Altered Dynamics upon Oligomerization Corresponds to Key Functional Sites

Abstract

It is known that over half of the proteins encoded by most organisms function as oligomeric complexes. Oligomerization confers structural stability and dynamics changes in proteins. We investigate the effects of oligomerization on protein dynamics and its functional significance for a set of 145 multimeric proteins. Using coarse-grained elastic network models, we inspect the changes in residue fluctuations upon oligomerization and then compare with residue conservation scores to identify the functional significance of these changes. Our study reveals conservation of about ½ of the fluctuations, with ¼ of the residues increasing in their mobilities and ¼ having reduced fluctuations. The residues with dampened fluctuations are evolutionarily more conserved and can serve as orthosteric binding sites, indicating their importance. We also use triosephosphate isomerase as a test case to understand why certain enzymes function only in their oligomeric forms despite the monomer including all required catalytic residues. To this end, we compare the residue communities (groups of residues which are highly correlated in their fluctuations) in the monomeric and dimeric forms of the enzyme. We observe significant changes to the dynamical community architecture of the catalytic core of this enzyme. This relates to its functional mechanism and is seen only in the oligomeric form of the protein, answering why proteins are oligomeric structures.

INTRODUCTION

Proteins are critical for diverse cellular functions, including structural integrity, transport, and catalysis of biochemical reactions. Some function as independent monomeric units and others in multimers, or even form large biological complexes. The process of forming oligomers, oligomerization, often confers increased stability and the ability to perform complex functions.^{1, 2} Oligomers can exist either as an assembly of identical subunits, homo-oligomers, or can combine in a mosaic of hetero-oligomers. Previous work reveals that homo-oligomers often tend to display structural symmetry that is generally associated with greater stability and robustness.^{3, 4} Apart from their specific architecture, oligomers can also be classified based on whether or not complexation is required for their biological activity. Obligate cases require oligomerization in order to execute their functions, while non-obligate oligomers are transient complexes with the subunits capable of performing their functions in isolation.⁵

Oligomeric complexes can perform complex functions, a role often not possible for monomers. For example, the homo-oligomeric complexes Hsp90 and calreticulin play significant roles in affecting protein folding⁶; the oligomeric forms of these proteins are known to bind misfolded proteins with higher affinity than their monomeric counterparts. Moreover, most oligomeric complexes exhibit longer-range allosteric regulation than in the monomer, which can be important for signal transduction.^{1, 7} Hemoglobin is a classic example that has been investigated frequently to elucidate aspects of allostery and cooperativity with respect to protein oligomerization. Also, the increased stability of protein complexes by oligomerization is an essential modification for thermophiles to prevent their dissociation under extreme temperatures.⁸

The dynamics of individual monomers persist in most oligomeric assemblies. However, some complexes can develop novel dynamics after oligomerization, especially when some critical motions are not accessible to the monomeric form. Previously Voth, et al.⁹, showed that the dimeric form of triosephosphate isomerase was required to obtain appropriate motions of the closing loop, while the monomer does not show such motions. Bahar et al.¹⁰ investigated the low frequency normal modes accessible to an individual subunit of amino acid kinases in the monomeric and oligomeric forms and proposed that changes to the dynamics upon oligomerization facilitate allostery and ligand binding. A molecular dynamics simulation of tryptophan synthase revealed that in its monomeric form the enzyme is more rigid and cannot undergo conformational transitions that are seen after oligomerization.¹¹ In addition, oligomerization is known to increase the catalytic efficiency of this enzyme in contrast to the isolated monomer. In another study, we reported a similar finding where the functional loops of triosephosphate isomerase preserve their dynamics in both natively dimeric and natively tetrameric forms.¹²

The conformational flexibilities of globular proteins have often been considered to be a central factor for their function.^13-15 Soft modes from elastic network models have frequently been used to predict energetically favorable conformational changes upon substrate binding, and these predictions bear a strong similarity to the different experimentally resolved structures.¹⁶ Previous studies indicated strong correlations between dynamic flexibility and conservation levels of amino acids, with the most conserved residues showing the smallest fluctuations. These studies emphasized the significance of regions having high packing density, low mobility and low solvent accessibility by their high level of conservation; this also underscores how important probing conformational dynamics is to decipher protein function.^17-19 These studies, however, have assigned functional significance based on residue flexibility in the native protein structure. For a native oligomeric protein, subunits of an assembly will exhibit different residue flexibility profiles when in isolation than when in the assembly owing to the differences in packing densities. A comparative study on residue flexibilities in the monomeric and oligomeric forms of a protein was not previously carried out for a diverse set of proteins - the aim of the present study, which will inform us about the importance of oligomerization for functional sites.

To understand the changes in dynamics that oligomerization introduces, we investigate a diverse set of 145 homo-oligomers with oligomeric states ranging from two (homo-dimer) to six (homo-hexamer). For each protein, we compute the change in mean square fluctuations (MSFs) of all residues in the monomer upon oligomerization. We then compare the residue conservation profiles of each protein with the MSF changes to ascribe functional significance to the changes in dynamics. We limit this study to a consideration of only homooligomers, owing to their greater abundance. We investigate the specific cases for four enzymes: glutamate dehydrogenase, arginase 1, glycine N-methyltransferase and D-amino acid oxidase to probe the functional importance of regions showing altered dynamics and then, provide more general results that associate changes in dynamics with functional significance. Our study reveals the importance of regions with dampened fluctuations following oligomerization. Using the specific cases of the four enzymes, we further confirm that the residues in regions with dampened mobilities often play a key role in the catalytic activity of the enzyme and hence, are orthosteric by nature. In the final section, we also address the question of why certain enzymes function only in their oligomeric state with triosephosphate isomerase (TIM) as a case study. Specifically we compare the residue communities (blocks of residues which are most highly correlated in their motions) for the monomeric and oligomeric forms of TIM. We observe a substantial shift in the community architecture of the catalytic core in the oligomer, the fundamental characteristic change necessary for the enzyme’s activity, and a further change upon substrate binding.

