Introductory Tutorials for Simulating Protein Dynamics with GROMACS.

Computing free energies of complex biomolecular systems via atomistic (AT) molecular dynamics (MD) simulations remains a challenge due to the need for adequate sampling and convergence. Recent coarse-grained (CG) methodology allows simulations of significantly larger systems (∼10(6) to 10(8) atoms) over longer (μs/ms) time scales. Such CG models appear to be capable of making semiquantitative predictions. However, their ability to reproduce accurate thermodynamic quantities remains uncertain. We have recently used CG MD simulations to compute the potential of mean force (PMF) or free energy profile of a small peptide toxin interacting with a lipid bilayer along a 1D reaction coordinate. The toxin studied was VSTx1 (Voltage Sensor Toxin 1) from spider venom which inhibits the archeabacterial voltage-gated potassium (Kv) channel KvAP by binding to the voltage-sensor (VS) domains. Here, we re-estimate this PMF profile using (i) AT MD simulations with explicit membrane and solvent and (ii) an implicit membrane and solvent (generalized Born; GBIM) model where only the peptide was explicit. We used the CG MD free energy simulations to guide the setup of the corresponding AT MD simulations. The aim was to avoid local minima in the AT simulations which would be difficult over shorter AT time scales. A cross-comparison of the PMF profiles revealed a conserved topology, although there were differences in the magnitude of the free energies. The CG and AT simulations predicted a membrane/water interface free energy well of -27 and -23 kcal/mol, respectively (with respect to water). The GBIM model, however, gave a reduced interfacial free energy well (-12 kcal/mol). In addition, the CG and GBIM models predicted a free energy barrier of +61 and +96 kcal/mol, respectively, for positioning the toxin at the center of the bilayer, which was considerably smaller in the AT simulations (+26 kcal/mol). Thus, we present a framework for serially combining CG and AT simulations to estimate the free energy of peptide/membrane interactions. Such approaches for combining simulations at different levels of granularity will become increasingly important in future studies of complex membrane/protein systems.

REACH Coarse-Grained Biomolecular Simulation: Transferability between Different Protein Structural Classes

Intrinsically disordered proteins (IDPs) are a set of proteins that lack a definite secondary structure in solution. IDPs can acquire tertiary structure when bound to their partners; therefore, the recognition process must also involve protein folding. The nature of the transition state (TS), structured or unstructured, determines the binding mechanism. The characterization of the TS has become a major challenge for experimental techniques and molecular simulations approaches since diffusion, recognition, and binding is coupled to folding. In this work we present atomistic molecular dynamics (MD) simulations that sample the free energy surface of the coupled folding and binding of the transcription factor c-myb to the cotranscription factor CREB binding protein (CBP). This process has been recently studied and became a model to study IDPs. Despite the plethora of available information, we still do not know how c-myb binds to CBP. We performed a set of atomistic biased MD simulations running a total of 15.6 μs. Our results show that c-myb folds very fast upon binding to CBP with no unique pathway for binding. The process can proceed through both structured or unstructured TS's with similar probabilities. This finding reconciles previous seemingly different experimental results. We also performed Go-type coarse-grained MD of several structured and unstructured models that indicate that coupled folding and binding follows a native contact mechanism. To the best of our knowledge, this is the first atomistic MD simulation that samples the free energy surface of the coupled folding and binding processes of IDPs.

Atomic-Level Protein Structure Refinement Using Fragment-Guided Molecular Dynamics Conformation Sampling

Gradient of mechanical properties in polymer nanocomposites: From atomistic scale to the strain gradient effective continuum

