Structure and energetics of ligand binding to proteins: Escherichia coli dihydrofolate reductase-trimethoprim, a drug-receptor system

A study of the binding of the antibacterial agent trimethoprim to Escherichia coli dihydrofolate reductase was carried out using energy minimization techniques with both a full, all-atom valence force field and a united atom force field. Convergence criteria ensured that no significant structural or energetic changes would occur with further minimization. Root-mean-square (RMS) deviations of both minimized structures with the experimental structure were calculated for selected regions of the protein. In the active site, the all-atom minimized structure fit the experimental structure much better than did the united atom structure. To ascertain what constitutes a good fit, the RMS deviations between crystal structures of the same enzyme either from different species or in different crystal environments were compared. The differences between the active site of the all-atom minimized structure and the experimental structure are similar to differences observed between crystal structures of the same protein. Finally, the energetics of ligand binding were analyzed for the all-atom minimized coordinates. Strain energy induced in the ligand, the corresponding entropy loss due to shifts in harmonic frequencies, and the role of specific residues in ligand binding were examined. Water molecules, even those not in direct contact with the ligand, were found to have significant interaction energies with the ligand. Thus, the inclusion of at least one shell of waters may be vital for accurate simulations of enzyme complexes.     

Modeling glycolipids: take one

Molecular dynamics simulations of glycolipid bilayers consisting of 1,2-di-O-palmitoyl-3-O-beta-D-glucosyl-sn-glycerol were performed using five different force field parameterizations. Comparing the results with experimental data revealed that only the all-atom model correctly reproduces both the phase behavior and the surface area per lipid. Only one of the united atom models studied reproduces the correct phase behavior.     

Simulations of the B-DNA molecular dynamics of d(CGCGAATTCGCG)2 and d(GCGCGCGCGC)2: an analysis of the role of initial geometry and a comparison of united and all-atom models

Molecular dynamics simulations on the sequence d(CGCGAATTCGCG)2 have been carried out using both united atom and all-atom representations, and starting the simulations both from a regular repeating B-DNA structure and from the x-ray single crystal B-DNA structure. An all-atom B-DNA simulation on the sequence d(GCGCGCGCGC)2 has also been carried out, in order to compare it with a previous united atom simulation. The helix repeats, H-bonding, sugar pucker profiles, and average torsional angles are all in the range observed in crystallographic and nmr studies for B-DNA helices. In some of the sequences, there is a significant bend in the DNA helices. The individual helix repeats, with focus on 3'CpG5' and 3'GpC5' units, show the opposite helix repeat to that suggested by Calladine's rules.     

Vapour-Liquid Phase Equilibria of n-alkanes by Direct Monte Carlo Simulations

Abstract

We report results of direct Monte Carlo simulations of n-pentane and n-decane at the liquidvapour interface for a number of temperatures. The intermolecular interactions are modeled using the last version of the anisotropic united atom model (AUA4). We have used the local long range correction energy and an algorithm allowing to select randomly with equal probability two different displacements. The liquid and vapour densities are in excellent agreement with experimental data and with those previously calculated using the GEMC method.     

Validation of all-atom phosphatidylcholine lipid force fields in the tensionless NPT ensemble

A recently defined charge set, to be used in conjunction with the all-atom CHARMM27r force field, has been validated for a series of phosphatidylcholine lipids. The work of Sonne et al. successfully replicated experimental bulk membrane behaviour for dipalmitoylphosphatidylcholine (DPPC) under the isothermal-isobaric (NPT) ensemble. Previous studies using the defined CHARMM27r charge set have resulted in lateral membrane contraction when used in the tensionless NPT ensemble, forcing the lipids to adopt a more ordered conformation than predicted experimentally. The current study has extended the newly defined charge set to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine (POPC) and 1-palmitoyl-2-docosahexaenoyl-sn-glycero-3-phosphatidylcholine (PDPC). Molecular dynamics simulations were run for each of the lipids (including DPPC) using both the CHARMM27r charge set and the newly defined modified charge set. In all three cases a significant improvement was seen in both bulk membrane properties and individual atomistic effects. Membrane width, area per lipid and the depth of water penetration were all seen to converge to experimental values. Deuterium order parameters generated with the new charge set showed increased disorder across the width of the bilayer and reflected both results from experiment and similar simulations run with united atom models. These newly validated models can now find use in mixed biological simulations under the tensionless ensemble without concern for lateral contraction.     