METHODS

Protein Structures

The initial dataset comprises Protein Data Bank (PDB) files of 174 different homooligomers downloaded from PDB. For each protein, the number of subunits in its functional quaternary state (biological assembly) ranges from two to six. We identify the biological assembly for each protein based on the assignment made by the authors and software in the PDB entry of the protein.

Homolog Selection and Multiple Sequence Alignment

For each protein in the initial dataset, we extract the sequence corresponding to a single chain (by default, we consider just the first chain) in the PDB file. We refer to these as query sequences. For each query sequence we search for homologous sequences using BLAST against the non-redundant protein sequence database with an e-value cutoff of 0.01, percentage identity in the range of ≥ 35% and ≤ 95% and query coverage of 80%. To filter duplicates, we then cluster the initial set of homologs with CD-Hit²⁰ at 95% sequence identity and then select only the representative sequences from each cluster. Our final dataset has 145 symmetric homooligomeric proteins (Supporting Information file ds145.xlsx), each having a minimum of 50 representative hits from BLAST. The diversity of the dataset in terms of oligomeric state and residues is depicted in Figure S1 (A and B).

We then perform Multiple Sequence Alignment (MSA) for the representative homologs collected for each protein with Clustal Omega²¹ with its default parameters.

Conservation Scores

Using Rate4Site²² with its default parameters for the evolutionary model (JTT) and rate inference method (Bayesian), we calculate the conservation scores for each protein from its respective MSA file. Rate4Site reports the extent of conservation at a position as a z-score, where a lower score indicates higher conservation.

Mean Square Fluctuations (MSF) from Elastic Network Model (ENM)

The fluctuations derived from ENM show remarkable agreement with the experimental fluctuations in B-factors.^23-25 Here, we use the Anisotropic Network Model (ANM)²³ to study the protein dynamics. We model individual proteins as coarse-grained elastic networks by representing each residue by its C^α atom and connecting residue pairs by harmonic springs. In equilibrium, the potential of this system is given as

$$V=\frac{1}{2}\Delta R^{T}H\Delta R$$ (1)

Here, Δ R is the vector of change in position for all residues, Δ R^T is the transpose of this vector and H is a 3N by 3N-dimensional Hessian matrix that has the second derivatives of the potential function. We vary the strength of spring γ between a residue pair by the inverse of their separation distance(d_ij), given by the following equation.

$$\gamma ={\left(\frac{1}{d_{ij}}\right)}^a$$ (2)

Diagonalizing the Hessian matrix results in 3N-6 modes (V) and eigen values (λ) which correspond to the non-rigid body dynamics of the system and we use these to calculate the MSF of residues with the following equation.

$$<\Delta R_i^2>=\frac{3K_{B}T}{\gamma }{\sum }_{j=1}^{3N-6}\frac{1}{{\lambda }_j}{\sum }_{i=3k-2}^{3k}{V}_{ji}^2$$ (3)

Here, K_B is the Boltzmann constant and T (set to 300) is the temperature in Kelvin. We then compute the theoretical B-factors (B factor^MSF) from these mean-square fluctuations (MSFs) as

$$B_i=\frac{8{\pi }^2<\Delta R_i^2>}{3}$$ (4)

and use them to describe residue positional fluctuations. We set a to 3 as it gives the highest median correlation with the experimental B-factors (Figure S1.C).

MSF of Monomer and Oligomer

We use an approach similar to that of Bahar¹⁰ and Chang¹¹ to obtain a protein’s monomeric form from the oligomeric assembly. For each protein, we extract only the first chain from the PDB file and consider it to be the isolated monomer (Monomer^isolated) and when the same chain is in the oligomeric assembly, we refer to it as Monomer^oligomer. Comparing the fluctuation profiles of Monomer^isolatedand Monomer^oligomer will give us insight into the changes in dynamics after oligomerization. As the dataset comprises only symmetric proteins, we assume that there is a high overlap in the dynamics of individual chains in the oligomer and thus, we proceed with monitoring the change in dynamics for the first chain only.

We calculate the Bfactor^MSFvectors for the isolated monomer and oligomer of each protein and refer to these as $Bfacto{r}_{Monome{r}^{isolated}}^{MSF}$ and $Bfacto{r}_{Oligomer}^{MSF}$ respectively. We then consider the MSF values of only the first chain of the oligomer to study the fluctuation profile of the monomer in the oligomer.

Z-score transformation of raw MSF and Fold Changes

For individual proteins, we standardize the raw fluctuation values obtained in the $Bfacto{r}_{oligomer}^{MSF}$ and $Bfacto{r}_{Monome{r}^{isolated}}^{MSF}$ vectors by converting them to z-scores. Transforming the raw scores into z-score helps express both vectors on the same scale, i.e. the number of standard deviations the fluctuation of a given residue is from the mean fluctuation value over all residues. It also helps eliminate any potential bias that may be introduced due to the difference in the number of residues in the Monomer^isolatedand the Monomer^oligomer. From the standardized $Bfacto{r}_{oligomer}^{MSF}$ and Monomer^isolated we obtain the standardized scores for the monomer in assembly and in isolation respectively. We refer to these standardized vectors as Z_Monomer^isolated and Z_Monomer^oligomer. We then convert these vectors into a positive scale as follows:

$$Z_{Monome{r}^{isolated}}^N=Z_{Monome{r}^{isolated}}^N+\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 1\hfill \\ \hfill 1\hfill \\ \hfill ⋮\hfill \end{array}\right].\mid \text{min}(Z_{Monome{r}^{isolated}}^N,Z_{Monome{r}^{oligomer}}^N)\mid$$ (5)

$$Z_{Monome{r}^{oligomer}}^N=Z_{Monome{r}^{oligomer}}^N+\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 1\hfill \\ \hfill 1\hfill \\ \hfill ⋮\hfill \end{array}\right].\mid \text{min}(Z_{Monome{r}^{isolated}}^N,Z_{Monome{r}^{oligomer}}^N)\mid$$ (6)

