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\begin{document}

\title{The alteration of structural network upon transient association between
proteins studied using graph theory}



\author[1]{Ramanathan Sowdhamini}%
\author[1]{Vasam Prabantu}%
\author[1]{Himani Tandon}%
\author[1]{Sankaran Sandhya}%
\author[1]{Narayanaswamy Srinivasan}%
\affil[1]{Indian Institute of Science Molecular Biophysics Unit}%


\vspace{-1em}



  
  \date{May 22, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Proteins such as enzymes perform their function by predominant
non-covalent bond interactions between transiently interacting units.
There is an impact on the overall structural topology of the protein,
albeit transient nature of such interactions, that enable proteins to
deactivate or activate. This aspect of the alteration of the structural
topology is studied by employing protein structural networks, which are
node-edge representative models of protein structure, reported as a
robust tool for capturing interactions between residues. Several methods
have been optimised to collect meaningful, functionally relevant
information by studying alteration of structural networks. In this
article, different methods of comparing protein structural networks are
employed, along with spectral decomposition of graphs to study the
subtle impact of protein-protein interactions. A detailed analysis of
the structural network of interacting partners is performed across a
dataset of around 900 pairs of bound complexes and corresponding unbound
protein structures. The variation in network parameters at, around and
far away from the interface are analysed. Finally, we present
interesting case studies, where an allosteric mechanism of structural
impact is understood from communication-path detection methods. The
results of this analysis are beneficial in understanding protein
stability, for future engineering and docking studies.%
\end{abstract}%



\sloppy


\textbf{The alteration of structural network upon transient association
between proteins studied using graph theory}

Vasam Manjveekar Prabantu\textsuperscript{1}, Himani
Tandon\textsuperscript{1,2}, Sankaran Sandhya \textsuperscript{3},
Ramanathan Sowdhamini \textsuperscript{1,4,5,*}, Narayanaswamy
Srinivasan\textsuperscript{1,*}

\textsuperscript{1} Molecular Biophysics Unit, Indian Institute of
Science, Bangalore, India

\textsuperscript{2} MRC Laboratory of Molecular Biology, Cambridge,
United Kingdom

\textsuperscript{3} Department of Biotechnology, Faculty of Life and
Health Sciences, Ramaiah University of Applied Sciences, Bangalore,
India

\textsuperscript{4} National Centre for Biological Sciences, TIFR,
Bangalore, India

\textsuperscript{5} Institute of Bioinformatics and Applied
Biotechnology, Electronic City, 560100, Bangalore, India

*Joint corresponding authors

\textbf{Abstract}

Proteins such as enzymes perform their function by predominant
non-covalent bond interactions between transiently interacting units.
There is an impact on the overall structural topology of the protein,
albeit transient nature of such interactions, that enable proteins to
deactivate or activate. This aspect of the alteration of the structural
topology is studied by employing protein structural networks, which are
node-edge representative models of protein structure, reported as a
robust tool for capturing interactions between residues. Several methods
have been optimised to collect meaningful, functionally relevant
information by studying alteration of structural networks. In this
article, different methods of comparing protein structural networks are
employed, along with spectral decomposition of graphs to study the
subtle impact of protein-protein interactions. A detailed analysis of
the structural network of interacting partners is performed across a
dataset of around 900 pairs of bound complexes and corresponding unbound
protein structures. The variation in network parameters at, around and
far away from the interface are analysed. Finally, we present
interesting case studies, where an allosteric mechanism of structural
impact is understood from communication-path detection methods. The
results of this analysis are beneficial in understanding protein
stability, for future engineering and docking studies.

\textbf{Keywords:} Protein structural networks, graph spectral analysis,
protein-protein interaction, transient association, allostery, network
alterations\textbf{1. Introduction}

The importance of molecular flexibility for a protein to function is
well documented. The analysis of different structural states helps in
analysing its function. Several proteins are very rigid and exist in
fewer distinct conformations. However, most proteins exist predominantly
in an inactive state and seldom in an active state. The difference
between the structural states arises from subtle changes in local
conformations at specific sites or from large structural excursions with
altered topology. Some proteins also populate an intermediate state
which may be stabilised in a dynamic equilibrium due to strong
interactions. The stabilisation of such a transient state is generally
brought about by external perturbations like post translational
modifications, mutations, or various binding partners. One such scenario
is the perturbation of the protein structure due to binding with another
protein. The changes brought about at the site of their interface is
generally allosterically transmitted across the structure of the protein
to impact or present its active site. Although this is intuitive to
understand, the mechanism of this signalling has not been thoroughly
analysed across all proteins.

