A Chemical Perspective on Allostery.

Review pubs.acs.org/CR

A Chemical Perspective on Allostery Andre A. S. T. Ribeiro and Vanessa Ortiz* Department of Chemical Engineering, Columbia University, New York, New York 10027, United States ABSTRACT: Much work has been done in the past decade to quantify the phenomenon of allosteric communication in proteins. Every new study unveils an extra piece of the puzzle in our search for an understanding of allostery that allows us to make predictions on the response of a protein to medically relevant stimuli such as pathological mutations or drug binding. This review summarizes recent advances in the analysis of mechanisms of allosteric communication in proteins, and combines this new knowledge to offer a perspective of allostery which is consistent with chemical views of molecular processes. First, we review recent work, particularly computational, on the characterization of signal propagation and conformational changes in allosteric proteins. We then compare different models of allostery, and discuss the significance of the concept of an allosteric pathway. We argue that allostery can be rationalized in terms of pathways of residues that efficiently transmit energy between different binding sites. We then provide examples that show how this picture could account for most of the observed data, since energy flow may be manifested as changes in both structure and dynamics. We conclude by acknowledging that the proposed view is still a simplification and should not be taken as a rigorous model of allosteric communication in proteins. Nevertheless, simple pictures like this can go a long way in improving our understanding of many complex phenomena observed in nature. structure or function.7−9 A thorough understanding of microscopic interactions and their effect on macroscopic properties of biomolecules not only expands our overall knowledge of nature, but it also allows us to make predictions concerning the outcomes of complex processes that are relevant for different technological applications. One of the most fascinating features of the cellular machinery is its ability to respond to changes in its environment. Cell signaling is a major area of biological research, and allosteric propagation in individual proteins is directly linked to complex cellular processes.10 The term “allostery” was coined by Monod and Jacob to describe long-range effects observed upon ligand binding to some substrates, where excess energy stemming from binding to a specific site triggers structural and/or dynamical changes in other regions of the biomolecule, allowing for efficient intramolecular control of metabolic processes.11−15 Rationalization of early experimental evidence led to the development of two important phenomenological models for allostery: the concerted model of Monod, Wyman, and Changeux (MWC)16 and the sequential model of Koshland, Némethy, and Filmer (KNF).17 Both models were originally developed to provide a description of allostery in hemoglobin and consider two major conformational states for the different protein domains. The MWC model further assumes that different domains are in the same conformational state and that ligand binding shifts the chemical equilibrium in favor of the high-affinity state, leading to cooperative ligand binding. On the

CONTENTS 1. Introduction 2. Identifying Structural or Dynamical Changes in Allosteric Proteins 2.1. MD-Based Methods 2.2. Markov State Models (MSM) 2.3. Normal Mode Analysis (NMA) 2.4. Principal Component Analysis (PCA) 2.5. Elasticity-Based Methods 3. Identification of Residues Important for Signal Propagation in Proteins 3.1. Statistical Coupling Analysis 3.2. Theoretical and Computational Methods 4. A Chemical Picture of Allostery in Terms of Pathways of Energetically Coupled Residues 5. Conclusions Author Information Corresponding Author Notes Biographies Acknowledgments References Note Added after ASAP Publication

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1. INTRODUCTION Proteins and other biomolecules are characterized by a multitude of interatomic interactions that ultimately determine their macroscopic behavior.1,2 This intricate balance of interactions results in complex energy landscapes3−6 and renders such molecules susceptible to subtle perturbations which, in several cases, can result in significant changes in © 2016 American Chemical Society

Special Issue: Protein Ensembles and Allostery Received: September 15, 2015 Published: January 7, 2016 6488

DOI: 10.1021/acs.chemrev.5b00543 Chem. Rev. 2016, 116, 6488−6502

Chemical Reviews

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can be obtained by identifying which amino acid residues are essential for signal propagation and what are the structural or dynamical changes elicited by the excess energy resulting from effector binding. In addition, chemists tend to think in terms of structure and specific interatomic interactions. A chemical perspective thus needs to characterize relevant interactions and structural motifs for allostery. As will be seen in the following sections, significant improvements have been achieved in addressing these questions in recent years. The Review will be structured as follows: section 2 will focus on the identification of structural and dynamical changes in allosteric proteins, section 3 will focus on the identification of residues important for signal propagation, and section 4 will discuss the significance of the concept of allosteric pathways and how a chemically appealing picture of allostery can be obtained.

other hand, the KNF model assumes an induced-fit mechanism where ligand binding to one domain triggers conformational changes in the other domain, and can thus be easily understood in terms of the propagation of a interdomain signal. A more recent ensemble allostery model (EAM) provides a generalization of both models, allowing for different conformational states to be populated (Figure 1).18 Advances in nuclear

2. IDENTIFYING STRUCTURAL OR DYNAMICAL CHANGES IN ALLOSTERIC PROTEINS Allosteric behavior is observed when ligand binding to a specific site affects physical and/or chemical properties at another region of the protein. It is therefore necessary to investigate what are the underlying structural or dynamical changes elicited by ligand binding. Experimental techniques such as X-ray crystallography and nuclear magnetic resonance can provide significant insights on structure and dynamics of biomolecules, and have been extensively applied to investigate allosteric proteins. A recent review focuses on the application of both techniques to study allostery in hemoglobin.27 In addition, experimental techniques28 such as disulfide trapping29,30 can be used to identify allosteric sites when studying structural changes elicited by ligand binding. Finally, experimental techniques provide the ultimate source of information for the validation and improvement of computational models of biomolecules. Interesting illustrations of this type of approach are the employment of NMR data to perform molecular dynamics simulations of proteins31,32 and the refinement of structurebased models with evolutionary data to explore protein conformational diversity.33 Properly designed experimental studies can provide direct measurements and information about complex molecular processes, and the amount of data on allosteric proteins has increased significantly in recent years.34 Nevertheless, experimental methods are frequently hindered by limitations in spatial and temporal resolution. Employing mathematical models to describe nature offers no such limitations, and a detailed microscopic characterization of the behavior of molecular systems can be obtained. Computational methods can be successfully applied to the characterization of conformational changes,35,36 as well as to identification of allosteric sites in proteins.37,38 Nevertheless, this type of method comes with a significant cost, as the quality of the results can only be as good as the quality of the model itself, and realistic models frequently lead to computationally intensive calculations that require specialized software and hardware.39,40 The study of conformational changes/dynamics in proteins has always represented a challenge for computer simulations because of the need to sample long time scales to capture this phenomenon, which for the purposes of a molecular simulation constitutes a “rare event”. Even when studying allostery, which generally involves relatively small conformational rearrangements (compared to, say, protein folding), and even today when our computational capacity is orders of magnitude larger than 10 years ago, the question of whether we have sampled our system enough to