Using Molecular Dynamics Simulations on Crambin to Evaluate the Suitability of Different Continuum Dielectric and Hydrogen Atom Models for Protein Simulations

Abstract

Molecular dynamics simulations of enzymes with enough explicit waters of solvation to realistically account for solute-solvent interactions can burden the computational resources required to perform the simulation by more than two orders of magnitude. Since enzyme simulations even with an implicit solvation model can be imposing for a supercomputer, it is important to assess the suitability of different continuum dielectric models for protein simulations. A series of 100-picosecond molecular dynamics simulations were performed on the X-ray crystal structure of the protein crambin to examine how well computed structures, obtained using seven continuum dielectric and two hydrogen atom models, agreed with the X-ray structure. The best level of agreement between computed and experimental structures was obtained using a constant dielectric of 2 and the all-hydrogen model. Continuum dielectric models of 1,1^*r, and 2^*r also led to computed structures in reasonably good agreement with the X-ray structure. In all cases, the all-hydrogen model gave better agreement than the united atom model, although, in one case, the difference was not significant. Dielectric models of 4, 80, and 4^*r with either hydrogen model yielded significantly poorer fits. It is especially noteworthy that the observed trends did not semiquantitatively converge until about 50 picoseconds into the simulations, suggesting that validation studies for protein calculations based on energy minimizations or short simulations should be viewed with caution.     

Folding time predictions from all-atom replica exchange simulations

We present an approach to predicting the folding time distribution from all-atom replica exchange simulations. This is accomplished by approximating the multidimensional folding process as stochastic reaction-coordinate dynamics for which effective drift velocities and diffusion coefficients are determined from the short-time replica exchange simulations. Our approach is applied to the folding of the second beta-hairpin of the B domain of protein G. The folding time prediction agrees quite well with experimental measurements. Therefore, we have in hand a fast numerical tool for calculating the folding kinetic properties from all-atom "first-principles" models.     

Crowding affects structural dynamics and contributes to membrane association of the NS3/4A complex

Using molecular dynamics simulations, we describe how crowded environments affect the internal dynamics and diffusion of the hepatitis C virus proteases NS3/4A. This protease plays a key role in viral replication and is successfully used as a target for antiviral treatment. The NS3 enzyme requires a peptide cofactor, called NS4A, with its central part interacting with the NS3 β-sheet, and flexible, protruding terminal tails that are unstructured in water solution. The simulations describe the enzyme and water molecules at atomistic resolution, whereas crowders are modeled via either all-atom or coarse-grained models to emphasize different aspects of crowding. Crowders reflect the polyethylene glycol (PEG) molecules used in the experiments to mimic the crowded surrounding. A bead-shell model of folded coarse-grained PEG molecules considers mainly the excluded volume effect, whereas all-atom PEG models afford more protein-like crowder interactions. Circular dichroism spectroscopy experiments of the NS4A N-terminal tail show that a helical structure is formed in the presence of PEG crowders. The simulations suggest that crowding may assist in the formation of an NS4A helical fragment, positioned exactly where a transmembrane helix would fold upon the NS4A contact with the membrane. In addition, partially interactive PEGs help the NS4A N-tail to detach from the protease surface, thus enabling the process of helix insertion and potentially helping the virus establish a replication machinery needed to produce new viruses. Results point to an active role of crowding in assisting structural changes in disordered protein fragments that are necessary for their biological function.     