The analysis of allosteric signalling can often be approached using
protein structural networks (PSN). It is a simplistic mathematical model
of the residue interactions that exist in a well-ordered globular
protein structure, where the residues are considered as nodes and any
interaction between them is considered by drawing an edge between them.
The edge signifies a relationship between the interacting residues,
generally pertaining to features such as non-covalent bonding, proximity
between atoms in space and sometimes also based on energy parameters
that can be defined for interactions.

A further advancement on the use of these structure networks is the
application of a graph-spectral method for the global comparison of
proteins. This method is robust and sensitive to even minute structural
perturbations that can be observed between any pair of networks that are
given as input. The method described by Vasundhara and co-workers is an
advanced comparison metric that has been applied in the validation of
protein structure models and in understanding the amount of structural
variability in an ensemble of structures of a given protein. The method
has been employed in the current work for the global comparison of PSNs.

We have compared the bound and the unbound forms of the same protein,
that has been crystallised when bound to interacting partners as well as
independently. The ProPairs database is a large consortium of available
bound and unbound proteins structures and provides this information. Any
changes in network parameters, both local and global, are discussed
along with interesting clinically relevant scenarios where the network
may have changed considerably without affecting its overall structure
topology. The rearrangement, gain and loss of network connectivity are
discussed further, illustrated using case studies.

\textbf{2. Materials and methods}

\emph{2.1 Dataset}

The Propairs database of legitimate protein-protein docking complexes
enlists crystal structures of bound complexes, defined as biological
complexes in the Protein Data Bank (PDB), and their corresponding
unbound protein structure(s). A total of 2378 bound complexes that have
corresponding unbound structures of the interacting partners were
collected. It was ensured that the crystal structures of the bound
complex are of better than 3\selectlanguage{ngerman}Å resolution. Structures in the bound form
were required to have the same oligomeric state as in the unbound form
to ensure that the perturbation is not influenced by the docking of any
other protein molecule. The dataset was further curated to remove
structures with missing residues. Any multiple occupancies were
corrected to obtain a conformer with single occupancy, based on highest
occupancy value, for all its atoms. 895 chains from a bound complex with
interfacial sites were paired with the corresponding chain in the
unbound form to make the working dataset for this analysis. The list of
all the protein chains along with the analysis of their network
information can be found in Supplementary Table 1.

\emph{2.2 Interface and non-interface definition based on atom
contacts.}

Non-covalent bonding between associating protein units form the
interface in-between partnering molecules that form a complex. In this
analysis, any pair of residues from the interacting partners, whose
atoms fall within a distance of 4.5 Å are considered to form the
interfacial sites. This concept is based on proximity and is called an
atom contact, is also similar to the method used in the construction of
edges to make a structural network of the protein. Any non-adjacent
residue within the structural network that comes directly in contact
with the interfacial sites by making atom contacts are termed as primary
contacts. These sites make up the rim of the interface around the
interfacial core. All the remaining residues that are away from the
interface makeup the non-interfacial sites.

\emph{2.3 Network construction and analysis}

The protein structural network (PSN) is a weighted graph representation
of residues interconnected to depict a network of interactions. Each
residue in the PSN is a node and they are connected to other nodes using
edges based on their 3D coordinates. Spatial distance, chemical
non-covalent bonds, charge, energy, or many other features are several
means of defining network edges. In the current analysis, inter-atomic
distance between atoms of non-adjacent residues are used to define
interactions. A distance proximity cut-off of 4.5Å is used to define
atom contacts. The weight of an edge is defined as the ratio of the
total number of atom contacts made between a pair of residues and the
maximum number of atom contacts found in the entire dataset between the
corresponding amino acids.

