Kinetic and thermodynamic allostery in the Ras protein family

Abstract

Allostery, the transfer of information between distant parts of a macromolecule, is a fundamental feature of protein function and regulation. However, allosteric mechanisms are usually not explained by protein structure, requiring information on correlated fluctuations uniquely accessible to molecular simulation. Existing work to extract allosteric pathways from molecular dynamics simulations has focused on thermodynamic correlations. Here, we show how kinetic correlations encode complementary information essential to explain observed variations in allosteric regulation. We applied kinetic and thermodynamic correlation analysis on atomistic simulations of H, K, and NRas isoforms in the apo, GTP, and GDP-bound states of Ras protein, with and without complexing to its downstream effector, Raf. We show that switch I and switch II are the primary components of thermodynamic and kinetic allosteric networks, consistent with the key roles of these two motifs. These networks connect the switches to an allosteric loop recently discovered from a crystal structure of HRas. This allosteric loop is inactive in KRas, but is coupled to the hydrolysis arm switch II in NRas and HRas. We find that the mechanism in the latter two isoforms are thermodynamic and kinetic, respectively. Binding of Raf-RBD further activates thermodynamic allostery in HRas and KRas but has limited effect on NRas. These results indicate that kinetic and thermodynamic correlations are both needed to explain protein function and allostery. These two distinct channels of allosteric regulation, and their combinatorial variability, may explain how subtle mutational differences can lead to diverse regulatory profiles among enzymatic proteins.

Significance

Using the Ras family proteins as a model system, this work demonstrates that networks of kinetic correlations are needed, in addition to standard thermodynamic measures, to predict mutant and ligand-dependent allosteric regulation in enzymes.

Introduction

Protein can transfer motion, and thus information, across the length of their structures. However, a mechanistic understanding of how this information flows is not yet established. While almost all drugs target protein active sites (1), very few target allosteric sites. With greater understanding of protein communication networks, new allosteric targeting sites could emerge for proteins that have eluded current drug screening methods. On a more fundamental level, a mechanistic understanding of allostery is required to build testable models of protein function and evolution. The first allosteric models were phenomenological. In the context of multiprotein cooperativity, the Monod et al. model (2) posited that ligand binding shifts the equilibrium between states in which all subunits change conformation in a concerted manner, whereas the Koshland et al. model (3) posited that ligand binding sequentially induced protein conformational change that promotes further ligand binding. Information transfer is enabled by symmetry and rigidity to facilitate long-range structural correlations (4). Perutz (5) was the first to use crystal structures to decipher allosteric mechanisms based on structural changes in hemoglobin upon binding of oxygen to the heme groups. Allostery was initially described in proteins with well-defined backbone structural changes between the active and inactive states. However, many researchers have since observed allosterically induced functional change without a difference in mean structure between functional states. For example, in the catabolite activator protein, two ligand binding sites communicate allosterically to change the protein’s affinity for DNA. This communication has been shown by NMR to be purely entropic (6). As a complementary method, statistical analysis of pairs of amino acid positions that jointly vary in multiple sequence alignments were used to reveal contiguous sectors of coevolving residues within proteins (7,8). Through clever attachment of a light-activated protein domain at surface sites of the sector in dihydrofolate reductase, allosteric communication through the sector was demonstrated (9). These results indicate that allosteric mechanisms are more diverse and nuanced than what can be inferred from static structure.

Our current understanding of allostery has evolved from a two-state model to a statistical ensemble-based model in which a protein samples a probability distribution over conformational states. Characterizing conformational states instead of relying on a single averaged protein structure, such as is done with x-ray crystallography, has proven to be important for understanding reaction mechanisms (10,11). Working under this ensemble model, Cooper and Dryden mathematically showed how allostery can occur without enthalpic changes (12). More specifically, they demonstrated two other possibilities: 1) allosteric regulation can modulate the number of conformational states accessed (the entropy), or 2) allosteric regulation can modulate the waiting time (kinetics) between conformational changes. This abstract framework underscores the need to understand and predict networks of thermodynamic and kinetic allostery from structural and dynamical data on real protein systems.

Experimental methods such as NMR and kinetic ITC studies (13,14,15) have shown that conformational entropy can have a greater effect on binding affinity than differences in backbone structure. Therefore, direct sampling of atomistic fluctuations on the single-molecule level is needed to extract correlated dynamics responsible for allostery. Molecular dynamics (MD) simulations provide atomically resolved protein dynamics on the functionally relevant timescale of picoseonds to milliseconds, thereby directly sampling the correlated motion of all protein atoms. The sampled protein conformations can be used to build coarse-grained Markov states of the entire protein, allowing estimation of rate constants between protein states. However, correlations between different parts within a protein, and therefore the allosteric pathways, are not directly mapped by this state-space formulation (16,17). Alternatively, insights into allosteric pathways have been inferred from structural models based on intramolecular contact networks. Intramolecular couplings are then predicted using normal mode analysis of structural perturbations (18) or graph theoretic measures that incorporate information about correlated dynamics via network edge weights (19). Here, we consider the challenge of extracting allosteric pathways from simulation data without imposing any structure-based mechanism of information transfer.