The min function takes the minimum of the two vectors. We then define Fold Change Ratio (FCR) as the ratio of the z-scores of the monomer in assembly to the z-scores of the monomer in isolation.

$$\mathrm{Fold}\mathrm{Change}\mathrm{Ratio}(\mathrm{FCR})=\frac{Z_{Monome{r}^{oligomer}}^N}{Z_{Monome{r}^{isolated}}^N}$$ (7)

To identify residues with significant increases or decreases in fluctuations, we use a cutoff of 1.5 FCR. A FCR greater than or equal to 1.5 indicates that the residue shows increased fluctuations upon oligomerization whereas, a FCR less than or equal to $\frac{1}{1.5}$ suggests a significant reduction in fluctuations after oligomerization. As the problem of finding residues with significant change in fluctuations has some similarity to the problem of identifying differentially expressed genes in RNA-Seq and microarray assays, we proceed with the cutoff of 1.5 which was shown to provide significant results for those types of experiments.^{26, 27}

Identifying Interface Residues

For a particular chain, we identify interface residues as those whose heavy atoms are within 4.5A from the atoms of residues from any of the other subunits.^{28, 29}

Packing Density Calculations

Residue level packing densities are computed from the atomic structure of each protein in the dataset. The packing density values are obtained using the software Voronoia.³⁰

Residue Community Analysis

We define residue communities as groups of residues which are highly correlated in their fluctuations and exhibit motion as rigid units. We perform community analysis for the monomer of TIM for 4 cases: the isolated monomer without substrate, the isolated monomer with substrate, the monomer in the context of the dimer without the substrate and the monomer as part of the dimer with substrate. We use the PDB 1tph as the substrate bound form and 8tim as the unbound form. For the substrate bound form of TIM (PDB 1tph) we coarse-grain the protein at the C^α level while, retaining the substrate in its all-atom form. We set the exponent for spring strength a to 2 as this gives high correlation with the experimental B Factors and model the interaction strength as given in Equation 2.

After diagonalization of the Hessian of this system, we use the first twenty low frequency modes to construct the inverse hessian matrix as follows.

$$H^{-1}=\sum \begin{array}{c}20\hfill \\ i=1\hfill \end{array}{\lambda }_i^{-1}{V}_i{V}_i^T$$ (8)

Here, V_i is the ith low frequency mode vector, $V_i^T$ the transpose of V_i and λ_i is the corresponding eigenfrequency of this mode. The H⁻¹ has dimensions 3N by 3N, N being the number of residues and gives the correlations between residue fluctuations in the x,y and z directions. Like the Hessian, the H⁻¹ can also be viewed as an N-dimensional matrix of sub-elements, these having a dimension of 3 by 3. We then calculate the correlation between the fluctuations of residues i and j as

$$c_{ij}=\frac{trace{H}_{ij}^{-1}}{\sqrt{trace{H}_{ii}^{-1}trace{H}_{jj}^{-1}}}$$ (9)

In the above equation, $H_{ij}^{-1}$ is a 3 by 3 block element of the inverse Hessian corresponding to residues i and j and it gives the correlation between the fluctutions of residues i and j in the x,y and z directions. $H_{ii}^{-1}$ and $H_{jj}^{-1}$ are the block elements corresponding to the self-correlations of residues i and j. The trace is the sum of the diagonal elements of each block matrix. In taking the trace of the block matrices, we are only accounting for the correlations of residue fluctuations in the same directions. Performing the above operation results in an N-dimensional symmetric correlation matrix, C.

We then express the above correlation matrix as a dissimilarity matrix by subtracting each element of C from 1.

$$c_{ij}^{dissimilarity}=1-c_{ij}$$ (10)

Hierarchical clustering of the dissimilarity matrix with complete linkage then yields a dendrogram, grouping residues which are correlated to similar extents in their motions. We cut the dendrograms for the ligand free form (8tim) and ligand bound form (1tph) of TIM at manually selected heights to generate two, three and four clusters and then map these clusters onto the structure for comparisons. To perform hierarchical clustering and generate the dendrograms, we use the MATLAB clustering module (https://www.mathworks.com/help/stats/hierarchical-clustering.html).

Probability distribution fit

We fit the residue conservation and packing density data to different distributions using the MATLAB function allfitdist (https://www.mathworks.com/matlabcentral/fileexchange/34943-fit-all-valid-parametric-probability-distributions-to-data/content/allfitdist.m).

Non-parametric test of significance

We perform the non-parameteric Kruskal-Wallis test to evaluate the significance of residue conservation scores for different levels of MSF change using the MATLAB kruskalwallis³¹ function.