The degree parameter and node strength obtained from the sum of all edge
weights connected to a node describes the connectivity around the
corresponding residues in the PSN. A higher degree would suggest that
the well-connected node is a hub in the network. Upon binding, any
significant change in the node strength or degree of sites, especially
hubs, corresponding to loss or gain of crucial connectivity in the PSN
are analysed.

\emph{2.4 Global network and structure comparison}

Structures in their bound form are aligned with the corresponding
structures in their unbound form and information of structural deviation
(RMSD) between all pairs of chains are obtained. TM-align is used to
compute the RMSD, which is a measure of C\selectlanguage{greek}α \selectlanguage{english}deviation between
topologically equivalent residues. This is followed by global network
comparison of the same equivalent residues using the network
dissimilarity method discussed by Gadiyaram and coworkers.

The method of computing network dissimilarity involves storing the PSN
as an adjacency matrix which is normalised to a Laplacian of the network
graph followed by its spectral decomposition to obtain the eigen values
and eigen vectors. A Forbenious norm of the difference between the
adjacency matrices of the two structural networks provides the edge
difference score (EDS). A difference in the local and global clustering
of residues in the network is captured using the Edge-weighted cosine
score (EWCS) and the correspondence scores respectively. The component
scores are then used to compile the Network Dissimilarity Score (NDS)
between the compared networks. Identical networks would have a NDS of
zero. No two networks can have a dissimilarity greater
than\(\sqrt{}3\).

\emph{2.5 Control dataset}

The global comparison of the structure network was performed earlier on
a dataset of single chain single domain proteins to determine their
structure variability. There, all pairs of available multiple conformers
of the same protein are compared to determine the network dissimilarity
(NDS) and structure deviation (RMSD) scores. In this work, the data from
the previous analysis has been used as a control to understand the
significance of the variability obtained upon transient association. The
two-sample Kolmogorov-Smirnov test (KS test) is performed to test the
significance of the data obtained in the working dataset as compared to
the corresponding scores of the control dataset.

\textbf{3. Results}

The dataset used for the analysis consists of 895 cases, corresponding
to a set of proteins that includes 285 enzymes, few transport protein
complexes, and other structural oligomers. Proteins from diverse
organisms including eukaryotes, plants and various animals are also
present in this working dataset. 366 cases in the dataset are human
proteins of which 96 are known to have enzymatic activity. In each case,
the protein chain from the bound complex is compared against its
corresponding chain in the unbound form. The structures are aligned to
identify topologically equivalent residues, modelled as nodes in the PSN
construct. Those residues that are in contact between the binding
partners are considered as interfacial sites and those in contact with
the interface are primary contacts.

A threshold of a minimum of 50 residues is used so that globular domains
are considered and not peptides. The smallest case with least number of
nodes is the ovalbumin enzyme inhibitor bound to different binding
partners (PDB ID 1HJA). Here, turkey ovalbumin protein of 51 residues is
complexed with the trimeric alpha-chymotrypsin to inhibit its function
(with 16 interfacial sites and 21 are primary contact sites). The
largest case, from PDB ID 2J8S, is the Acriflavine resistance protein B
trimer of 1032 residues in each chain bound to two molecules of designed
inhibitor (DARPin). One of the chains from the trimer is unbound and the
other two have differential contact. While one chain has 20 interfacial
sites with 31 primary contacts, the other has only 7 interfacial sites
with 20 primary contacts.

\emph{3.1 Analysing alteration in PSN upon transient association}

Preliminary analysis of the constructed PSNs was performed to study the
alteration of basic network parameters like average degree and strength,
change in hub status, loss or gain of edges and centrality information.
Supplementary Figure 1 shows the degree of all nodes in the dataset. The
maximum degree of any node in all PSNs analysed in this dataset is 19.
Nodes in the PSNs that have a very high degree are special hotspots with
high connectivity that can alter the overall network when perturbed.
These nodes in the PSNs are identified as hubs. From the degree
distribution of the dataset, it is observed that nodes with degree equal
to 11 crosses the 90\textsuperscript{th} percentile. Henceforth, for
this analysis, any node with degree greater than 10 is considered as a
hub node.

