Nonequilibrium,multiple-timescale simulations of ligand-receptor interactions in structured protein systems

Predicting the long-time, nonequilibrium dynamics of receptor-ligand interactions for structured proteins in a host fluid is a formidable task, but of great importance to predicting and analyzing cell-signaling processes and small molecule drug efficacies. Such processes take place on timescales on the order of milliseconds to seconds, so "brute-force" real-time, molecular or atomic simulations to determine absolute ligand-binding rates to receptor targets and over a statistical ensemble of systems are not currently feasible. In the current study, we implement on real protein systems a previously developed 3-5 hybrid molecular dynamics/Brownian dynamics algorithm, which takes advantage of the underlying, disparate timescales involved and overcomes the limitations of brute-force approaches. The algorithm is based on a multiple timescale analysis of the total system Hamiltonian, including all atomic and molecular structure information for the system: water, ligand, and receptor. In general, the method can account for the complex hydrodynamic, translational-orientational diffusion aspects of ligand-docking dynamics as well as predict the actual or absolute rates of ligand binding. To test some of the underlying features of the method, simulations were conducted here for an artificially constructed spherical protein "made" from the real protein insulin. Excellent comparisons of simulation calculations of the so-called grand particle friction tensor to analytical values were obtained for this system when protein charge effects were neglected. When protein charges were included, we found anomalous results caused by the alteration of the spatial, microscopic structure of water proximal to the protein surface. Protein charge effects were found to be highly significant and consistent with the recent hypothesis of Hoppert and Mayer (Am Sci 1999;87:518-525) for charged macromolecules in water, which involves the formation of a "water dense region" proximal to the charged protein surface followed by a "dilute water region." We further studied the algorithm on a D-peptide/HIV capside protein system and demonstrated the algorithms utility to study the nonequilibrium docking dynamics in this contemporary problem. In general, protein charge effects, which alter water structural properties in an anomalous fashion proximal to the protein surface, were found to be much more important than the so-called hydrodynamic interaction effects between ligand and receptor. The diminished role of hydrodynamic interactions in protein systems allows for a much simpler overall dynamic algorithm for the nonequilibrium protein-docking process. Further studies are now underway to critically examine this simpler overall algorithm in analyzing the nonequilibrium protein-docking problem.     

Investigating the local flexibility of functional residues in hemoproteins

It is now widely accepted that protein function depends not only on structure, but also on flexibility. However, the way mechanical properties contribute to catalytic mechanisms remains unclear. Here, we propose a method for investigating local flexibility within protein structures that combines a reduced protein representation with Brownian dynamics simulations. An analysis of residue fluctuations during the dynamics simulation yields a rigidity profile for the protein made up of force constants describing the ease of displacing each residue with respect to the rest of the structure. This approach has been applied to the analysis of a set of hemoproteins, one of the functionally most diverse protein families. Six proteins containing one or two heme groups have been studied, paying particular attention to the mechanical properties of the active-site residues. The calculated rigidity profiles show that active site residues are generally associated with high force constants and thus rigidly held in place. This observation also holds for diheme proteins if their mechanical properties are analyzed domain by domain. We note, however, that residues other than those in the active site can also have high force constants, as in the case of residues belonging to the folding nucleus of c-type hemoproteins.     

Investigations of Takeout proteins’ ligand binding and release mechanism using molecular dynamics simulation

Takeout (To) proteins exist in a diverse range of insect species. They are involved in many important processes of insect physiology and behaviors. As the ligand carriers, To proteins can transport the small molecule to the target tissues. However, ligand release mechanism of To proteins is unclear so far. In this contribution, the process and pathway of the ligand binding and release are revealed by conventional molecular dynamics simulation, steered molecular dynamics simulation and umbrella sampling methods. Our results show that the α4-side of the protein is the unique gate for the ligand binding and release. The structural analysis confirms that the internal cavity of the protein has high rigidity, which is in accordance with the recent experimental results. By using the potential of mean force calculations in combination with residue cross correlation calculation, we concluded that the binding between the ligand and To proteins is a process of conformational selection. Furthermore, the conformational changes of To proteins and the hydrophobic interactions both are the key factors for ligand binding and release.     

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.     