Kinetic versus thermodynamic allostery

Allosteric regulation of entropy is sometimes referred to as “dynamic allostery” to differentiate it from enthalpic regulation; however, we denote any combination of enthalpic and/or entropic regulation as “thermodynamic allostery.” Whether primarily entropic or enthalpic in nature, thermodynamic allostery is relatively intuitive: it can be quantified by the extent to which the probability distribution sampled by the allosteric and active sites are not independent. However, kinetic allostery, quantified by correlations in the waiting times between different structural transitions, is relatively unexplored. Consider a protein with an allosterically deactivated state A which transitions to an allosterically activated state B. With each type of allostery, a different change in the energy landscape of the conformational ensemble is expected (Fig. 1 a). Enthalpic allostery results from changing the relative stability between states (e.g., in hemoglobin (5)), whereas entropic allostery changes the number of conformations accessible to one of the states (e.g., tetracycline receptor (11) (Fig. 1 a). Kinetic allostery results from raising or lowering the energy barrier between states, resulting in changes to the waiting time between subsequent interstate transitions. Parts of the protein with long mean waiting times indicate regions of dynamical frustration; if the waiting times of different parts of the protein vary in time in a correlated manner, they constitute a kinetic coupling network. If this network includes surface sites whose waiting times can be modulated by external perturbation, then such a network is a kinetic allosteric network. Because entropy and enthalpy are time-independent equilibrium measures, allosteric mechanisms driven by enthalpic and entropic changes can be quantified by probing the protein ensemble without considering the arrow of time. For example, thermodynamic couplings have been quantified by calculating the cross correlation or covariance between the Cartesian coordinates (20) and often further simplified by projecting them onto lower-dimensional principal components (21). Normal mode analysis has also provided insights into collective motions and their sensitivity to sequence perturbations (22). Structure-based approaches have also incorporated graph theoretic approaches to predict information pathways within proteins (19). However, a kinetic measure must depend on time; to quantify kinetic allostery requires discrete event statistics to measure correlations between the frequency of conformational dynamics. Although methods exist to augment thermodynamic correlations with temporal information (23), relatively little progress has been made to quantify kinetic allostery, which would require capturing correlated changes in the timescale of motion rather than the motion itself. We previously introduced a purely temporal measure of correlations in the waiting time between protein dihedral changes, called the conditional activity (CA), and demonstrated its potential for mapping kinetic allosteric pathways (24). In this study we will apply this framework to quantify kinetic allostery.

Figure 1.

Types of allostery. (a) Energy landscapes for two protein states, A and B, where A is an inactive state and B is an activated state. Enthalpic and entropic allostery correspond to changing the relative energy or number of conformations (i.e., microstates) of state B, respectively. Kinetic allostery can be thought of as a change in the barrier height between states. (b) Michaelis-Menten kinetics (details in text) for two enzymes, one with a high $k_r$ and $k_f$, and one with low $k_r$ and $k_f$, but the same ratio of $k_r/k_f$. If $k_{cat}$ is low, enzyme velocity under nonsaturating substrate is independent of $k_f$. For high $k_{cat}$, velocity becomes $k_f$ dependent. (c) Sample dihedral distributions from HRas MD simulations. For three very similar distributions, vastly different persistence times (${\tau }_p$) and self-conditional activity (CA[x][x], i.e., dynamical memory) are present. To see this figure in color, go online.

Ras protein family as a model system for kinetic allostery

Ras is a GTPase upstream of the MAPK/ERK pathway that regulates cell fate and proliferation in response to growth factor stimulation at the cell membrane. They are enzymatic proteins that go through a cycle of binding GTP (the active state), hydrolyzing it to GDP (the inactive state), and releasing the GDP into the cytosol. Ras has been studied in depth because it is one of the most commonly mutated proteins across cancer (25). Nevertheless, fundamental properties of Ras function and regulation are not mechanistically understood. There are three primary Ras isoforms: HRas, KRas, and NRas. The catalytic lobe of the protein (residues 1–86), which contains the hydrolysis machinery, is 100% conserved between isoforms, while the allosteric lobe of the protein (residues 87–166) is 80% conserved between isoforms. Despite high sequence conservation, the isoforms exhibit different hydrolysis rates, mutation rates and associated cancer types, intracellular localization, transcriptional network targets, and sensitivity to modulation by regulatory proteins GTPase-activating proteins (GAPs) and guanine nucleotide exchange factors (GEFs) (26,27,28). These differences in regulation suggest that there are distinct communication networks in the three isoforms despite sequence similarity. This is supported by the discovery of allosteric sites for KRas (29) as well as a putative longer-distance allosteric site for HRas identified from crystal structures (30), suggesting that allosteric mechanisms may not be shared across isoforms (30,31). Because the hydrolysis step of the Ras cycle is an irreversible nonequilibrium process, Ras is a viable candidate for kinetic allostery. The Ras family proteins are therefore ideal model systems to compare kinetic versus thermodynamic allostery, and to use these networks to explain differences in protein function arising from mutational variation, as well as differential regulation of protein function by ligand and cofactor binding.