The change of degree and strength at all sites between the PSNs of the
bound and unbound forms of the proteins were next analysed. The
alteration at the interfacial sites, primary contacts and
non-interfacial sites were considered as the changes at, around and away
from the interface, respectively. Supplementary Figure 2 summarises the
changes observed across all sites in the dataset. The variation upon
transient association are recognised by treating the unbound form as the
reference structure and measuring all changes in the network when
complexed. Hence, any edges that are unique to the unbound form are
considered to be lost and those unique to the bound form are found to be
gained. Likewise, altering the hub status of nodes in the networks are
also noted. If the size of the protein is large and has a compact
structure, there is an increased chance of finding more hubs. Loss or
gain of numerous hubs can point to change in local conformation of
sidechains. The information on gain and loss of edges and hubs in all
cases is reported in Supplementary Table 1.

Across the dataset, a net gain in hubs is observed more: In terms of
hubs, the net gain, loss and indifference are 437, 333 and 125 cases,
respectively. Human serum albumin in complex with beta-2-microglobulin
and IgG receptor (PDB ID 4K71) has the highest net gain in the number of
hubs (23) across the dataset. However, taking percentage gain
proportional to the length of the protein, the highest gain in hubs is
observed in another IgG Fab fragment (PDB ID 1NSN) where there is a gain
of 15 hubs in the 187-residue structure, which is more than 8\% of the
protein. Such a tremendous gain in hubs upon binding would suggest that
the residues move closer to each other, and the structure would be more
compact upon binding. On the other hand, the highest loss (33 hubs and
103 edges) is observed in the case of Glutathione S-transferase when
bound to Jasmonic amino acid synthetase (PDB ID 5GZZ). Interestingly,
164 edges are lost whereas only 61 edges are gained and the loss of hubs
from unbound form is not accompanied by any gain of hubs when bound,
which suggest that there is a severe loss of connectivity in the protein
as a result of protein binding. The information necessary to analyse
each case in the dataset is provided in Supplementary Table 1.

\emph{3.2 Global comparison in working dataset as compared to control}

Next, the 895 cases from the bound \emph{versus} unbound pairs of
protein chains are subject to global comparison by computing the network
dissimilarity score (NDS) and RMSD for structure deviation between
backbone conformations. The information obtained from the working
dataset is illustrated as a scatter plot as shown in Figure 1A. Similar
information obtained in the control where only multiple structures of
the same protein that are known to be single chain single domain is also
plotted in the background of the scatter. The statistics of the data
points corresponding to each of the datasets is marked with horizontal
and vertical lines to depict the mean of the data points. The structure
deviation in the control was about 0.34 \selectlanguage{ngerman}Å with a standard deviation of
about 0.3 Å, whereas the mean deviation of the working dataset is about
1.14 Å with a standard deviation of about 0.94 Å. By performing a KS
test, it is also understood that the RMSD scores obtained in the working
dataset is significantly much higher than what was observed in the
control (p-value \textless{} 0.0001). Hence, the spread of the
topological variation of the backbone is much larger when proteins
undergo transient associations than the structural variability obtained
from multiple conformers of the same protein.

Likewise, the network dissimilarity observed in the control had a mean
of 0.112 ± 0.047 whereas that observed from the working dataset is 0.173
± 0.065. Also, KS-test results (p-value \textless{} 0.0001) show that
the dissimilarity in the networks is significantly higher in transiently
binding proteins as compared to the dissimilarity in PSNs of multiple
conformers of the same protein (control dataset). It is interesting to
analyse those cases where the variability in the network arises without
much change in the backbone conformation. The contribution to network
dissimilarity specifically arises from variability in local sidechain
conformations. The network comparison scores, and structure deviation of
these cases are greater and lower than mean of the dataset, respectively
and can be found clustered on the top left of the scatter shown in
Figure 1A. 194 cases from the working dataset show such a trend (with
RMSD \textless{} 1.14 Å and NDS \textgreater{} 0.173). A list of top
twelve cases with such network alterations are listed in Figure 1B, a
few highlighted cases are studied in detail.