Molecular dynamics study of interaction of dimyristoyl phosphotidyl choline with water

We present here results of molecular dynamics (MD) simulations on hydrated bilayers of 40 molecules of 1-2-dimyristoyl-sn-glycero-3-phosphatidyl choline (DMPC) in liquid crystalline (Lα) phase using two different models (i) with same (A) conformation for all DMPC molecules, (ii) with alternate rows having different (A and B reported in crystallographic studies on DMPC) conformations. The bilayers were hydrated using 776 and 1064 water molecules. Simulations have been carried out at 310K with AMBER 4.0 program, using united atom force field for 200 pico seconds (ps) after equilibration. During heating and equilibration constant pressure temperature (PT) conditions were maintained while in simulation of equillibrated bilayers constant volume temperature (VT) conditions were used. Subaveraged atomic coordinates were used to calculate geometric parameters of lipid molecules and lipid water interaction. Our results show larger flexibility of polar head group and glycerol region in Lα phase compared to gel or non-hydrated bilayers. Chain disorder was more towards end. Sn-2 chains were more disordered. Use of two types of starting conformations increased disorder. Trans fraction of chain torsional angle was higher in non-hydrated bilayer. However it was more disordered due to ‘swing’ movement of chains because of distortion in torsional angles α2 and 03 due to absence of water molecules. Trans fraction of the chains, order parameter and water penetration showed general agreement with the available experimental results. On the whole MD technique was found to be quite useful for depicting microscopic behaviour of liquid crystalline system and correlating the same with macroscopic changes observed experimentally.     

Studies of folding and misfolding using simplified models

Computer simulations are as vital to our studies of biological systems as experiments. They bridge and rationalize experimental observations, extend the experimental "field of view", which is often limited to a specific time or length scale, and, most importantly, provide novel insights into biological systems, offering hypotheses about yet-to-be uncovered phenomena. These hypotheses spur further experimental discoveries. Simplified molecular models have a special place in the field of computational biology. Branded as less accurate than all-atom protein models, they have offered what all-atom molecular dynamics simulations could not--the resolution of the length and time scales of biological phenomena. Not only have simplified models proven to be accurate in explaining or reproducing several biological phenomena, they have also offered a novel multiscale computational strategy for accessing a broad range of time and length scales upon integration with traditional all-atom simulations. Recent computer simulations of simplified models have shaken or advanced the established understanding of biological phenomena. It was demonstrated that simplified models can be as accurate as traditional molecular dynamics approaches in identifying native conformations of proteins. Their application to protein structure prediction yielded phenomenal accuracy in recapitulating native protein conformations. New studies that utilize the synergy of simplified protein models with all-atom models and experiments yielded novel insights into complex biological processes, such as protein folding, aggregation and the formation of large protein complexes.     

Protein modeling and structure prediction with a reduced representation

Protein modeling could be done on various levels of structural details, from simplified lattice or continuous representations, through high resolution reduced models, employing the united atom representation, to all-atom models of the molecular mechanics. Here I describe a new high resolution reduced model, its force field and applications in the structural proteomics. The model uses a lattice representation with 800 possible orientations of the virtual alpha carbon-alpha carbon bonds. The sampling scheme of the conformational space employs the Replica Exchange Monte Carlo method. Knowledge-based potentials of the force field include: generic protein-like conformational biases, statistical potentials for the short-range conformational propensities, a model of the main chain hydrogen bonds and context-dependent statistical potentials describing the side group interactions. The model is more accurate than the previously designed lattice models and in many applications it is complementary and competitive in respect to the all-atom techniques. The test applications include: the ab initio structure prediction, multitemplate comparative modeling and structure prediction based on sparse experimental data. Especially, the new approach to comparative modeling could be a valuable tool of the structural proteomics. It is shown that the new approach goes beyond the range of applicability of the traditional methods of the protein comparative modeling.     