Here, we generate atomistic MD data on the three main Ras isoforms to quantify backbone kinetic allostery using the CA measure and compare this with the thermodynamic allosteric network. We systematically studied the effect of ligand state and downstream effector binding on kinetic and thermodynamic correlation networks. We show that both are needed to explain differences in intrinsic versus Raf-dependent catalysis rates among the isoforms, and both types of networks predict coupling of the functional switches to the allosteric site, although the different isoforms vary in their use of kinetic versus thermodynamic allostery.

Quantifying thermodynamic and kinetic allostery

To simplify terminology and ensure an unambiguous metric, we quantify allostery by the extent of coupling between sites in a protein, without consideration of the additional requirement that the allosteric site should be susceptible to modulation by an external signal such as a ligand. The computational approach contains three main components: calculating 1) the mutual information (MI), 2) the CA from dihedral barcode trajectories, and 3) generating the dihedral barcode trajectories from the raw simulation data.

The mutual information as a metric for thermodynamic allostery

Consistent with previous work, we use the mutual information (MI) as a metric of thermodynamic allostery between dihedrals (32,33). If two dihedrals X and Y can occupy discrete states parameterized by the variables x and y, respectively, then the MI between X and Y is (33):

$$I\left(X;Y\right)=\sum _{x,y}P\left(x,y\right)\ln P\left(x,y\right)-\sum _{x}P\left(x\right)\ln P\left(x\right)-\sum _{y}P\left(y\right)\ln P\left(y\right)\text{,}$$ (1)

where $P\left(x\right)$ denotes the probability of observing X being in state x in the simulation, and $P\left(x,y\right)$ denotes the joint probability of simultaneously observing X in state x and Y in state y. $-\sum _{x}P\left(x\right)\ln P\left(x\right)$ is the entropy of dihedral X calculated over all possible values x.

The conditional activity as a metric for kinetic allostery

Kinetics of conformational transitions are the result of motions at several timescales: side-chain rotations and small loop motions over picoseconds to nanoseconds (ps–ns), and larger domain movements over microseconds to milliseconds (34). The fastest functionally relevant protein motions are ps–ns motions, and have been shown to play a role in allostery for several systems (6,35,36,37).

We do not expect waiting times (i.e., kinetic changes) to affect the activity of a protein that performs a reversible task that reaches local equilibrium, such as binding a target, because only the ratio of forward and backward reaction rates matters in that case. However, if the protein performs a nonequilibrium function, such as an irreversible enzymatic reaction (Fig. 1 b), altering waiting times can influence function. For example, in the standard Michaelis-Menten kinetics model of enzymatic reactions, the Michaelis constant $K_M$ is the concentration of substrate for which the enzyme achieves half of its maximum reaction rate ($V_{\max }$). $K_M$ is related to the microscopic kinetic rate constants (38): $K_M=k_r/k_f+k_{cat}/k_f$, where $k_r/k_f$ is the thermodynamic term that represents the probability that the enzyme is unbound, and $k_{cat}/k_f$ is the kinetic term that represents the quotient of the rate of catalysis once the ligand is bound and the rate of binding. If the enzyme is coupled to a slow irreversible process (small $k_{cat}$), the thermodynamic term $k_r/k_f$ dominates, and $k_{cat}$ does not significantly influence the rate of formation of product. However, if the enzyme is coupled to a fast irreversible process, the kinetic term ($k_{cat}/k_f$) dominates. In the latter scenario, a change in waiting times that alters $k_f$ can influence the rate of product formation by influencing the likelihood that a binding event will result in product formation (Fig. 1 b). This is true even if the $k_r/k_f$ ratio is unchanged. For such a catalytic protein, one would expect that long-range modulation of $k_f$ can serve as a purely kinetic form of allosteric regulation.

