Data availability statement extraction
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Training data and model checkpoints for DAS extraction
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10.34133_2022_9870149.pdf
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Code Availability. The source codes for our CS framework are
available at https://github.com/bianzhiyu/ContinuityScaling.
|
Additional Points Code Availability. The source codes for our CS framework are available at https://github.com/bianzhiyu/ContinuityScaling .
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AAAS
Research
Volume 2022, Article ID 9870149, 10 pages
https://doi.org/10.34133/2022/9870149
Research Article
Continuity Scaling: A Rigorous Framework for Detecting and
Quantifying Causality Accurately
Xiong Ying,1,2,3 Si-Yang Leng ,2,4 Huan-Fei Ma ,5 Qing Nie
and Wei Lin 1,2,3,8
,6 Ying-Cheng Lai
,7
1School of Mathematical Sciences, SCMS, and SCAM, Fudan University, Shanghai 200433, China
2Research Institute for Intelligent Complex Systems, CCSB, and LCNBI, Fudan University, Shanghai 200433, China
3State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain Science, Institutes of Brain Science,
Fudan University, Shanghai 200032, China
4Institute of AI and Robotics, Academy for Engineering and Technology, Fudan University, Shanghai 200433, China
5School of Mathematical Sciences, Soochow University, Suzhou 215006, China
6Department of Mathematics, Department of Developmental and Cell Biology, And NSF-Simons Center for Multiscale Cell
Fate Research, University of California, Irvine, CA 92697-3875, USA
7School of Electrical, Computer, And Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA
8Shanghai Artificial Intelligence Laboratory, Shanghai 200232, China
Correspondence should be addressed to Wei Lin; [email protected]
Received 7 March 2022; Accepted 24 March 2022; Published 4 May 2022
Copyright © 2022 Xiong Ying et al. Exclusive Licensee Science and Technology Review Publishing House. Distributed under a
Creative Commons Attribution License (CC BY 4.0).
Data-based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to
science, engineering, and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques,
we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which
is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross-map
as conventionally implemented, we define causation through measuring the scaling law for the continuity of the investigated
dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and
assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The
continuity scaling-based framework is rigorously established and demonstrated using datasets from model complex systems
and the real world.
1. Introduction
Identifying and ascertaining causal relations are a problem
of paramount importance to science and engineering with
broad applications [1–3]. For example, accurate detection
of causation is the key to identifying the origin of diseases
in precision medicine [4] and is important to fields such as
psychiatry [5]. Traditionally, associational concepts are often
misinterpreted as causation [6, 7], while causal analysis in
fact goes one step further beyond association in a sense that,
instead of using static conditions, causation is induced under
changing conditions [8]. The principle of Granger causality
formalizes a paradigmatic framework [9–11], quantifying
causality in terms of prediction improvements, but, because
of its linear, multivariate, and statistical regression nature,
the various derived methods require extensive data [12].
Entropy-based methods [13–20] face a similar difficulty.
Another issue with the Granger causality is the fundamental
requirement of separability of the underlying dynamical var-
iables, which usually cannot be met in the real world sys-
tems. To overcome these difficulties, the cross-map-based
techniques, paradigms tailored to dynamical systems, have
been developed and have gained widespread attention in
the past decade [21–36].
2
Research
The cross-map is originated from nonlinear time series
analysis [37–42]. A brief understanding of such a map is as
follows. Consider two subsystems: X and Y. In the recon-
structed phase space of X, if for any state vector at a time a
set of neighboring vectors can be found, the set of the
cross-mapped vectors, which are the partners with equal
time of X, could be available in Y. The cross-map underlying
the reconstructed spaces can be written as Y t = ΦðXtÞ
(where Xt and Y t are delay coordinates with sufficiently
large dimensions) for the case of Y unidirectionally causing
X while, mathematically,
its inverse map does not exist
[34]. In practice, using the prior knowledge on the true cau-
sality in toy models or/and the assumption on the expanding
property of Φ (representing by its Jacobian’s singular value
larger than one in the topological causality framework
[24]), scientists developed many practically useful tech-
niques based on the cross-map for causality detection. For
instance, the “activity” method, originally designed to mea-
sure the continuity of the inverse of the cross-map, com-
pares the divergence of the cross-mapped vectors to the
state vector in X with the divergence of the independently-
selected neighboring vectors to the same state vector [22,
23]. The topological causality measures the divergence rate
of the cross-mapped vectors from the state vectors in Y
[24], and the convergent cross-mapping (CCM), increasing
the length of time series, compares the true state vector Y
with the average of the cross-mapped vectors, as the estima-
tion of Y [21, 25–36]. Then, the change of the divergence or
the accuracy of the estimation is statistically evaluated for
determining the causation from Y to X. Inversely, the causa-
tion from X to Y can be evaluated in an analogous manner.
The above evaluations [21, 24, 26–36] can be understood at a
conceptional and qualitative level and perform well in many
demonstrations.
In this work, striving for a comprehensive understanding
of causal mechanisms and inspired by the cross-map-based
techniques, we develop a mathematically rigorous frame-
work for detecting causality in nonlinear dynamical systems,
turning eyes towards investigating the original systems from
their cross-maps, which is also logically consistent with the
natural interpretation of causality as functional dependences
[2, 8]. The skills used in cross-map-based methods are
assimilated in our framework, while we directly study the
original dynamical systems or the reconstructed systems
instead of the cross-maps. The foundation of our framework
is the scaling law for the changing relation of ε with δ arising
from the continuity for the investigated system, henceforth
the term “continuity scaling”. In addition to providing a the-
ory, we demonstrate, using synthetic and real-world data,
that our continuity scaling framework is accurate, computa-
tionally efficient, widely applicable, showing advantages over
the existing methods.
2. Continuity Scaling Framework
To explain the mathematical idea behind the development of
our framework, we use the following class of discrete time
dynamical systems: xt+1 = fðxt, ytÞ and yt+1 = gðxt, ytÞ for t
∈ ℕ, where the state variables fxtgt∈ℕ, fytgt∈ℕ evolve in
the compact manifolds M, N of dimension DM, DN under
sufficiently smooth map f, g, respectively. We adopt the
common recognition of causality in dynamical systems.
Definition 1. If the dependence of fðx, yÞ on y is nontrivial (i.
e., a directional coupling exists), a variation in y results in a
change in the value of fðx, yÞ for any given x, which, accord-
ing to the natural interpretation of causality [2, 43], admits
that y : fytgt∈ℕ has a direct causal effect on x : fxtgt∈ℕ,
denoted by y↪x, as shown in the upper panel of Figure 1(a).
We now interpret the causal relationship stipulated by
ð·Þ ≜ fðxg, ·Þ for a given
the continuity of a function. Let fxg
∈ N , we denote its image under
∈ M. For any yP
point xg
≜ fxg
the given function by xI
ðyPÞ. Applying the logic state-
ment of a continuous function to fxg
ð·Þ, we have that, for
any neighborhood OðxI, εÞ centered at xI and of radius ε >
0, there exists a neighborhood OðyP, δÞ centered at yP of
radius δ > 0, such that fxg
ðOðyP, δÞÞ ⊂ OðxI, εÞ. The neigh-
borhood and its radius are defined by
O p, hð
Þ = s ∈ S distS
f
j
s, pð
Þ < h
g, p ∈ S, h > 0,
ð1Þ
where distSð·, · Þ represents an appropriate metric describ-
ing the distance between two given points in a specified
manifold S with S = M or N . The meaning of this mathe-
matical statement is that, if we have a neighborhood of the
resulting variable xI first, we can then find a neighborhood
for the causal variable yP to satisfy the above mapping and
inclusion relation. This operation of “first-ε-then-δ” pro-
vides a rigorous base for the principle that the information
about the resulting variable can be used to estimate the
information of the causal variable and therefore to ascertain
causation, as indicated by the long arrow in the middle
panels of Figure 1(a). Note that, the existence of the δ > 0
neighborhood is always guaranteed for a continuous map
. In fact, due to the compactness of the manifold N , a
fxg
largest value of δ exists. However, if yP does not have an
explicit causal effect on the variable xI, i.e., fxg
is independent
of yP, the existence of δ is still assured but it is independent
of the value of ε, as shown in the upper panel of Figure 1(b).
This means that merely determining the existence of a δ-
neighborhood is not enough for inferring causation - it is
necessary to vary ε systematically and to examine the scaling
relation between δ and ε. In the following we discuss a num-
ber of scenarios.
Case I. Dynamical variables fðxt, ytÞgt∈ℕ are fully measur-
x > 0, the set fxτ ∈ Mjτ ∈ It
able. For any given constant ε
ðε
xÞg can be used to approximate the neighborhood Oðxt+1,
ε
xÞ, where the time index set is
x
It
x
ε
xð
Þ ≜ τ ∈ ℕ distMj
f
ð
xt+1, xτ
Þ < ε
x
g:
ð2Þ
The radius δt
y = δt
yðε
xÞ of the neighborhood Oðyt, δt
yÞ
Research
3
(a)
(b)
Figure 1: Illustration of causal relation between two sets of dynamical variables. (a) Existence of causation from y in N to x in M, where
each correspondence from xt+1 to yt is one-to-one, represented by the line or the arrow, respectively, in the upper and the middle panels. In
y (the lower panel) with ε
this case, a change in ln ε
y denoting the neighborhood size of the resulting
variable x and of the causal variable y, respectively. (b) Absence of causation from y to x, where every point on each trajectory, fytg, in N
could be the correspondent point from xt+1 in M (the upper panel) and thus every point in N belongs to the largest δ-neighborhood of yt
(the middle panel). In this case, δ
x (the lower panel). Also refer to the supplemental animation for illustration.
x results in a direct change in δ
y does not depend on ε
x and δ
satisfying fxg=xt ðOðyt, δt
yÞÞ ⊂ Oðxt+1, ε
xÞ can be estimated as
n
h
Þ ≜ # (cid:2)It
x
ε
xð
Þ
δt
y
ε
xð
i
o−1 〠
τ∈(cid:2)It
x
ε
xð
Þ
distN yt, yτ−1
ð
Þ,
ð3Þ
xg.
xðε
xÞ ≜ fτ ∈ It
where #½·(cid:2) is the cardinality of the given set and the index set
is (cid:2)It
xÞjdistMðxt, xτ−1Þ < ε
xðε
The strict mathematical steps for estimating δt
y are given
in Section II of Supplementary Information (SI). We empha-
size that here correspondence between xt+1 and yt is investi-
gated, differing from the cross-map-based methods, with
one-step time difference naturally arising. This consider-
ation yields a key condition [DD], which is only need when
considering the original iteration/flow and whose detailed
description and universality are demonstrated in SI. We
reveal a linear scaling law between hδt
yit∈ℕ and ln ε
x, as
shown in the lower panels of Figure 1, whose slope s
y↪x is
an indicator of the correspondent relation between ε and δ
and hence the causal relation y↪x. Here, h·it∈ℕ denotes
the average over time. In particular, a larger slope value
implies a stronger causation in the direction from y to x as
represented by the map functions fðxt, ytÞ (Figure 1(a)),
while a near zero slope indicates null causation in this direc-
tion (Figure 1(b)). Likewise, possible causation in the
reversed direction, x↪y, as represented by the function gð
xt, ytÞ, can be assessed analogously. And the unidirectional
case when fðx, yÞ = f0ðxÞ independent of y is uniformly con-
sidered in Case II. We summarize the consideration below
and an argument for the generic existence of the scaling
law is provided in Section II of SI.
Theorem 2. For dynamical variables fðxt, ytÞgt∈ℕ measured
directly from the dynamical systems, if the slope s
y↪x defined
above is zero, no causation exists from y to x. Otherwise, a
directional coupling can be confirmed from y to x and the
slope s
y↪x increases monotonically with the coupling strength.
Case II. The dynamical variables fðxt, ytÞgt∈ℕ are not
directly accessible but measurable time series futgt∈ℕ and
fvtgt∈ℕ are available, where ut = uðxtÞ and vt = vðytÞ with
u: M ⟶ ℝru and v: N ⟶ ℝrv being smooth observational
functions. To assess causation from y to x, we assume one-
dimensional observational time series (for simplicity): ru =
rv = 1, and use the classical delay-coordinate embedding
method [37–42, 44] to reconstruct the phase space: ut =
T
ðut, ut+τu,⋯,ut+ðdu−1ÞτuÞ
and vt = ðvt, vt+τv ,⋯,vt+ðdv−1Þτv Þ
,
where τu,v is the delay time and du,v > 2ðDM + DN Þ is the
embedding dimension that can be determined using some
standard criteria [45]. As illustrated in Figure 2, the dynam-
ical evolution of the reconstructed states fðut, vtÞgt∈ℕ is gov-
erned by
T
ut+1 =
~
f ut, vt
ð
Þ, vt+1 = ~g ut, vt
ð
Þ:
ð4Þ
The map functions can be calculated as
∘ E−1
~
fðu, vÞ ≜ Eu ∘
∘ E−1
∘ E−1
u ðuÞ, Π
u
1
∘ E−1
v ðvÞÞ, where the embedding (diffeomorphism)
v ðvÞÞ, ~gðu, vÞ ≜ Ev ∘ ½f, g(cid:2)ðΠ
1
2
½ f, g(cid:2)ðΠ
ðuÞ, Π
2
4
Research
(f(x, y), g(x, y))
M × N
M × N
y↪x or x↪y
)
u
(
1
u
–
E
°
1
П
)
v
(
1
–
v
E
°
2
П
)
y
,
x
(
u
E
)
y
,
x
(
v
E
˜
˜
Lu × Lv
˜
˜
Lu × Lv
v↪u or u↪v
˜
˜
(f(u,v),g(u,v))
{ut(x)}t𝜖N {vt(y)}t𝜖N
Figure 2:
Illustration of system dynamics before and after
embedding for Case II. In the left panel, the arrows describe how
~
f, ~gÞ after
the original systems ðf, gÞ is equivalent to the system ð
embedding. In the right panel, causation between the internal
variables x and y can be ascertained by detecting the causation
between the variables u and v reconstructed from measured time
series.