Experiments have revealed that DNA solvation dynamics is characterized by multiple time scales ranging from a few picoseconds to a few hundred nanoseconds and in some cases even up to several microseconds. The last part of decay is not only slow but can also be described by a power law (PL). The microscopic origin of this PL is yet to be clearly established. Here we present a theoretical study employing multiple approaches from time dependent statistical mechanics and computer simulations. The present study shows that water dynamics may not account for the slow PL decay because the longest time scales describing water dynamics could be at most of the order of 100 ps. We find that the DNA solvation dynamics is complex, due to multiple different contributions to solvation energy. Our investigations also show that the primary candidates for this exotic nature of solvation dynamics are the response of the counterions and ions of the buffer solution. We first employ the well-known Oosawa model of polyelectrolyte solution that includes effects of counterion fluctuations to construct a frequency dependent dielectric function. We use it in the continuum model of Bagchi, Fleming, and Oxtoby (BOF). We find that it fails to explain the slow PL decay of DNA solvation dynamics. We then extend the Oosawa model by employing the continuous time random walk technique developed by Scher, Montroll and Lax. We find that this approach could explain the long time PL decay, in terms of the collective response of the counterions. To check the nature of random walk of counterions along the phosphate backbone, we carry out atomistic molecular dynamics (MD) simulations with a long (38 base pair) DNA. We indeed find frequent occurrence of random walk of tagged counterions along the phosphate backbone. We next propose a generalized random walk model for counterion hopping on phosphate backbone (observed in our MD simulations) and carry out kinetic Monte Carlo simulations to show that the nonexponential contribution to solvation dynamics can indeed come from dynamics of such ions. We also employ a mode coupling theory (MCT) analysis to understand the slow relaxation that can originate from ions in solution due to the use of the buffer. Explicit evaluation suggests that buffer ion contribution could explain a logarithmic time dependence in the nanosecond time scale but not a power law. To further understand the nonexponentiality of solvation dynamics at relatively shorter times (less than 100 ps) we carry out atomistic MD simulations with explicit water molecules. Log-normal distributions of relaxation times of water dynamics inside the grooves may be responsible for the initial multiexponential decay of solvation dynamics. We find that the observed faster solvation of groove bound probe than that of the intercalated probe could arise from the self-motion of the probe.

Fluorescence of environment-sensitive dyes is widely applied to monitor local structure and solvation dynamics of biomolecules. It has been shown that, in comparison with a parent indole fluorophore, fluorescence of 2-(2'-pyridyl)-5-methylindole (5M-PyIn-0) and 2-[2'-(4',6'-dimethylpyrimidyl)]-indole (DMPmIn-0) is remarkably sensitive to hydrogen bonding with protic partners. Strong fluorescence, observed for these compounds in nonpolar and polar aprotic solvents, is efficiently quenched in aqueous solution. This study demonstrates that 5M-PyIn-0 and DMPmIn-0, which are almost nonemitting in aqueous solution, become highly fluorescent upon titrating with phospholipid vesicles. The fluorescence enhancement is accompanied by a significant blue shift of emission maximum. The Gibbs free energy of membrane partitioning, measured by the increase in the steady-state fluorescence intensities during transfer from an aqueous environment to a lipid bilayer, is very favorable for both compounds, being in a range from -7.1 to -8.0 kcal/mol and depending only slightly on lipid composition of the membrane. The fluorescence enhancement upon membrane partitioning is indicative of the loss of the specific hydrogen-bonding interactions between the excited fluorophore and water molecules, causing efficient fluorescence quenching in bulk water. This conclusion is supported by atomistic molecular dynamics (MD) simulations, demonstrating that both 5M-PyIn-0 and DMPmIn-0 bind rapidly and partition deeply into a lipid bilayer. MD simulations also show a rapid, nanosecond-scale decrease in the probability of solute-solvent hydrogen bonding during passive diffusion of the probe molecules from bulk water into a lipid bilayer. At equilibrium conditions, both 5M-PyIn-0 and DMPmIn-0 prefer deep localization within the hydrophobic, water-free region of the bilayer. A free energy profile of penetration across a bilayer estimated using MD umbrella sampling shows that both indole derivatives favor residence in a rather wide potential energy well located 10-15 Å from the bilayer center.

Phospholemman (PLM) is a 72-residue bitopic cardiac transmembrane protein, which acts as a modulator of the Na(+)/K(+)-ATPase and the Na(+)/Ca(2+) exchanger and possibly forms taurine channels in nonheart tissue. This work presents a high resolution structural model obtained from a combination of site-specific infrared spectroscopy and experimentally constrained high throughput molecular dynamics (MD) simulations. Altogether, 37 experimental constraints, including nine long range orientational constraints, have been used during MD simulations in an explicit lipid bilayer/water system. The resulting tetrameric alpha-helical bundle has an average helix tilt of 7.3 degrees and a crossing angle close to 0 degrees . It does not reveal a hydrophilic pore, but instead strong interactions between various residues occlude any pore. The helix-helix packing is unusual, with Gly(19) and Gly(20) pointing to the outside of the helical bundle, facilitating potential interaction with other transmembrane proteins, thus providing a structural basis for the modulatory effect of PLM on the Na(+)/K(+)-ATPase. A two-stage model of interaction between PLM and the Na(+)/K(+)-ATPase is discussed involving PLM-ATPase interaction and subsequent formation of an unstable PLM trimer, which readily interacts with surrounding ATPase molecules. Further unconstrained MD simulations identified other packing models of PLM, one of which could potentially undergo a conformational transition to an open pore.