We quantify kinetic allostery using the conditional activity (CA) metric we previously introduced (24):

The CA (24) is defined as:

$$CA\left[X\right]\left[Y\right]\equiv -\mathit{ln}\left[\frac{{\tau }_x\left[X\right]\left[Y\right]}{{\tau }_p\left[X\right]}\right]$$ (2)

where (${\tau }_p\left[X\right]$) is the persistence time and (${\tau }_x\left[X\right]\left[Y\right]$) is the exchange time. The persistence time is (${\tau }_p\left[X\right]$), the amount of time that passes, i.e. the waiting time, between a randomly-selected starting time point and the next transition in X. The exchange time is (${\tau }_x\left[X\right]\left[Y\right]$), the waiting time between a transition in Y and the next transition in X. In other words, given a time series of switching events of discrete variables X and Y, the CA of X on Y is the log of the reduction of the expected waiting time until the next X event immediately after a Y event. Therefore, processes that are dynamically correlated and anticorrelated will have positive and negative CA, respectively (see methodological details in (24)). In previous work, side-chain CA was observed to have long-range correlations across the length of entire proteins, whereas side-chain MI was strictly short range (24).

Generating discrete conformational barcodes from MD simulations

Currently, most protein structural studies are based on Cartesian coordinates, where there is no threshold that can be used to determine if an event occurred. Calculating CA requires a reliable measurement of the timing of an event, and the degrees of freedom must reside in a finite set of discrete states. Protein dihedral angles, measured using microseconds-long MD simulations, meet this criteria because they sample probability distributions that are well separated into distinct basins. The transition time of a dihedral conformation change is then the time it takes to hop from one dihedral basin to another (see materials and methods for vibrational filtering and transition commitment threshold). In addition, because dihedral coordinates represent protein degrees of freedom subject to covalent bond length and angle constraints, they are the natural internal coordinates to represent protein conformations (39).

To calculate the CA, statistics of transition events are required, necessitating the construction of a “dihedral barcode” for each time point, in which every position on the barcode represents a different backbone dihedral, and the discrete value of that position corresponds to the dihedral’s basin at that time point. The barcodes were constructed from the MD simulation data by first extracting dihedral angle probability distributions over the MD trajectory (Fig. 2 a, top). Dihedral peaks were assigned using a MATLAB peak-finding function (40), with each peak corresponding to a discrete dihedral state (Fig. 2 b), and assignment of a dihedral value to a dihedral state were based on the peak closest to the dihedral value, generating a discrete conformational barcode over time (Fig. 2 a, bottom). To compare thermodynamic allostery to kinetic allostery, the MI between dihedrals was calculated using the same dihedral barcode states used to calculate the CA.

Figure 2.

Conformational barcodes from MD simulations. Vibrational filtering and barcoding applied as an example to HRas simulation data. (a) Conversion of continuous backbone dihedral data (top) into discrete dihedral basins binned by basin index (bottom). Each dihedral basin is assigned a number from 1-N, where N is the total number of basins observed for that dihedral distribution. Here, each basin from 1-N is assigned a different color, unless there are more than 4 basins, in which case the 4th and greater basins are all red. The 166 amino acid protein has 332 backbone dihedrals (φ+ψ for each amino acid) and are shown here in order of protein sequence. Secondary structure map at top with β-strands (arrow), α-helices (rectangle) and loops (line). (b) Example of vibrationally unfiltered dihedrals (top) and vibrationally filtered and binned rotamers (bottom) from a single dihedral distribution. To see this figure in color, go online.

Materials and methods

MD simulations

All-atom MD simulations were performed for Ras isoforms in their apo, GTP-bound, GDP-bound states, as well as the state of being bound to both GTP and Raf-RBD. There are two splicing variants of KRas, KRas4A and KRas4B, and we simulated KRas4B (referred to as KRas in this work). The initial structures for the simulations were obtained from the PDB and were altered as described in Table 1. Because Ras hydrolyzes GTP, GNP (phosphoaminophosphonic acid guanylate ester), a nonhydrolyzable analog of GTP, is used in crystal structures of Ras. For our GTP-bound simulations we replaced GNP by GTP by substituting the nitrogen with an oxygen atom in the PDB file. Simulations were performed with GROMACS (41,42) at the BIOHPC computing facility at UT Southwestern. V-sites (43) were used to freeze hydrogen vibrations in apo simulations, allowing for a 5 fs timestep for those simulations, and 2 fs timesteps were used without V-sites for all non-apo simulations. Coordinates were saved every 10 ps for each simulation except for apo HRas and KRas simulations, which were saved every 25 ps. All simulations were run with the CHARMM36 force field (44) and a cubic periodic box with 1 nm solvent buffer distance was used (see Table S1 for system sizes). The SPC/E water model (45) was used and Na⁺ atoms were added to maintain overall charge neutrality. The systems were energy minimized, heated to 300 K over the course of 10 ns using the Berendsen et al. (46) thermostat, and pre-equilibrated for 1000 ns under NPT conditions using the Nosé-Hoover thermostat (47,48) and the Parrinello and Raman barostat (49). A Verlet cutoff scheme was used for nonbonding interactions, and particle mesh Ewald (50) was used for long-range electrostatics calculations with periodic boundary conditions. PyMOL (51) was used for molecular graphics (51).