Es: M × N ⟶ ~L s ⊂ ℝds with
given by
~L s ≜ EsðM × N Þ, s = u or v, is
Eu x, y
ð
f, g½
Ev x, y
ð
f, g½
∘
1
∘ f, g½
Þ ≜ uð xð Þ, u ∘ Π
(cid:2)2τu x, y
ð
Þ ≜ vð yð Þ, v ∘ Π
2
(cid:2)2τv x, y
ð
τu x, y
(cid:2)
ð
du−1
Þ, ⋯, u ∘ Π
∘ f, g½
(cid:2)
1
τv x, y
∘ f, g½
(cid:2)
ð
dv−1
∘ f, g½
ð
Þ, ⋯, v ∘ Π
Þ, u ∘ Π
1
Þτu x, y
ð
Þ, v ∘ Π
2
Þτv x, y
ð
(cid:2)
ð
ÞÞ,
∘
ÞÞ,
2
ð5Þ
k
~L s, ½f, g(cid:2)
s defined on
1ðx, yÞ = x and Π
with the inverse function E−1
represent-
ing the kth iteration of the map and the projection mappings
as Π
2ðx, yÞ = y. Case II has now been
reduced to Case I, and our continuity scaling framework
can be used to ascertain the causation from v to u based on
the measured time series with the indices It
uÞ and
s
v↪u (equations (2) and (3)).
uÞ, δt
uðε
vðε
~
f0ðutÞ and vt+1 = ~gðut, vtÞ, where
Does the causation from v to u imply causation from y to
x? The answer is affirmative, which can be argued, as follows.
If the original map function f is independent of y: fðx, yÞ =
f0ðxÞ, there is no causation from y to x. In this case, the
embedding Euðx, yÞ becomes independent of y, degenerating
into the form of Euðx, yÞ = Eu0ðxÞ, a diffeomorphism from M
~L u0 = Eu0ðMÞ only. As a result, equation (4) becomes
to
~
∘ f ∘ E−1
ut+1 =
f0ðuÞ = Eu0
u0ð
~
f0 is independent of v. The
uÞ and the resulting mapping
independence can be validated by computing the slope
v↪u associated with the scaling relation between hδt
s
vit∈ℕ
and ln ε
u, where a zero slope indicates null causation from
v to u and hence null causation from y to x. Conversely, a
finite slope signifies causation between the variables. Thus,
any type of causal relation (unidirectional or bi-directional)
detected
variables
fðut, vtÞgt∈ℕ implies the same type of causal relation
between the internal but inaccessible variables x and y of
the original system.
reconstructed
between
state
the
T
Case III. The structure of the internal variables is completely
unknown. Given the observational functions ~u, ~v: M × N
⟶ ℝ with ~ut = ~uðxt, ytÞ and ~vt = ~vðxt, ytÞ, we first recon-
struct the state space: ~ut = ð~ut, ~ut+τ,⋯,~ut+ðd−1ÞτÞ
and ~vt =
ð~vt, ~vt+τ,⋯,~vt+ðd−1ÞτÞ
. To detect and quantify causation
from ~v to ~u (or vice versa), we carry out a continuity scaling
analysis with the modified indices It
~vðε~uÞ and s~v↪~u.
Differing from Case II, here, due to the lack of knowledge
about the correspondence structure between the internal
and observational variables, a causal relation for the latter
does not definitely imply the same for the former.
~uðε~uÞ, δt
T
Case IV. Continuous-time dynamical systems possessing a
sufficiently smooth flow fSt ; t ∈ ℝg on a compact manifold
H : dStðu0Þ/dt = χðStðu0ÞÞ, where χ is the vector field. Let
f̂ut=ωn+νgn∈ℤ and f̂vt=ωn+νgn∈ℤ be two respective time series
from the smooth observational functions ̂u, ̂v: H ⟶ ℝ with
̂ut = ̂uðStÞ and ̂vt = ̂vðStÞ, where 1/ω is the sampling rate and
ν is the time shift. Defining Ξ ≜ Sω: H ⟶ H and ̂Sn ≜
Sωn+νðu0Þ, we obtain a discrete-time system as ̂Sn+1 = Ξð̂SnÞ
with the observational functions as ̂un = ̂uð̂SnÞ and ̂vn = ̂vð
̂SnÞ, reducing the case to Case III and rendering applicable
our continuity scaling analysis to unveil and quantify the
causal relation between f̂ut=ωn+νgn∈ℤ and f̂vt=ωn+νgn∈ℤ. If
the domains of ̂u and ̂v have their own restrictions on some
particular subspaces, e.g., ̂u: H u ⟶ ℝ and ̂v: H v ⟶ ℝ
with H = H u ⊕ H v, the case is further reduced to Case II,
so the detected causal relation between the observational
variables imply causation between the internal variables
belonging to their respective subspaces.
3. Demonstrations: From Complex Dynamical
Models to Real-World Networks
To demonstrate the efficacy of our continuity scaling frame-
work and its superior performance, we have carried out
extensive numerical tests with a large number of synthetic
and empirical datasets, including those from gene regulatory
networks as well as those of air pollution and hospital
admission. The practical steps of the continuity scaling
framework together with the significance test procedures
are described in Methods. We present three representative
examples here, while leaving others of significance to SI.
2,t+1 = x
The first example is an ecological model of two unidirec-
tionally interacting species: x
1,tð3:8 − 3:8x
1,t − μ
1,t+1 = x
12
x
2,t − μ
2,tÞ and x
x
2,tð3:7 − 3:7x
1,tÞ. With time series
2,tÞgt∈ℕ obtained from different values of the cou-
1,t, x
fðx
pling parameters, our continuity scaling framework yields
correct results of different degree of unidirectional causa-
tion, as shown in Figures 3(a) and 3(b). In all cases, there
exists a reasonable range of ln εx
(neither too small nor
too large) from which the slope sx
of the linear scaling
can be extracted. The statistical significance of the estimated
slope values and consequently the strength of causation can
be assessed with the standard p-value test [46] (Methods and
SI). An ecological model with bidirectional coupling has also
been tested (see Section III of SI). Figures 3(c) and 3(d)
↪x
21
2
1
2
Research
5
0.6
0.4
t
〉
1
x
𝛿
〈
t
0.2
0.6
0.4
t
〉
2
x
𝛿
〈
t
0.2
0
–8
–6
–2
0
–4
ln 𝜀x2
0
–8
–6
–2
0
–4
ln 𝜀x1
𝜇21 = 0.00
𝜇21 = 0.05
𝜇21 = 0.10
𝜇21 = 0.15
(a)
𝜇12 = 0.00
𝜇12 = 0.00
𝜇12 = 0.00
𝜇12 = 0.00
(b)
t
c
e
ff
E
x5
x4
x3
x2
x1
j
x
↪
x
s
i
e
p
o
l
S
t
c
e
ff
E
x5
x4
x3
x2
x1
0.12
0.1
0.08
0.06
0.04
0.02
0
j
x
↪
x
s
i
e
p
o
l
S
0.15
0.12
0.09
0.06
0.03
0
x1
x2
x4
x5
x3
Cause
(d)
x1
x2
x4
x5
x3
Cause
(c)
Figure 3: Ascertaining and characterizing causation in various ecological systems of interacting species. (a, b) Unidirectional causation of
two coupled species. In (a), the values of the slope sx
2 are approximately 0.0004, 0.1167, 0.1203,
and 0.1238 for four different values of the coupling parameter μ
indicating its
nonexistence. (c, d) Inferred causal network of five species whose interacting structure is, respectively, that of a ring: xi↪xi+1ðmod 5Þ
(i = 1, ⋯, 5) and of a tree: x j↪xj+1,j+3 (j = 1, 2), where the estimated slope values are color-coded. Results of a statistical analysis of the
accuracy and reliability of the determined causal interactions are presented in SI Section III. Time series of length 5000 are used in all
these simulations. The embedding parameters are τs = 1 and ds = 3 with s = x
21. (b) Near zero slope values sx
associated with the causal relation x
for x
↪x
↪x
1,
↪x
↪x
1
2
2
1
1
2
1, ⋯, x
5.
show the results from ecological networks of five mutually
interacting species on a ring and on a tree structure, respec-
tively, where the color-coded slope values reflect accurately
the interaction patterns in both cases.
The second example is the coupled Lorenz system: _xi =
σiðyi − xiÞ + μijx j, _yi = xiðρi − ziÞ − yi, _zi = xiyi − βizi with i,
j = 1, 2 and i=j. We use time series fy
2,tgt=nω for
detecting different configurations of causation (see Section
III of SI). Figure 4 presents the overall result, where the
color-coded estimated values of the slope from the continu-
ity scaling are shown for different combinations of the sam-
pling rate 1/ω and coupling strength. Even with relatively
low sampling rate, our continuity scaling framework can
successfully detect and quantify the strength of causation.
Note that the accuracy does not vary monotonously with
the sampling rate, indicating the potential of our framework
1,t, y
to ascertain and quantify causation even with rare data.
Moreover, the proposed index can accurately reflect the true
causal strength (denoting by the coupling parameter), which
is also evidenced by numerical tests in Sections III and IV of
SI. Robustness tests against different noise perturbations are
provided in Section III of SI demonstrating the practical
usefulness of our framework. Additionally, analogous to
the first example, we present in SI several examples on cau-
sation detection in the coupled Lorenz system with nonlin-
ear couplings, and the Rössler-Lorenz system, etc., which
further demonstrates the generic efficacy of our framework.
In addition, we present study on several real-world data-
set, which brings new insights to the evolutionary mecha-
nism of underlying systems. We study gene expression
data from DREAM4 in silico Network Challenge [47, 48],
whose intrinsic gene regulatory networks (GRNs) are known
for verification (Figure 5(a) and Figure S17 of SI). Applying
6
Research
1
2
𝜇
6
4
2
0
5
4
3
2
1
0
2
y
↪
1
y
s
e
p
o
l
S
1
2
𝜇
6
4
2
0
1
y
↪
2
y
s
e
p
o
l
S
5
4
3
2
1
0
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sampling duration/0.001
(a)
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sampling duration/0.001
(b)
Figure 4: Detecting causation in the unidirectionally coupled Lorenz system. The results are for different values of μ
sampling rate 1/ω. (a, b) Color-coded values of the slopes sy
embedding parameters are ds = 7, τs ≈ 0:05 with ωjτs (s = y
including the time series lengths used in the simulations.
12 = 0) and
, respectively. The integration time step is 10−3 and the
and sy
2). See Section III and Table S9 of SI for all the other parameters
1 or y
21 (μ
↪y
↪y
1
2
1
2
100
45
44
43
1
0.8
0.6
0.4
0.2
e
t
a
r
e
v
i
t
i
s
o
p
e
u
r
T
0
0
75
36
69
37
67
25
85
38
10
62
72
96
23
83
87
73
Enhancer
Inhibitor
(a)
0.2
0.4
0.6
0.8
1
False positive rate
1, AUROC = 0.765
2, AUROC = 0.667
3, AUROC = 0.693
4, AUROC = 0.693
5, AUROC = 0.868
(b)
Figure 5: Detecting causal interactions in five GRNs. (a) One representative GRN containing 20 randomly selected genes. Other four
structures can be found in Figure S17 of SI. (b) The ROC curves as well as their AUROC values demonstrate the efficacy of our framework.
our framework to these data, we ascertain the causations
between each pair of genes by using the continuity scaling
framework. The corresponding ROC curves for five different
networks as well as their AUROC values are shown in
Figure 5(b), which indicates a high detection accuracy in
dealing with real-world data.
We then test the causal relationship in a marine ecosys-
tem consisting of Pacific sardine landings, northern anchovy
landings and sea surface temperature (SST). We reveal new
findings to support the competing relationship hypothesis
stated in [49] which cannot be detected by CCM [25]. As
pointed out in Figure 6, while common influence from SST
to both species is verified with both methods, our continuity
scaling additionally illuminates notable influence from
anchovy to sardine with its reverse direction being less sig-
nificant. While competing relationship plays an important
role in ecosystems, continuity scaling can reveal more essen-
tial interaction mechanism. See Section III.E of SI for more
details.
Moreover, we study the transmission mechanism of the
recent COVID-19 pandemic. Particularly, we analyze the
daily new cases of COVID-19 of representative countries
for two stages: day 1 (January 22 nd 2020) to day 100 (April
30 th 2020) and day 101 (May 1 st 2020) to day 391 (February
15 th 2021). Our continuity scaling is pairwisely applied to
reconstruct the transmission causal network. As shown in
Figure 7, China shows a significant effect on a few countries
at the first stage and this effect disappears at the second
stage. However, other countries show a different situation
with China, whose external effect lasts as shown in Section
III.E and Figure S18 of SI. Our results accord with that
China holds stringent epidemic control strategies with
Research
7
SST
SST
Sardine
Anchovy
Sardine
Anchovy
Continuity scaling
CCM
Figure 6: The comparison of causal network structure detected by continuity scaling and CCM among sea surface temperature, sardine, and
anchovy.
Figure 7: The causal effect from China to other countries of the COVID-19 pandemic detected by continuity scaling between stages 1 and 2.