Figure 1. Comparison of allostery models, as described by Hilser and co-workers.18 Rectangles and circles represent different conformational states of two protein domains, while shaded shapes represent effector binding to a specific domain. Possible conformational states of the different models are highlighted by black ellipses. The MWC model only allows matching conformational states in both domains, while the KNF model yields an induced-fit mechanism. The ensemble allostery model considers additional combinations of domain conformational state/effector binding.

magnetic resonance (NMR) and the widespread employment of computer simulations of biomolecules also led to the recognition of the role of dynamics in protein function19,20 and allostery.21,22 This is even more relevant given experimental evidence23 supporting the early theoretical proposal that allostery may be manifested exclusively through changes in the dynamical behavior of proteins, with no significant structural shifts.24 The overall complexity of allostery and signal propagation in proteins render relatively simple models such as MWC and KNF unable to fully account for experimental evidence on different allosteric proteins.25,26 On the other hand, more complex models often lack a simple qualitative picture that can be very appealing and useful. Chemists are very familiar with this type of compromise: while a full quantum-mechanical description of a molecular system involves complex multidimensional wave functions, the concept of a chemical bond with localized electrons remains extremely important and is widely used to rationalize different chemical processes. The purpose of this Review is to highlight advances in obtaining a mechanistic perspective on allostery, therefore contributing to yield a chemically appealing picture of this complex biological process. Within the framework of the MWC model, allostery is a consequence of dynamical coupling between the different binding sites and a resulting restriction of their conformational states. On the other hand, a series of structural deformations propagate from one binding site to the other in the KNF model. In any case, the binding sites are energetically coupled and a chemical perspective on allostery 6489


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catalytic domain (Cel7BCD), which was induced by binding of a glucan chain.46 Analysis of residue−residue distances from 100 ns AA MD simulations showed how the loop that includes residues Trp320 to Gly333 changes conformation upon glucan chain binding. Another study used residue−residue distances, as well as cluster analysis and solvent accessible surface area to analyze AA MD trajectories to characterize the conformational changes associated with ATP binding and hydrolysis in serine/ threonine protein kinase Akt1, which lead to dephosphorylation of residue T308.47 Using these measures, the authors demonstrated that ATP binding to Akt1 stabilizes the closed conformation, protecting phophorylated T308 (pT308) by restricting access from phosphatase. However, upon ATP hydrolysis to ADP, a conformational change exposes pT308 to allow dephosphorylation. Similar analysis was also applied to trajectories obtained from Brownian dynamics simulations of a self-organized polymer model that was used to describe the allosterically induced rigor (R) to postrigor (PR) conformational transition in myosin V.48 Angles and residue−residue distances, as well as root-mean-square fluctuation measurements, were used to show how, upon ATP binding, a series of loop movements and helix rotations lead to the structural rearrangements that eventually cause the myosin motor domain to detach from actin. Equilibrium MD simulations have also been used in combination with targeted MD simulations to study conformational changes in allosteric transitions. Residue root mean square fluctuations and atomic motion correlations are measured from equilibrium MD simulations, while specific backbone angles and residue distances are monitored in targeted MD simulations in which a harmonic force is applied to a subset of residues in one conformational state, to force them to adopt the conformation observed in the structure associated with the other state. Analysis of equilibrium and targeted MD trajectories were applied to study the conformational changes involved in tetracycline (Tc)-binding-induced DNA unbinding from Tet repressor (TetR).49 Harmonic forces were applied to the residues surrounding the Tc binding site of the DNA-bound structure of TetR, to make them adopt the conformation observed in the TetR−Tc complex. The results showed significant conformational changes in two helices, helices 6 and 4, of which helix 4’s N-terminal forms part of TetR’s DNA interface. This destabilization of the TetR−DNA interface was proposed to lead to the observed dissociation of TetR from its operator DNA upon binding of Tc. This approach was also used to study the calcium-induced conformational transition from the tense (T) state to the relaxed (R) state in recoverin.50 Here, the transition was found to follow a two-step process that involved (1) destabilization of the T structure by breakage of three salt-bridges, and swiveling of the N- and C-terminal domains, and (2) separation of two helices and stabilization of the interfacial domain. Following a similar idea to that involved in the use of targeted MD, Laine and co-workers51 used steered MD simulations to generate a conformational path connecting the closed and open conformations of adenylyl cyclase (EF). EF is the etiologic agent of anthrax; it raises the levels of cAMP in the human body when its catalytic site for conversion of ATP to cAMP becomes activated upon binding of calmodulin (CaM). Since both closed and open conformations were known for EF, steered MD was used to apply harmonic forces to move the atoms in the closed structure to their respective positions in the open structure. Intermediate conformations were collected and

obtain an accurate and reliable view of the conformational dynamics of our protein continues to be as valid as it ever was. For this reason, we keep trying to come up with “tricks” that help us improve our sampling while avoiding months of simulation and gigabytes of data that only contribute to the background noise. Two of the most common tricks involve simplifying the molecular description of the molecule using some form of coarse graining, and reducing the size of the conformational space sampled by picking a set of “reaction coordinates” that are believed to dominate the transition from one conformational state to the other. In the following sections, we will go over some of the methods that have been used to characterize conformational changes/dynamics in allosteric proteins, and the tricks behind them. 2.1. MD-Based Methods

Much of the work done to characterize conformational changes in allosteric proteins relies on the analysis of trajectories obtained from molecular dynamics (MD) simulations. In MD simulations, Newton’s equations of motion are integrated over time to generate the trajectories followed by each particle in the system, in three-dimensional (3D) space. These simulations can be performed using an all-atom (AA) description of the molecule, or using a coarse-grained (CG) description, which represents groups of atoms in the molecule by a single particle. The AA representation allows inclusion of specific interactions such as hydrogen bonding and salt bridges. This makes for a more accurate description of the mechanisms at play, but limits conformational sampling of the molecule in two ways: (1) having a more complex conformational energy landscape provides the possibility that the molecule gets trapped in a minimum, and (2) computations are more expensive (all degrees of freedom are taken into account) limiting the total amount of time the simulation can reach. On the other hand, CG models are usually softer, which reduces specificity in the interactions but allows increased sampling of the molecular conformational space. It is also possible to reduce the complexity of the energy landscape by using structure-based models, which essentially restrict the phase space to a specific energy basin. The earliest example of this type of approach is the Go̅ model,41 and recent generalizations for multiple energy basins have been used to study allosteric transitions.7,33,42,43 Chu and Voth performed a CG analysis on AA MD simulations of ATP-bound and ADP-bound G-actin, to show that the coil-to-helix transition that G-actin’s DNase I-binding loop (DB loop) undergoes upon ATP hydrolysis causes a weakening of the intermonomer interactions in actin assemblies.44 This effect is strong enough to show a reduction of almost half in the persistence length of the F-actin upon ATP hydrolysis. This allosteric communication was proposed by the authors as one of the factors contributing to the dynamic behavior of F-actin. This work was extended to examine the role of severing protein, actin depolymerization factor (ADF)/ cofilin, on actin filament stability.45 By applying their CG analysis of AA MD simulations, the authors showed that binding of ADF/cofilin to an actin monomer induces substantial structural changes to the DB loop of the adjacent monomer. This was also seen to weaken intermonomer interactions and increase flexibility of the filament. Analysis of time evolution of residue−residue distances from MD simulations can also provide insights into relevant conformational changes. This type of measurements helped identify a conformational change in the endoglucanase I 6490