Table 1.

Protein systems simulated

System	PDB	Simulation time (μs)
H-Ras Apo	5P21	53
H-Ras GTP	5P21	60
H-Ras GDP	1CRQ	51
K-Ras Apo	6GOD	35
K-Ras GTP	6GOD	50
K-Ras GDP	6MBT	52
N-Ras Apo	5UHV	47
N-Ras GTP	5UHV	47
N-Ras GDP	5UHV	41
H-Ras GTP + Raf RBD	4G0N	16
K-Ras GTP + Raf-RBD	6GOD	17
N-Ras GTP + Raf-RBD	5UHV	17

Slowly hydrolyzing GTP analogue GNP from PDB files were replaced with GTP before simulation. Missing atoms of Raf-RBD were also modeled.

Data coarse graining

Dihedral angle trajectories were used to generate probability distributions of each backbone and side-chain dihedral angle over time. Each amino acid has three backbone dihedrals: φ, ψ, and ω. Only φ and ψ dihedrals were analyzed, since ω dihedrals remain in one rotameric state. The peaks in these probability distributions were assigned using a MATLAB peak-finding function (40), and assignment of individual rotamers to peak basins were based on the peak closest to the rotamer. From this information, the raw 0–360° dihedral trajectories are converted into “peak trajectories,” where vibration in the raw data is filtered out (Fig. 2). Because occupancy of dihedral wells was insensitive to temporal resolution above 10 ns, for downstream calculation of MI, the 10 ps resolution peak trajectory is made into a 10 ns resolution consensus trajectory by finding the peak consensus within 10 ns time chunks. In contrast, we observed short-lived dynamical fluctuations below this time resolution, and consequently used the 25 ps resolution peak trajectories for CA analysis. For ease of visualization, we used the 10ns consensus trajectory to build the “dihedral barcodes,” which represents the discrete backbone dihedral configuration as a function of time (Fig. 2 a). Unless otherwise noted, programming was done using Python3 (52).

Correlation analysis

The CA (24) is defined as

$$A\left[X\right]\left[Y\right]\equiv -\mathit{ln}\left[\frac{{\tau }_x\left[X\right]\left[Y\right]}{{\tau }_p\left[X\right]}\right]$$

where $\tau \equiv T\left(X,N\left(X\right)\right)$ is the observation time. The transition time function is $T\left(X,i\right)$, which is the time of the ith transition of X. The waiting time function, $W\left(X,t\right)$, is the time interval, starting at time t until the next transition of X. The persistence time is ${\tau }_p\left[X\right]=\frac{1}{2\tau }{\sum }_{i=1}^{N\left(X\right)}W{\left(X,T\left(X,i\right)\right)}^2$ and the exchange time is ${\tau }_x\left[X\right]\left[Y\right]=\frac{1}{\tau }{\sum }_{i=1}^{N\left(Y\right)-1}W\left(X,T\left(Y,i+1\right)\right)W\left(Y,T\left(Y,i\right)\right)$.

Results

Ras function and structure

In the active GTP-bound state, the Ras switch I domain can bind to Raf kinase (Fig. 3 a), modulating Raf autoinhibition to activate Raf phosphorylation of downstream MEK (53,54,55,56). After product release, the Ras active site is subsequently occupied by GTP due to 10-fold GTP/GDP concentration in the cell (57). Before binding to Raf, GEFs accelerate the rate at which GDP is released from Ras and thus serve to activate Ras. GAPs increase the rate of GTP hydrolysis to GDP, thus deactivating the protein. Ras uses switch I (residues 30–40) and switch II (residues 60–76) for GTP hydrolysis (Fig. 3 a) as well as for binding of these effector proteins.

Figure 3.

Dihedral entropy and persistence times in GTP-bound Ras. (a) HRas-Raf RBD structure (PDB: 4G0N). Allosteric lobe is represented in red, switch I, switch II in blue and green respectively. Raf-RBD is represented in orange. View of Ras-Raf-RBD interface at switch I shown on right. (b) Experimental hydrolysis time data adapted from (26). (c) Mean persistence time for each domain of Ras colored according to legend in (a). This Ras-Raf structure contains the Ras-binding domain (RBD) of Raf only. (d) Sum of individual dihedral entropies of Ras showing contribution from each domain of the protein. There are two domains in Raf that bind to Ras: the RBD and the cysteine-rich domain (CRD). The CRD was disordered in the crystal structure and is thus omitted. The CRD binds on either side of the RBD binding site of switch I. To see this figure in color, go online.