Here, stage 1 is from January 22 nd 2020 to April 30 th 2020, and stage 2 is from May 1 st 2020 to February 15 th 2021. For those detected
causal links between all countries, refer to Section III.E and Figure S18 of SI. These maps are for illustration only.
sporadic domestic infections, as evidenced by official daily
briefings, demonstrating the potential of continuity scaling
in detecting causal networks for ongoing complex systems.
Additionally, We emphasize that day 100 is a suitable
critical day to distinguish the early severe stage and the late
well-under-control stage of the pandemic (see Figure S18(a)
of SI), while slight change of the critical day will not nullify
our result. As shown in Figure S18(b) of SI, when the
critical day varies from day 94 to day 106, no significant
change (less than 5%) of the detected causal links occurs at
both stages, and the number of countries under influence of
China at Stage 2 remains zero. See more details in Section
III.E of SI.
Additional real world examples including air pollutants
and hospital admission record from Hong Kong are also
shown in Section III of SI.
4. Discussion
To summarize, we have developed a novel framework for
data-based detection and quantification of causation in com-
plex dynamical systems. On the basis of the widely used
cross-map-based techniques, our framework enjoys a rigor-
ous foundation, focusing on the continuity scaling law of
the concerned system directly instead of only investigating
the continuity of its cross-map. Therefore, our framework
is consistent with the standard interpretation of causality,
and works even in the typical cases where several existing
typical methods do not perform that well or even they fail
(see the comparison results in Section IV of SI). In addition,
the mathematical reasoning leading to the core of our frame-
work, the continuity scaling, helps resolve the long-standing
issue associated with techniques directly using cross-map
that information about the resulting variables is required to
project
the causal variables,
whereas several works in the literature [50], which directly
studied the continuity or the smoothness of the cross-map,
likely yielded confused detected results on causal directions.
Computational complexity. The computational com-
plexity of the algorithm is OðT 2NεÞ, which is relatively
smaller than the CCM method, whose computational com-
plexity is OðT 2 log TÞ.
the dynamical behavior of
Limitations and future works. Nevertheless, there are
still some spaces for improving the presently proposed
framework. First, currently, only bivariate detection algo-
rithm is designed, so generalization to multivariate network
inference requires further considerations, as analogous to
those works presented in Refs. [51–53]. Second, the causal
time delay has not been taken into account in the current
framework, so it also could be further investigated, similar
to the work reported in Ref. [33]. Also, more advanced algo-
rithms, such as the one developed in Ref. [54], could be
8
Research
integrated into this framework for detecting those temporal
causal structures. Definitely, we will settle these questions
in our future work.
Detecting causality in complex dynamical systems has
broad applications not only in science and engineering, but
also in many aspects of the modern society, demanding
accurate, efficient, and rigorously justified and hence trust-
worthy methodologies. Our present work provides a vehicle
along this feat and indeed resolves the puzzles arising in the
use of those influential methods.
5. Methods
Continuity scaling framework: a detailed description of algo-
rithms. Let futgt=1,2,⋯,T and fvtgt=1,2,⋯,T be two experimen-
tally measured time series of internal variables fðxt, ytÞgt∈ℕ.
Typically, if the dynamical variables fðxt, ytÞgt∈ℕ are accessi-
ble, fðut, vtÞg reduce to one-dimensional coordinate of the
internal system. The key computational steps of our conti-
nuity scaling framework are described, as follows.
We reconstruct
the phase space using the classical
method of delay coordinate embedding [37] with the opti-
mal embedding dimension dz and time lag τz determined
by the methods in Refs. [55, 56] (i.e., the false nearest neigh-
bors and the delayed mutual information, respectively):
n
(cid:2)
L z ≜ z tð Þ = zt, zt+τz , ⋯, zt+ dz−1
ð
Þτz
(cid:3)
j
o
t = 1, ⋯, T
0
,
ð6Þ
z = u, v, T
where
Euclidean distance is used for both L u,v.
0 = min fT − ðdz − 1Þτzjz = u, vg,
and
We present the steps for causation detection using the
case of v↪u as an example.
We calculate the respective diameters for L u,v as
(cid:4)
Dz ≜ max distLz z tð Þ, z τð Þ
ð
Þ 1 ≤ t, τ ≤ T
j
(cid:5)
,
0
ð7Þ
where z = u, v, and z = u, v. We set up a group of numbers,
fε
u,N ε = Du, with the other ele-
u,jgj=1,⋯,N ε
ments satisfying
u,1 = e · Du, ε
, as ε
ln ε
u,j − ln ε
j − 1
u,1
=
ln ε
− ln ε
u,N ε
Nε − 1
u,1
,
ð8Þ
for j = 2, ⋯, N ε − 1. Then, in light of (2) with (3), we have
δt
v
ε
uð
(cid:6)
Þ = # It
u
ε
uð
Þ
(cid:7)−1 〠
τ∈It
u
ε
uð
Þ
distL v v tð Þ, v τ − 1
ð
ð
Þ
Þ,
ð9Þ
with
It
u
ε
uð
(cid:4)
(cid:8)
(cid:8)
Þ = τ ∈ ℕ distLu
u t + 1
ð
Þ, u τð Þ
ð
Þ < ε
u, t + 1 − τ
j
(cid:5)
j > E
ð10Þ
where numerically, ε
set fε
u,jgj=1,⋯,N ε
u alters its value successively from the
, and the threshold E is a positive number
0
0
vðε
chosen to avoid the situation where the nearest neighboring
points are induced by the consecutive time order only.
u,jÞg
vðε
u, where ℕT
As defined, hδt
uÞit∈ℕ is the average of δt
vðε
uÞ over all
t. We use a finite number of pairs
possible time
fðhδt
, ln ε
vðε
u,jÞit∈ℕT
to approximate the scaling
j=1,⋯,N ε
relation between hδt
uÞit∈ℕ and ln ε
= f1,
2,⋯,T
0g. Theoretically, a larger value of N ε and a smaller
value of e will result in a more accurate approximation of
the scaling relation. In practice, the accuracy is determined
by the length of the observational time series, the sampling
duration, and different types of noise perturbations. In
numerical simulations, we set e = 0:001 and N ε = 33. In addi-
tion, a too large or a too small value of ε
u can induce insuffi-
cient data to restore the neighborhood and/or the entire
manifold. We thus set δt
u,jÞ = δt
u,j+1Þ as a practical tech-
nique as the number of points is limited practically in a small
neighborhood. As a result, near zero slope values would
appear on both sides of the scaling curve hδt
uÞit∈ℕ-ln ε
u,
as demonstrated in Figure 3 and in SI. In such a case, to esti-
mate the slope of the scaling relation, we take the following
approach.
vðε
vðε
vðε
Define a group of numbers by
(cid:11)
(cid:9)
− δt
v
− ln ε
Sj ≜
ln ε
u,j+1
δt
v
t∈ℕT
(cid:11)
(cid:12)
(cid:10)
ε
0
u,j+1
u,j
(cid:9)
(cid:10)
(cid:12)
ε
u,j
t∈ℕT
0
,
ð11Þ
where j = 1, ⋯, Nε − 1, sort them in a descending order,
from which we determine the ½Nε + 1/2(cid:2) largest numbers,
collect their subscripts - j’s together as an index set ̂J, and
set H ≜ fj, j + 1jj ∈ ̂Jg. Applying the least squares method
to the linear regression model:
(cid:11)
(cid:12)
δt
v
ε
uð
Þ
t∈ℕ = S · ln ε
u + b
ð12Þ
with the dataset fðhδt
optimal values ð̂S,
finally obtain the slope of the scaling relation as s
, we get the
̂bÞ for the parameters ðS, bÞ in (12) and
u,jÞit∈ℕT
, ln ε
≜ ̂S.
u,jÞg
vðε
j∈H
0
v↪u
For the other causal direction from u to v, these steps are
equally applicable to estimating the slope s
u↪v.
0
To assess the statistical significance of the numerically
determined causation, we devise the following surrogate test
using the case of v causing u as an illustrative example.
Divide the time series fuðtÞgt∈ℕT
into NG consecutive
segments of equal length (except for the last segment - the
shortest segment). Randomly shuffle these segments and
then regroup them into a surrogate sequence f̂uðtÞgt∈ℕT
.
Applying such a random permutation method to fvðtÞgt∈ℕT
generates another surrogate sequence f̂vðtÞgt∈ℕT
. Carrying
out the slope computation yields ŝv↪̂u. The procedure can
be repeated for a sufficient number of times, say Q, which
consequently yields a group of estimated slopes, denoted as
fsq
̂v↪̂u is set as s
v↪u obtained from the
original time series. For all the estimated slopes, we calculate
̂v↪̂ugq=0,1⋯,Q, where s0
0
0
0
Research
9
their mean bμ
-value for s
v↪u is calculated as
v↪u and the standard deviation bσ
v↪u. The p
(cid:13)
s
ps
v↪u
≜ 1 − normcdf
(cid:14)
,
v↪u
ð13Þ
v↪u
bσ
− bμ
v↪u
where normcdf ½·(cid:2) is the cumulative Gaussian distribution
function. The principle of statistical hypothesis testing guar-
antees the existence of causation from v to u if ps
< 0:05.
In simulations, we set the number of segments to be
N G = 25 and the number of times for random permutations
to be Q ≥ 20.
v↪u
Additional Points
Code Availability. The source codes for our CS framework are
available at https://github.com/bianzhiyu/ContinuityScaling.
Conflicts of Interest
The authors declare no competing interests.
Authors’ Contributions
W.L. conceived idea. X.Y., S.-Y.L., and W.L. designed and
performed the research. X.Y., S.-Y.L., H.-F.M., and W.L.
analyzed the data. H.-F.M., Y.-C.L., and Q.N. contributed
data and analysis tools, and all the authors wrote the paper.
X.Y. and S.-Y.L. equally contributed to this work.
Acknowledgments
W.L. is supported by the National Key R&D Program of
China (Grant No. 2018YFC0116600), by the National Natu-
ral Science Foundation of China (Grant Nos. 11925103 and
61773125), by the STCSM (Grant No. 18DZ1201000), and
by the Shanghai Municipal Science and Technology Major
Project (No. 2021SHZDZX0103). Y.-C.L. is supported by
AFOSR (Grant No. FA9550-21-1-0438). S.-Y.L. is supported
by the National Natural Science Foundation of China (No.
12101133) and “Chenguang Program” supported by Shang-
hai Education Development Foundation and Shanghai
Municipal Education Commission (No. 20CG01). Q.N. is
partially supported by NSF (Grant No. DMS1763272) and
the Simons Foundation (Grant No. 594598). H.-F.M. is sup-
ported by the National Natural Science Foundation of China
(Grant No. 12171350) and by the National Key R&D Pro-
gram of China (Grant No. 2018YFA0801100).
Supplementary Materials
Supplementary materials: SI.pdf (where we include analytic
and computational details of the results in the main text.
This SI is helpful but not essential for understanding the
main results of the paper.) (Supplementary Materials)
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| null |
10.1088_1361-6501_ad180c.pdf
|
Data availability statement
The data cannot be made publicly available upon publication
because they are owned by a third party and the terms of use
prevent public distribution. The data that support the findings
of this study are available upon reasonable request from the
authors.
|
Data availability statement The data cannot be made publicly available upon publication because they are owned by a third party and the terms of use prevent public distribution. The data that support the findings of this study are available upon reasonable request from the authors.
|
Meas. Sci. Technol. 35 (2024) 035605 (12pp)
Measurement Science and Technology
https://doi.org/10.1088/1361-6501/ad180c
Automated defect detection in precision
forging ultrasonic images based on
deep learning
Jianjun Zhao1, Yuxin Zhang1, Xiaozhong Du1,3,∗
and Xiaoming Sun2
1 School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024,
People’s Republic of China
2 College of Mechanical and Electrical Engineering, Central South University, Changsha 410083,
People’s Republic of China
3 School of Energy and Materials Engineering, Taiyuan University of Science and Technology, Jincheng
048000, People’s Republic of China
E-mail: [email protected]
Received 26 July 2023, revised 6 December 2023
Accepted for publication 21 December 2023
Published 29 December 2023
Abstract
Ultrasonic testing is a widely used non-destructive testing technique for precision forgings.
However, assessing defects in ultrasonic B-scan images can be prone to errors, misses, and
inefficiencies due to human judgment. To address these challenges, we propose a method based
on deep learning to automate the evaluation of such images. We started by creating a dataset
comprising 8000 images, each measuring 224 × 224 pixels. These images were cropped from
ultrasonic B-scan images of 7 specimens, each featuring different sizes and locations of holes
and crack defects. We then used state-of-the-art deep learning models to benchmark the dataset
and identified YOLOv5s as the best-performing baseline model for our study. To address the
challenges of deploying deep learning models and the issue of small defects being easily
confused with the background in ultrasonic B-scan images, we made lightweight improvements
to the deep learning model. Additionally, we enhanced the quality of data labels through data
cleaning. Our experiments show that our method achieved a precision of 97.8%, a recall of
98.1%, [email protected] of 99.0%, and [email protected]:.95 of 67.6%, with a frames per second (FPS) of
74.5. Furthermore, the number of model parameters was reduced by 43.2%, while maintaining
high detection accuracy. Overall, our proposed method offers a significant improvement over
the original model, making it a more reliable and efficient tool for automated defect assessment
in ultrasonic B-scan images.