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bound and unbound systems and suggested a role for the induced fit mechanism during drug binding to cryptic sites. One can also use experimental data to build the MSM. This is what Zemkova et al. did when studying the allosterically regulated pore dilation of the P2X4 receptor channel.55 They used experimental data generated in their own lab to build MSM that describe how ivermectin (IVM) allosterically regulates the ability of adenosine 5′-triphosphate (ATP) to activate the P2X4 receptor channel. They showed that IVM has the ability to rescue the P2X4 receptor from desensitization and subsequent internalization by dilating the receptor channel pore. Boras and co-workers also used an MSM built from experimental data to study the allosteric mechanisms by which cAMP binding activates protein kinase A (PKA).56 The PKA complex (known as R2C2) is composed of two regulatory (R) subunits and two catalytic (C) subunits. Each R subunit has two cyclic nucleotide binding domains (CBD-A and CBD-B), to which four cAMP molecules bind to activate and release the C subunits. The authors used previously published experimental data to build MSM of the PKA-RIα isoform, and the results from their simulations suggest that one C subunit is released first, upon binding of cAMP to the CBDB. This observation was explained by the authors as being a result of a conformational selection mechanism driving the first part of the allosteric activation process. Release of the second C subunit was found to happen only after all four cAMP molecules are bound to the R2C2 complex. The authors followed up with a second study that used MSM built from atomistic MD simulations to study the conformational freeenergy landscape of the CBD-A domain, in both the apo (cAMP-free) and cAMP-bound states.57 In this second study, it was found that both apo and cAMP-bound systems show relatively flat free-energy landscapes, which allow exchange between the active and inactive states, consistent with a conformational selection mechanism of allostery. The authors observed that CBD−cAMP interactions have the effect of slowing motion in the ensemble, which in turn modulates the transition rate of going from active to inactive but not that of going from inactive to active. In addition, they identified a change in dynamics of a specific α-helix (the B/C helix) as being the rate-limiting step for activation.

refined using a modified version of the conjugate peak refinement method. The resulting “conformational transition path” revealed the presence of a pocket on the surface of EF, which underwent significant structural changes during the closed-to-open transition. The authors then used virtual screening to find potential EF inhibitors, of which some were confirmed to inhibit the activation of EF in in vitro essays. 2.2. Markov State Models (MSM)

Markov state models take advantage of the idea that proteins have a very rugged conformational free-energy landscape, with many minima being separated by a relatively small barrier. This means that, given sufficient thermal energy, a molecule will be able to sample all minima separated by small energy barriers. We can then assume that all those states can be represented by a single “average” kinetically metastable state, which will be separated from other kinetically metastable states by larger energy barriers. This significantly reduces the number of states we need to sample. The second assumption MSM make is that the transitions between these average states can be described as a Markovian process (the probability distribution for the next transition depends only on the current state of the system). This second assumption allows us to describe the kinetics of a system with N states with the equation P(nτ ) = P(0)[Γ(τ )]n

(1)

where τ = propagation time step, n = total number of propagation steps, P(nτ) = probability that each state is occupied at time nτ (a 1 × N vector), P(0) = probability that each state is occupied at time 0 (a 1 × N vector), and Γ(τ) is the transition probability matrix (TPM), an N × N matrix containing the transition probability from state i to state j. The TPM is generally constructed using data from molecular dynamics (MD) trajectories. For more details on MSM implementation, please refer to the excellent book chapter by Da and co-workers.52 While a recent development, MSM have already been successfully applied to the study of several allosteric systems. In 2011, Silva and co-workers reported on the use of MSM built from atomistic MD simulations to study the kinds of conformational changes that are triggered by the binding of arginine to lysine-, arginine-, ornithine-binding (LAO) protein.53 The authors were not only able to predict the bound state, but could also identify two main steps in the opento-closed transition that LAO undergoes upon arginine binding. The first step involved binding of arginine to form an “encounter complex”, and it was found to be driven by both induced fit and conformational selection. The second step involved closing of the molecule to form the bound state, and was found to be driven by only induced fit. Another very interesting study was able to apply MSM to find a large number of cryptic allosteric sites on β-lactamase, interleukin-2, and RNase H.54 The authors defined cryptic allosteric sites as transient pockets that are allosterically coupled to the protein’s active site and, therefore, could potentially serve as novel drug target sites for the molecule. The MSM were derived from long atomistic MD simulations of both unbound and bound states. MSM of the unbound systems were found to sample conformations that were very similar to the bound state, which prompted the authors to point at the mechanism of conformational selection as a possibility when describing ligand binding. However, the authors also compared results from

2.3. Normal Mode Analysis (NMA)

The main assumption in NMA is that, at equilibrium, all conformations adopted by a molecule can be considered to arise as thermally induced harmonic fluctuations around a single well-defined conformation. Essentially, each minimum in the conformational energy surface of the molecule is considered to be a perfect parabola, an assumption that is known to be incorrect at physiological temperatures. A second assumption is made when applying NMA to the study of conformational dynamics of macromolecules; this is that protein function correlates with large conformational fluctuations (low frequency modes), and therefore only these need to be considered. This relation has been confirmed by many studies, and is now widely accepted to the point that it is used as a condition to confirm the presence of allostery in a molecule.58 For a molecular structure composed of N atoms, a standard NMA calculation involves minimizing the conformational potential energy of the structure, calculating the Hessian matrix (a 3N × 3N matrix of second derivatives of the potential energy 6491