\emph{3.3 Network alteration without change in the overall topology}

The scenario where the protein connectivity is altered upon transient
association without much deviation in the backbone conformation are
interesting. This suggests that the signal from the interface to
non-interface residues can be transmitted via small, concerted,
side-chain conformational changes without undergoing any large backbone
conformational changes. The data points corresponding to such cases can
be found on the upper left quadrant of the scatter plot, where the NDS
is high and RMSD is very low. A detailed list of all the cases that fall
into this category can be found in Supplementary Table 3 along with
their computed comparison metrics. Of the 194 cases that show such
variability, few interesting cases have been chosen for detailed studies
below.

\emph{3.3.1 The acriflavine resistance protein B (AcrB) undergoes
network rearrangement.}

The acriflavine resistance protein B is a multidrug efflux pump found in
the inner membrane component of the AcrAB-ToiC drug efflux system found
in \emph{E coli} . The overexpression of this protein machinery in the
organism renders it resistant to a wide range of drugs as it functions
to efflux the molecules out of the cell. The mechanism of function of
the protein have been well studied. There are three distinct domains in
each subunit of the AcrB protein, the transmembrane domain (TM-domain),
pore domain and the ToiC docking domain. Drug molecules enter the
protein from the central cavity in the TM-domain domain which are passed
into the pore through channels that can open and close based on
conformation coupling in the helices of the protein. The molecules
efflux into the docking domain via the central funnel.

In the bound form, the AcrB trimer is bound to two molecules of designed
ankyrin-repeat protein (DARPin) inhibitors (PDB ID 2J8S shown in
Supplementary Figure 3A). This binding mimics the different functional
states of the proteins, where the three chains of AcrB are locked in
three different states which reveal the mechanism of drug efflux from
the channels of each chain. Alteration of the network around the channel
in the pore domain of AcrB (Chain A) is observed upon binding with the
DARPin molecule (Figure 2A). The pore domain has an open channel that
allows for the efflux of drug molecules which is closed in the inhibitor
bound form of the protein. The closing of this channel is mediated by
rearrangement of sidechain interactions facing outwards of the channel
to face inwards thus closing the gate. This leads to a significant
rearrangement of the network in the protein and hence the high network
dissimilarity is observed.

\selectlanguage{greek}\emph{3.3.2 Net loss of connectivity in Pancriatic α-amylase protein
when bound to inhibitor}\selectlanguage{english}

The porcine pancreatic \selectlanguage{greek}α-\selectlanguage{english}amylase protein (PPA) that is secreted by
pancreatic acinar cells is responsible for the catalysing the initial
step in starch hydrolysis and is an essential enzyme for producing
glucose. Function of the protein is the endohydrolysis of
(1-4)-alpha-D-glucosidic linkages in polysaccharides containing three or
more (1-4)-alpha-linked D-glucose units. This is performed when the
carboxylic oxygens of the catalytically competent residues Glu233 and
Asp300 make hydrogen bonds with the ``glycosidic'' NH group of the
acarviosine group. This protein is a major component of pancreatic fluid
making it the primary target for the treatment of type 2 diabetes. Also,
its interaction with several inhibitors is well documented as it is
studied from perspective of several different diseases.

In our case study, the protein is bound to the microbial inhibitor
tendamistat (PDB ID 1BVN shown in Supplementary Figure 3B). This bound
form has the same topological fold as the unbound PPA however their
network is found to be altered. A net loss of hubs and edges is observed
along with loss of essential connectivity around the active site
residue, 233E which functions as a proton donor. Most of the lost edges
are found in the C-terminal domain of the proteins which binds to the
tedamistat inhibitor where, 17 hubs are lost, of which one is an active
site and only four hubs are gained (Figure 2B). Hence, the connectivity
in the functional C-terminal domain is lowered when bound to the
inhibitor which also blocks the active site of protein from performing
hydrolysis.