Ras MD simulations

All-atom MD simulations were performed for Ras isoforms in their apo, GDP-bound, and GTP-bound states; the GTP-bound states were further divided into simulations with and without binding to Raf-RBD, the domain of the downstream signaling partner that (active)GTP-bound Ras binds to (see Table 1 and materials and methods). There are two splicing variants of KRas, KRas4A and 4B, and here we simulate KRas4B. The initial structures for the simulations were obtained from the PDB (https://www.rcsb.org) (see materials and methods for system preparation and simulation details). The tens of microsecond simulations were sufficiently long for the CA between dihedral pairs to converge (Fig. S1).

Thermodynamic and kinetic features of Ras are isoform specific and sensitive to Raf binding

Raf is a downstream effector of Ras that binds near the active site of Ras at switch I (Fig. 3 a), and only binds when GTP is bound (58). Experimental measurements of the GTP hydrolysis times of the three isoforms (26), both bound and unbound to Raf, are shown in Fig. 3 b. These kinetic measurements reveal two trends among Ras isoforms. The first is that, in the absence of Raf, HRas hydrolyzes GTP faster than KRas and NRas. The second is that, while KRas hydrolysis speed is faster when bound to Raf, binding of Raf does not affect hydrolysis rate of HRas and NRas.

We simulated wild-type GTP-bound NRas, KRas, and HRas, both bound and unbound to Raf-RBD, and calculated dihedral angle entropies and waiting time statistics. Although the relationship between GTP hydrolysis rate and the thermodynamic and kinetic attributes of a protein is complex and beyond the scope of this work, we can nevertheless use our framework to generate mechanistic hypotheses based on thermodynamic and kinetic modulation of the switches (green and blue regions in Fig. 3). The persistence time is a kinetic measure of frustration, which can lead to long residence times in configurations necessary for catalysis. The persistence time is defined as the mean waiting time until a dihedral transition—a switch from one dihedral basin to another—starting from a random time point. The fast GTP hydrolysis of HRas is correlated with the much longer persistence times of the dihedrals in the HRas hydrolysis machinery (switches I and II; Fig. 3 c). The backbone dihedral entropy summed across switches I and II are similar across the three isoforms (Fig. 3 d). Therefore, the difference in the intrinsic hydrolysis rate can be explained by differences in kinetics, suggesting that fast hydrolysis in HRas may be enabled by slowing down the fluctuations of its switches.

In contrast to the intrinsic hydrolysis rate, the effect of Ras binding on GTP hydrolysis is modulated by changes in both kinetics and thermodynamics. The effect of Raf binding decreases the switch II persistence time in HRas and KRas, but not NRas (Fig. S2; switch I persistence time could not be calculated due to insufficient conformational sampling of switch I during the Raf-bound simulations). Binding of an effector protein is expected to increase the rigidity of the protein at the binding site, as fluctuating residues in the prebound state become locked into a single conformation to stabilize the interaction with the effector protein. Upon binding of Raf, the summed dihedral entropy decreases (Fig. 3 c) across all isoforms, with the largest decrease in KRas (Fig. 3 c). In HRas, the decreased switch II persistence time (expected to slow hydrolysis) is accompanied by an entropy decrease in the switches (expected to speed up hydrolysis), perhaps explaining why there is no change in the hydrolysis rate of HRas upon Raf binding (Fig. 3 b). When Raf is bound to NRas, surprisingly the decrease in switch I entropy is counteracted by an increase in switch II entropy, leading to a small overall entropy change. Combining this with the observation that NRas switch II persistence time is also unaffected by Raf binding may explain why NRas hydrolysis rate is unaffected by Raf binding (Fig. 3 a). Finally, when Raf is bound to KRas, the decreased switch II persistence time is accompanied by the largest decrease in entropy in the switches (Fig. 3 d). This supports the previous hypothesis that the high fluidity of KRas requires Raf to stabilize switch I to stabilize the surrounding GTP hydrolysis machinery (26). We hypothesize that this entropy difference is large enough to overcome the persistence time decrease, thereby leading to faster hydrolysis in KRas. That Raf binding significantly changes switch II entropy despite no direct contact indicates that there is thermodynamic allostery between switch I and switch II (see MI analysis below).

These results indicate that thermodynamic and kinetic analyses are both necessary to explain protein function, even within a single protein, and motivate the analysis of waiting time correlations between dihedrals to infer kinetic allostery.