Keywords: deep learning, ultrasonic testing, automated detection, lightweight improvement
1. Introduction
The non-destructive testing of precision machined complex
forgings is crucial, as they are irreplaceable core components
in mechanical equipment. Ultrasonic testing is widely utilized
in non-destructive testing of precision forgings due to its ease
of use and ability to accurately locate defects [1]. While the
acquisition of ultrasonic data is largely automated, the analysis
∗
Author to whom any correspondence should be addressed.
of the acquired data is predominantly conducted manually by
professionally trained experts. The quality of the analysis res-
ults depends entirely on the knowledge and experience of the
analysts, which can lead to issues such as missed detections,
incorrect detections, and lengthy consumption times. As a res-
ult, numerous researchers have made efforts to develop auto-
mated methods for defect detection to streamline the analysis
process.
Figure 1 illustrates the basic scanning methods used in
ultrasonic testing imaging, including A-scans, B-scans, and
C-scans. In the past, most studies focused on using A-scan
1
© 2023 IOP Publishing Ltd
Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 1. Basic way of imaging with ultrasonic testing.
data for automated analysis of ultrasonic data due to the poor
imaging quality of B-scans images. For instance, in 2004,
Bettayeb et al [2] proposed an automated ultrasonic NDE
system that utilizes wavelet transform to suppress noise and
enhance defect localization in ultrasonic signals, along with
an artificial neural network classification algorithm, which
achieved defect classification. In 2006, Matz et al [3] util-
ized an ultrasonic signal filtering method with discrete wave-
let transform and a pattern recognition method with support
vector machines (SVMs) to classify A-scans signals into three
categories: fault echoes, weld echoes, and back wall echoes.
In 2007, Khelil et al [4] employed the principal component
analysis method to optimize the wavelet parameters extrac-
ted from ultrasonic echoes and establish a SVM algorithm
to classify planar and volumetric defects. In 2011, Sambath
et al [5] chose 12 coefficients from the wavelet representa-
tion of the echo signal as features, such as mean, variance,
energy, and amplitude, and inputted them to a neural net-
work with two hidden layers for training to identify four types
of defects with a 94% accuracy rate. In 2014, Chen et al
[6] proposed a hierarchical multiclass SVM (LMSVM) with
parameter optimization and feature selection using BA. The
method was proven to be robust, accurate, and reliable for
ultrasonic defect classification through experiments conducted
on a welding defect dataset. In 2017, Cruz et al [7] used three
different feature extraction methods, including the discrete
Fourier transform, wavelet transform, and cosine transform,
as well as two different artificial neural network architectures
to automatically classify welding defects. They achieved effi-
cient identification of defects using this approach. Meng et al
[8] proposed a deep convolutional neural network (CNN) with
a linear SVM top layer to classify cavity-layered ultrasonic
signals in carbon fiber-reinforced polymer (CFRP) samples.
In 2018, Munir et al [9] evaluated the performance of deep
and shallow neural networks for automatic classification of
weld defect ultrasonic signal data. They found that deep neural
networks had better performance, achieving the highest accur-
acy of 91.89% on a mixed-frequency dataset. In 2019, Munir
et al [10] applied CNNs to noisy ultrasonic features to improve
the classification performance and applicability of defects in
welded parts. Their experimental results showed that CNNs
can achieve fairly high defect classification accuracy even for
noisy signals. Guo et al [11] combined principal component
analysis (PCA) on adaptive enhancement (Adaboost), extreme
gradient enhancement (XGBboost), and SVM—three machine
learning models widely used in NDT—to compare their per-
formance on 220 laser ultrasonic signal data collected from 22
samples with different subsurface defect sizes. PCA XGBoost
achieved the highest recognition rate of 98.48%.
While many researchers have achieved good results with
automated analysis of A-scans, the evaluation datasets used
have only contained a few hundred or a few thousand A-scans.
Such datasets are hardly a complete representation of all pos-
sible shape variations when compared to the millions of A-
scans used in actual inspection tasks. Moreover, the lack of
surrounding information in the A-scans makes it challenging
to distinguish between noise and defect signals, which is not
conducive to defect classification.
Ultrasonic B-scan images provide valuable spatial inform-
ation for automated analysis of ultrasonic testing, and recent
advances in ultrasonic testing equipment have significantly
improved their imaging quality. In 2019, Posilovic et al [12]
2
Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 2. System framework.
tested the performance of YOLO and SSD models in detecting
defects from 98 real B-scan data by means of data augmenta-
tion, and YOLO achieved better detection results with an aver-
age accuracy (AP) of 89.7%. Virupakshappa et al [13] simu-
lated a total of 400 ultrasonic B-scan images of various defect
types and demonstrated that deep learning methods, such as
CNN, can be used for defect identification in ultrasonic NDT
with high classification accuracies. In 2021, Ye et al [14] cre-
ated a new ‘USimgAIST’ dataset of over 7000 real ultrasonic
testing images of 17 types of defects and benchmarked the
dataset using state-of-the-art deep learning models. DenseNet
achieved the best result with an f1 score of 95.33% in the work
of Virkkunen et al [15], who used data augmentation to bring
the deep learning network to human evaluation levels of per-
formance in identifying cracks in pipe welds. Latete et al [16]
used simulated and experimental data to train the Faster R-
CNN, which allowed accurate identification, localization and
sizing of flat bottom holes and side drilled holes in the speci-
men. Medak et al [17] achieved 89.6% mAP for the detection
of extreme aspect ratio defects commonly found in ultrasonic
images by training the EfficientDet deep learning framework
with adjusted hyperparameters.
These studies demonstrate that deep learning has great
potential for ultrasonic testing image recognition, and the com-
bination of deep learning algorithms with ultrasonic testing B-
scan images recognition has considerable significance in terms
of improving detection efficiency and ensuring discriminatory
accuracy. However, most of the research has been conducted
based on simulation data, and there are no scholars who have
systematically studied various aspects of data acquisition, data
cleaning, deep learning model selection and model improve-
ment in practical industrial applications.
In this study, we have conducted comprehensive research
on Dataset creation, benchmark selection for deep learn-
ing models and model improvement methods. The overall
framework of our approach is illustrated in figure 2. We
have evaluated the performance of the latest deep learning
models for automated defect evaluation of ultrasonic images
in precision forgings using our self-built datasets. We have
used YOLOv5s as the baseline and fine-tuned the automated
ultrasonic image detection process through lightweight model
improvements and data cleaning methods. Our study provides
some insight into the deployment of deep learning models
for automated defect assessment applications in ultrasonic
images.
2. Construction of ultrasonic image dataset
There is currently a lack of publicly available large-scale data-
sets for ultrasonic testing due to the diversity and variability of
defects and the difficulty in obtaining sample data. To address
this gap and develop an automated evaluation algorithm for
ultrasonic testing images, we collected data from 7 samples
containing hole defects ranging from 0.5 mm to 1 mm in dia-
meter and crack defects less than 1 mm in width. Data was
acquired using an AOS phased-array ultrasonic real-time total
focus imaging system, as shown in figure 3. The phased-array
transducer utilized had a frequency of f = 5 MHz, 128 arrays,
a width of e = 0.65 mm, a gap of g = 0.1 mm between
arrays, a center distance of p = 0.75 mm, and a height of
w = 10 mm.
A total of 30 ultrasonic B-scan images were acquired using
the Total Focus Imaging Algorithm (TFM), comprising 28
images with defects and 2 images without defects. To enhance
the sample size for improved training of the deep learning
model, the images were randomly cropped to generate 8000
B-scan images of 224 × 224 pixels. These images were ana-
lyzed and labeled by multiple engineers to identify the types
and locations of defects, as illustrated in table 1. The dataset
was divided into a training set, validation set, and test set in a
3:1:1 ratio.
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Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 3. Phased array ultrasonic real-time total focus imaging system.
Table 1. Dataset division.
Number of
hole defects
Number of
crack defects
Number of
defective images
Number of
defect-free images
Total number
of images
Training set
Validation set
Test set
Total
7543
2471
2465
12 470
1190
362
368
1920
4088
1379
1380
6847
692
231
230
1153
4780
1610
1610
8000
Figure 4 displays ultrasonic B-scan images of the defect-
ive and healthy samples we acquired, which contain holes
and cracks. While crack defects are clearly visible through
inspection, some tiny hole defects are not eas-
visual
ily distinguishable from the background. This difficulty in
detection can lead to missed or false detections during
analysis.
Due to the small size of hole defect targets and the pres-
ence of some background noise in B-scan images, engineers
may encounter problems during annotation, such as miss-
ing defect annotations, mislabeled types, oversized bound-
ing boxes, and bounding boxes with center points outside the
image. To address these issues, we used the method shown in
figure 5 to automatically retrieve data and obtained over 200
images with problematic annotations. We then re-annotated
these images.
The dataset after data cleaning was divided as shown in
table 2.
3. Baseline testing
trained all models on a machine equipped with a single
NVIDIA GTX 1070 (8G) graphics card, using the default
hyperparameter settings and the maximum batch size accept-
able for that card.
To evaluate the performance of each model, we used four
statistics: TP (True Positive), FP (False Positive), TN (True
Negative), and FN (False Negative). Based on these statist-
ics, we introduced six evaluation metrics: Precision (P), Recall
(R), [email protected], [email protected]:.95, number of model parameters
(Params), and frames per second (FPS).
Precision, which refers to the probability of detecting the
correct target in all detected targets, can be calculated using
equation (1). Recall, which refers to the probability of correct
recognition among all positive samples, can be derived from
equation (2)
Precision =
TP
TP + FP
Recall =
TP
TP + FN
.
(1)
(2)
In this study, we aimed to evaluate the performance of various
deep learning models on our acquired ultrasonic defect dataset.
Specifically, we compared YOLOv3 [18], YOLOv5, YOLOv7
[19], YOLOR [20], EffcientDet [21], and the two-stage detec-
tion model Faster-RCNN [22], which are among the most
commonly used models in the field of object detection. We
A Precision-Recall curve can be plotted from an array con-
taining Precision and Recall values, and the average precision
AP is the area under the curve, calculated as follows:
1ˆ
AP =
p (r) dr.
(3)
0
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Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 4. Ultrasonic B-scan images of (a) holes, (b) cracks, (c) no defects.
mAP is the mean of all classes of AP:
the YOLOv5s model was chosen as the baseline for further
research.
mAP =
1
n
n∑
i =1
APi
(4)
4. Methods
where n represents the type of defect, [email protected] represents the
mAP value when IoU is set to 0.5, and [email protected]:.95 represents
the average mAP at different IoU thresholds (from 0.5 to 0.95,
step size 0.05).
Table 3 shows that among the deep learning models tested,
the YOLOv5s model achieved the highest levels of preci-
sion, [email protected]:.95, and FPS. While the recall rate was only
3.0% lower than the best-performing YOLOR-P6 model.
Compared to the best performing EfficientDet d0, the differ-
ence in [email protected] was only 0.7%. As the localization effect
of defects and re-al-time detection are of more importance,
Although the YOLOv5s model already exhibits good infer-
ence speed and detection performance, this study still faces
some challenges that need to be addressed. Firstly, during the
detection of hole defects, the small size of the target leads to
a low Precision and Recall of YOLOv5s, resulting in missed
detections. Secondly, the large number of convolutional and
deep neural network structures can lead to excessive model
complexity, which is not suitable for deployment to mobile or
embedded systems.
To address these issues, this study optimized the model
structure and used data cleaning methods to improve the
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Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 5. Data cleaning process.
Table 2. Data cleaning results.
Number of
hole defects
Number of
crack defects
Number of
defective images
Number of
defect-free images
Total number
of images
Training set
Validation set
Test set
Total
7502
2481
2458
12 441
1190
362
368
1920
4082
1383
1371
6836
698
227
239
1164
4780
1610
1610
8000
Table 3. Benchmarking experiments.
Model
Faster-RCNN(resnet50)
YOLOv3 spp
YOLOv5s
YOLOv7
YOLOR-P6
EffcientDet d0
Size
224
512
640
640
640
512
P
0.899
0.864
0.937
0.882
0.653
0.941
R
0.902
0.871
0.936
0.901
0.966
0.937
6
[email protected]
[email protected]:.95
FPS
Params
0.936
0.901
0.96
0.925
0.933
0.967
0.558
0.471
0.591
0.471
0.506
0.537
17
21
72
23
35
29
41.8M
62.5M
7.02M
36.9M
36.8M
3.9M
Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 6. Improved YOLOv5s model.
Figure 7. CBS_CBAM module.
efficiency of automated defect detection in ultrasonic images.
The optimized YOLOv5s model structure is shown in figure 6.
4.1. YOLOv5s model improvement
To improve detection efficiency and enhance the network’s
focus on the target, we incorporated CBAM into the CBS
module in layers 1, 3, and 5 of the backbone network.
As shown in figure 7,
the CBAM module [23] sequen-
tially infers the attention graph through the channel atten-
tion module and the spatial attention module. The chan-
nel attention module leverages the information between fea-
ture channels, while the spatial attention module leverages
the information between feature spaces. The attention graph
is then multiplied with the input feature graph for adapt-
ive feature optimization, which effectively attends to small
targets.
To fulfill the requirements of industrial applications, we
introduced the Ghost module [24] for a lightweight net-
work design, by replacing the CBS module at layer 7 with
GhostConv. In figure 8(a), GhostConv is performed in two
steps: firstly, using normal convolution to obtain fewer fea-
ture maps, then applying a second convolution on top of it
to obtain more feature maps, and finally concatenating the
different feature maps together to produce a new output. We
replaced the C3 module in Backbone with C3Ghost, whose
structure is shown in figure 8(c), mainly consisting of ordinary
convolution and the GhostBottleneck as shown in figure 8(b).
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Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Figure 8. (a) GhostConv, (b) GhostBottleneck and (c) C3Ghost modules.
The GhostBottleneck module allows sufficient or redundant
information to be provided in the feature layer, to always
ensure the model’s understanding of the input data.