\emph{3.3.3 Iota toxin-component has increased connectivity when bound
to actin protein.}

The Iota toxin component Ia is an ADP ribosylating toxin (ADPRT). The
C-terminal domain that houses the active site of this protein complexed
to NAD is essential for its function. It is known that the active site
loop along with residues Tyr60-Tyr62 of the toxin binds to actin protein
and inhibits its activity. Actin specific ADPRTs perform ADP
ribosylation of G-actin at Arg117, leading to disorganisation of the
cytoskeleton and cell death.

In our analysis, significant dissimilarity is observed between the actin
bound form of the protein (PDB ID 3BUZ shown in Supplementary Figure 3C)
and the unbound toxin. The actin bound protein has few more new
interactions at the binding site and a net overall gain in connectivity.
New edges are found to be gained at the functional sites Arg352, Glu378,
Glu380 of the protein. A net gain in number of edges and hubs is
observed, which shows a more compact structure especially around the
binding site (Figure 2C).

\emph{3.3.4 Dihydrolipoyl dehydrogenase loses connectivity away from the
binding site.}

The human mitochondrial dihydrolipoyl dehydrogenase (DLD, hE3 or E3)
along with pyruvate dehydrogenase (E1) and dihydrolipoyl transacetylase
(E2) form the pyruvate dehydrogenase complex (PDC) which is known to
link the glycolysis metabolic pathway with the citric acid cycle. The
primary function of the complex is to convert pyruvate to acetyl-CoA
which is necessary for cellular respiration. The DLD protein exists as a
homodimer, where each subunit consists of a FAD and NAD binding domain
along with a central and an interface domain that interacts with the E3
binding protein (E3BP) to form the PDC. At the FAD binding domain active
site, Flavin mediated oxidation takes place to oxidise the substrate
which is reversed to FAD resting state using
NAD\textsuperscript{+}resulting in NADH and H. Deficiency of this
protein is associated with autosomal recessive metabolic disorders.

In this case, the E3 homodimer is bound to E3 binding domain of E3BP
forming a subcomplex with a strong hydrophobic interface (PDB ID 1ZY8
shown in Supplementary Figure 3D). It is reported that the central
hydrophobic patch along with numerous ionic and hydrogen bonds between
residues of the three chains add to the stability of the subcomplex. The
network dissimilarity between the bound and the unbound form of this
protein is found to be very high. A significant loss in the number of
edges, mostly far from the site of the interface is observed (Figure
2D). While 19 hubs are lost all around the protein only three hubs are
gained leading to a net severe loss of connectivity.

\textbf{4. Discussion}

The ability of a protein to make and break interactions with another
protein in order to bind to it temporarily and perform a certain
function allows for transient association between the proteins. The
binding event is mostly brought about by non-covalent bonds at the
interface between the interacting proteins which also determine the
nature and strength of interaction. The implication of such an event can
range from no structural change (due to weak interaction) to long range
(allosteric communication) of the perturbation signal. The focus of our
work was to study how direct associations play a role in perturbing the
connectivity of residues in globular proteins. The effect of the
perturbation at, around and away from the interface is studied by
constructing a protein structural network (PSN) of the connectivity
within the protein and analysing the alteration of the network.

A collection of structures from the ProPairs database was used for the
analysis. After filtering structures based on their crystallographic
properties, 895 protein chains have been identified that transiently
associate with other proteins and have the same oligomeric state in the
bound complex as well as the unbound form. The structure of the protein
chain obtained as a part of a protein complex, which is the bound form
of the protein, is compared with the structure of the same protein chain
when it is not bound to the interacting partner but yet in the same
oligomeric state. At the local level, the change in network parameters
such as number of edges, hubs and centrality measures are studied. The
global comparison is made in terms of the topological change, as in,
their backbone deviation (RMSD) and in terms of their structural network
dissimilarity (NDS).

Graph spectral comparison methods are used in computing the
dissimilarity between the networks which involves spectral decomposition
to obtain the eigen vectors and eigen values of the PSNs. Few case
studies with high network variation were identified using the global and
basic network comparison. A major contribution to the NDS in these cases
arises from its component, EWCS which is mostly responsible to compute
the change in local clustering of residues. The Fiedler vectors (Fv)
between a pair of PSNs can be examined to identify the sites with high
variations in the clustering of nodes. The eigen vector corresponding to
the second smallest eigen value is called the Fiedler vector. This
vector can provide meaningful information on the algebraic connectivity
of the network and can be used in partitioning the network into
clusters. This is illustrated with a case study.