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the system. Ming and Wall67 derived the equations and calculated these quantities for the allosteric system composed of lysozyme and the ligand tri-N-acetyl-D-glucosamine. In their derivation, the authors split the change in the conformational distribution of the system into three contributions: changes in the eigenvalue spectrum, changes in the mean conformation, and changes in the eigenvectors. They showed that the term that corresponds to contributions from changes in the eigenvectors can be used to identify potential binding sites in proteins. Because of all the approximations involved, NMA can be considered sometimes to be of limited use, but when combined with other computational methods and experimental data, it can be quite powerful. One example of this is the work of the group of Qiang Cui, which used NMA in combination with detailed MD simulations to study the allosteric effects of phosphorylation on the activation of bacteria chemotaxis Y protein (CheY).68 NMA helped identify the β4−α4 loop as one of the major conformational changes associated with the CheY activation transition. When combined with other analysis, the authors determined that phosphorylation does not cause, but rather stabilizes, the new conformation of the β4−α4 loop. In another example, Zhuravleva et al. combined NMA with PCA (see section 2.4) and NMR data to identify the mechanisms of allosteric inhibition of barstar on ribonuclease barnase.69 Here, NMA of a Gaussian network model was used to help identify mobile interfaces that serve as “hinges” to allow reorganization of blocks of relatively rigid residues. It was suggested by the authors that these mobile interfaces could provide pathways for the propagation of allosteric signals between distant sites. The group of Roland Stote has also made several contributions to the study of protein allostery using NMA. An NMA study of the Inserted domain (I-domain) from the lymphocyte function-associated antigen-1 (LFA-1) identified structural changes important for the activation of this integrin protein.70 It also showed marked differences in the atomic-level dynamics of LFA-1 when binding of the natural ligand versus binding of an allosteric inhibitor. This was followed up with an NMA/PCA study of the dynamics of β3 integrin I-like and Hybrid domains,71 in which the modes driving the conformational transition from closed to open were identified, as well as their connection to the ligand binding event. Allosterically coupled conformational changes in oligomerization have also been studied with NMA. The group of Ivet Bahar used NMA to study oligomerization of enzymes belonging to the amino acid kinase family.180 By splitting the Hessian matrix into submatrices, the authors were able to quantify the effects of oligomerization on the dynamics of the monomers, and vice versa. Monomers were seen to pass on their intrinsic dynamic features to the oligomers they formed, while the monomer−monomer interface created upon oligomerization was found to provide a stiff “glue” that allowed the oligomer rigid-body motion. NMA was also applied to study the conformational changes involved in the allosteric coupling of the ATPase and helicase activities in hepatitis C virus NS3 helicase.72 Here, NMA of an ENM of the NS3 helicase was used to identify the lowest frequency modes of motion, and then a deformation analysis process was applied to confirm these modes. In the deformation analysis, the crystal structures of the open and closed states of the protein were superimposed, then external forces were applied to the ATP-binding residues of the open structure to move them toward the close one, and the global

with respect to the coordinates), and diagonalizing the Hessian to obtain the eigenvalues and eigenvectors (normal modes). This last matrix-diagonalization step makes this analysis so computationally expensive that it limits its applicability to only small proteins in vacuum, or with solvent described implicitly. To make NMA accessible to a larger set of molecules, one must apply a third approximation: that the atomic interactions can be described at a coarse-grained level, with elastic network models (ENM) being the model of choice by many. ENM describe an entire protein structure as a set of particles (placed at the positions of the Cα) that are connected by springs (placed between any two Cα’s that are within a predetermined cutoff distance). All spring pairs in the model are decided using a single cutoff distance, Rc, and all springs have exactly the same spring constant, γ. But even with all these approximations, NMA has become very popular because it brings with it the benefit of extracting low-frequency modes of motion not readily accessible with the more rigorous atomistic MD simulations. One of the first studies that applied NMA to the understanding of conformational transitions in allosteric proteins was that of the group of Perahia on hemoglobin59,60 and aspartate transcarbamylase (ATCase).61−63 The authors modeled the crystal structures of both tensed (T) and relaxed (R) states using a united-atom model (nonpolar hydrogen atoms are described implicitly) to describe the protein atoms, and a linear distance-dependent dielectric constant plus weighting of atomic charges at the ends of charged amino acid side chains to model the effects of the water. Analysis of low-frequency modes in the T-state showed displacements that made the structure approach the R-state, while low-frequency modes on the R-state showed displacements toward the T-state structure. The authors used this information to identify the types of tertiary and quaternary structural changes that drive the T−R transition in hemoglobin and ATCase. Mukherjee et al.64 applied NMA to identify the structural changes associated with the allosterically activated DNA mismatch repair cycle. Using their results from NMA on the crystal structures of bacterial MutS and eukaryotic MSH2MSH6, with and without mismatch DNA, the authors were able to construct possible conformational states for all the steps in the mismatch recognition/repair cycle: DNA scanning, mismatch recognition, repair initiation, and sliding along DNA after mismatch recognition. NMA has also been used to construct a series of structures that span the transition between the open and closed conformations of adenylate kinase (AKE).65,66 AKE is allosterically activated by ATP binding to undergo large conformational changes, which allow for the catalysis of the reaction of ATP with AMP to produce ADP. At each “step” along the closing, the authors would generate a new set of normal modes for an intermediate structure using an elastic network model. This approach allowed inclusion of nonlinearities, such as local unfolding, involved in the full open-to-closed transition. In the first study, the authors found that these local unfolding (or cracking) events had an allosteric catalytic effect on enzyme function by acting as added denaturant.65 The second study revealed that the motion of the LID domain, dominated by intrinsic structural fluctuations, always preceded the motion of the NMP domain, which was dominated by ligand−protein interactions and cracking.66 Normal modes can also be used to calculate the allosteric potential and the change in the conformational distribution of 6492


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study the cooperativity in their oligomerization and ligand binding processes. From the normal modes obtained from ligand-free and ligand-bound forms of the monomer and dimer, the authors calculated configurational entropies that provided the entropic cost associated with changes in the vibrational activity in the system. Comparison of these configurational entropies showed a smaller entropy cost for both processes of oligomerization and ligand binding occurring together, than for them occurring separately, consistent with the observation of cooperativity in experimental studies. PCA was also used to identify conformational changes connecting ATP binding and hydrolysis to solute transport in ATP-binding cassette (ABC)3 transporters. PCA was applied to trajectories of the ATP-bound, ADP-bound, and apo states of monomeric MJ0796 to show how ATP binding and hydrolysis causes rotation of a helical domain, mediated by interactions between the catalytic metal and a glutamine residue. Analysis of the dimer showed large structural changes in a helical domain, which caused the dimer to become asymmetric. Kantarci-Carsibasi et al.78 combined PCA with Monte Carlo (MC) simulations to model the transition between open and closed conformations of adenylate kinase, and between tense and relaxed states in hemoglobin. The technique allowed the authors to identify and characterize important events involved in the transition, in a computationally efficient manner. Collective motions in GluA2 and GluA3 AMPA receptors (AMPARs) N-terminal domains (NTDs) were also examined using PCA to investigate the possibility of allosteric regulation of channel activity, in a fashion similar to that observed with ionotropic glutamate receptors (iGluRs).79 PCA confirmed the existence of motions in GluA2 and GluA3 AMPARs NTDs, which were consistent with the allosteric mechanisms of signal propagation in iGluRs. This finding opened the door for the search for potential ligands for GluA2 and GluA3 AMPARs NTDs that could allosterically regulate their channel opening for cognitive enhancement. An interesting study used a combination of analysis methods, including PCA, to identify residues that are important for signal propagation in hyperthermophilic acylaminoacyl peptidase (AAP).80 By performing an in silico alanine scanning, the authors identified V13A, among others, as a mutation that could destabilize the protein structure. However, PCA analysis of this mutant showed a dynamical fingerprint that was almost identical to that of the wild-type AAP. In a similar approach, Johnson and co-workers81 combined PCA with glycine scanning to develop a method that allows identification of motions that are important for allosteric communication in a protein. The method applies PCA to identify important collective modes on contacts that have been selected based on their highly dynamic behavior (contacts that have 20−80% probability of being formed). The authors tested their method by studying the allosteric regulation that the binding of ligand 9C to retinoid X receptor (RXR) exerts on the binding of ligand T3 to thyroid hormone receptor (TR) in the TR−RXR nuclear receptor complex. They found that binding of 9C to RXR applies a perturbation to the RXR binding site, which propagates through the TR−RXR interface and has the effect of “loosening” TR−T3 binding. Finally, PCA was recently used in a new tool to build ensembles of protein conformations and construct conformational energy landscapes for proteins.82 The new tool, called SIfTER, was applied to study effects of mutations on the allosteric signaling of the H-Ras catalytic domain. The mutation