To address the small and medium-sized target defects in this
study, which are mainly concentrated in the shallow part of the
neural network, we reduced the number of C3Ghost modules
in layers 2, 4, and 6 of the backbone network from the ori-
ginal [3, 6, 9] to [2, 4, 6]. This adjustment effectively improves
the network’s detection capability for small and medium-sized
targets.
To reduce computational complexity and network structure
while maintaining accuracy, the CBS module of the neck net-
work was replaced with GhostConv, and the C3 module was
replaced with C3Ghost, effectively compressing the network
parameters of YOLOv5s.
IOU =
B1 ∩ B2
B1 ∪ B2
(6)
where ρ2 (b, bgt) represents the Euclidean distance between the
centroids of the prediction frame and the true frame. c repres-
ents the diagonal distance of the smallest closed area that can
contain both the prediction box and the true box, B1 for the
true box and B2 for the prediction box.
a =
v
1 − IOU + v
(
v =
4
π 2
arctan
wgt
hgt
− arctan
)
2
w
h
LOSSCIOU = 1 − IOU +
ρ2 (b, bgt)
c2
+ av
(7)
(8)
(9)
4.2. Comparison of loss functions
YOLOv5 defaults to using the CIOU loss function, and CIOU
Loss takes into account the overlap area, centroid distance and
aspect ratio of the bounding box regression though. As shown
in equation (5):
CIOU = IOU − ρ2 (b, bgt)
c2
− av
(5)
where a is the weight function and v reflects the difference in
aspect ratio rather than the true difference between the aspect
ratio and its confidence level respectively, so this can some-
times prevent the model from optimizing similarity effect-
ively, for which we introduced the EIOU loss function and
compared it with the CIOU loss function. EIOU loss was pro-
posed by Zhang et al [25] in 2021, which minimizes the differ-
ence between the width and height of the target frame and the
8
Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Anchor, producing faster convergence and better localization
results.
in Precision, a 0.8% increase in Recall, a 43.2% reduction in
the amount of parameters, and an increase in FPS to 75.1.
The comparison of solutions A, D, E, and G reveals that
although optimizing the backbone network can reduce the
model’s parameter count, it does not significantly improve
the FPS. This is because the introduction of the CBAM
attention mechanism in the improved backbone network
increased the network layers, thus affecting the inference
speed.
Solution D involved lightweight design specifically for
the backbone and neck networks, achieving a superior bal-
ance between mAP and params. This approach resulted
in the best detection performance. While ensuring detec-
tion accuracy,
it significantly reduced the model’s para-
meter count, enhancing detection efficiency. It meets the
requirements of accuracy and real-time performance in
the lightweight
industrial defect detection. Additionally,
model is well-suited for practical deployment in production
environments.
In order to demonstrate the impact of data quality on
the model’s detection accuracy, this study trained and tested
the original YOLOv5s model and the improved model on
the cleaned dataset. The results are presented in table 5,
which clearly shows that data cleaning can effectively improve
all aspects of model metrics. Precision improved by 4.5%
and [email protected] by 3.2%. Moreover, compared to the original
YOLOv5s model, the improved model has only 0.1% lower
[email protected]:.95, but the number of model parameters is reduced
by 43.2%, FPS is also slightly improved, and several other
indicators have not changed significantly. Therefore, in prac-
tical applications, it is more productive to identify the deep
learning model first and then look for ways to improve the
data.
Figure 9 illustrates a comparison of the mAP between
the improved algorithm and the original algorithm during the
training phase. It can be observed that the convergence rate of
the improved model is similar to that of the original model,
indicating that the improvements made in this study do not
affect the model’s convergence.
Figure 10 illustrates the detection results of the YOLOv5s
model before and after the improvement. The green circles
represent the defects that were missed. Compared to the
YOLOv5s model, the improved method in this study still
has some cases of missing detection for small defects that
are difficult to distinguish with the naked eye. However, it
achieves a high accuracy rate of detection overall. This indic-
ates that the lightweight model proposed in this study has
excellent detection performance and can meet the accuracy
and real-time performance requirements in industrial defect
detection.
The equation for EIOU loss is as follows:
LOSSEIOU = LOSSIOU + LOSSdis + LOSSasp
= 1 − IOU +
ρ2 (b, bgt)
c2
+
ρ2 (w, wgt)
C2
w
+
ρ2 (h, hgt)
C2
h
(10)
where C2
rectangle of the predicted and real boxes.
w and C2
h are the width and height of the smallest outer
The EIOU equation consists of three parts. LOSSIOU is the
loss of overlap between the predicted and true frames, LOSSdis
is the loss of distance between the center of the predicted and
true frames, which is the same as that of CIOU, and LOSSasp is
the loss of width and height of the predicted and true frames.
5. Experimental results and discussion
To validate the impact of the improvements described in this
study on the detection performance of the model, an evaluation
was carried out on the ultrasound B-scan dataset that we col-
lected. We set up 7 solutions to analyze the different improve-
ment components, each using the same training parameters.
Table 4 shows the results of the evaluation. Solution A
optimizes the backbone network by using the CBS_CBAM
structure, adding a channel attention module and a spatial
attention module to enhance the detection of small targets,
replacing the Conv module at layer 7 with GhostConv, and
replacing the C3 module with C3Ghost. The [email protected]:.95
only reduced by 0.6%, while the amount of model paramet-
ers was reduced by 24.8%, and the FPS increased to 73.6.
Solution B improves the neck network by replacing the
Conv module with GhostConv and the C3 module with
C3Ghost, reducing the amount of model parameters by 18.5%
and increasing the FPS considerably to 85.7. Solution C uses
the EIOU loss function to replace the original CIOU loss to
improve the localization accuracy of the model bounding box,
with effective improvements in Precision, Recall, and FPS.
Solutions D, E, and F were subjected to two-by-two cross-
validation, and the comparison revealed that improving the
backbone and neck networks could significantly reduce the
number of model parameters. Improving the IOU loss could
improve the Recall rate and reduce defect misses.
Solution G has been improved for all three areas. Although
[email protected] is reduced by 0.2% and [email protected]:.95 by 2.2% com-
pared to the original YOLOv5s model, there is a 0.6% increase
9
Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
Model
Backbone
Neck
EIOU
P
R
[email protected]
[email protected]:.95
Params
FPS
Table 4. Ablation experiments.
YOLOv5s
Solution A
Solution B
Solution C
Solution D
Solution E
Solution F
Solution G
3
3
3
3
3
3
3
3
3
3
3
3
0.937
0.936
0.935
0.945
0.941
0.943
0.943
0.942
0.936
0.936
0.931
0.944
0.936
0.944
0.943
0.944
0.96
0.957
0.958
0.961
0.961
0.962
0.96
0.958
0.591
0.585
0.586
0.589
0.572
0.588
0.582
0.569
7.02M
5.28M
5.72M
7.02M
3.99M
5.28M
5.72M
3.99M
Table 5. Data cleaning test results.
Model
YOLOv5s
YOLOv5s + Data cleaning
Solution D + Data cleaning
P
0.937
0.982
0.978
R
0.936
0.981
0.981
[email protected]
[email protected]:.95
0.96
0.992
0.990
0.591
0.677
0.676
Params
7.02M
7.02M
3.99M
72.6
73.6
85.7
86.1
74.5
74.4
85.5
75.1
FPS
72.6
72.6
74.5
Figure 9. Comparison of (a) [email protected] and (b) [email protected]:.95 for Solution D and YOLOv5s.
Figure 10. Detection results of (a) YOLOv5s and (b) Solution D.
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Meas. Sci. Technol. 35 (2024) 035605
J Zhao et al
6. Conclusion
Consent for publication
To achieve effective automation in the detection of ultrasound
B-scan images, this study proposes an improved YOLOv5
model, making the following contributions:
All authors have consented to have this work published and
have approved of submission to the Measurement Science and
Technology.
(1) A baseline test was conducted on the constructed data-
set, comparing the performance of YOLOv3, YOLOv5,
YOLOv7, YOLOR, EfficientDet, and Faster-RCNN. The
YOLOv5 model was identified as the most efficient
method for analyzing ultrasound B-scan images currently
available.
(2) The YOLOv5 model was enhanced by incorporating
the CBAM attention mechanism and GhostConv light-
weight convolution, simplifying the model complexity and
improving detection efficiency.
(3) From a
data
nificantly
accuracy.
data-centric
perspective,
an
cleaning method was
employed
enhance
the
algorithm’s
automated
to
sig-
detection
The primary objective of this study is to validate the feasib-
ility and effectiveness of the developed method. It is acknow-
ledged that defects in real-world applications might be even
more intricate. The breadth of collected ultrasound data and
the extent of automated quantitative analysis will be explored
in future work.
Data availability statement
The data cannot be made publicly available upon publication
because they are owned by a third party and the terms of use
prevent public distribution. The data that support the findings
of this study are available upon reasonable request from the
authors.
Acknowledgments
The author would like to thank the anonymous reviewers
for constructive comments and suggestions which led to an
improved presentation.
Funding
This work was supported by the General Project of the
National Natural Science Foundation of China, Project No.
in
51875501; Postgraduate Education Innovation Project
Shanxi Province of China, Project No. 2022Y671, and the
Natural Science Foundation of Shanxi Province, China,
Project No. 202103021224273.
Conflict of interest
The authors declare that we have no competing interest.
11
Authors’ contributions
Z J and D X wrote most of the manuscript text and gener-
ated all the graphics. Z J and Z Y developed the algorithm and
wrote the program. S X wrote the introduction and provided
background information and references.
ORCID iD
Jianjun Zhao https://orcid.org/0009-0003-2931-0379
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12
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10.1038_s41467-022-30406-4.pdf
|
Data availability
The cryo-EM particle stacks, maps and models generated in this study have been
deposited in EMPIAR image archive, EMDB database and the Protein Data Bank,
respectively, under accession codes EMPIAR-10969, EMD-25757 and PDB-7T9G) for
VcINDY-Na+ (300 mM) structure and under accession codes EMPIAR-10970, EMD-
25756 and PDB-7T9F) for VcINDY-Ch+ structure. Source Data for Fig. 4 are available
with the paper.
|
Data availability The cryo-EM particle stacks, maps and models generated in this study have been deposited in EMPIAR image archive, EMDB database and the Protein Data Bank, respectively, under accession codes EMPIAR-10969, EMD-25757 and PDB-7T9G ) for VcINDY-Na + (300 mM) structure and under accession codes EMPIAR-10970, EMD- 25756 and PDB-7T9F ) for VcINDY-Ch + structure. Source Data for Fig. 4 are available with the paper.
|
ARTICLE
https://doi.org/10.1038/s41467-022-30406-4
OPEN
Structural basis of ion – substrate coupling in the
Na+-dependent dicarboxylate transporter VcINDY
David B. Sauer1,2,4, Jennifer J. Marden1,2, Joseph C. Sudar
Da-Neng Wang
1,2✉
2, Jinmei Song1,2, Christopher Mulligan
3✉
&
;
,
:
)
(
0
9
8
7
6
5
4
3
2
1
The Na+-dependent dicarboxylate transporter from Vibrio cholerae (VcINDY) is a prototype
for the divalent anion sodium symporter (DASS) family. While the utilization of an electro-
chemical Na+ gradient to power substrate transport is well established for VcINDY, the
structural basis of this coupling between sodium and substrate binding is not currently
understood. Here, using a combination of cryo-EM structure determination, succinate binding
and site-directed cysteine alkylation assays, we demonstrate that the VcINDY protein
couples sodium- and substrate-binding via a previously unseen cooperative mechanism by
conformational selection. In the absence of sodium, substrate binding is abolished, with the
succinate binding regions exhibiting increased flexibility, including HPinb, TM10b and the
substrate clamshell motifs. Upon sodium binding, these regions become structurally ordered
and create a proper binding site for the substrate. Taken together, these results provide
strong evidence that VcINDY’s conformational selection mechanism is a result of the
sodium-dependent formation of the substrate binding site.
1 Department of Cell Biology, New York University School of Medicine, New York, NY 10016, USA. 2 Skirball Institute of Biomolecular Medicine, New York
University School of Medicine, New York, NY 10016, USA. 3 School of Biosciences, University of Kent, Canterbury, Kent, UK. 4Present address: Centre for
Medicines Discovery, Nuffield Department of Medicine, University of Oxford, Oxford, UK.
email: [email protected]; [email protected]
✉
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VcINDY is a Na+-dependent dicarboxylate transporter that
imports TCA cycle intermediates across the inner mem-
brane of Vibrio cholerae1,2. The detailed structural and
mechanistic understanding of VcINDY1–4 has made the protein
a prototype of the divalent anion sodium symporter (DASS)
family (Supplementary Fig. 1a, b)5. Within the human genome,
the SLC13 genes encode for DASS members including the
Na+-dependent, citrate transporter (NaCT) and dicarboxylate
transporters 1 and 3 (NaDC1 and NaDC3)6. Besides functioning
as TCA cycle intermediates, DASS-imported substrates are cen-
tral to a number of cellular processes. In bacteria C4-carboxylates
can serve as the sole carbon source for growth7, while imported
citrate and tartrate are electron acceptors during fumarate
respiration8. Citrate is also a precursor for both fatty acid bio-
synthesis and histone acetylation in mammals9,10. Dicarboxylates
such as succinate and α-ketoglutarate act as signaling molecules
that regulate the fate of naive embryonic stem cells and certain
types of cancer cells11,12. As a result of these roles in regulating
cellular di- and tricarboxylate levels, mutations in DASS trans-
porters have dramatic physiological consequences. Deletion of
bacterial DASS transporters can abolish growth on particular
dicarboxylates7,8. Mutations in the human NaCT transporter
cause SLC13A5-Epilepsy in newborns13, whereas variants in
the dicarboxylate transporter NaDC3 lead to acute reversible
leukoencephalopathy14. In mice, knocking out NaCT results in
protection from obesity and insulin resistance15. Such roles of
SLC13 proteins in cell metabolism have made them attractive
targets for the treatment against obesity, diabetes, cancer and
epilepsy16–18. Therefore, mechanistic characterization of
the
prototype transporter VcINDY will help us to better understand
the transport mechanism of the entire DASS family, including the
human di- and tricarboxylate transporters.