Ion interactions with nucleic acids (both DNA and RNA) are an important and evolving field of investigation. Positively charged cations may interact with highly negatively charged nucleic acids via simple electrostatic interactions to help screen the electrostatic repulsion along the nucleic acids and assist their folding and/or compaction. Cations may also bind at specific sites and become integral parts of the structures, possibly playing important enzymatic roles. Two popular methods for computationally exploring a nucleic acid’s ion atmosphere are atomistic molecular dynamics (MD) simulations and the Poisson–Boltzmann (PB) equation. In general, monovalent ion results obtained from MD simulations and the PB equation agree well with experiment. However, Bai et al. (2007) observed discrepancies between experiment and the PB equation while examining the competitive binding of monovalent and divalent ions, with more significant discrepancies for divalent ions. The goal of this project was to thoroughly investigate monovalent (Na+) and divalent (Mg2+) ion distributions formed around a DNA duplex with MD simulations and the PB equation. We simulated three different cation concentrations, and matched the equilibrated bulk ion concentration for our theoretical calculations with the PB equation. Based on previous work, our Mg2+ ions were fully solvated, the expected state of Mg2+ ions when interacting with a duplex, when the production simulations began and remained throughout the simulations (Kirmizialtin, 2010; Robbins, 2012). Na+ ion distributions and number of Na+ ions within 10 Å of the DNA obtained from our two methods agreed well. However, results differed for Mg2+ ions, with a lower number of ions within the cut-off distance obtained from the PB equation when compared to MD simulations. The Mg2+ ion distributions around the DNA obtained via the two methods also differed. Based on our results, we conclude that the PB equation will systematically underestimate Mg2+ ions bound to DNA, and much of this deviation is attributed to dielectric saturation associated with high valency ions.

Modeling Macromolecular Motions by X-Ray-Scattering-Constrained Molecular Dynamics

Major histocompatibility complex class I (MHC-I), a key element of the acquired immune system, plays essential roles in activating CD8+ T cells by recognizing intracellular antigens derived from pa...

Atomistic molecular dynamics simulations of intrinsically disordered proteins.

The increased production of unconventional hydrocarbons emphasizes the need to understand the transport of fluids through narrow pores. Although it is well-known that confinement affects fluids structure and transport, it is not yet possible to quantitatively predict properties such as diffusivity as a function of pore width in the range of 1-50 nm. Such pores are commonly found not only in shale rocks but also in a wide range of engineering materials, including catalysts. We propose here a novel and computationally efficient methodology to obtain accurate diffusion coefficient predictions as a function of pore width for pores carved out of common materials, such as silica, alumina, magnesium oxide, calcite, and muscovite. We implement atomistic molecular dynamics (MD) simulations to quantify fluid structure and transport within 5 nm-wide pores, with particular focus on the diffusion coefficient within different pore regions. We then use these data as input to a bespoke stochastic kinetic Monte Carlo (KMC) model, developed to predict fluid transport in mesopores. The KMC model is used to extrapolate the fluid diffusivity for pores of increasing width. We validate the approach against atomistic MD simulation results obtained for wider pores. When applied to supercritical methane in slit-shaped pores, our methodology yields data within 10% of the atomistic simulation results, with significant savings in computational time. The proposed methodology, which combines the advantages of MD and KMC simulations, is used to generate a digital library for the diffusivity of gases as a function of pore chemistry and pore width and could be relevant for a number of applications, from the prediction of hydrocarbon transport in shale rocks to the optimization of catalysts, when surface-fluid interactions impact transport.

Toward a mechanistic understanding of cesium adsorption to todorokite: A molecular dynamics simulation study

Molecular dynamics simulations as support for experimental studies on surfactant interfacial layers