structural changes on the molecule, induced by the local applied forces, were calculated. Finally, the structural changes were analyzed using dynamical domain partition to show that the main conformational changes are indeed captured by the first two modes obtained from NMA using the ENM. However, the use of ENMs in NMA does not always return reliable results. Dykeman and co-workers developed a method that allows the computationally efficient application of NMA to a large protein using an all-atom description.73 The method employs an energy functional which is minimized to find modes of a classical dynamical matrix below a fixed level. They applied this method to study the conformational transition, from symmetric to asymmetric, of bacteriophage MS2 coat protein dimers, which is caused by binding of its allosteric effector, an RNA stem-loop (TR). Analysis of the normal modes obtained for TR-bound and RNA-free coat protein dimers showed that TR binding causes a loop in one of the monomers (the FG loop) to become more dynamic while the same loop on the other monomer rigidifies.74 NMA using an ENM showed increased flexibility for both loops.75 2.4. Principal Component Analysis (PCA)

Like NMA, PCA also assumes that the molecular motions relevant to protein function are all included in the major collective modes. However, PCA does not assume a harmonic potential around a conformational energy minimum. For this reason, PCA is also known as quasi-harmonic normal-mode analysis. In PCA, a set of structural conformations of a molecule (that may be obtained experimentally or from an MD simulation) are superimposed with each other and used to construct the symmetric variance−covariance matrix of positional fluctuations: C = ⟨(x i − ⟨x⟩)(x i − ⟨x⟩)T ⟩

(2)

where xi are the coordinates for each individual frame, and ⟨x⟩ are the coordinates for the “average” frame. Then, C is diagonalized by solving the eigenvalue problem λ = ATCA

(3)

where λ and A are the eigenvalues and eigenvectors of C, respectively. Because PCA does not apply the harmonic approximation, frequency cannot be used to identify the relevant modes. Instead, the largest amplitude modes are used, which are the eigenvectors corresponding to the largest eigenvalues. In the application of PCA to the study of protein allostery, the McCammon group published a paper in 2001 in which PCA was used to identify the collective motions involved in the opening of the gorge of mouse acetylcholinesterase (AChE).76 While allosteric mechanisms were not the main subject of the publication, the authors did note the correlation between motion in the gorge and motion in other parts of the protein. They speculated that the mechanism of inhibition employed by Fas2 (a known AChE inhibitor) could involve restricting groups on the surface of AChE, which they had identified as having large concerted motions with the gorge. A later study focused on the use of PCA to understand mechanisms of allostery that do not necessarily involve structural changes, but changes in the vibrational activity of the molecule.77 Here the authors simulated small systems of glycopeptide antibiotics chloroeremomycin, vancomycin, and dechlorovancomycin in explicit water (6000 atoms in total), to 6493


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in oncogenic variant Q61L was found to decrease flexibility in H-Ras, affecting its GTP hydrolysis activity.

elsewhere and elicit structural or dynamical changes. The notion of an allosteric pathway is usually defined in terms of function, being a set of amino acid residues experimentally known to be required for allosteric behavior of a given protein. In the following we will focus on the determination of both types of pathway, therefore linking the functional definition of allostery with the chemical picture of energy flow through specific interatomic interactions. Several experimental and theoretical methods have been used in recent years to study energy transport in biomolecules.86−89 Anisotropic energy flow between distant regions in proteins has been directly linked to allosteric pathways by a number of theoretical studies. Obtaining experimental evidence of this phenomenon is not trivial, but advances in spectroscopic techniques have allowed for detailed studies of vibrational energy transfer in molecules of increasing complexity.90−97 Ultrafast pump−probe spectroscopy has been the standard approach for experimental investigation of vibrational energy transfer (VET) in molecular systems. Transient-absorption spectroscopy can be used to study vibrational energy redistribution in small molecules.98 Larger molecules such as proteins are usually characterized by congested absorption spectra due to overlapping Franck−Condon transitions, resulting in a need for other techniques to be employed. In the case of heme proteins, time-resolved resonance Raman spectroscopy has been particularly useful. Early studies determined that energy transfer from the excited heme to surrounding protein atoms occurs within a few picoseconds.99,100 Energy dissipation from the protein to solvent has also been monitored by time-resolved IR101 and thermal phase grating spectroscopy,102 yielding time constants of ∼20 ps. A recent development in time-resolved spectroscopy applied to proteins has been achieved by the Mizutani group. Timeresolved anti-Stokes ultraviolet resonance Raman (UVRR) was used to monitor populations of a vibrationally excited amino acid residue following heme photoexcitation, providing direct observation of VET in the cytochrome c protein.103 It was found that energy flow from the heme group to the only Trp residue in this protein, located within 4 Å of the heme moiety,104 has a time constant of ∼3 ps, while release of energy from this residue to surrounding atoms occurs within ∼8 ps. A beautiful combination of this technique with site-directed mutagenesis has been recently reported, allowing for an investigation of the dependence of VET kinetics with the distance to the excited heme group.105 Mutants with Trp residues within 7 and 12 Å of the heme moiety were studied, and the authors found the energy flow distance dependence to be in qualitative agreement with classical thermal diffusion. However, the results obtained for a mutant with a Trp residue within 16 Å of the heme moiety were significantly different, and the authors argued that a more complex model at the molecular level would be necessary to explain the results.105 This corroborates evidence from theoretical studies89 and, more specifically, raises the important question as to which types of interatomic interactions contribute to efficient energy propagation in proteins. Another application of femtosecond spectroscopy has been recently reported by Li and co-workers.106 The authors investigated energy flow in bovine serum albumin (BSA). A heater dye was bound to a fatty acid binding site that is allosterically coupled to a binding site in another subdomain. The connection between energy flow and allostery was directly