Estimation of Respiratory Nasal Pressure and Flow Rate Signals Using Different Respiratory Sound Features

BackgroundRespiratory sounds are associated with the flow rate, nasal flow pressure, and physical characteristics of airways. In this study, we aimed to develop the flow rate and nasal flow pressure estimation models for the clinical application, and find out the optimal feature set for estimation to achieve the optimal model performance.MethodsRespiratory sounds and flow rate were acquired from nine healthy volunteers. Respiratory sounds and nasal flow pressure were acquired from twenty-three healthy volunteers. Four types of respiratory sound features were extracted for flow rate and nasal flow pressure estimation using different estimation models. Effects of estimations using these features were evaluated using Bland-Altman analysis, estimation error, and respiratory sound feature calculation time. Besides, expiratory and inspiratory phases divided estimation errors were compared with united estimation errors.ResultsThe personalized logarithm model was selected as the optimal flow rate estimation model. Respiratory nasal flow pressure estimation based on this model was also performed. For the four different respiratory sound features, there is no statistically significant difference in flow rate and pressure estimation errors. LogEnvelope was, therefore, chosen as the optimal feature because of the lowest computational cost. In addition, for any type of respiratory sound feature, no statistically significant difference was observed between divided and united estimation errors (flow rate and pressure).ConclusionRespiratory flow rate and nasal flow pressure can be estimated accurately using respiratory sound features. Expiratory and inspiratory phases united estimation using respiratory sounds is a more reasonable estimation method than divided estimation. LogEnvelope can be used for this united respiratory flow rate and nasal flow pressure estimation with minimum computational cost and acceptable estimation error.     

Small Molecule Diffusion into Swelling Iota-Carrageenan Gels: A Fluorescence Study

Abstract

Small molecule diffusion into Iota-Carrageenan gel was studied by using steady-state fluorescence (SSF) technique. Pyranine, dissolved in water was used as fluorescence probe. Fluorescence emission intensity, I_p, and scattered light intensity, I_sc, were monitored to study diffusion and swelling processes at various temperatures respectively. Fickian and Li-Tanaka models were elaborated to produce diffusion, D, and collective diffusion, D ₀, coefficients. Diffusion and swelling activation energies were also obtained and found to be 20.5 kj mol^?1 and 28.2 kj mol^?1, respectively.     

Using molecular dynamics simulations on crambin to evaluate the suitability of different continuum dielectric and hydrogen atom models for protein simulations

Molecular dynamics simulations of enzymes with enough explicit waters of solvation to realistically account for solute-solvent interactions can burden the computational resources required to perform the simulation by more than two orders of magnitude. Since enzyme simulations even with an implicit solvation model can be imposing for a supercomputer, it is important to assess the suitability of different continuum dielectric models for protein simulations. A series of 100-picosecond molecular dynamics simulations were performed on the X-ray crystal structure of the protein crambin to examine how well computed structures, obtained using seven continuum dielectric and two hydrogen atom models, agreed with the X-ray structure. The best level of agreement between computed and experimental structures was obtained using a constant dielectric of 2 and the all-hydrogen model. Continuum dielectric models of 1, 1r, and 2r also led to computed structures in reasonably good agreement with the X-ray structure. In all cases, the all-hydrogen model gave better agreement than the united atom model, although, in one case, the difference was not significant. Dielectric models of 4, 80, and 4r with either hydrogen model yielded significantly poorer fits. It is especially noteworthy that the observed trends did not semiquantitatively converge until about 50 picoseconds into the simulations, suggesting that validation studies for protein calculations based on energy minimizations or short simulations should be viewed with caution.     