The VcINDY protein is a homodimer consisting of a scaffold
domain and a transport domain (Supplementary Fig. 1b–f)1. The
conservation of this architecture throughout the DASS/SLC13
family has been confirmed by X-ray crystallography and cryo-
electron microscopy (cryo-EM) structures of VcINDY, LaINDY,
a dicarboxylate exchanger from Lactobacillus acidophilus, and the
human citrate transporter NaCT1,4,19,20. Comparison of VcINDY
in its inward-facing (Ci) conformation with the outward-facing
(Co) structure of LaINDY, along with MD simulations, reveals
that an elevator-type movement of the transport domain, through
an ~12 Å translation along with an ~35° rotation, facilitates
translocation of the substrate from one side of the membrane
to the other19. In fact, the structural and mechanistic conserva-
tion may extend beyond DASS to the broader Ion Transport
Superfamily (ITS)5,21.
Substrate transport of VcINDY is driven by the inwardly-
directed Na+ gradient, with dicarboxylate import coupled to the co-
transport of three sodium ions (Supplementary Fig. 1a, b)1,2,22. The
binding sites for the substrate and two central Na+s have been
identified in the structures of VcINDY in its Na+- and substrate-
bound inward-facing (Ci-Na+-S) state (Supplementary Fig. 1e, f)1,4.
The Na1 site on the N-terminal half of the transport domain is
defined by a clamshell formed by loop L5ab and the tip of hairpin
HPin. A second clamshell encloses Na2, related to Na1 by inverted-
repeat pseudo-symmetry in the sequence and structure, and formed
by L10ab and the tip of hairpin HPout (Supplementary Fig. 1c).
In addition to binding the Na+s, both hairpin tips also form parts of
located between the Na+ sites. Each
the substrate-binding site,
hairpin tip consists of a conserved Ser-Asn-Thr (SNT) motif, and
the two SNT motifs form part of the substrate-binding site, making
direct contact with carboxylate groups of the substrate. Whereas
these two SNT signature motifs are responsible for recognizing
carboxylate, additional residues in neighboring loops have been
proposed to distinguish between different kinds of substrates4.
Furthermore, VcINDY’s structure with sodium in the absence of a
substrate (the Ci-Na+ state), determined in 100 mM Na+, is very
similar to that of the Na+- and substrate-bound state Ci-Na+-S19.
While the Na+- and substrate-binding sites in VcINDY have
been well-characterized1,4,23, the coupling mechanism between
the electrochemical gradient and substrate transport24 is less well
understood. There is strong evidence that charge compensation
by sodium ions is essential in lowering the energy barrier for
transporting the di- and trivalent anionic substrates across the
membrane19. However, such charge compensation alone does not
necessarily result in substrate binding as Li+ is able to bind to
VcINDY similarly to Na+, but results in a lower affinity substrate
binding site and considerably reduced transport rates2,23. More
importantly, charge neutralization cannot explain the sequential
binding observed for VcINDY. As is the case for other DASS
proteins25–28, all available experimental evidence from both
whole cells and reconstituted systems supports the notion that in
VcINDY sodium ions and substrate bind in a sequential manner,
with Na+s binding first, followed by dicarboxylate2,3,23,29. As a
secondary-active transporter can transport substrate in either
direction, it follows that the release of the substrate and Na+s is
also ordered, with the substrates being released first.
Structures of VcINDY in the Na+- and substrate-bound state
Ci-Na+-S, in which the Na+ sites share residues with the sub-
strate site in their center, allowed us to propose that substrate
binding in VcINDY follows a cooperative binding mechanism via
conformational selection1,30. In this mechanism, the binding
of sodium ions helps to induce a proper binding site for the
substrate (Supplementary Fig. 1a, b). Conversely, in the absence
of bound sodium ions the substrate-binding site will change
significantly, such that the substrate cannot bind. Not only can
such a mechanism be part of Na+—substrate coupling, it may
also explain the sequential binding observed for VcINDY.
This conformational selection mechanism of substrate binding
enables us to make two explicit, experimentally testable predic-
tions. First, the affinity of the transporter to a substrate must
be much higher in the presence of Na+ than in its absence.
Second, substantial structural changes will occur at the Na+ sites
in the absence of sodium, affecting substrate binding.
In this work, we aim to test these two predictions using a
combination of structure determination by single-particle cryo-EM,
substrate-binding affinity measurements by intrinsic tryptophan
fluorescence quenching, and position accessibility quantification
via a newly-developed site-directed cysteine alkylation assay29. In
particular, we characterize VcINDY in sodium-saturating and
sodium-free conditions, including structures in Ci-Na+ and Ci-apo
states. These experimental results allow us to directly test the
conformational selection binding model of VcINDY.
Results
Succinate binding depends on the presence of Na+. To test the
first of
the predictions generated from our conformational
selection hypothesis, we measured VcINDY’s binding affinity for
the model substrate, succinate, in both the presence and absence
of Na+ (Supplementary Fig. 2). We reasoned that VcINDY’s
tryptophans, particularly Trp148 located at
the tip of HPin
of the Na1 site, may change its position or environment upon
Na+-/substrate-binding. Thus, we used intrinsic tryptophan
fluorescence quenching, a technique that has been successfully
applied to measure substrate binding for various membrane
transporters20,31–36. In the presence of 100 mM Na+, detergent-
purified VcINDY was found to bind succinate with an apparent
Kd of 92.2 ± 47.4 μM (Fig. 1a, Supplementary Fig. 2b). For
comparison, the human NaCT in the same protein family binds
its substrate citrate at an apparent Kd of 148 ± 28 μM20.
2
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ARTICLE
Fig. 1 Cryo-EM structure of VcINDY in the Ci-Na+ state determined in 300 mM Na+. a Measurements of succinate binding to detergent-purified VcINDY
in the presence of 100 mM NaCl, using intrinsic tryptophan fluorescence quenching (N = 4). Data are presented as mean values ± SEM. The apparent Kd
was determined to be 92.2 ± 47.4 mM. When NaCl was replaced with Choline chloride, no binding of succinate to VcINDY could be measured (N = 4).
b Cryo-EM map of VcINDY determined in the presence of 300 mM NaCl. The map is colored by local resolution (Å) and contoured at 5.1 σ. The overall
map resolution is 2.83 Å. c Structure of VcINDY in the Ci-Na+ state. The structure is colored by the B-factor. d Na1 site structure and Coulomb map.
e Na2 site structure and Coulomb map. f Overlay of VcINDY structures around the substrate and sodium binding sites in the Ci-Na+ state (green) and Ci-
Na+-S state (PDB ID: 5UL7, blue). There is very little structural change observed between the two states.
To measure the binding affinity of succinate to VcINDY with
empty Na+ binding sites, we searched for a cation to replace Na+ in
the purification buffer. This ion should not occupy the Na1 or
Na2 sites while still allowing the transporter protein to remain
stable in the solution. K+ is unable to power substrate transport in
VcINDY, but was found to be unsuitable as the protein precipitated
when purified in the presence of 100 mM KCl. We next tested the
organic cation choline (C5H14NO+, Ch+ in abbreviation). We
reasoned that Ch+ would be more stabilizing than K+ based on its
position in the Hofmeister series37, and that its size would preclude
it from occupying Na+ binding sites38. Indeed, VcINDY purified in
100 mM NaCl remained soluble at 0.5–1.0 mg/mL after diluting the
sample 11,000-fold in 100 mM ChCl. VcINDY was therefore
purified in the presence of 100 mM Ch+ as the only monovalent
cation. The protein eluted as a sharp, symmetrical peak on a size-
exclusion chromatography column (Supplementary Fig. 2a), con-
firming its stability and structural homogeneity.
intrinsic tryptophan fluorescence quenching with
VcINDY purified and assayed in the presence of 100 mM Ch+
revealed no succinate binding (Fig. 1a, Supplementary Fig. 2c).
Thus, the binding measurements in the presence and absence of
Na+ are consistent with a conformational selection model where
bound sodium ions are necessary to VcINDY forming a proper
binding site for succinate. Encouraged by these findings and our
ability to produce stable, structurally homogeneous and Na+-free
VcINDY, we next sought to uncover the structural basis of this
Na+—substrate
transporter’s
structures using cryo-EM in different states.
coupling by determining the
Notably,
Structure of VcINDY in 300 mM Na+. Generally speaking, the
transport mechanism of a secondary-active transporter is rever-
sible, in which the direction of substrate translocation depends on
the direction and magnitude of the driving force (Supplementary
Fig. 1a, b). Consequently, substrate binding is structurally
equivalent to substrate release. Therefore, to provide structural
insights into VcINDY’s binding process, we aimed to characterize
the substrate release process in the inward-facing (Ci) con-
formations by capturing the structures of VcINDY in the fol-
lowing states: its Na+-and substrate-bound state (Ci-Na+-S), its
Na+-bound state (Ci-Na+) and its Na+- and substrate-free state
(Ci-apo).
The Ci-Na+-S structure of VcINDY has previously been solved
using X-ray crystallography1,4. Additionally, we had characterized
the Ci-Na+ state using a cryo-EM structure of VcINDY purified
in 100 mM Na+ without substrate19. However, as the apparent
K0.5 for Na+ for VcINDY was measured to be 41.7 mM2, our
earlier VcINDY sample in 100 mM Na+ likely represents a
mixture of the Ci-Na+ and Ci-apo states. It is unclear whether the
subsequent cryo-EM image processing of the particles was able to
exclude all particles of the Na+-free Ci-apo state. To more clearly
and definitively resolve the Ci-Na+ state structure, in the current
work we purified and determined a structure of VcINDY in
300 mM Na+. This ion concentration was optimized to increase
the Na+ occupancy, while, at the same time, ensuring a low
enough noise level in the cryo-EM images to determine a Ci-Na+
state structure of this small membrane protein (total dimer mass:
126 kDa) at 2.83 Å resolution (Fig. 1b, c, Supplementary Figs. 3
and 4a–c, Table 1).
Compared with the two previously determined cryo-EM
structures of VcINDY in the presence of 100 mM NaCl19, the
herein reported structure in 300 mM Na+ (Fig. 1c, Supplementary
Fig. 4b) is identical to the one bound to a Fab and embedded in
lipid nanodisc (PDB ID: 6WW5)19 (r.m.s.d. of 0.460 Å for all the
non-hydrogen atoms), except for the position of the last three
residues at the C-terminus, which interact with the Fab molecule
used for structure determination (Supplementary Fig. 4d). Further-
though the map obtained in 300 mM Na+ conditions
more,
clarified the loop connecting HPoutb and TM10b, the model in
300 mM NaCl is effectively identical to the other previous Ci-Na+
structure in 100 mM NaCl, determined in amphipol and without
Fab (PDB ID: 6WU3)19, with an r.m.s.d of 0.358 Å after excluding
Val392 – Pro400 (Supplementary Fig. 4d).
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As expected from the higher Na+ occupancy in the 300 mM
sample, better-defined densities appeared within both the Na1
and Na2 clamshells (Fig. 1d, e), which were absent in the previous
100 mM Na+ maps19. In addition to coordination by side chains
and backbone carbonyl oxygens, the sodium ion at the Na1 site is
stabilized by the helix dipole moments from HPinb and TM5b
(Fig. 1f; Supplementary Fig. 1e, f), as previously observed in other
membrane proteins39,40. Similarly, the Na+ ion in the Na2 site is
stabilized by HPoutb and TM10b.
Finally, this higher resolution map confirmed our earlier
observations that succinate release caused only limited changes
at the substrate-binding site without relaxing the two Na+
clamshells19. Both the overall structure and the sodium- and
substrate-binding sites in the Ci-Na+ state are similar to those in
the sodium- and substrate-bound Ci-Na+-S state (Fig. 1e, f,
Supplementary Fig. 4e). The similarity of these structures agrees
with our conformational selection model of Na+ – substrate
coupling, which requires sodium-binding induce a Ci-Na+ state
structure that can bind substrate directly as in the Ci-Na+-S
state (Supplementary Fig. 1a, b).
Apo structure of VcINDY in Choline+. With the structures of
sodium- and succinate-bound1,4 and Na+-only bound (Fig. 1) states
in hand, the missing piece of the puzzle to validate the Na+ con-
formational selection mechanism was the Ci-apo state structure of
the transporter protein. As a Ch+ ion is too large to fit into a Na+
binding site36,38, and VcINDY was stable and monodisperse in the
presence of 100 mM ChCl (Supplementary Fig. 2a), such a pre-
paration allowed us to obtain cryo-EM maps of the Ci-apo state
(Fig. 2, Supplementary Figs. 5 and 6, Table 1). Unlike the VcINDY
map in 300 mM Na+ for which 3D classification converged to a
single map (Supplementary Fig. 3), the VcINDY-choline dataset
yielded four distinct classes at a resolution range of 3.6—4.4 Å
resolution (Supplementary Figs. 5 and 7). The 3D class with the
highest resolution was further refined to 3.23 Å resolution (Fig. 2a, b,
Supplementary Fig. 6c). The least well-resolved regions of the map,
and highest B-factors of the model, are found in L4-HPin and L9-
HPout, two previously-identified hinge regions that facilitate move-
ment of the transport domain19. Whereas the overall fold of the
protein in Ch+ remains the same (Supplementary Fig. 6d, f), Na+
densities within the Na1 and Na2 clamshells are totally absent.