2.5. Elasticity-Based Methods

Elasticity-based methods part from the premise that, when applied a perturbation, a protein structure will respond by undergoing local conformational changes in spots that offer the least resistance to motion, namely, regions of high flexibility (or low stiffness). Therefore, if one knows which are the highly flexible regions in a protein structure, one can use this information to predict the kinds of conformational changes that the molecule will undergo as a response to perturbation. Lawton et al.83 extracted the stiffness, K, for different parts of the molecule from the Hessian matrix, which is the matrix of second derivatives of the energy with respect to interparticle distances (Kii = ∂2Eij/∂xi2). To reduce computational cost, they used a reduced description of the interatomic interactions which emphasized motions of nodal backbone atoms. Starting with the crystallographic structure of deoxyhemoglobin, the authors applied distance constraints to atom pairs surrounding the oxygen binding pocket to simulate oxygen binding. Then, they applied their stiffness matrix to generate the oxyhemoglobin structure, and compared it to its crystallographic counterpart to calculate the root mean squared distance (rmsd) difference between their prediction and the crystallographic structure. While in some instances they were able to obtain an rmsd less than 1 Å, the results seemed to be highly dependent on the choice of atoms to which the initial distance constraints were applied. More recently, we applied a method developed by Riggleman and co-workers84 for the calculation of atomic elasticities to the characterization of conformational changes in the allosteric Lac repressor (LacI) protein.85 The method involves application of a small strain to the molecule and, after energy minimization, calculation of the atomic stresses (σi) and strains (εi) to finally calculate the atomic elasticity, Ki, using the macroscopic definition (Ki = σi/εi). A 3D map of elasticity was built for LacI, in which the crystal structure was colored according to the stiffness values obtained from the calculation. This map was compared to the map obtained by superimposing the crystal structures of LacI with inducer and with anti-inducer molecules. The regions of high flexibility in the stiffness map were in good agreement with regions that showed high deformation in the superposition map. The stiffness map built using an elastic network model to describe energetic interactions did not show good agreement with the experimental crystal structures, highlighting the need to use an all-atom description to fully capture allosteric mechanisms in LacI.

3. IDENTIFICATION OF RESIDUES IMPORTANT FOR SIGNAL PROPAGATION IN PROTEINS Signal propagation in proteins is a highly complex biomolecular process that is often fundamental for the biological function of a given protein. These molecules are subject to numerous intraand intermolecular forces that determine their behavior. Strong interactions such as chemical and hydrogen bonds, and weak van der Waals interactions both play important roles in determining structure and function. 1 This network of interactions also implies that perturbations of a group of atoms may be propagated to other regions of the molecule through specific interactions, therefore defining pathways of energy flow. This is directly linked to allostery, allowing for excess energy stemming from ligand binding to be directed 6494


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protein-coupled receptors (GPCR) and hemoglobins. In the case of the studied GPCRs, most positions were found to be independent from all remaining positions. It was also found that statistically coupled interactions can be roughly divided in three classes, with the first two being relatively short-range interactions. The third class was identified as a sparse but contiguous network of residues linking the ligand-binding pocket to the cytoplasmic surface, with many of the involved residues being essential for allosteric activation of GPCRs.114 A sparse network of physically connected residues was also found for the hemoglobins, and the involved residues are consistent with the known mechanism of allosteric signaling in these proteins. The aforementioned results show that SCA can be a very powerful method for determination of allosteric pathways in proteins. Indeed, the method has been employed to identify residues important for signal propagation in a number of proteins.115−121 Despite the demonstrated usefulness of studying evolutionary covariances, it should be noted that not all such correlations are necessarily relevant. Indeed, correlations may arise from MSA sampling limitations and phylogenetic effects. Halabi and co-workers used random matrix theory to analyze the SCA covariance for a family of serine proteases.122 Their main finding is that residues taking part in relevant interactions can be divided into statistically independent groups that occupy different regions within the core of the tertiary structure and are associated with different biochemical properties. Furthermore, they represent coevolving groups of residues that have diverged independently in the evolution of the protein family. The name “protein sector” was introduced to describe these groups of residues, and it was found that they typically comprise protein active sites and connect to other functional sites through pathways in the protein core.123 Recent work has shown that residues that take part in a protein sector are functionally sensitive to mutation, whereas nonsector positions are more tolerant to substitution.124 Interestingly, it was also found that standard measures of functional importance, including positional conservation, are not able to identify as many functionally relevant positions as sector analysis.124 The SCA method focuses on identifying correlations in a set of homologous protein sequences; however, it should be noted that a given protein family may include proteins that exhibit different biological functions despite high sequence similarity. This is especially relevant for large multidomain proteins. An interesting study by Smock and co-workers focused on the family of Hsp70-like proteins, including both the allosteric Hsp70 and nonallosteric Hsp110 proteins. Employing singlevalue decomposition of the SCA matrix to compare functional divergence with positional coevolution, a sector responsible for interdomain signal propagation in Hsp70 was identified.125 The aforementioned results clearly indicate the importance of statistical coupling analysis for determining allosteric pathways in proteins. Nevertheless, analysis of evolutionary data does not allow for mechanisms of signal propagation to be dissected, therefore lacking the necessary spatial resolution to fully determine the microscopic requirements for allostery. As will be discussed below, a range of methods based on computer simulations of biomolecules is especially suitable to address this issue.

evaluated by performing the experiments with BSA bound to its allosteric effector sodium myristate. It was found that effector binding results in a significant increase of anisotropic energy flow through the protein without heating of the rigid helix bundles that connect the allosterically coupled sites.106 3.1. Statistical Coupling Analysis

Spectroscopic techniques constitute the most direct way of investigating energy transfer and linking it to signal propagation in proteins; nevertheless, the required experimental setup is complex and the resulting spatial resolution is limited. Furthermore, while protein engineering techniques can be used to allow the study of energy transfer to different sites in a protein, the determination of a pathway for signal propagation would require the characterization of all the relevant VET kinetics in a single molecular entity. Direct determination of allosteric pathways through spectroscopic methods is therefore currently unfeasible. Nevertheless, indirect evidence for determining pathways of signal propagation may be gained by mutagenesis studies, with mutations at key residues deteriorating the efficiency of energy transport and leading to a loss of biological function.107 Relevant inter-residue interactions for signaling can be mapped with thermodynamic mutant cycle analysis, a technique that focuses on the assignment of pairwise interactions through the measurement of energetic coupling between different residues.108 However, employing this method for a systematic identification of functionally important interactions in complex proteins is hindered by significant technical limitations. A more successful approach has been provided by the usage of evolutionary data to identify correlated mutations.109 A beautiful application of this kind of analysis is exemplified by the statistical coupling analysis (SCA) method of Lockless and Ranganatham.110 The proposed method is based on the notion that evolution of protein sequences is a random process subject to constraints imposed by biological function. Strong evolutionary constraints in a given position will result in sequence conservation or, in other words, a probability distribution for different amino acid residues that is significantly different from the overall distribution for the protein family. Indeed, it is well-known that highly conserved residues tend to occur in functionally important protein regions.111−113 However, an analysis of conserved positions does not take into account the fact that specific inter-residue interactions are frequently important for biological function. In the case of allosteric proteins, it is exactly these interactions that determine the pathways for signal propagation. In order to identify conserved interactions between different residues, the SCA method considers pairwise correlations between sequence positions in the multiple sequence alignments (MSA) of a protein family. The method was originally applied to a single active site residue in a PDZ domain family. A set of coupled positions was predicted, including unexpected long-range interactions, therefore defining a pathway through the protein structure that may allow for efficient energy propagation. This seminal work has motivated several investigations to confirm the proposed signal propagation pathway in the PDZ domain, as will be discussed below. The statistical coupling method can be obviously applied to the entire protein sequence, instead of focusing on a single residue, yielding a conservation-weighted covariance matrix. This was first reported by Süel and co-workers.114 The authors investigated three families of allosteric proteins, including G 6495