Protein structure visualization and mapping of critical residues onto structures

We use Pymol to map and visualize the key functional residues and clusters on the protein structure.³²

RESULTS

Our dataset includes 145 different homo-oligomeric proteins having between two (homo-dimer) and six (homo-hexamer) subunits. For each protein, we choose a single subunit (the first chain from the PDB file) to represent its monomeric form. This method of using a single subunit from the oligomeric protein assembly to represent the isolated monomer is similar to the approach taken by Bahar¹⁰ and Chang¹¹. We also verify the reliability of this approach by considering the case of protein tyrosine phosphatase that has been crystallized in both monomeric (PDB 1L8G) and oligomeric (PDB 2CM3) forms. Comparison of the dynamics of the crystallized monomer with that of the monomer extracted from the oligomer shows a strong correlation in the residue fluctuations for the two forms (Figure S2), which further verifies this approach.

To investigate the effect of oligomerization on protein dynamics, for each protein, we compute the Mean Square Fluctuations (MSF) for residues when it is an isolated monomer and compare with the fluctuations when the same monomer is in its oligomeric assembly. Then, we simply look at the ratio of changes in the scalar mobilities (fold change ratio or FCR); with an arbitrary cutoff at 50% either reduced or increased, we identify residues that have undergone significant changes in their mobilities upon oligomerization. We attribute functional significance to the changes in mobilities by considering them together with the degree of conservation of residues, which we compute using Rate4Site.²² Regions which are critical to the protein’s function, such as catalytic sites, evolve more slowly and hence, are usually more conserved.

Influence of oligomerization on key functional residues

First we inspect the effect of oligomerization for four enzymes: bovine glutamate dehydrogenase (an enzyme known for its allosteric behavior), arginase 1 (a critical enzyme in the urea cycle), glycine N-methyltransferase (playing a critical role in methionine metabolism) and D-amino acid oxidase (oxidizes D amino acids and enables yeast to use D-amino acids for nutrition). For each, we identify from the literature those residues known to have functional significance and map them onto the protein structure to focus on the changes in fluctuations for these. Here, we address the fundamental question: does the mobility of the identified critical residues for a protein change significantly upon oligomerization? If it does, then do these functional residues undergo significant reductions or increases in their mobilities upon oligomerization?

Glutamate dehydrogenase

Glutamate dehydrogenase (GDH) plays a pivotal role in the metabolism of ammonia and is universal throughout most domains of life. It catalyzes the inter-conversion of L-glutamate into α-ketoglutarate and ammonia. In mammals, enriched GDH activity is found in liver, kidney, brain and pancreas, and the ammonia produced from glutamate is utilized in the urea cycle.³³ GDH in mammals exists as a homohexamer with dihedral symmetry and is comprised of about 500 residues. It has two structural domains: the NAD⁺-binding domain where, the coenzyme NADH binds and the glutamate-binding domain where the substrate glutamate binds. In contrast to its isoforms in other life forms, mammalian GDH demonstrates allostery.³⁴ Previous studies have shown that the mobility of the enzyme’s NAD⁺-binding domain (Figure 1) is essential to mediate the enzyme’s allosteric behavior.^{34, 35} Also, the ‘antenna’ protrusion in the enzyme’s structure is present only in mammalian GDH, and its role has been implicated in the allosteric regulation of the enzyme.³⁶

Figure 1.

Domains and structural aspects of bovine glutamate dehydrogenase (GDH). The mobility of the NAD⁺-binding domain mediates allostery in the enzyme. Glutamate-binding domain is responsible for binding the substrate glutamate. The antenna feature is unique only to animal GDH and is also hypothesized to play some role in the allosteric behavior of the protein. Table S1 provides details of the functionally significant residues and their roles.

The most commonly known allosteric effectors for the enzyme are ADP, GTP and NADH, while the enzyme is also known to be regulated by other metabolites such as leucine and monocarboxylic acids.³⁴ GTP and NADH regulate the enzyme by facilitating its conformational transition to the inactive state in which the NAD⁺-binding domain has a closed conformation and helps in the modification of the glutamate substrate. ADP on the other hand is responsible for activating the enzyme to release the substrate during which the NAD⁺-binding domain attains the open conformation. While GTP binds on the NAD⁺-binding domain below the pivot helix, the binding site for ADP is uncertain.^{33, 35}

We probe the influence of oligomerization on the dynamics of glutamate dehydrogenase using the PDB structure 3mw9. We observe that the NAD⁺-binding domain becomes more flexible upon oligomerization while the glutamate binding domain undergoes considerable reduction in its mobility (Figure 2A). Residues K90, K114, K126, R211 and S381 have been shown to interact with glutamate³³ and are of prime importance for the enzyme’s catalytic activity. Interestingly, four of these residues (K90, K114, K126 and S381) map to regions with reduced fluctuations (Figure 2A and Table S1). Residues that bind to allosteric regulator GTP, on the other hand, are found either in regions with increased fluctuations or where there are no significant changes in fluctuations. Residues H209, R217, R261 and R265 which interact with the allosteric inhibitor GTP fall into this category.

Figure 2.

Flexibility change and sequence conservation of four enzymes. For each enzyme (A, B, C and D), a figure has three parts. The first part (Left) has the enzyme colored by interface (pale yellow) and non-interface (teal). Next, it is colored by change in residue fluctuations (Middle). Regions with increases in MSF (50% increase or more) are shown in red, regions with reduced MSF (50% decrease or more) in blue and those without any significant changes in gray. The third part of the figure (Right) shows the enzyme colored by residue conservation scores with blue and red marking the lower and upper end of the conservation, respectively. In all the three parts, the key functional residues of each enzyme are shown as spheres. (A) Bovine GDH, (B) Arginase 1, (C) Glycine n-methyltransferase (GNMT), and (D) D-aminoacid oxidase. The details of the key functional residues for each enzyme are provided in the Supporting Information.

