A Universal Pattern in the Percolation and Dissipation of Protein

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A Universal Pattern in the Percolation and Dissipation of Protein Structural Perturbations Nandakumar Rajasekaran, Ashok Sekhar, and Athi N. Naganathan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02021 • Publication Date (Web): 14 Sep 2017 Downloaded from http://pubs.acs.org on September 20, 2017

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The Journal of Physical Chemistry Letters

A Universal Pattern in the Percolation and Dissipation of Protein Structural Perturbations Nandakumar Rajasekaran,1 Ashok Sekhar2 & Athi N. Naganathan1* 1

Department of Biotechnology, Bhupat & Jyoti Mehta School of Biosciences, Indian Institute of

Technology Madras, Chennai 600036, India. 2

Departments of Molecular Genetics, Biochemistry and Chemistry, The University of Toronto,

Toronto, ON, Canada M5S 1A8. AUTHOR INFORMATION Corresponding Author e-mail: [email protected] Phone: +91-44-2257 4140

ACS Paragon Plus Environment

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ABSTRACT

Understanding the extent to which information is transmitted through the intra-molecular interaction network of proteins upon a perturbation, i.e. an allosteric effect, has long remained an unsolved problem. Through an analysis of high-resolution NMR data from the literature on 28 different proteins and 49 structural perturbations, we show that the extent of induced structural changes through mutations, and molecular events including protein-protein, protein-peptide, protein-ligand binding and post-translational modifications exhibit a near-universal exponential functional form. The extent of percolation into the protein structures can be up to 20-25 Å despite no apparent change in the three-dimensional structures. These observations are also consistent with theoretical expectations, elementary graph theoretic analysis of protein structures, detailed MD simulations and experimental double-mutant cycles. Our analysis highlights that most molecular events would contribute to allosteric effects independent of protein structure, topology or identity and provides a simple avenue to test and potentially model their effects.

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Binding of a ligand, be it a protein, peptide or a co-factor, to a protein is one of the fundamental molecular events that regulates an array of downstream signaling cascades within the cell. The binding event can also result in post-translational modifications (PTMs) of the protein including phosphorylation, methylation etc. In many cases, such binding events or PTMs translate into conformational changes of the protein thereby regulating the specificity or affinity of a different or the same ligand at distal site that does not overlap with the original binding site. Such ‘action at a distance’ is termed allostery and was originally inspired by the binding cooperativity of oxygen to hemoglobin.1,2 Since then numerous approaches have been developed to explore and understand whether a binding event contributes to a conformational change and the underlying molecular principles associated with conformational transitions and population shifts.3-11 A dramatic structural change is, however, not a necessary criterion for an allosteric response, as shown from the perspective of theory,12 experiments13-19 and computational models20-24 (‘dynamic allostery’). The precise microscopic mechanism of how the signaling occurs in such cases and the extent (i.e. the distance) to which such an event can be ‘felt’ around the structure are still open questions. This is because of the intrinsic complexity and idiosyncratic nature of proteins that are held together by a unique network of weak non-covalent interactions determined by the primary sequence. The complexity is particularly evident in the differential and apparently context-dependent responses of proteins to specific mutational perturbations.25-28 It is also well established that the information generated by a binding event is transmitted through the buried non-covalent interaction network29-31 that is more fluid-like than previously thought.32,33 The related observations that mutations can mimic or modulate binding events34-36 suggest that


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mutations and the effect of a ligand-binding event translate into similar structural responses as they involve perturbations to the protein core. Taken together, this raises the question of whether allostery is a conserved or an intrinsic property of proteins37 or any macromolecule stabilized by non-covalent interaction network. Allosteric effects are typically identified by distal modulations of protein function and hence are challenging to identify when there is no trivial functional output. In this regard, backbone chemical shift perturbations (CSPs) generated from high-resolution NMR experiments are powerful tools to probe for minor changes in packing density, as they are sensitive to the local electronic environment of nuclei. In fact, CSPs upon ligand binding or mutations and relaxation dispersion experiments have been successfully employed to identify allosteric networks and minor conformational sub-states.38-42 In this work, we show that simple CSP experiments can highlight not only the coupled residues but also the extent to which they are coupled. We find that such distal effects are independent of protein structural class, binding event (protein-protein, protein-peptide, protein-ligand), or mutation type. The distance dependence of perturbations reveals a universal functional form highlighting a beautiful simplicity in otherwise apparently complex structural perturbations. To explore the extent to which mutational effects are felt in a structure, we collected backbone chemical shift differences between the wild-type and mutant (chemical shift perturbations or CSPs) from the literature on 12 different proteins for a total of 25 different single-point substitutions (Supporting Figure S1, Table 1 in the Supporting Information, SI). The mutations include side-chain truncation substitutions (say, LA), changes in backbone rigidity (glycine substitutions) and charge status, and those that increase the side-chain volume. No major structural re-arrangements