A diverse view of protein dynamics from NMR studies of HIV-1 protease flaps

Internal motion in proteins fulfills a multitude of roles in biological processes. NMR spectroscopy has been applied to elucidate protein dynamics at the atomic level, albeit at a low resolution, and is often complemented by molecular dynamics simulation. However, it is critical to justify the consistency between simulation results and conclusions often drawn from multiple experiments in which uncertainties arising from assumed motional models may not be explicitly evaluated. To understand the role of the flaps of HIV-1 protease dimer in substrate recognition and protease function, many molecular dynamics simulations have been performed. The simulations have resulted in various proposed models of the flap dynamics, some of which are more consistent than others with our working model previously derived from experiments. However, using the working model to discriminate among the simulation results is not straightforward because the working model was derived from a combination of NMR experiments and crystal structure data. In this study, we use the NMR chemical shifts and relaxation data of the protease "monomer" rather than structural data to narrow down the possible conformations of the flaps of the "dimer". For the first time, we show that the tips of the flaps in the unliganded protease dimer interact with each other in solution. Accordingly, we discuss the consistency of the simulations with the model derived from all experimental data.     

Inferring Diffusion Dynamics from FCS in Heterogeneous Nuclear Environments

Fluorescence correlation spectroscopy (FCS) is a noninvasive technique that probes the diffusion dynamics of proteins down to single-molecule sensitivity in living cells. Critical mechanistic insight is often drawn from FCS experiments by fitting the resulting time-intensity correlation function, G(t), to known diffusion models. When simple models fail, the complex diffusion dynamics of proteins within heterogeneous cellular environments can be fit to anomalous diffusion models with adjustable anomalous exponents. Here, we take a different approach. We use the maximum entropy method to show—first using synthetic data—that a model for proteins diffusing while stochastically binding/unbinding to various affinity sites in living cells gives rise to a G(t) that could otherwise be equally well fit using anomalous diffusion models. We explain the mechanistic insight derived from our method. In particular, using real FCS data, we describe how the effects of cell crowding and binding to affinity sites manifest themselves in the behavior of G(t). Our focus is on the diffusive behavior of an engineered protein in 1) the heterochromatin region of the cell’s nucleus as well as 2) in the cell’s cytoplasm and 3) in solution. The protein consists of the basic region-leucine zipper (BZip) domain of the CCAAT/enhancer-binding protein (C/EBP) fused to fluorescent proteins.     

Cell behaviour as a dynamic attractor in the intracellular signalling system

We present a model of the cell signalling network based on the generic properties of interactions between protein kinases (PKs) and protein phosphatases (PPs) inside cells. The model is designed to examine the global properties and intrinsic dynamics of the phosphorylation system. A genetic algorithm (GA) is used to evolve populations of "cells". The GA selects cells and ranks them based on an analysis of the dynamics of the proteins within the networks from a series of different random starting conditions. The fittest cells are taken to be those which can generate a variety of different "behaviours" from a series of different initial conditions. During the GA, intracellular protein interactions evolve via mutation and an analogue of domain shuffling between protein types that is thought to occur during biological evolution. The dynamics of the simulated networks are presented and we discuss the hypothesis that changes in the behaviour of a cell may be interpretable as a switch between attractor basins in the intracellular signalling network.     

Lifetime of actin-dependent protein nanoclusters

Protein nanoclusters (PNCs) are dynamic collections of a few proteins that spatially organize in nanometer-length clusters. PNCs are one of the principal forms of spatial organization of membrane proteins, and they have been shown or hypothesized to be important in various cellular processes, including cell signaling. PNCs show remarkable diversity in size, shape, and lifetime. In particular, the lifetime of PNCs can vary over a wide range of timescales. The diversity in size and shape can be explained by the interaction of the clustering proteins with the actin cytoskeleton or the lipid membrane, but very little is known about the processes that determine the lifetime of the nanoclusters. In this paper, using mathematical modeling of the cluster dynamics, we model the biophysical processes that determine the lifetime of actin-dependent PNCs. In particular, we investigated the role of actin aster fragmentation, which had been suggested to be a key determinant of the PNC lifetime, and we found that it is important only for a small class of PNCs. A simple extension of our model allowed us to investigate the kinetics of protein-ligand interaction near PNCs. We found an anomalous increase in the lifetime of ligands near PNCs, which agrees remarkably well with experimental data on RAS-RAF kinetics. In particular, analysis of the RAS-RAF data through our model provides falsifiable predictions and novel hypotheses that will not only shed light on the role of RAS-RAF kinetics in various cancers, but also will be useful in studying membrane protein clustering in general.     