Raf-dependent allosteric pathways across Ras isoforms

A putative HRas allosteric site at loop 7 (Fig. 4 a) was identified based on a crystal structure (30,31). While the endogenous ligand is not known for this site, it is suspected to play a role in Ras function based on observed binding of calcium and acetate, which results in an ordering of switch II that places Q61, the main amino acid assisting in hydrolysis, into the active site (30,31). This allosteric site is suspected to modulate hydrolysis in the presence of Raf because binding at this site results in a conformational change in switch II, which is outside the Raf binding site. A key question is whether this allosteric region and its ligand-dependent communication mechanism are revealed as part of the network analysis of the simulation data.

Figure 4.

(a) Two views of HRas (5P21) structure with important structural motifs labeled: switch I in blue, switch II in green, and loops 7, 8, and 10 in red. (b) Mutual information and conditional activity for simulations of HRas bound to GTP and GDP. The corresponding KRas and NRas heatmaps are given in Figs S3 and S4. Mutual information and conditional activity units are in bits. Red arrows highlight differences in MI and CA for loops 7 and 8 upon GTP hydrolysis. Note different color scales for MI and CA. To see this figure in color, go online.

For each of our simulations, we calculated the interdihedral CA and MI matrices to determine kinetic and thermodynamic pathways of allostery, respectively. In all Ras isoforms and regardless of nucleotide binding, the MI and CA communication networks (Figs. 4, S3, and S4), switch I and switch II contain the greatest amount of correlation, and this communication is mainly inter- and intraswitch communication. The MI and CA matrices in Fig. 4 also demonstrate that the presence of the γ-phosphate substantially alters communication networks in HRas, and this phenomenon is consistent across isoforms (Figs. S3 and S4). The GDP and apo (Fig. S8) states both contain greater amounts of communication than the GTP state in the allosteric lobe, indicating that the γ-phosphate quenches some communication networks within the protein. In the GDP-bound state, the function of Ras is mainly to release the GDP into the cytosol so that a GTP can bind in its place. This release function involves the coordination of residues in the allosteric lobe, including the breaking of a salt bridge between loop 8 (red, Fig. 4) and loop 10. These loops contain conserved (59,60) NKCD (143–147) and ETSAK (116–119) motifs, which are also responsible for the specificity of the guanine nucleotide and stabilizing nucleotide binding, respectively.

The increased communication observed in the allosteric lobe in the GDP-bound state matrices is consistent with this function of the GDP-bound state. Changing the ligand from GTP to GDP increases entropy of loops 7 and 8 in HRas (Fig. 4 b) and loop 7 in KRas (Fig. S3 b), with no significant change in NRas (Fig. S4 b). This is consistent with the picture of loops 7 and 8 acting as entropic reservoirs that help to stabilize GDP-bound Ras. In HRas (Fig. 4 b), loop 8 shares significant MI with switch I and switch II, suggesting that regulation of switch I and switch II conformations by GEFs could allosterically lower the entropic favorability of the GDP-bound state via loop 8. Orthogonal to this thermodynamic picture, kinetic correlations in HRas are oppositely affected by the change from GTP to GDP binding. Despite loop 7 having lower entropy and lower MI with the switches in the GTP-bound state (Fig. 4 b, top), analysis of the CA shows that the fluctuations in loop 7 are much more kinetically coupled to the fluctuations in the switches in the GTP bound state (Fig. 4 b, bottom). In contrast, loop 7 is thermodynamically uncoupled to the rest of the protein in the GTP and GDP bound states (Fig. 4 b, top). This suggests that allosteric modulation of loop 7 in the GTP-bound state in the absence of GAP binding is kinetically controlled in HRas. These thermodynamic and kinetic correlations are not observed in the other two Ras isoforms (Figs. S3 and S4), indicating that, although trends in entropy are consistent across isoforms, mutual entropy and kinetic correlations are more sensitive to mutational modulation.

For each of the Ras simulations, we diagonalized the MI and (symmetrized) CA matrices to find the principal eigenvectors. These eigenvectors show the most prominent CA and MI correlation networks for each simulation. For GTP-bound HRas, the magnitude of the principal eigenvector components of the φ and ψ dihedrals are shown proportional to the radius of their corresponding C-α and carbonyl carbon atoms, respectively (Fig. 5 a), and the corresponding eigenvalue compared with the other top eigenvalues of the spectrum (Fig. 5 b). The main signaling function of Ras is to activate the downstream effector Raf. In the GTP-bound state, Ras can either bind to Raf (at switch I) or hydrolyze the GTP to GDP (involving switch I and switch II). Consistent with this expectation, the top MI and CA eigenvectors are dominated by switch I and switch II at the GTP-bound step of the Ras cycle (Fig. 5 a, left). When the structure is simulated with Raf bound at switch I, the switch I dihedrals no longer participate in the dominant correlated network (blue spheres in Fig. 5 a). These Raf-induced changes are similar for thermodynamic and kinetic networks at the level of the switches, despite variation in the specific dihedrals within the switches that contribute most to the networks.