Oligomerization increases the packing density of interface residues and as a consequence, it is reasonable to speculate that the flexibility of these residues will be diminished in the assembly. However, in Figure 2A we observe that some residues that are not in the interface also undergo reductions in their fluctuations and some of these residues are orthosteric (involved in the catalytic activity of the enzyme) by nature. Our findings also corroborate results from previous studies which suggest the importance of the mobility of the NAD⁺ binding domain for the enzyme’s allosteric behavior.³³ Importantly, the mobility of this domain is significantly higher in the oligomer than in the monomer.

Arginase I

Mammalian arginase plays a vital role in the urea cycle, a cascade of chemical reactions that help to eliminate toxic chemicals inside the body. The enzyme is known to exist in two isoforms: arginase I, which catalyzes the hydrolysis of L-arginine to form ornithine and urea in the final step of the urea cycle, and arginase II, which regulates the concentrations of arginine and ornithine. Both enzymes have significant roles in maintaining homeostasis inside the body and in facilitating the elimination of toxic chemicals.³⁷ We investigate the effect of oligomerization on the arginase I enzyme from Rattus norvegicus (PDB 1rla), which is active as a trimer.

On comparing the MSFs of residues of the independent monomer with the monomer taken as part of its trimeric assembly, we observe that residues located at the interface undergo significant reductions in their mobilities. Some exposed residues which are not part of the interface exhibit increases in fluctuations following oligomerization. We also note that there are residues not at the interface undergoing reduced mobilities. Arginase I uses Mn²⁺ as a cofactor to catalyze the hydrolysis of arginine. Residues H101, D124, H126, D128, D232 and D234 form the manganese binding cluster in the enzyme while, H141 and E277 have been shown to interact with the substrate and are responsible for its catalytic modification (Table S2).³⁸ Previously, mutation studies of these sites indicated that these severely impair the enzyme’s function either by reducing the binding affinity of the enzyme for the cofactor or by reducing its catalytic activity.^{38, 39} We explore whether these residues have a special preference to exist in regions with increased or dampened mobilities upon oligomerization by mapping them onto the structure and verifying their fluctuation changes. All six residues, where mutation studies were carried out, map to regions having reduced fluctuations after oligomerization. Moreover, residues interacting with the substrate are also seen to be further stabilized in the assembly. Interestingly, all of these residues are in the non-interface parts of the enzyme and yet they displayed significant reductions in their mobilities upon oligomerization (Figure 2B).

Glycine N-methyltransferase

Glycine N-methyltransferase (GNMT) is an essential enzyme involved in the metabolism of methyl groups. It uses glycine and S-adenosylmethionine (SAM) as substrates and catalyzes their conversion into S-adenosylhomocysteine (SAH) and sarcosine. The reaction involves the transfer of a methyl group from SAM to glycine. The enzyme is known to be active in its tetrameric form and is found in abundance in mammalian liver cells. It maintains the SAM/SAH ratio in the cell and thus, controls methylation in the cell.⁴⁰ Besides, in humans this enzyme is known to play an important role in gluconeogenesis⁴¹ and the expression of the GNMT gene is also linked to prostate cancer proliferation.⁴²

For the effects of oligomerization on the dynamics of the monomer (PDB 1bhj), we observe, similar to the previous cases, a major fraction of residues at the interface showing reduced fluctuations while, some residues on the surface showing an increase in mobility. Also, we notice that certain residues in the non-interface regions show reductions in their fluctuations. We then study the changes in flexibility of key residues that interact with substrates. For the rat GNMT, residues Y21, W30, R40, A64, D85, N116, W117, L136, H142 have been shown to interact with the substrate SAM while, residues Y33, G137, N138, R175,Y194,Y220 and Y242 are known to interact with glycine (Table S3).⁴³ We observe a similar pattern as we did for the other enzymes: the key functional residues are located in regions where the flexibility is reduced upon oligomerization. While most residues involved in binding SAM are located in the interface, residues which bind to glycine are found in non-interface parts of the enzyme and show stabilization upon oligomerization (Figure 2C). Mutations to certain glycine and SAM-binding residues (Y21, Y33, Y194 and Y220) have been shown to be important in contributing to the catalytic efficiency of the enzyme⁴³, and of these, three residues map to regions with reduced fluctuations (Table S3).

D-amino acid oxidase

D-amino acid oxidase catalyzes the dehydrogenation of D-amino acids into their corresponding imino acids. The reaction uses flavine adenine dinucleotide (FAD) as the cofactor and results in the reduction of the cofactor. It is an important enzyme in yeast where cell growth is dependent on the effective utilization of D-amino acids. In mammals, the enzyme is found in a few organs and is known to be catalytically less efficient than its yeast counterpart. In yeast, the enzyme exists as a stable homodimer. Previous studies provided evidence that the enzyme dimerizes upon addition of the cofactor FAD, suggesting that the transition from the apo to the holoenzyme is essential for dimerization.^44-46

From the probing of the dynamic effects of oligomerization on a single subunit (PDB 1c0k), we observe that most of the enzyme shows no significant changes in mobility. Interestingly, we do not find regions with increased mobility for the cutoff of 50% change. However, by relaxing the change cutoff to only 25%, we observe that residues on the surface and distal to the oligomerization interface exhibit greater flexibilities than in their isolated form (Figure 2D). While the dynamic flexibility of most of the residues that form the catalytic chamber of the enzyme and interact with substrate (Y1223, Y1238, R1285 and S1335)⁴⁴ remain relatively unchanged, a larger fraction of residues that bind to the FAD coenzyme (S1012, S1015, A1034, R1035, A1047, S1048, G1052, N1054, V1162, S1334, S1335, G1337, Y1338, Q1339) show reduction in their mobilities (Table S4 and S5 and Figure 2D). All of these critical residues map onto the non-interface regions of the enzyme.