Additional local changes are observed for the protein parts near the
Na1 and Na2 sites (Fig. 2c), with a loss of density in each Ci-apo
map at the HPinb and TM10b helices (Fig. 3b), indicating increased
local structural flexibility.
Flexibility of Apo VcINDY near the Na1 and Na2 sites. While
the VcINDY Ci-apo state overall structure is similar to those in
the 300 mM Na+ (r.m.s.d of 0.672 Å) (Supplementary Fig. 6f), the
model exhibited significant changes near the Na1 and N2 sites
(Figs. 2c and 3a, b). The tip of HPin and the L10a-b loop have
moved away from the Na1 and Na2 sites, respectively, with the
carbonyls of Ala376 and Ala420, and the side chain of Asn378
also rotated away from the Na2 site. Notably, HPinb near the
Na1 site and TM10b near the Na2 site and their connecting loops
showed marked decreased density in the cryo-EM map, corre-
sponding to the increased flexibility of these regions (Fig. 3a, b).
Correspondingly, the model exhibited significantly higher relative
B-factors in the same regions compared to the rest of the model
(Fig. 3c, d). However, we recognized that such a single, averaged
model might not fully describe the true structural ensemble, and
sought a method to describe the Ci-apo state’s mobility.
To further analyze such local flexibility, we used simulated
annealing41,42 in a model refinement protocol analogous to protein
structure determination by NMR spectroscopy43. We reasoned that
in multiple, separate refinements with simulated annealing the rigid
parts of the VcINDY would converge to the same coordinates, while
mobile portions of the protein would arrive at distinct atomic
positions in each run. We term this as NMR-style analysis in
recognition of NMR’s power to characterize protein dynamics,
though in cryo-EM the constraints are Coulomb potential maps
rather than distances.
Most parts of the VcINDY structure exhibit no variation in the
Ci-Na+ state, including HPinb and TM10b in the 300 mM Na+
condition (Fig. 3e, Supplementary Fig. 8a). In contrast, in the Ci-
apo state the NMR-style analysis clearly illustrated the structural
heterogeneity near the Na1 and Na2 sites (Fig. 3f, Supplementary
Fig. 8b). Instead of converging to one structure, the simulated
annealing resulted in an ensemble of structures, with the greatest
variations occurring in the HPinb and TM10b regions. The mean
r.m.s.d. of the transport domain’s backbone atoms for the Ci-apo
protomers is 0.589 Å, as opposed to 0.099 Å among Ci-Na+
protomers refined using the same protocol to the same resolution.
As the 3.23 Å apo map imposes C2 symmetry on one of four
classes of particles in ChCl (Supplementary Fig. 5), and all four
classes are different
the degree of
flexibility of these helices in the Ci-apo state is likely to be even
greater. Such helix flexibility results from the absence of Na+
interactions with residues in the clamshells and with the dipoles
of HPinb and TM10b44,45.
(Supplementary Fig. 7),
Site-directed alkylation supports structural changes to Na1 and
Na2 sites. To confirm the local conformational changes and helix
flexibility observed in our VcINDY structures, we implemented a
site-directed cysteine alkylation strategy that can directly assess
the solvent accessibility of specific positions in a protein. In this
a
L4-HPout
b
c
4.0
3.5
3.0
2.5
L9-HPin
N378
A376
Na1
I149
N151
Na2
A420
P422
HPinb
TM10b
Fig. 2 Cryo-EM structure of VcINDY in the Ci-apo state determined in Choline+. a Cryo-EM map of VcINDY preserved in amphipol determined in the
presence of 100 mM Choline Chloride. The map is colored by local resolution (Å) on the same scale as Fig. 1b and contoured at 4.8 σ. The overall map
resolution is 3.23 Å. The two previously-identified hinge regions which facilitate movement of the transport domain19, L4-HPin and L9-HPout, are found to
be most flexible. b Structure of VcINDY in the Ci-apo state. The structure is colored by the B-factor on the same scale as Fig. 1b. c Overlay of VcINDY
structures around substrate and sodium binding sites in the sodium-bound Ci-Na+ state (green) and the Ci-apo state (pink). The structures of the two Na1
and Na2 clamshells have changed in the absence of sodium ions, particularly around residues Ile149, Asn151, Ala376, Asn378, Ala420 and Pro422.
4
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a
c
e
Na1
Na2
TM10b
HPinb
b
Na1
Na2
TM10b
HPinb
d
Na1
Na2
Na1
Na2
TM10b
HPinb
TM10b
HPinb
f
Na1
Na2
Na1
Na2
TM10b
HPinb
TM10b
HPinb
Fig. 3 VcINDY flexibility changes near the Na1 and Na2 sites between the
Ci-Na+ state and Ci-apo states. a Cryo-EM density map in 300 mM NaCl.
b. Cryo-EM density map in 100 mM Choline Chloride. In a and b, the
respective protein models’ backbones are fitted into the densities. Maps are
contoured such that the scaffold domains have equal volume. c. Structure
of VcINDY in its Ci-Na+ state. d. Structure of VcINDY in its Ci-apo state. In
c and d, the structures are colored by normalized B-factors. e NMR-style
analysis of the VcINDY structure in Na+. f NMR-style analysis of the
VcINDY structure in Choline+. The resolution for refinement of both
structures in e and f was truncated to 3.23 Å. In the absence of sodium, the
helices on the cytosolic side of Na1 and Na2, particularly HPinb and TM10b
and their connecting loops, show markedly increase flexibility. Instead of a
single structure, the Ci-apo model consists of an ensemble of structures.
approach, single cysteines are introduced into a Cys-less version
of VcINDY, which is capable of robust Na+-driven transport2,3.
Following purification, the cysteine mutants of VcINDY are
incubated with the thiol-reactive methoxypolyethylene glycol
maleimide 5 K (mPEG5K). This tag reacts with solvent-accessible
cysteines and increases the protein mass by ~5 kDa, which is
separable from unmodified protein on an SDS-PAGE gel. As
mPEG5K will react faster with cysteines that are more accessible,
monitoring PEGylation over time provides us with the ability to
follow changes in the accessibility of particular parts of the pro-
tein under different conditions29.
To test our conformational selection model using biochemical
approaches, we designed a panel of single-cysteine mutants of
VcINDY that would report on the Na+-dependent accessibility
changes at the Na1 and Na2 sites predicted from structures
(Fig. 4a, Supplementary Fig. 8d). We selected residues that, if our
cooperative binding model is accurate, will exhibit a higher rate of
PEGylation in the absence of Na+ compared to its presence due
to the increased mobility of HPin and TM10b. To create our panel
proximal to the Na1 site, we purified four cysteine mutants whose
reactive thiol groups are buried in the Ci-Na+ state behind HPin
(L138C on HPina, A155C and V162C on HPinb and A189C on
TM5a). However, similar cysteine substitutions near Na2 (Val427,
Ile433, Gly442 and Met438) resulted in diminished expression
levels, likely indicating the importance of these residues to the
stability of the protein. Fortunately, cysteine mutation of Val441 to
cysteine, a residue located on TM11 and behind TM10b (Fig. 4a,
Supplementary Fig. 8d), expressed well and allowed for purifica-
tion. Typically, well-expressing single cysteine VcINDY mutants
that can be purified are capable of Na+-driven succinate
transport29.
We monitored the PEGylation of each mutant in the presence
and absence of Na+. Under these reaction conditions there is no
PEGylation of the Cys-less variant, demonstrating no background
labelling that could hinder analysis (Fig. 4b, top row). In the
presence of 300 mM Na+ we observed complete inhibition of
PEGylation at every position (Leu138, Ala155, Val162, Ala189
and Val411) over the time course of 60 min (Fig. 4b, left panels),
in agreement with our model that these residues are buried in the
Na+-bound state. However, in the absence of Na+ (but with
300 mM Ch+), every mutant showed escalated levels of PEGyla-
tion over time (Fig. 4b, right panels), indicating the increased
flexibility of HPinb and TM10b.
To ensure that the change in PEGylation rate that we observed
was due to changes in residue accessibility and not caused by an
unforeseen effect
the cations may have on the PEGylation
reaction, we monitored the reaction rate of a position for which
we observed no accessibility change in the structural analysis. A
cysteine mutant at Ser436, positioned at the periphery of the
transporter protein (Fig. 4a), exhibited minimal Na+-dependent
accessibility changes (Fig. 4b, bottom row).
These accessibility measurements, along with our previous
PEGylation results on three other VcINDY residues near the
Na1 site (T154C, M157C and T177C, Supplementary Fig. 8e)29,
fully support the changes in protein dynamics predicted upon
occupation of the Na1 and Na2 sites, and are consistent with a
conformational selection coupling model.
Structural comparison of Ci-Na+-S, Ci-Na+ and Ci-apo states.
The VcINDY structures determined in 300 mM Na+ and apo as
reported here, together with previously-determined X-ray struc-
ture of the protein with both sodium and substrate bound1,4,
allowed us to examine the structural changes of the transporter
between the Ci-Na+-S, Ci-Na+ and Ci-apo states. In addition to
the flexibility observed in HPinb and TM10b, we observed amino
acid sidechain movements both at the interface between the
scaffold domain and the transport domain, as well as on the
periplasmic surface of the protein.
At the scaffold–transport domain interface, side chains of
several bulky amino acids rotated or shifted between the three
states, including Phe100, His111 and Phe326 (Fig. 5a). On the
periplasmic surface, Trp461 at the C-terminus is buried in the apo
and Na+-bound structures (Fig. 5b). However, in the Ci-Na+-S
structure, the ring of the nearby Phe220 was rotated by ~90°,
pushing out the side chain of Trp461, leaving the C-terminus
pointing to the periplasmic space. Accordingly, the loop between
HPoutb and TM10a moved into the periplasmic space of the apo
VcINDY structure, displacing Glu394 and breaking its salt bridge
with Lys337. Whereas no single switch was identified that can
trigger conformational exchanges between the inward- and
outward-facing states,
local structural changes observed here
suggest that small changes at multiple locations are required for
inter-conformation transitions in VcINDY.
In comparing maps of the three states, we noted the VcINDY
Ci-Na+ map reported herein was sufficiently detailed to identify
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a
Na1
HPina
138
HPinb
Na2
441
TM10b
TM5a
189
155
162
90
HPina
138
162
Na1
HPinb
441
TM5a
189
155
TM10b
436
Na2
b
kDa
55
+ Na+
Na+
Cys-less
L138C
436
A155C
35
25
55
35
25
55
35
25
55
35
25
55
35
25
55
35
25
55
35
25
P
U
P
U
P
U
P
U
P
U
P
U
P
U
0 5 10 30 60
0 5 10 30 60 min
V162C
A189C
V441C
S436C
Fig. 4 Cysteine alkylation with mPEG5K of VcINDY near the Na1 and Na2 sites in the presence and absence of Na+. a Location of cysteine mutations.
Our structures suggested that HPinb and TM10b become flexible in the absence of sodium, increasing the solvent accessibility of Leu138, Ala155, Val162
and Ala189 near the Na1 site, and Val441 near the Na2 site. Position Ser436, for which no accessibility change was observed between our structures, is
used as a control. On a Cys-less background, residues at these positions were individually mutated to a cysteine for mPEG5K labeling. For clarity, only
amino acid numbers are labeled and the types are omitted. b Coomassie Brilliant Blue-stained non-reducing polyacrylamide gels showing the site-directed
PEGylation of each cysteine mutant over time in the presence and absence of Na+. P: PEGylated protein; U: Un-PEGylated protein. Each reaction was
performed on two separate occasions with the same result. Source data is provided as Source Data file.
a
b
F326
F100
H111
five ordered water molecules buried at
the dimer interface
(Supplementary Fig. 8c). The water molecules are not visible in
previous maps, or the VcINDY-apo map, indicating the high-
the VcINDY Ci-Na+ map reported here was
resolution of
necessary for their identification. These waters are arranged in a
square pyramidal configuration in the largely hydrophobic
pocket, coordinated by only the symmetry-related carbonyls of
Phe92 and inter-water hydrogen bonds. The role of these waters
in VcINDY folding or transport are unclear, though protein
folding defects underlie several pathogenic mutations on the
equivalent dimerization interface of NaCT5.
F220
W461
TM10a
HPoutb
E394
K337
Fig. 5 Movement of VcINDY’s amino acid side chains between its
Ci-Na+-S, Ci-Na+ and Ci-apo states. VcINDY structures in three states are
overlaid: Ci-Na+-S (blue), Ci-Na+ (green) and Ci-apo (pink) states. a At the
scaffold-transport domain interface, the side chains of Phe100, His111 and
Phe326 rotate between states. b On the periplasmic surface, some loops
and side chains move between the states, including Phe220, Lys337,
Glu394 and Trp462.
Discussion
Despite great advances in structural and mechanistic studies on
the
membrane transporters over the past
ion–substrate coupling mechanism is well characterized for only
very few co-transporters,
this
fundamental aspect of the secondary-active transport mechanism.
Here, we have described the structural basis of ion–substrate
coupling for VcINDY, which reveals a distinct conformational
selection mechanism that ensures obligatory coupling.
limiting our understanding of
twenty years46–50,
While Na+ sites in some other Na+-dependent transporters are
buried in the middle of the protein38,48,49,51, the sodium sites in
VcINDY are directly accessible from the extramembrane space.