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3.2. Theoretical and Computational Methods

the simulation. The method was used to study signal propagation in a PDZ domain, and the obtained results are consistent with the statistical coupling analysis method described above.110 A method similar in spirit to PPMD is anisotropic thermal diffusion (ATD).148 Here, nonequilibrium MD is performed with a single amino acid residue coupled to a heat bath, allowing for characterization of vibrational energy flow through the protein. A number of computational studies have focused explicitly on investigating vibrational energy transfer in proteins, and employed methodologies have included normal mode calculations,149,150 master equation simulations,87 and a generalization of the ATD method described above.151 Detailed accounting of interatomic forces in equilibrium MD simulations has also been used to determine signal propagation pathways.152 Finally, a mathematical approach that has seen significant success in modeling signal propagation is based on graph theory. A coarse-grained representation of a complex biomolecule can be obtained by modeling it as a network, with nodes usually representing amino acid residues and edges linking nodes that are deemed connected. Network modeling can be used both to perform inexpensive calculations of structural fluctuations153,154 and to analyze the results of atomistic MD simulations.146,155,156 A recent review provides an excellent account of the basic theory and applications of graph theory to model allosteric proteins.157

Theoretical studies of allostery and signal propagation have been performed for several decades, and employed methods include an early mathematical model linking hemoglobin structure to biological function and state-of-the-art molecular dynamics simulations using dedicated hardware.35,36,126 As previously discussed, the computational cost of atomistic MD simulations can be very significant, and carefully developed models of reduced complexity can be useful alternatives for providing insights on biological function. A powerful example is the COREX algorithm originally developed by Hilser and Freire.127 This method is based on Monte Carlo simulations of local unfolding of groups of amino acid residues in the native state structure and has been used to study protein folding and to identify residues important for allosteric communication in a number of proteins,8,128−131 including a detailed account of allostery in the enzyme dihydrofolate reductase.128 A recent paper described very interesting results on the employment of COREX and an ensemble allostery model18,132 as part of a strategy to design switch proteins.133 COREX was used to assess changes in conformational entropy caused by the incorporation of engineered linkers in a nonallosteric fusion protein, resulting in a modified energy landscape that triggers allosteric behavior. The authors suggest that their approach could be a general strategy for introduction of allostery in nonallosteric proteins.133 The COREX algorithm relies on a model that was parametrized based on surface area calculations and calorimetric data of a number of proteins.134 Another approach for designing coarse-grained models of proteins relies on extensive analysis of structural information.135,136 This type of knowledge-based contact potential can be rationalized in terms of energy landscape theory.137,138 A key concept arising from this type of approach is that proteins and other biomolecules are characterized by minimally frustrated interactions, allowing for complex processes such as protein folding to occur with relatively fast kinetic rates.3 It has been shown that this type of interaction can play a significant role in allosteric proteins.6,139 The previous results show that relatively simple models can give valuable information about signal propagation in proteins. Nevertheless, the computational technique that has been most used for studying allostery is undoubtedly atomistic MD simulations in one of its many forms. The importance and popularity of MD simulations is clearly shown by the fact that, despite the increased complexity of the underlying model and corresponding algorithmic implementations, performing a MD simulation of a protein is relatively straightforward with any of the several well-known MD simulation packages.140−144 Molecular dynamics simulations typically generate enormous amounts of high-dimensional data, and careful analysis of the molecular trajectories can give insights about allosteric pathways and signal propagation in proteins. The most straightforward approach for studying allostery with MD is to run simulations of both the apo and effector-bound protein structures, comparing structural and/or dynamical fluctuations in both trajectories.36 It should be noted that a full characterization of these fluctuations may represent significant sampling requirements. In order to decrease the associated computational cost, enhanced sampling techniques may be used.145,146 A method that has been specifically designed for studying signal propagation is pump−probe MD (PPMD),147 where a subset of protein atoms is subject to oscillating forces during

4. A CHEMICAL PICTURE OF ALLOSTERY IN TERMS OF PATHWAYS OF ENERGETICALLY COUPLED RESIDUES Section 3 focused on the determination of signaling pathways in proteins, and it was shown that several experimental and theoretical methods can be used to identify residues important for energy transfer and allostery. However, when all the experimental and computational evidence is combined, it becomes clear that the notion of a single pathway of coupled residues linking different binding sites offers only a limited view. A more general approach is to consider the possible existence of multiple pathways,158 and a computational method able to identify degenerate allosteric pathways has been recently proposed.159 This increased complexity may also be used to question the usefulness of the concept of allosteric pathways. Indeed, the ensemble allostery model (EAM) of Hilser and coworkers18 posits that allostery in a multidomain protein should be rationalized in terms of free energies of conformational change within different domains and interdomain energetic coupling (Figure 1). This model, however, does not provide explicit consideration of structure or specific interatomic interactions, and therefore it does not contribute to a chemically appealing picture of allostery. One of the main features of EAM is an inverse relationship between allosteric coupling and stability within the molecule.18 Indeed, the role of intrinsically disordered (ID) proteins in allostery has been increasingly acknowledged.160−162 Allostery in ID proteins obviously challenges a mechanical picture of allostery with structural pathways going through residues adjacent in tertiary structure. But maybe we can solve this discrepancy by reevaluating our definition of the term “signaling pathway”. As previously mentioned, an allosteric pathway is usually defined in terms of function, corresponding to a set of residues essential for allosteric behavior of a given protein. On the other 6496