Functional significance of dynamic change

Is there a general consensus as observed for the four enzymes above, with most of the functional sites undergoing a significant dampening in their fluctuations upon oligomerization? Or put conversely, are regions with reduced mobilities more conserved? To answer these questions, we consider the residue conservation profiles for all the proteins in the dataset calculated using Rate4Site and investigate the underlying distributions of the conservation scores. On fitting the residue conservation scores to different distributions, we observe that the conservation scores are best fit with the generalized extreme value distribution (Figure S5) as has often been observed for biological sequences.⁴⁷

In Figure 3, we classify residues as either interface (A) or non-interface (B) and for each category we report the distribution of residue conservation scores for the following three classes.

Figure 3.

Relationship between changes in MSF and residue conservation. (A) For interface residues, the distribution of conservation scores is sharper for regions with reduced MSF, followed by regions with no relative change. The regions which show increases in flexibility upon oligomerization are least conserved and have a broader distribution of conservation scores. (B) For non-interface residues, the same pattern is observed i.e. residues with reduced fluctuations are observed to be more conserved than their counterparts. Conservation scores are computed from Rate4Site with lower scores indicating higher conservation.

1. Residues with significant increases in MSF (MSF Increased)

2. Residues with significant decreases in MSF (MSF Decreased)

3. Residues with no significant changes in MSF (MSF Unchanged)

We identify a residue as an interface residue if any of its heavy atoms is within 4.5Å of the heavy atoms of the residues from an adjacent subunit of the oligomer. We observe that the extent of conservation is higher for both interface and non-interface residues showing reduced fluctuations than the residues that show either increases or no significant changes in their mobilities following oligomerization. Figure 3 also suggests that residues with increased mobilities upon oligomerization have a tendency to evolve more quickly than others. We also evaluate the statistical significance of the observed results. A non-parametric test for statistical significance reveals that the observed differences in residue conservation between the three classes is significant both for interface and non-interface residues (Figure S7). Also, the distributions are similar for the choice of different fold change ratio (FCR) cutoffs (Figure S6). To verify the consistency of these observations, we create two smaller data sets from the ds145 set, having 40 and 80 structures each, and repeat the calculations at FCR cutoff 1.5. For both sets we observe a similar distribution of the conservation scores (Figure S8, A and B) which suggest that the results are consistent across multiple data sets.

Global changes in dynamics upon oligomerization

Oligomerization not only reduces the mobilities, but also increases the mobilities of certain residues. This is seen in the four enzymes we described first. We then ask what fraction of residues in the entire dataset have significantly reduced or increased mobilities upon oligomerization. We investigate the changes in residue fluctuations for the threshold of 1.5 FCR that is, 50 % or more increase or decrease in fluctuations. In this way, we observe that 51.5 % of residues across all the proteins in our dataset show no significant changes in their mobilities upon oligomerization, while 26.2 % of the residues undergo a substantial reduction in their mobilities upon oligomerization (Figure S3 and Table 1).

Table 1. Extent of Changes in Mobilities.

Counts of the number of interface and non-interface residues showing increased, decreased and unchanged mobilities for 145 proteins. Changes indicate at least a 50% gain or loss in mobility.

Class	Oligomer Interface Residues (Counts and Percentage)	Oligomer Non- Interface Residues (Counts and Percentage)	Total (Counts and Percentage)
MSF Increased	238 (2.7%)	7780 (28.2%)	8018 (22.2%)
MSF Unchanged	2409 (28.2%)	16185 (58.6%)	18594 (51.5%)
MSF Decreased	5871 (68.9%)	3622 (13.12%)	9493 (26.2%)
Total	8518 (23.5%)	27587 (76.4%)	36105 (99.9%)

This aligns with one of the most widely accepted consequences of oligomerization, i.e., the dampening of residue mobilities at the binding interface. However, we also observe that 22.2 % of all residues exhibit increases in their flexibilities. 86 % of the proteins (124/145) in the dataset exhibit an increase for at least 10 percent of their residues. Interestingly, a small percentage of the residues (~ 3 %) with increased fluctuations are actually located at the interface of the oligomeric assembly (Table 1, Figure S4.A). These interface residues with increased fluctuations are found in regions with a significantly lower packing density in contrast to the other interface residues having reduced fluctuations (Figure S4.B and S4.C). We also perform this analysis on individual cases, that is, by identifying fractions of residues with increased, decreased or unchanged fluctuations upon oligomerization for each protein and then plotting the results for each category as box plots (Figure 4). We still observe that while almost half the residues for each protein show no change in their fluctuations, about a quarter show reduced and another quarter show increased mobilities. These observations suggest that oligomerization is not just a mechanism that dampens the mobility of residues, but is also a means of increasing the flexibility of certain regions of the protein, very nearly a conservation of the extent of internal mobility. Those regions with increased mobilities, as we saw for bovine glutamate dehydrogenase can play an important role in regulating the allosteric behavior of the protein.

Figure 4.

Boxplot showing fraction of residues with increased, unchanged and decreased fluctuations across all proteins. Residues with no significant changes in fluctuations have the highest mean fraction (0.474) while, the average fraction of residues with reduced MSF are nearly the same as the fraction of residues with increased (0.278 and 0.246 respectively).

Effect of oligomerization on residue communities: a case study on Triosephosphate isomerase (TIM)

Triosephosphate isomerase (TIM) plays an important role in the glycolytic pathway by catalyzing the reversible interconversion between isomers, dihydroxyacetone phosphate (DHAP) and D-glyceraldehyde 3-phosphate (GAP). The enzyme has a “TIM barrel” fold and is active as a homodimer in most mesophilic organisms. The catalytic chamber of the enzyme is located at the center of each TIM barrel and catalysis is carried out by a Lys-His-Glu triad (Figure 5). Glu165 and His95 are critical for proton transfer while, Lys13 bonds with the substrate oxygen.⁴⁸ Residues 166-176 correspond to the loop 6 which plays a critical role in the presentation and orientation of the ligand to interact with the active site residues. Previous studies showed that the dynamics of this loop is essential for the enzymatic activity, especially in protecting the substrate from solvent and preventing the formation of byproducts.⁴⁹

Figure 5.