The first step is to identify the Fv from the spectra of the pair of
graphs. Figure 3A shows the aligned Fv between the bound and the unbound
form of the DLD protein. The absolute difference between the aligned
vectors is computed to find regions of the protein that are not in
agreement. Figure 3B shows the difference between the Fv and highlights
the region with variation between the vectors. The sites with the most
variation, having the highest absolute difference are shown as sticks in
Figure 3C. The cartoon diagram of the chain A of DLD is coloured based
on the absolute difference between the vectors and chain B is shown as
grey surface. The interacting partner E3BP protein is shown using yellow
surface representation. Side chains of the top five residues with
highest absolute difference, yellow in the bound form and red in the
unbound form, are shown using spheres.

Any alteration of network parameters close to the site of interface is
expected as the interfacial sites make new interactions with the binding
partner. However, more often, alterations are also observed far from the
site of binding due to allostery which is the transmission of the
perturbation. The path of this allosteric signal can be analysed by
drawing the shortest path between the site of perturbation to the site
of significant network alteration. The change in shortest path between
the site of binding to the site of perturbation is analysed in the case
study and discussed in the Supplementary Figure 4. A new edge between
spatially proximal nodes GLU 437 and ASP 350 in the bound form reduces
the shortest path when compared to the several possible short paths in
the unbound form.

Most of the variability observed in the dataset occurs at the
non-interfacial sites. This is also evident from the variation of degree
and strength at, around and away from the interface observed in
Supplementary Figure 2. The network variation obtained only by
considering the structure network of non-interface sites says that in
almost 89\% of the cases the network dissimilarity is greater than 50\%
of the NDS scored from all residues. This result also suggest that most
of the network away from the binding site is affected by the
perturbation, but all sites are not perturbed proportionally. As viewed
from the absolute difference between Fv of the DLD protein case study
only five nodes of the entire length of the long protein were strongly
affected to cluster differently. The effect on all other sites are
feeble and is an effect of subtle changes in the local conformation of
sidechains. Which shows that most residues predominantly still remain in
the same topology, any interactions that are broken are counteracted by
other interactions being made. Hence there is predominantly a
rearrangement of interactions that is being observed. However, in about
60\% of the 285 cases that are identified as enzymes, in the working
dataset, a net loss in connectivity is observed. Hence when the
interacting protein is an enzyme, the structure of the bound form may be
less compact than the unbound form which may serve the process of
functioning to catalyse several different reactions.

The case studies have been chosen such that their analysis has certain
clinical relevance and an impact on understanding their mechanism. The
alteration of the network in all the case studies can be related to
several human disease conditions like antibacterial resistance,
diabetes, toxin induced cell death and Latic acidosis. We also related
to known information about the mechanisms of their function. Hence, the
analysis of the structure network is a necessary and beneficial tool in
the analysis of structural excursions. The development of such tools
that can analyse the impact of protein-protein interactions will help in
understanding allostery mechanism and the network analysis of protein
structures for stability engineering and docking studies.

\textbf{5. Conclusion}

The alteration of the structure network upon transient interactions
between the structure of a protein complex of interacting partners is
analysed by comparing it against an available unbound structure as a
reference. Studying the effect of perturbations using a network graph of
residue-residue interactions within the protein is a beneficial and
robust tool in the analysis of structural excursions. Comparing several
basic network parameters and using advanced graph spectral approaches a
local and global difference between the unbound and the bound form of
protein chains is identified. It is understood that even when there is
no significant change in the overall fold of a given protein the network
of interactions may rearrange themselves to yield a preferred function
or phenotype. Change of protein function can be analysed by studying the
change in network parameters at the active site. The protein binding
event is found to increase the connectivity within a protein in the case
of a non-enzymatic toxin inhibitor. A significant loss of connectivity
in the case of DLD protein is associated with the formation of a strong
hydrophobic patch in the bound form of this homodimer enzyme. Probing
the spectral properties of the protein structural network yielded
Fiedler vectors which are compared to find nodes which jump from one
cluster to another. The path of communication from the site of binding
to the highest perturbed site is obtained by building the shortest path
between the nodes. These methods of studying the effect of perturbations
throw light on understanding the allostery mechanisms.