Previous experimental data support that Na+-driven DASS co-
transporters operate via an ordered binding and release2,25–29.
Specifically, Na+ binding occurs before substrate binding, while
substrate release precedes Na+ release. For VcINDY, we have
now observed that sodium release from the Na1 and Na2 sites in
the cytoplasm allows increased conformational diversity going
from the Ci-Na+ to the Ci-apo states, whereas the Ci-Na+ and Ci-
6
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Co
Co-Na+
Co-Na+-S
TM10b
HPin
Ci
TM10b
HPin
TM10b
HPin
Ci-Na+
Ci-Na+-S
Fig. 6 Schematic model of conformational selection mechanism for
sodium—substrate coupling in VcINDY. In the absence of sodium ions,
HPinb and TM10b, along with their connecting loops responsible for sodium
and substrate binding, are flexible. From the ensemble of flexible structures,
the binding of sodium ions (blue circles) selects a conformation with a
proper binding site for the substrate, allowing its binding (red oval). The
scaffold and transport domains in each protomer are colored as green and
pink, respectively. Only the Na1 and Na2 sites are illustrated. Transport
domain movements in the two protomers are shown as symmetric for
simplicity but are functionally independent.
Na+-S states are structurally similar (Fig. 6). Specifically, the
movement of helices HPinb and TM10b is tightly coupled to Na+
binding. At the Na1 and Na2 sites, the sodium ions are stabilized
via direct and ion—dipole interaction with the two helices.
Therefore, upon Na+-release, the elimination of these interac-
tions caused the relaxation of the HPinb and TM10b helices44,45,
leading to increased mobility in the connected loops responsible
for substrate binding. In the reverse reaction, ions binding at the
Na1 and Na2 sites, concurrent with helix re-ordering, select from
the ensemble a structure with the proper binding site for the
substrate. While the effects of VcINDY’s cryptic third Na+ are
still to be determined, we now have established a structural
understanding of the Na+—substrate coupling mechanism for
this co-transporter. By extension, other DASS transporters may
utilise a similar structural mechanism for Na+—substrate cou-
pling (Fig. 6).
The structural basis of Na+-substrate coupling for VcINDY
is distinct
from that of GltPh/GltTk from the dicarboxylate/
amino acid:cation symporter family which otherwise share several
commonalities with VcINDY including the presence of re-entrant
hairpin
elevator-like
mechanism1,3,4,48,52–56. In addition, as we have shown here for
VcINDY, a cooperative binding mechanism has been suggested for
both GltPh and GltTk, which requires the initial binding of Na+ in
order to prime the binding site for the substrate, aspartate38,57.
However, the structural basis of Na+-substrate coupling in GltPh/
GltTk differs substantially from the coupling mechanism we observe
for VcINDY. Rather than the general relaxation of a helix governing
substrate-binding site formation, the binding of Na+ to GltPh/GltTk
induces discrete conformational changes of a small number of
amino acid residues centered on the highly conserved NMDGT
motif53,57,58. As is the case here for VcINDY (Fig. 6), the fully loaded
and Na+-only bound structures of GltPh/GltTk are
largely
identical52,53,57,58, demonstrating that Na+ binding drives the for-
mation of the substrate-binding site, and not the substrate itself.
utilization
loops
and
the
an
of
In addition to conformational selection, another mechanism for
ion–substrate coupling of co-transporters has been proposed to be
charge compensation5,19. Such a mechanism can greatly minimize
the energy penalty for translocating charged substrates across the
hydrophobic lipid bilayer59,60. Unlike for DASS exchangers19,
where charge compensation is the major force for overcoming the
←→ Ci transition, both local structural
energy barrier in the Co
ordering and charge balance are needed for Na+-coupled co-
transporters within the DASS family.
Comparison of the VcINDY structures reported here with
those determined earlier1,4,19, of three states in total, also sheds
new light on the mechanism of the transporter’s conformational
switching between the two sides of the membrane. As the Ci-apo
structure is significantly different from that of the Ci-Na+-S state,
their corresponding transitions to the outward-facing state:
Ci-apo to Co-apo and Ci-Na+-S to Co-Na+-S, are different at the
transport-scaffold domain interface (Fig. 6). Whereas the transi-
tion between Ci-Na+-S and Co-Na+-S state can be described as
rigid-body movement, as was seen in the DASS exchangers5,
the co-transporters’ Co-apo ←→ Ci-apo state transition likely
involves large structural rearrangements of the transport domain.
Considering the pseudo-symmetry of the DASS fold, the Ci-apo →
Co-apo movement would require refolding of TM10b to pack
against
the scaffold domain, and possibly the concurrent
unfolding of TM5b. This potential asymmetry between the apo-
state transition (Co-apo ←→ Ci-apo) and transition of the fully-
loaded transporter (Ci-Na+-S ←→ Co-Na+-S) needs further
investigation. Finally, the pseudo-symmetry within the DASS fold
and sequence1,3,19 and Na+ dependent solvent accessibility of the
S381C mutant on HPoutb of VcINDY, which we investigated
previously29, seem to indicate the Co state also undergoes Na+
dependent conformational selection to enable substrate binding.
However, verifying this hypothesis will require structural char-
acterization of a DASS symporter’s outward-facing state.
Methods
VcINDY expression and purification. Expression and purification of VcINDY
were carried out according to our previous protocol1. Briefly, E. coli BL21-AI cells
(Invitrogen) were transformed with a modified pET vector61 encoding N-terminal
10x His tagged VcINDY. Cells were grown at 32 °C until OD595 reached 0.8,
protein expression occurred at 19 °C following IPTG induction, and cells were
harvested 16 h post-induction. Cell membranes were solubilized in 1.2 % DDM and
the protein was purified on a Ni2+-NTA column. For cryo-EM and substrate
binding experiments, the protein was purified using size-exclusion chromatography
(SEC) in different buffers. The protein used for the cysteine alkylation assays was
produced as described previously29.
Tryptophan fluorescence quenching assay. Tryptophan fluorescence quenching
was used to measure affinity of succinate to purified VcINDY in detergent, using a
protocol adapted from earlier work on other membrane transporters20,31–34.
VcINDY purified by SEC in a buffer of 25 mM Tris pH 7.5, 100 mM NaCl and
0.05% DDM was used to measure succinate affinity, while the 100 mM NaCl was
replaced by 100 mM ChCl for affinity measurements in the absence of sodium.
Protein was diluted to a final concentration of 4 μM in SEC buffer. Using a Horiba
FluoroMax-4 fluorometer (Kyoto, Japan) at 22 °C and a 280 nm excitation wave-
length, the emission spectrum was recorded between 290 and 400 nm. The emis-
sion maximum was determined to be 335 nm. Subsequently, the change in
fluorescent emission at 335 nm was monitored with increasing concentrations of
succinic acid (pH 7.5), from 0.1 μM to 1 mM. Each experimental condition was
repeated 4 times. The binding curve was fit in Prism using a quadratic binding
equation to account for bound substrate62.
Amphipol exchange and cryo-EM sample preparation. From Ni2+-NTA pur-
ified VcINDY, DDM detergent was exchanged to PMAL-C8 (Anatrace, Maumee,
OH) as previously described19,63. Following further purification by SEC in buffer
containing 25 mM Tris pH 7.5, 100 mM NaCl and 0.2 mM TCEP, the NaCl con-
centration was increased to 300 mM and the protein sample was concentrated to
1.3 mg/mL. For the apo protein preparation, NaCl in the abovementioned SEC
buffer was replaced with 100 mM ChCl, and the protein sample was concentrated
to 1.3 mg/mL.
Cryo-EM grids were prepared by applying 3 μL of protein to a glow-discharged
QuantiAuFoil R1.2/1.3 300-mesh grid (Quantifoil, Germany) and blotted for 2.5 to
4 s under 100% humidity at 4 °C before plunging into liquid ethane using a Mark
IV Vitrobot (FEI).
Cryo-EM data collection. Cryo-EM data were acquired on a Titan Krios micro-
scope with a K3 direct electron detector, using a GIF-Quantum energy filter with a
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20-eV slit width. SerialEM was used for automated data collection64. Each micro-
graph was dose-fractioned over 60 frames, with an accumulated dose of 65 e-/Å2.
Cryo-EM image processing and model building. Motion correction, CTF esti-
mation, particle picking, 2D classification, ab initio model generation, hetero-
genous and non-uniform refinement, and per-particle CTF refinement were all
performed with cryoSPARC65. Each dataset was processed using the same protocol,
except as noted.
Micrographs underwent patch motion correction and patch CTF estimation,
and those with an overall resolution worse than 8 Å were excluded from
subsequent steps. An ellipse-based particle picker identified particles used to
generate initial 2D classes. These classes were used for template-based particle
picking. Template identified particles were extracted and subjected to 2D
classification. A subset of well-resolved 2D classes were used for the initial ab initio
model building, while all picked particles were subsequently used for heterogeneous
3D refinement. After multiple rounds of 3D classification (ab initio model
generation and heterogeneous 3D refinement with two or more classes), a single
class was selected for nonuniform 3D refinement with C2 symmetry imposed,
resulting in the final map.
All Cryo-EM maps were sharpened using Auto-sharpen Map in Phenix66,
models were built in Coot67, and refined in Phenix real space refine68. The model
for VcINDY in NaCl was built using the structure of VcINDY embedded in a lipid
nanodisc (PDB: 6WW5) as an initial model, with lipid and antibody fragments
removed. The VcINDY model in choline used the structure of VcINDY in 300 mM
NaCl, with ions and waters removed, as the starting model.
The NMR-style analysis used 5 independent runs of phenix.real_space_refine66 to
refine the models of VcINDY in apo and in 300 mM NaCl, with ions and waters
removed, using unique computational seeds for each run. Each refinement was
performed with simulated annealing, without NCS constraints or secondary structure
restraints, and a refinement resolution limit of 3.23 Å for both maps. Analysis with or
without map sharpening, or randomizing initial atomic positions using
phenix.pdbtools, gave similar results. Transport domain maps were scaled to equivalent
contours using the scaffold domain’s volume as an internal standard after extracting
with phenix.map_box. Figures were made using UCSF Chimera69 and PyMOL70.
Cysteine alkylation assay. For the cysteine alkylation experiments, each purified
cysteine mutant was exchanged into reaction buffer containing 50 mM Tris, pH 7,
5% glycerol, 0.1% DDM and either 300 mM NaCl or 300 mM ChCl (Na+-free
conditions). Protein samples were incubated with 6 mM mPEG5K and samples
were taken at the indicated timepoints and immediately quenched by addition of
SDS-PAGE samples buffer containing 100 mM methyl methanesulfonate (MMTS).
Samples were analyzed with Coomassie Brilliant Blue-stained non-reducing
polyacrylamide gels.
Reporting summary. Further information on research design is available in the Nature
Research Reporting Summary linked to this article.
Data availability
The cryo-EM particle stacks, maps and models generated in this study have been
deposited in EMPIAR image archive, EMDB database and the Protein Data Bank,
respectively, under accession codes EMPIAR-10969, EMD-25757 and PDB-7T9G) for
VcINDY-Na+ (300 mM) structure and under accession codes EMPIAR-10970, EMD-
25756 and PDB-7T9F) for VcINDY-Ch+ structure. Source Data for Fig. 4 are available
with the paper.
Received: 11 January 2022; Accepted: 28 April 2022;
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Acknowledgements
This work was financially supported by the NIH (R01NS108151, R01GM121994 and R01-
DK099023), the G. Harold & Leila Y. Mathers Foundation and the TESS Research Foun-
dation (to D.N.W); and Wellcome Trust (210121/Z/18/Z) and BBSRC (BB/V007424/1) (to
C.M.). D.B.S. was supported by the American Cancer Society Postdoctoral Fellowship
(129844-PF-17-135-01-TBE) and Department of Defense Horizon Award (W81XWH-16-1-
0153). We thank the following colleagues for helpful discussions: N. Coudray, R. Gonzalez
Jr., M. Lopez Redondo, J.A. Mindell and E. Tajkhorshid. We are also grateful to colleagues at
the Biophysics Colab, C. Grewer, R.M. Ryan and X. Wang, for commenting on the
manuscript. We thank the staff at the NYU Cryo-EM Facility and the NYU Microscopy Core
for assistance in grid screening and the Pacific Northwest Center for Cryo-EM in data
collection. EM data processing used computing resources at the HPC Facility of NYULMC.
Author contributions
J.J.M., J.S. and C.M. purified the proteins. J.J.M., J.C.S. and D.B.S. collected and analyzed
the substrate-binding data. C.M. did all the cysteine PEGylation experiments. D.B.S
collected and processed the cryo-EM images and built the atomic models. D.B.S and
D.N.W. analyzed the structures. D.B.S., C.M. and D.N.W. wrote the manuscript. All
authors participated in the discussion and manuscript editing. C.M. and D.N.W.
supervised the research.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41467-022-30406-4.
Correspondence and requests for materials should be addressed to Christopher
Mulligan or Da-Neng Wang.
Peer review information Nature Communications thanks Jeff Abramson, Reinhart
Reithmeier and the other, anonymous, reviewer(s) for their contribution to the peer
review of this work. Peer reviewer reports are available.
Reprints and permission information is available at http://www.nature.com/reprints
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in
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Open Access This article is licensed under a Creative Commons
Attribution 4.0 International License, which permits use, sharing,
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indicated otherwise in a credit line to the material. If material is not included in the
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regulation or exceeds the permitted use, you will need to obtain permission directly from
the copyright holder. To view a copy of this license, visit http://creativecommons.org/
licenses/by/4.0/.
© The Author(s) 2022
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