Figure 5.

HRas principal eigenvectors. HRas-GTP and HRas-GTP + RAF-RBD MI and CA principal eigenvectors projected onto PDB structure (5P21). Sphere size is scaled to the size of the contribution of the nearest dihedral in the principal eigenvector. We use a minimum sphere size of 0.2 (CA or MI = 0) and a maximum sphere size of 1.2, in order to represent all dihedrals visually. φ dihedrals are represented by C-α atoms and ψ dihedrals are represented by carbonyl carbon atoms. (b) Top 10 Eigenvectors and their percentages of the eigenvalue. To see this figure in color, go online.

In contrast, kinetic and thermodynamic communication networks, and their regulation by Raf, qualitatively differ in terms of the involvement of the allosteric site within loop 7 (red in Fig. 5 a). This allosteric region, previously suggested based on crystal structures (30,31), is the only localized region predicted by our network analysis aside from the two switch regions. Hydrolysis is suspected to be mediated by binding of a ligand at the allosteric site at the C-terminus of switch II that functions exclusively in the Raf-bound state by ordering switch II and positioning Q61 in the active site (26). In the absence of Raf, the principal eigenvector contains no intrinsic thermodynamic coupling to the allosteric site (Fig. 5 a, top left), but significant kinetic coupling (Fig. 5 a, bottom left) between the putative allosteric site and switch II. However, the Raf-bound simulations show that thermodynamic and kinetic allostery can be differentially activated by Raf (GAP) binding. Although Raf binding does not enhance kinetic allostery (Fig. 5 a, bottom right), it is sufficient to activate thermodynamic allostery (Fig. 5 a, top right). This differential regulation of kinetic versus thermodynamic allostery by Raf binding is also observed in KRas and NRas, but with isoform-dependent variation (Figs S5 and S6). In particular, Raf binding activates both thermodynamic and kinetic allostery in KRas (Fig. S5), whereas Raf binding does not significantly affect allosteric engagement in NRas (Fig. S6).

Discussion

Cooper and Dryden were the first to demonstrate that kinetic changes, in addition to thermodynamic changes, can in principle tune protein function. However, in the almost 40 years since, how kinetic changes are coupled at the molecular scale to form allosteric networks remains largely unexplored. Computational advances increasingly allow interrogation of correlated motions responsible for allostery. In this study, we addressed this question by applying a recently developed measure of kinetic correlation to transition dynamics between dihedral states collected from atomistic simulations of the Ras protein family totaling half a millisecond. In the case of the hydrolysis machinery, these networks are consistent across functional states of the protein (GTP bound versus GDP bound) as well as across isoforms. The coupling analysis correctly identifies the important switches of the protein and their communication with each other, as well as a previously suspected allosteric region. The analysis also reveals new insights into the nature of kinetic versus thermodynamic coupling between these regions, as well as key loop regions, and how these couplings differ among the Ras isoforms. Therefore, these networks have both robust as well as tunable features. By comparing the resultant kinetic correlation networks with the mutual-information-based thermodynamic correlation networks, we demonstrate that kinetic control and kinetic allosteric networks are distinct from their thermodynamic counterparts. In fact, kinetic and thermodynamic characterizations are both needed in order to explain the diversity of cofactor-dependent catalytic activities and allosteric responses observed experimentally. The kinetic communication hotspots do not follow the boundaries of secondary structural elements, supporting the idea that dynamical modules are not necessarily structural modules (61).

This kinetic analysis framework opens up important new avenues of research in the study of allostery. Further insight can be gained with simulation of additional mutated Ras systems, and with longer simulations of the systems presented here. An exciting path forward will be found in analyzing kinetic and thermodynamic communication networks in multiprotein complexes. For example, recent computational studies indicate that Raf binding to Ras dampens Ras fluctuations, consistent with our calculated entropy change upon Raf binding, thereby promoting subsequent Ras dimerization (62). Computational studies of KRas suggest that Ras dimerization could catalyze an alternative pathway of GTP hydrolysis and therefore alter Raf binding (63), suggesting a rich network of feedback regulation. We hope that the framework presented could identify the allosteric networks responsible for multi-input computation in these extended protein complexes, as well as systematically predict new allosteric sites for enzymatic proteins more generally.

Author contributions

L.J.M. and M.M.L. designed the research. L.J.M. performed the research. L.J.M. and M.M.L. contributed analytic tools and wrote the paper.

Editor: Chris Neale.