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Figure 1 Identifying coupled residues through single point mutations. Chemical shift perturbations involving the backbone amide atoms (∆δ), the amide hydrogen alone (∆δ 1HN) or the hydrogen on the alpha-carbon (∆δ 1Hα) are shown as a function of distance from the mutated site. Distance (d) is measured from Cα atom of mutated residue except in the case of Thymidylate Synthase for which distance is measured from Sγ of cysteine 146 (panel f). Two-parameter exponential fits to the function a = a0 e

− d /dC

, where a0 is the amplitude and dC is the coupling

distance, are shown in red. The sparse data points and large scatter preclude exponential fits to the mutations in panels h, m-o.


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have been reported in any of these proteins. Remarkably, even in this dataset, we find that the chemical shifts deviate from the WT to a large extent with the effect felt as far as 20 Å from the mutated site (measured as the Cα-Cα distances from the mutated site; Figure 1). The pattern seems to be independent of the nature of the mutation or protein identity. Importantly, control plots of CSPs from unfolded proteins (i.e. difference in chemical shifts between unfolded variants with and without the mutation) indicate little deviation or any specific trends (Figure S2). Despite the limited dataset, this analysis clearly implies that our observations in Figure 1 represent the propagation of the mutational effect around the perturbed site driven by alterations of the packing density resulting in the observable electronic effects. We further collected published CSPs upon protein-protein (8 pairs; green in Figure 2) or proteinpeptide binding (2 pairs; gray in Figure 2), protein-ligand (4 pairs; cyan in Figure 2) and also from di-Ubiquitin chains (Ubq chains linked at 7 different lysine positions, yellow in Figure 2; Figure S3 and Table 2 in SI). A ligand-(or protein-) binding site is defined as the collection of residues that are within 4 Å of the ligand in protein-ligand (or protein-protein) complex. Distances are then calculated from the coordinate center of Cα atoms of ligand (or protein) binding site and Cα atoms of each residue in the protein. Plotting the experimental CSPs as a function of the calculated distance, we find that a protein-protein or a protein-ligand binding event percolates far into the structure (~20-25 Å), very similar to that of mutations (Figure 2). The effect again appears to be independent of the nature of the underlying binding event or the identity of the protein/ligand involved and importantly without any perceptible structural change. Interestingly, the effect of phosphorylation (a post-translational modification; Table 3 in SI and Figure S4) also seems to influence distant residues though to a lesser extent (Figure 3).


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Figure 2 Propagation of perturbations into the protein structure induced by binding events. Backbone chemical shift perturbations (∆δ) are shown as a function of distance from the ligand binding site. Plots for protein-protein interactions are shown in green, protein-peptide interactions in gray, protein-ligand interactions in cyan and perturbations from ubiquitinubiquitin linkage at different sites in yellow. Abnormal chemical shift (2.10 ppm) for residue 12 has been excluded from the fit for Pin1 domain (panels k and l). Panel p reports the root mean square (RMS) difference in chemical shifts from different nuclei between apo- and holo-forms of the protein Bet. Exponential fits are shown in red (see the legend to Figure 1 and main text). The larger scatter in protein-ligand interactions, primarily due to the multiple-aromatic rings/longcarbon-chain nature of the ligands (Table 2, SI), precludes an exponential fit though the distancedependent trends are similar to other perturbations.


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Figure 3 Long-range effects induced by phosphorylation. Plots of backbone chemical shift perturbations (∆δ) are shown as function of distance from phosphorylated site for the indicated proteins. Exponential fits are shown in black.