Neutron frequency windows and the protein dynamical transition

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, , that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations---an "equilibrium" model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a "frequency window" model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.     

Rigidity of protein structure revealed by incoherent neutron scattering

The rigidity and flexibility of a protein is reflected in its structural dynamics. Studies on protein dynamics often focus on flexibility and softness; this review focuses on protein structural rigidity. The extent of rigidity can be assessed experimentally with incoherent neutron scattering; a method that is complementary to molecular dynamics simulation. This experimental technique can provide information about protein dynamics in timescales of pico- to nanoseconds and at spatial scales of nanometers; these dynamics can help quantify the rigidity of a protein by indices such as force constant, Boson peak, dynamical transition, and dynamical heterogeneity. These indicators also reflect the rigidity of a protein's secondary and tertiary structures. In addition, the indices reveal how rigidity is influenced by different environmental parameters, such as hydration, temperature, pressure, and protein-protein interactions. Hydration affects both rigidity and softness more than other environmental factors. Interestingly, hydration affects harmonic and anharmonic motions in opposite ways. This difference is probably due to the protein's dynamic coupling with water molecules via hydrogen bonding.     

A comparative molecular dynamics study of thermophilic and mesophilic ribonuclease HI enzymes

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Protein probabilities in shotgun proteomics: evaluating different estimation methods using a semi-random sampling model

The calculation of protein probabilities is one of the most intractable problems in large-scale proteomic research. Current available estimating methods, for example, ProteinProphet, PROT_PROBE, Poisson model and two-peptide hits, employ different models trying to resolve this problem. Until now, no efficient method is used for comparative evaluation of the above methods in large-scale datasets. In order to evaluate these various methods, we developed a semi-random sampling model to simulate large-scale proteomic data. In this model, the identified peptides were sampled from the designed proteins and their cross-correlation scores were simulated according to the results from reverse database searching. The simulated result of 18 control proteins was consistent with the experimental one, demonstrating the efficiency of our model. According to the simulated results of human liver sample, ProteinProphet returned slightly higher probabilities and lower specificity than real cases. PROT_PROBE was a more efficient method with higher specificity. Predicted results from a Poisson model roughly coincide with real datasets, and the method of two-peptide hits seems solid but imprecise. However, the probabilities of identified proteins are strongly correlated with several experimental factors including spectra number, database size and protein abundance distribution.     

Studying the Unfolding Kinetics of Proteins under Pressure Using Long Molecular Dynamic Simulation Runs

The usefulness of computational methods such as molecular dynamics simulation has been extensively established for studying systems in equilibrium. Nevertheless, its application to complex non-equilibrium biological processes such as protein unfolding has been generally regarded as producing results which cannot be interpreted straightforwardly. In the present study, we present results for the kinetics of unfolding of apomyoglobin, based on the analysis of long simulation runs of this protein in solution at 3 kbar (1 atm = 1.01325, bar = 101 325 Pa). We hereby demonstrate that the analysis of the data collected within a simulated time span of 0.18 μs suffices for producing results, which coincide remarkably with the available unfolding kinetics experimental data. This not only validates molecular dynamics simulation as a valuable alternative for studying non-equilibrium processes, but also enables a detailed analysis of the actual structural mechanism which underlies the unfolding process of proteins under elusive denaturing conditions such as high pressure.     

Self-similar dynamics of proteins under hydrostatic pressure—Computer simulations and experiments

Different experimental techniques, such as kinetic studies of ligand binding and fluorescence correlation spectroscopy, have revealed that the diffusive, internal dynamics of proteins exhibits autosimilarity on the time scale from microseconds to hours. Computer simulations have demonstrated that this type of dynamics is already established on the much shorter nanosecond time scale, which is also covered by quasielastic neutron scattering experiments. The autosimilarity of protein dynamics is reflected in long-time memory effects in the underlying diffusion processes, which lead to a non-exponential decay of the observed time correlation functions. Fractional Brownian dynamics is an empirical model which is able to capture the essential aspects of internal protein dynamics. Here we give a brief introduction into the theory and show how the model can be used to interpret neutron scattering experiments and molecular dynamics simulation of proteins in solution under hydrostatic pressure.     