Architecture of Triosephosphate isomerase (TIM). The enzyme has a TIM barrel structure with the catalytic residues located at the center of the molecule. The catalytic triad is formed by Lys13-His95-Glu165 (sticks). The mobility of loop 6 plays a key role in bringing in the substrate, protecting the ligand when it is bound, and removing the products.

We study the influence of oligomerization on residue clusters that exhibit significant correlation in their mobilities (referred here as residue communities) in the isolated monomer. Oligomerization, we hypothesize, by changing the geometry of the molecule can facilitate creation of new rigid blocks, often critical for the enzyme’s function. These newly introduced communities, present only in the oligomeric state of the molecule, could possibly explain why some enzymes are functionally active only in their oligomeric form.

Mesophilic TIM is known to be active only in its dimeric form. Interestingly, the enzyme does not form an active site shared between the adjacent subunits at the oligomeric interface.⁴⁸ The monomeric form of the enzyme is equipped with all the required catalytic residues to carry out its reaction on the substrate. The question then arises, why is oligomerization necessary for TIM if it is catalytically complete in the monomeric form. In this context, we investigate the changes in residue communities upon oligomerization and their importance for the enzyme’s function.

We use two forms of TIM: an unbound form (PDB: 8tim) and a substrate bound form (PDB: 1tph). Our aim is to investigate residue communities for four cases: a. single monomer from 8tim as an isolated monomer, b. single monomer from 1tph as an isolated monomer, c. 8tim as a dimer, and d. 1tph as a dimer. For each case, we study the rigid residue blocks in a single chain (by taking the first chain in the PDB file) and observing how they change upon oligomerization. For both forms we coarse-grain the protein by using only the C^α atoms, while modeling the substrate in 1tph at an all-atom level. We then model the dynamics of the isolated monomer and the monomer bound in the oligomer as elastic networks, the strength of interactions between residue pairs given by Equation 2. We obtain the matrix for correlated fluctuations from the inverse of the Hessian which is constructed using the first twenty soft modes, since these modes convey the most important motions (Equations 8 and 9). By using a single mode or a combination of these modes, proteins have been shown to undergo conformational transitions essential to their function.^{10, 17, 50} To obtain residue communities, we first transform the matrix of fluctuation correlations into a dissimilarity matrix (Equation 10) by subtracting each element from 1 and then perform hierarchical clustering with complete linkage on this matrix.⁵¹ The results of hierarchical clustering are displayed as a dendrogram (Figure S9). We truncate the dendrogram at different levels to obtain two, three and four clusters and treat them as structural blocks having highly correlated fluctuations, refer them as residue communities, and then investigate the influence of oligomerization on these communities.

In Figure 6 we have mapped the clusters formed by cutting the dendrograms at 90 percent of their maximum heights onto the TIM structures. Truncation at this level results in 2 clusters for 1tph and 8tim both in isolation and in their dimeric assembly. Figure 6A shows the mapped residue communities observed for 8tim and 1tph in isolation (i and ii respectively) and when in association with its adjacent unit (iii and iv respectively). As seen in Figure 6A (i and ii), the community structure of TIM in isolation doesn’t change much when the substrate is included in the structure. However, the change in the community structure is significant when the molecule is in its oligomeric form and the substrate is included (Figure 6A.iv).

Figure 6.

Effect of oligomerization on the distribution of residues into correlated communities for TIM. The communities formed upon truncating of the dendrograms at 90 percent (both 8tim and 1tph) are mapped onto the enzyme. (A) The community structure of TIM in isolation without substrate (i), with substrate (ii), as part of the oligomeric complex without substrate (iii), and oligomer with substrate (iv). (B) Communities in 1tph in isolation and in oligomeric association with bound substrate. Close-up view of the architecture of the active site residues and loop 6 for monomeric TIM with substrate (C) and oligomeric TIM with substrate (D) The two communities are colored red and blue. The substrate is shown as sticks and the active site triad as spheres. Glu165 and the phosphate group of the substrate can be seen to be dynamically correlated with loop 6 only in the oligomeric form of the enzyme.

The oligomeric and monomeric forms of TIM show quite different community structures in the presence of substrate (Figure 6B). A close up view of the active site of 1tph in its isolated form (Figure 6C) and in its oligomeric form (Figure 6D) shows the splitting of the active site into two communities (blue and red) in the oligomer while it remains rigid in the monomer. While two of the active site residues (Lys13 and His95) are part of a larger community, Glu165 displays coordinated motion with loop 6 and is part of the second community. We also observe the splitting of the substrate into two communities in the oligomeric form of the enzyme, with the phosphate group of the molecule moving in coordination with Glu165 and loop 6. When the dendrogram for the oligomeric form of TIM was cut to yield 3 clusters, Glu165 still moves in coordination with loop 6 while Lys13 and His95 are still part of the same community. Interestingly, at this level of clustering we begin to observe the coordination of Glu165 with loop 6 even in the unbound oligomeric form of TIM (8tim) as shown in Figure S10A.c. However, the observed rigidity of the active site in the monomeric form of TIM is preserved even after cutting the dendrogram for 1tph at different levels to yield three and four clusters (Figure S10B).