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Any perturbation of the protein structure, be it through a mutation or a ligand binding event, is expected to be non-trivial. However, when the experimentally observable changes to the protein structure (chemical shift perturbations) are plotted as a function of distance from the mutated site or the coordinate center of the ligand binding site, the resulting pattern appears to be universal; the perturbations are maximal next to the binding site and are diminished in magnitude beyond, but the overall trend is conserved. What is the origin of this unique dependence and what functional form could best explain this dissipation? Theoretical analysis of protein structures and perturbations from lattice simulations suggest that the coupling between adjacent residues decay approximately in an exponential manner.31 In fact, the degree of thermodynamic coupling gleaned from double-mutant cycles hints at a similar dependence.30,43 Recently, an analysis of mutational effects from the perspective of multiple models at various levels of complexity graph theory, one microsecond long MD simulations of 7 mutants of ubiquitin and a detailed statistical mechanical model - reveal that mutational effects propagate through the intra-protein interaction network and dissipate in an exponential fashion44. An empirical structural perturbation approach also results in an exponential decay of energetic coupling while explaining a variety of phenomena including the results of statistical coupling analysis, stability changes induced by point mutations, and potential origins of folding cooperativity.45 In the exponential function employed to analyze the varied data discussed above, the parameter dC in the function, a = a0 e

− d /dC

where a is the observable and d is the distance (in Å units), is

termed the distance constant or the coupling distance; it is a measure of the extent to which the perturbed residue is coupled to its neighbors energetically.44 Perturbation analysis of intraprotein interactions networks and MD simulations involving several mutations of ubiquitin


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Figure 4 A consistent view of the percolation and dissipation of protein perturbations. Exponential fits are shown in red. (a) A plot of changes in betweenness centrality, the sum of the fraction of shortest path between pairs of nodes that pass through a given node, upon perturbing each residue in ubiquitin residue interaction network as a function of distance from the mutated site.44 (b) Distance dependence of mean absolute changes in van der Waals interaction energy (in kJ mol-1) obtained from microsecond-long molecular dynamics simulation of seven aliphatic mutants of ubiquitin.44 Note the errors bars are the standard deviations and the standard errors of mean are ~0.45 kJ mol-1 indicating that the average behavior is well defined.44 (c) Experimental thermodynamic coupling indices (|∆∆∆G| in kJ mol-1) versus distance for PDZ (green), SNase (pink) and PDZ3 domain (blue) from double mutant studies. (d, e) A global view of the distance dependence of chemical shift perturbations (gray circles) involving backbone atoms (panel d) or amide hydrogen (panel e) from the mutational database. Exponential fits to the gray circles are shown in red. The averages from within bins of width 3 Å are shown in green circles and they follow the expected exponential distribution. The ordinates are shown till 0.3 ppm and account for at least 96% of the all the perturbations. (f) Same as panel d, but for binding events.


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reveal a dC~5-6 Å (Figure 4a,b).44 These coupling distances are well defined as they are estimated by binning the large amount of data derived from computational approaches.44 A reanalysis of the double-mutant cycle data (that measures the thermodynamic coupling) from PDZ29,43 and SNase46 again reveals that the perturbed residues are on average coupled with a dC~12 Å (Figure 4c). This suggests that the raw data presented in Figure 1-3 should follow a similar exponentially decaying function, but the errors are expected to be larger as the underlying simple distribution would be confounded by non-trivial factors including the specifics of the protein structure, mutation (context-dependence), fewer CSP points and experimental errors (Table 4). In fact, a weak trend is evident when the coupling distances estimated for each of the proteins are a plotted as a function of the mean packing density (the average number of residue neighbors in a protein) - the better packed a protein, the stronger is the energetic coupling between adjacent residues and hence larger is the extent of percolation (Supporting Figure S5). However, a majority of the distance vs. CSP data for the three perturbations (mutation, binding, phosphorylation) fall within a narrow range of ~6-13 Å coupling distances (curves in Figures 14) suggesting that such confounding factors manifest only as higher order effects. To extract the underlying zeroth-order distance dependence function from experiments, we grouped together similar experimental data (either backbone CSPs or amide hydrogen CSP) from mutations and ligand binding (Figure 4d-4f). This allows for a more accurate estimate of the coupling distances as it minimizes any protein- and nuclei-specific effects; exponential fits result in a dC of 8.2/9.3 Å (backbone/amide hydrogen CSP) and 10.1 Å for mutations and ligand binding, respectively (red in Figure 4d-4f). Importantly, a simple binning analysis (green circles in Figure 4d-4f) follows a similar trend to the global exponential fit highlighting that it is a robust functional form.