Dynamics and unfolding pathways of a hyperthermophilic and a mesophilic rubredoxin.

Molecular dynamics simulations in solution are performed for a rubredoxin from the hyperthermophilic archaeon Pyrococcus furiosus (RdPf) and one from the mesophilic organism Desulfovibrio vulgaris (RdDv). The two proteins are simulated at four temperatures: 300 K, 373 K, 473 K (two sets), and 500 K; the various simulations extended from 200 ps to 1,020 ps. At room temperature, the two proteins are stable, remain close to the crystal structure, and exhibit similar dynamic behavior; the RMS residue fluctuations are slightly smaller in the hyperthermophilic protein. An analysis of the average energy contributions in the two proteins is made; the results suggest that the intraprotein energy stabilizes RdPf relative to RdDv. At 373 K, the mesophilic protein unfolds rapidly (it begins to unfold at 300 ps), whereas the hyperthermophilic does not unfold over the simulation of 600 ps. This is in accord with the expected stability of the two proteins. At 473 K, where both proteins are expected to be unstable, unfolding behavior is observed within 200 ps and the mesophilic protein unfolds faster than the hyperthermophilic one. At 500 K, both proteins unfold; the hyperthermophilic protein does so faster than the mesophilic protein. The unfolding behavior for the two proteins is found to be very similar. Although the exact order of events differs from one trajectory to another, both proteins unfold first by opening of the loop region to expose the hydrophobic core. This is followed by unzipping of the beta-sheet. The results obtained in the simulation are discussed in terms of the factors involved in flexibility and thermostability.     

A Comparative Molecular Dynamics Study of Thermophilic and Mesophilic Ribonuclease HI Enzymes

Abstract

We studied a pair of homologous thermophilic and mesophilic ribonuclease HI enzymes by molecular dynamics simulations. Each protein was subjected to three 5 ns simulations in explicit water at both 310 K and 340 K. The thermophilic enzyme showed larger overall positional fluctuations at both temperatures, while only the mesophilic enzyme at the higher temperature showed significant instability. When the temperature is changed, the relative flexibility of different local segments on the two proteins changed differently. Principal component analysis showed that the simulations of the two proteins explored largely overlapping regions in the conformational space. However, at 340 K, the collective structure variations of the thermophilic protein are different from those of the mesophilic protein. Our results, although not in accordance with the view that hyperthermostability of proteins may originate from their conformational rigidity, are consistent with several recent experimental and simulation studies which showed that thermophilic proteins may be conformationally more flexible than their mesophilic counterparts. The decorrelation between conformational rigidity and hyperthermostability may be attributed to the temperature dependence and long range nature of electrostatic interactions that play more important roles in the structural stability of thermophilic proteins.     

Protein Folding Requires Crowd Control in a Simulated Cell

Macromolecular crowding has a profound effect upon biochemical processes in the cell. We have computationally studied the effect of crowding upon protein folding for 12 small domains in a simulated cell using a coarse-grained protein model, which is based upon Langevin dynamics, designed to unify the often disjoint goals of protein folding simulation and structure prediction. The model can make predictions of native conformation with accuracy comparable with that of the best current template-free models. It is fast enough to enable a more extensive analysis of crowding than previously attempted, studying several proteins at many crowding levels and further random repetitions designed to more closely approximate the ensemble of conformations. We found that when crowding approaches 40% excluded volume, the maximum level found in the cell, proteins fold to fewer native-like states. Notably, when crowding is increased beyond this level, there is a sudden failure of protein folding: proteins fix upon a structure more quickly and become trapped in extended conformations. These results suggest that the ability of small protein domains to fold without the help of chaperones may be an important factor in limiting the degree of macromolecular crowding in the cell. Here, we discuss the possible implications regarding the relationship between protein expression level, protein size, chaperone activity and aggregation.