DISCUSSION

Dynamics is critical for the functioning of globular proteins. From its native state, a protein can frequently access an ensemble of low energy conformational changes which help it to carry out its function. In many cases, however, there is a set of conformations that cannot be visited from a protein’s native state as it incurs a huge increase in the net free energy of the protein. This energy overhead can be overcome through events like ligand binding that can shift the equilibrium population of conformers towards the required conformation by reducing the energy barrier. From the perspective of the Monod-Wyman-Changeux (MWC) model for allostery^{7, 52}, oligomerization is a mechanism to introduce larger scale allostery in proteins through conformational equilibrium shifts. The results presented here, in part, support this hypothesis.

We observe that a major fraction of the proteins in our dataset have a significant number of residues that increase in their mobility upon oligomerization. From the case study on bovine GDH, it is evident that the NAD⁺-binding domain is more mobile in the oligomer than in the monomer. Oligomerization enables tethering of one end of the enzyme (the oligomeric interface and GLU-binding domain), while allowing the distal end to exhibit increased mobility about the pivot helix. Such mobility, as the MSF comparisons indicate, was not possible when the enzyme was in its monomeric form. Previously, researchers have proposed that the mobility of the NAD⁺-binding domain can potentially aid in the enzyme’s allosteric behavior. If this is true, based on the results presented here it appears reasonable to propose that the enzyme may exhibit diminished allosteric behavior in its monomer form.

The new conformational flexibility introduced upon oligomerization may also be explained in terms of energy-entropy compensation. For bovine GDH enzyme, an increase in the entropy of the NAD⁺ domain upon oligomerization is compensated by the energetic stabilization of the GLU-binding domain and at the oligomeric interface, which exhibit a significant reduction in mobility. This explanation is also supported by Figure 4 which demonstrates that, upon oligomerization, while half the residues in a protein show no significant change in flexibility, the remaining fraction are almost equally divided between those exhibiting increased and reduced MSF values. Oligomerization could thus be a key contributing factor to the functioning of multi-domain enzymes where one domain is required to be stable and another, mobile. Owing to the observed rigidity in the NAD⁺ domain, GDH may be also be catalytically less efficient as a monomer. With the newly acquired flexibility in its oligomeric form, the enzyme can now sample new conformations which may not have been accessible to the monomeric form owing to their energetic overhead. Allosteric regulators can exploit this newly introduced conformational flexibility which occurs only in the oligomeric state of the enzyme.

The second part of this study reveals the localization of functionally significant sites in regions having reduced flexibility. The results suggest that residues with reduced flexibility upon oligomerization are more conserved than residues with either increased or no significant changes in flexibility. For the current study, this is true for proteins with oligomeric states ranging from two to six, and we observe similar distributions with varying choices of the FCR cutoff (Figure S6). From the case studies, these residues can be in regions distant from the oligomeric interface and can present themselves as orthosteric sites where mutations may negatively impact the protein’s function. There are also regions which have no experimentally assigned functional role that exhibit reductions in fluctuations. As can be seen from our four case studies, these residues are present as neighbors to key functional sites. We speculate that these residues could possibly serve as key anchoring sites, whose structural robustness may be critical for the efficient catalytic activity of the enzyme. This however remains to be confirmed experimentally.

The final section of this study investigates the changes in residue communities upon oligomerization and their functional role for triosephosphate isomerase (TIM). The study of TIM shows the critical role of oligomerization in changing the community structure of the active site residues. While the Lys-His-Glu triad remains rigid in the monomer at different levels of hierarchical clustering, oligomerization facilitates a change in this dynamic architecture and promotes the coordination of the Glu165 with loop 6. Previous studies have confirmed a strong correlation between the mobility of loop 6 and Glu165.⁵³ The mobility of Glu165 has also been proposed to play a key role in placing the substrate into its proper orientation, a requisite step prior to its catalysis. We also observe that the phosphate group of the substrate moves collectively with the same community as loop 6 and Glu165. This is in agreement with previous observations according to which the phosphate forms hydrogen bond with Gly171 in the closed conformation of the loop.⁵³ Interestingly, the enzymatic splitting of the substrate is seen only in the oligomeric form. And this separate community analysis reflecting the anti-correlated motions of the active site appears to relate closely to the enzyme mechanism, with these motions assisting the chemical reaction and removal of product. The monomeric form of TIM has all the residues required for its catalytic activity and doesn’t form such a divided active site as seen in its oligomeric form. In principle it might function as a monomer, however it does not. The mixed coarse-grained model used here to investigate the change in communities shows that the coordination of Glu165 with loop 6 is observed only when the enzyme is in its oligomeric form. As stated earlier, the dynamics of these two key elements is critical for the enzyme’s function and hence, the results presented here, in the context of residue community changes at the active site elements could explain the inactivity of the monomeric TIM. Oligomerization, as seen in the previous test cases, facilitates the enzyme’s access to certain critical conformations that are inaccessible or require high energy for the monomeric form to change the dynamic architecture of the enzyme.

CONCLUSION

Our work outlines two key elements of oligomerization. First, it emphasizes the importance of sites whose flexibility is reduced upon oligomerization. Given that the conservation profile of residues follows an extreme value distribution, a large fraction of residues are conserved, making it difficult to identify on this basis alone the potential drug binding sites in a protein. In current practice, residues at the oligomeric interface are often investigated for candidate drug targets.^{54, 55} From this investigation, we conclude that for homooligomeric complexes, regions with reduced fluctuations might also be explored as potential drug targets even though these regions may not always be on the interface. Second, the test case on triosephosphate isomerase states the importance of the residue community changes, providing a possible explanation as to why certain enzymes function only in their oligomeric form. Both these findings can be further explored to better understand oligomeric systems and identify key aspects of their dynamics.