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We effectively find that protein structural perturbations consistently propagate to large distances from the source of perturbation and dissipate in a universal manner in diverse mutations and protein-ligand binding events. The minimalistic functional form that best describes this pattern is a simple exponential, from which protein- or residue-specific coupling distances can be extracted. It also allows for condensing the observations into a simple two-parameter function while other functional forms would require more parameters that might not be warranted given the spread in the data. Note that the observations presented in Figures 1-4 are the first large-scale analysis of protein structural perturbations; therefore, the reported long-distance percolation (that can be observed visually) holds true irrespective of the nature of functional forms that best describe the data, as they are quantities directly derived from NMR experiments without any model-specific analysis. An exponential dissipation is, however, consistent with expectations from lattice simulations of proteins,31 experimental double-mutant cycles,30,43 graph-theoretic analysis of protein structures,44 distance-dependent weakening of van der Waals interactions from all-atom MD simulations of WT and mutant proteins,44 and the pattern of energetic coupling derived from a structural perturbation approach.45 An exponential dependence arises from the fact that the coupling is maximal when the residues are in physical contact and is substantially less when moving away from the perturbed site. A more complex dependence could definitely be envisaged including a power series or even a power-law behavior. However, the dynamic range on the abscissa is just over one order of magnitude precluding a more detailed analysis. Our observations have several implications in the understanding of packing energetics in protein structures and the structural origins of allostery. First, it suggests that the information generated upon a binding event or mutation will be transmitted far into the structure (up to 20-25 Å) even


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in the absence of a conformational change, as originally proposed by Cooper and Dryden from theoretical considerations.12 While our observations do not reveal the precise mechanism of signal transmission that could be through subtle packing rearrangements or changes in internal side-chain and/or backbone dynamics, they provide a first comprehensive look at the extent to which the structural features are affected. Since binding is driven by a precise relative arrangement of residue side-chains and their intrinsic dynamics,14,47 the observed systematic alteration of the chemical shift pattern suggests that the electronic environment is distinctly affected that could modulate the binding of partners at distant sites. Second, distal effects (observed in this case through chemical shift perturbations) will therefore always occur irrespective of whether the perturbed residue is functional or not, as it depends only on how it is energetically coupled to its neighbors and not on its ‘functionality’. In other words, every site is allosteric (as can be seen from Figures 1-3) and can modulate the protein function if the active site is within its sphere of influence, potentially highlighting the origins of ‘cryptic allostery’.48 Third, such long-range effects are therefore not a feature that can be restricted to specific proteins (so-called allosteric proteins), but is a robust and intrinsic property of all proteins as their interior is stabilized by specific pattern of weak non-covalent interactions that are coupled to each other. Any perturbation event will necessarily propagate into the structure and dissipate exponentially as observed not just in intra-molecular networks but also in protein-protein interaction networks.49 Fourth, our observations provide a simple structural rationale for the results of sequence conservation patterns around the active site of enzymes that point to a strong conservation of residues not just around (~6 Å) the active site but till ~25 Å.50 Last and importantly, any binding event could potentially be modeled as a collection of perturbations around the binding site as shown recently from a structural perturbation approach.45 The


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chemical shift perturbations can also be employed as benchmarks to computationally model or restrain conformational ensembles of protein-ligand binding or mutational effects. This will reveal rich information on the functionally relevant minor and generally invisible conformational sub-states whose populations are modulated in response to perturbations.


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ASSOCIATED CONTENT Supporting Information. Tables with additional information on proteins analyzed, their structures, figure highlighting the lack of any specific trends when comparing the chemical shift differences between the denatured states of WT and mutant proteins, and the dependence of the coupling distance on packing density. (PDF) AUTHOR INFORMATION Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was funded by the new faculty seed grant from the Indian Institute of Technology Madras (IITM), India. We would like to thank Prof. Lewis E. Kay for providing the 1H and 15N chemical shift assignments of V148I apoSOD12SH. A. N. N is a Wellcome Trust/ DBT India Alliance Intermediate Fellow.


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Figure 1 117x76mm (300 x 300 DPI)



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Figure 2 117x76mm (300 x 300 DPI)


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Figure 3 32x12mm (300 x 300 DPI)



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Figure 4 86x41mm (300 x 300 DPI)


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TOC Figure 25x12mm (300 x 300 DPI)


A Universal Pattern in the Percolation and Dissipation of Protein

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