\textbf{6. Acknowledgements}

VMP would like to thank the continuous support and mentoring from
Professor Saraswathi Vishveshwara and Dr Vasundhara Gadiyaram. The work
would not have been completed without the helpful suggestions provided
by all our colleagues from NS and RS lab. This article is dedicated to
one of the authors, late Prof N. Srinivasan.

\textbf{7. Funding statement:}

Research from NS group is supported by the Department of Science and
Technology (DST), University grants commission (UGC), Department of
Biotechnology (DBT), Government of India. RS acknowledges funding and
support provided by JC Bose Fellowship (JBR/2021/000006) from Science
and Engineering Research Board, India and Bioinformatics Centre Grant
funded by Department of Biotechnology, India
(BT/PR40187/BTIS/137/9/2021). RS would also like to thank Institute of
Bioinformatics and Applied Biotechnology for the funding through her
Mazumdar-Shaw Chair in Computational Biology (IBAB/MSCB/182/2022).

\textbf{8. References}

\textbf{9. Figure legends}

\textbf{Figure 1:} Diversity in structural network and backbone topology
upon transient association. \textbf{(A)} The structure deviation
information obtained by computing C\selectlanguage{greek}α-\selectlanguage{english}RMSD (\selectlanguage{ngerman}Å) is compared against
network dissimilarity score (NDS) information obtained by comparing
structural networks based on atom contacts. The RMSD is plot on the
x-axis and the NDS is plot on the y-axis. The variability observed in
46\% of the cases is lower than the mean comparison scores. About 194
cases (21.65\%) show strong dissimilarity in network even though there
is no significant change in their topology, the alteration of the
network in these cases is analysed in detail. The control data shown in
yellow dots correspond to similar information obtained from structure
variability of single chain single domain proteins that do not associate
transiently. The mean of the working dataset is significantly greater
than the mean of the control. \textbf{(B)} Those cases with high network
dissimilarity without much structural deviation found on the top left
region of the scatter plot as listed. Only the top 12 cases out of which
four interesting cases are picked for detailed case studies are
highlighted. Their corresponding datapoints are marked on the scatter
plot shown on the left. The list of 197 cases that fall in this region
are tabulated in Supplementary Figure 4.

\textbf{Figure 2:} Alteration of structural network in case studies
analysed from change in basic network parameters. The observed changes
are illustrated on cartoon diagram of the structure networks. Edges that
are gained and lost are shown as orange and blue lines respectively.
Those hubs that are gained and lost are shown as orange and blue spheres
respectively. \textbf{(A)} rearrangement of edges in the pore domain of
the chain A in AcrB protein is shown, where most of the edges around the
pore are lost and those within the pore are gained. \textbf{(B)} Loss of
hubs in the C-terminal domain of the amylase protein is
observed.\textbf{(C)} Several edges and hubs are gained around the
binding site of the Iota toxin component upon interaction with actin
protein.\textbf{(D)} Loss of edges far form the binding site is observed
in human DLD protein.

\textbf{Figure 3:} Absolute difference between Fiedler vectors (Fv) of
DLD protein. Fv components cluster the nodes of the PSN into
groups.\textbf{(A)} shows the aligned Fv components of the bound and
unbound PSN of DLD protein. The clustering of most sites look almost
similar since the topological change in the backbone is not much.
\textbf{(B)}The absolute difference between the vectors point to those
nodes whose local clustering have changed due to variation of edge
weights. When the absolute difference between these vectors is taken, it
is found that there are spikes at specific sites which have been
perturbed by being clustered differently. \textbf{(C)} these specific
sites are mapped onto the cartoon diagram of the bound protein. The
binding partners are shown as surface. The sidechains of identified
sites in the bound and unbound structures are shown as yellow and red
spheres respectively.\selectlanguage{english}
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