A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

Multiscale Coarse-Grained Approach to Investigate Self-Association of Antibodies

Self-association of therapeutic monoclonal antibodies (mabs) are thought to modulate the undesirably high viscosity observed in their concentrated solutions. Computational prediction of such a self-association behavior is advantageous early during mab drug candidate selection when material availability is limited. Here, we present a coarse-grained (CG) simulation method that enables microsecond molecular dynamics simulations of full-length antibodies at high concentrations. The proposed approach differs from others in two ways: first, charges are assigned to CG beads in an effort to reproduce molecular multipole moments and charge asymmetry of full-length antibodies instead of only localized charges. This leads to great improvements in the agreement between CG and all-atom electrostatic fields. Second, the distinctive hydrophobic character of each antibody is incorporated through empirical adjustments to the short-range van der Waals terms dictated by cosolvent all-atom molecular dynamics simulations of antibody variable regions. CG simulations performed on a set of 15 different mabs reveal that diffusion coefficients in crowded environments are markedly impacted by intermolecular interactions. Diffusion coefficients computed from the simulations are in correlation with experimentally measured observables, including viscosities at a high concentration. Further, we show that the evaluation of electrostatic and hydrophobic characters of the mabs is useful in predicting the nonuniform effect of salt on the viscosity of mab solutions. This CG modeling approach is particularly applicable as a material-free screening tool for selecting antibody candidates with desirable viscosity properties.     

Molecular dynamics estimates of ion diffusion in model hydrophobic and KcsA potassium channels

Molecular dynamics simulations are carried out to obtain estimates of diffusion coefficients of biologically important Na+, K+, Ca2+ and Cl- ions in hydrophobic cylindrical channels with varying radii and large reservoirs. Calculations for the cylindrical channels are compared to those for the KcsA potassium channel, for which the protein structure has recently been determined from X-ray diffraction experiments. Our results show that ion diffusion is maintained at reasonably high levels even within narrow channels, and does not support the very small diffusion coefficients used in some continuum models in order to fit experimental data. The present estimates of ion diffusion coefficients are useful in the calculation of channel conductance using the Poisson-Nernst-Planck theory, or Brownian dynamics.     

From coarse-grain to all-atom: toward multiscale analysis of protein landscapes

Multiscale methods are becoming increasingly promising as a way to characterize the dynamics of large protein systems on biologically relevant time-scales. The underlying assumption in multiscale simulations is that it is possible to move reliably between different resolutions. We present a method that efficiently generates realistic all-atom protein structures starting from the C(alpha) atom positions, as obtained for instance from extensive coarse-grain simulations. The method, a reconstruction algorithm for coarse-grain structures (RACOGS), is validated by reconstructing ensembles of coarse-grain structures obtained during folding simulations of the proteins src-SH3 and S6. The results show that RACOGS consistently produces low energy, all-atom structures. A comparison of the free energy landscapes calculated using the coarse-grain structures versus the all-atom structures shows good correspondence and little distortion in the protein folding landscape.     

Conformational equilibria of valine studied by dynamics simulation.

The conformational probability distribution of a valine residue in the valine dipeptide and of the valine side chain in an alpha-helix, as well as the change in helix stability for replacing alanine with valine, has been calculated by molecular dynamics simulations of explicitly hydrated systems: dipeptide, tetrapeptide and 10-, 14- and 18-residue oligoalanine helices. All computed free-energy differences are means from at least eight separate slow-growth simulations, four in each direction and are reported with their root-mean-square deviations. Different values for the change in free energy of folding (delta delta G degrees) have been calculated with the use of forcefields having an all-atom and a central-atom representation of methyl groups, etc. The value obtained with the all-atom forcefield agrees well with new experimental values (3 kJ/mol = 0.7 kcal/mol). Furthermore, the most stable valine side-chain rotamer in the helix is different for these two representations. The most stable rotamer for the all atom conformation is the same one that predominates for valines in alpha-helices in proteins of known conformation. The lower conformational freedom of the valine side chain in the helix contributes 1 kJ/mol to the difference in stability computed with the all-atom potential; unfavorable interactions of the side chain with helix, even in the most stable conformation, further increase delta delta G degrees.