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structural fluctuations observed during the simulation). The calculated pathways thus conform to the notion of a pathway of energetically coupled residues. This method was able to identify residues important for allostery in the enzyme imidazole glycerol phosphate synthase (IGPS), while networks based on correlation coefficients were not. The proposed method of protein energy networks (PEN) gives maximum weights to chemical bonds and strong interresidue interactions such as hydrogen bonds and salt bridges, thus implying that allostery is linked to efficient energy propagation through strong interactions. The successful results with the IGPS enzyme led us to investigate this assumption more thoroughly, and we introduced a measure of efficiency of signal propagation, named “network coupling”, to address this issue.179 We employed the PEN method and the network coupling analysis to study the lactose repressor protein (LacI), a classic example of allosteric system.179 It was shown that the network energetic coupling was able to discriminate between allosterically active and inactive mutants of LacI. Interestingly, we found that the method also worked for mutants involving residues that do not form strong nonbonded interactions. The corresponding network nodes thus have edges with low weights that are, in principle, not important for signal propagation. Nevertheless, allowing for structural relaxation with sufficient MD sampling led to network rearrangements, ultimately resulting in decreased network coupling for allosterically inactive mutants. These results were not reproduced by networks defined in terms of correlation coefficients.179 The network energetic coupling analysis of LacI provided further evidence that the chemical picture of allostery linked to efficient energy propagation through strong interatomic interactions is indeed useful. Nevertheless, fully establishing this link requires the comparison of the network coupling with an actual measure of energy flow in proteins. We carried this analysis for the catabolite activator protein (CAP),179 a model system for allostery without conformational change.23 We performed an extensive characterization of energy flow in CAP, starting from a fully minimized protein in explicit solvent, and monitored local changes in both kinetic and potential energy following thermal excitation of a single residue. This was, to the best of our knowledge, the first such attempt on a fully minimized protein described at the atomistic level with explicit solvent molecules. We also calculated the network energetic coupling values for regular MD simulations of wild-type CAP and an allosterically inactive mutant. We found that both the network analysis and the energy propagation simulations predicted lower signal propagation efficiency for the allosterically inactive mutant of CAP. The successful application of the PEN method raises an interesting issue. As previously discussed, the method relies on the assumption that pathways of strongly interacting residues are essential for allostery, thus providing a picture of signal propagation in proteins which is in line with chemical views of molecular processes. It should also be noted that pathways of energetically coupled residues do not necessarily require a stable tertiary structure, and allostery in intrinsically disordered proteins can be rationalized in terms of efficient signal propagation through the protein backbone. To test this hypothesis, we performed energy propagation simulations on the folded and fully extended conformations of the postsynaptic density protein 95 (PSD-95). We found that the protein

hand, a structural or mechanical pathway can be defined as a set of residues that suffer coupled structural deformations following a mechanical perturbation at a given site.163−165 However, if we define a pathway as a set of residues that efficiently transmit energy between different binding sites, this more general notion could encompass both of the previous definitions since energy flow may be manifested as changes in both structure and dynamics. It is evident that this concept is a simplification, as excess energy stemming from ligand binding will diffuse over different degrees of freedom, including heat transfer to solvent molecules. Nevertheless, it can be a useful picture, and it is supported by recent experimental evidence.106 Several recent studies of allosteric proteins employing network theory also highlight common definitions of signaling pathways.166−173 As mentioned above, network theory can be used to model a protein structure (or an ensemble of structures stemming from MD simulations) at a coarse-grained level. Protein networks are usually mapped at the residue level, with each node representing a single amino acid residue. Defining a network topology also requires drawing connections between different nodes, thus defining network edges. Finally, it is often useful to employ weighted networks, where a specific weight is assigned to each network edge. This mathematical framework is especially convenient to study signal propagation, as shortest pathways can be easily calculated with specific algorithms.174,175 It therefore follows that the connection between allostery and the network model lies in the proper assignment of edges and edge weights. The assignment of network edges is somewhat straightforward. It is obvious that residues should be relatively close to each other in order to interact and mediate signal propagation, so employing an arbitrary geometrical cutoff value is a potentially reasonable approach. Nevertheless, it has been recently shown that small changes in the cutoff value can result in significant differences in the resulting analysis of signaling pathways.155 Assigning edge weights requires more careful consideration, and most studies have used weights based on inter-residue atom−atom contacts154,167,176,177 and correlation coefficients extracted from MD simulations.146,156,178 As mentioned above, different choices of network definition reflect different assumptions regarding the underlying mechanism of signal propagation. Assignment of network topologies based on geometrical cutoffs and inter-residue atom−atom contacts implies that residues close in tertiary structure are able to mediate signal propagation due to the formed contacts. It should be noted that this type of definition does not take into account the existence of different types of atoms and interatomic interactions. On the other hand, usage of correlation coefficients results in pathways defined in terms of coupled conformational fluctuations. This introduces significant problems in the analysis, as motion correlation is not necessarily associated with a direct interaction. In addition, this analysis does not discriminate between different types of interatomic interactions. We believe that a chemical picture of allostery should take into account different interatomic interactions. Indeed, we recently showed that defining network edges in terms of interaction energies has significant advantages over other approaches.155 It is important to note that there is no need to employ arbitrary cutoff values within this framework (as the edges represent direct inter-residue interactions), and the employed energies are ensemble averages extracted from molecular dynamics simulations (thus taking into account 6497


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backbone may provide a more efficient route for energy transfer than secondary and tertiary contacts.179

5. CONCLUSIONS We have reviewed new knowledge that has been obtained on the mechanisms by which allosteric proteins propagate signals and trigger conformational changes to enable changes in their behavior. We have then evaluated this new knowledge on the basis of different models of allostery and different definitions of allosteric pathways. In our search for a definition of allosteric pathway, which can encompass a large portion of the data and, at the same time, can conform to standard chemical views of molecular processes, we have arrived at a method that assumes that efficient energy transfer through strongly coupled residues is important for allosteric communication. The results discussed above indicate that this simple chemical picture of allostery based on pathways of energetically coupled residues can be very useful. Finally, it should be noted that this picture of energy pathways is a simplification, and does not provide a rigorous model of allosteric communication in proteins. Nevertheless, simple pictures of complex phenomena can be extremely powerful, as the example of the chemical bond clearly demonstrates.

Vanessa Ortiz was trained as a chemical engineer, receiving her B.S. from the University of Puerto RicoMayaguez and her Ph.D. from the University of Pennsylvania. At Penn, she worked under the guidance of Drs. Dennis E. Discher and Michael L. Klein, to conduct computational studies of aqueous block copolymer assemblies and protein stability under applied forces. She then did postdoctoral work in the group of Juan J. de Pablo at the University of Wisconsin Madison, modeling DNA to investigate the connections between DNA sequence and its mechanical properties. As an assistant professor in the Department of Chemical Engineering at Columbia University, Dr. Ortiz focuses on using computational methods to study the ways in which biomolecules use their ability to deform, to transmit signals, and to perform their function.

ACKNOWLEDGMENTS This material is based upon work supported by a Parkinson’s Disease Foundation Columbia University Center Pilot grant program.

AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Notes

REFERENCES

The authors declare no competing financial interest.

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Biographies

Andre Ribeiro obtained his B.S. and Ph.D. degrees in chemistry from the Federal University of Rio de Janeiro, Brazil. His doctoral thesis, under the supervision of Prof. Dr. Ricardo Bicca de Alencastro, described the implementation of an enhanced sampling method combining Monte Carlo and molecular dynamics simulations. He is currently a postdoctoral research fellow in the Ortiz Group at Columbia University, and his research focuses on the development of tools for analyzing biomolecular simulations. 6498


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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on January 7, 2016, with a missing reference. This reference has been added to the reference list, and it has been cited in the text in the version of this paper published to the Web on February 12, 2016.

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