Session T39: Computational Molecular Biophysics

Simulation of pH-dependent Behavior of Liposome

Optimized liposome for biomedical delivery applications has been a field of vigorous research for past few decades. While experimental techniques of fluorescence spectroscopy, differential scanning calorimetry and dynamic light scattering report physical suitabilities in several applications of liposomes, molecular dynamics simulation can provide more detailed feature at atomistic level for such biophysical systems. In recent times, experimental results of liposome's physical properties in different pH environment have widely been reported. The system draws interest for potential applications in several biomedical areas. We will present our molecular simulation results for such system highlighting the effect of pH on hydrogen bonding as well as correlation of dynamics to observed phase behavior.   

\textit{In silico} investigation of molecular effects caused by missense mutations in creatine transporter protein

Creatine transporter (CT) protein, which is encoded by SLC6A8 gene, is essential for taking up the creatine in the cell, which in turn plays a key role in the spatial and temporal maintenance of energy in skeletal and cardiac muscle cells. It was shown that some missense mutations in CT cause mental retardation, while others are harmless non-synonymous single nucleoside polymorphism (nsSNP). Currently fifteen missense mutations in CT are known, among which twelve are disease-causing. Sequence analysis reveals that there is no clear trend distinguishing disease-causing from harmless missense mutations. Because of that, we built 3D model of the CT using highly homologous template and use the model to investigate the effects of mutations of CT stability and hydrogen bond network. It is demonstrated that disease-causing mutations affect the folding free energy and ionization states of titratable group in much greater extend as compared with harmless mutations.   

Investigating the mechanism of DNA bulk hybridization with Forward Flux Sampling

DNA has become increasingly common as a building block for constructing nanomaterials. However, the mechanism by which DNA hybridization occurs is largely unknown, even in the bulk. Previous work using Transition Path Sampling and a coarse grain DNA model has shown that DNA bulk hybridization occurs via a ``slithering'' mechanism for repetitive sequences and a distinct nucleation event for random sequences. This mechanistic description remains somewhat incomplete as only configurations within the general vicinity of the transition state ensemble have been examined. In this work, we use Forward Flux Sampling and Langevin Dynamics to examine configurations along the entire transition pathway. We find that, for random sequences, barriers to hybridization arise at certain points in the hybridization pathway requiring reorientation of the two strands. Such barriers are not as pronounced for repetitive sequences where rearrangement occurs without the large scale disruption of hydrogen bonding. The formalism which we use has allowed us to calculate reaction constants for hybridization that are consistent with experiments. It has also allowed us to explain the precipitous decay of reaction rates that is observed when molecular weight is increased.   

A backbone based protein model with explicit solvent

The computational expense of folding atomistically detailed protein models is prohibitive. Hence minimalist models of proteins are a popular choice. The minimalist models developed so far have excluded water, and treated the hydrophobic effect as an effective attraction between hydrophobic monomers. This simplified treatment does not capture the temperature-dependent variations in entropy and enthalpy of water molecules. Proteins have a predominantly water-screened hydrophobic core and water-exposed polar groups. This structural feature should alter the dynamics of proteins and surrounding water from that of a hydrophobic homopolymer in water. To include these features in a minimalist model, we designed heteropolymers of polar and hydrophobic monomers in explicit water-like medium. The polar monomers and water molecules were modeled with the Jagla potential, which has been shown to reproduce many water-like thermodynamic properties, and the hydrophobic monomers as hard spheres. We discuss a methodology for optimizing the sequence of these heteropolymers and how the hydrophobic collapse of these heteropolymers differs from that of a random heteropolymer.   

Connecting ion channel simulations to experiment

A simple theoretical framework is used to connect MD simulation with ion channel permeation experiments. MD simulations of potassium channels typically exhibit at least two stable selectivity filter states, one with double occupancy and another with triple occupancy. In the association/dissociation (A/D) model, transitions between these two states occur via concerted motion of all three ions in a shunt-on shunt-off mechanism that is consistent with a large group of published MD simulations. This is the simplest model that explains the universal saturating behavior observed experimentally for many ion channels. Published permeation experiments through the MaxiK channel over a wide range of concentrations and positive voltages are shown to be remarkably consistent with the predictions of this model. Published MD simulations of the Kv1.2 potassium channel exhibit an extended shunt-on shunt-off mechanism at one end of the selectivity filter and a pop-off pop-on mechanism at the other end. This two-step mechanism is incorporated into an asymmetric variant of the A/D model that successfully explains published permeation data through the Shaker potassium channel at physiological concentrations, and successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive voltage data (that appear linear). Support from NSF 0836833 is gratefully acknowledged.   

On the Minimum Energy Path to Membrane Pore Formation

Several experimental methods have been developed to study the mechanical response of vesicles under an applied tension. Of particular note are the micropipette aspiration techniques and the use of a viscous solution to extend the lifetime of pores. MD simulations have also been used to study the energetic and structural properties of these transient pores on a molecular level. However, they often require extremely high tensions beyond the regime where pore formation is a thermally-activated event. We approach the nucleation problem by combining the string method with dynamic self-consistent field (DSCF) theory to obtain the full minimum energy path (MEP) to pore formation for a range of surface tensions $\gamma$. We compare our results with classical nucleation theory (CNT). Near the coexistence ($\gamma \rightarrow 0$) the rim of the pore is well-defined and the line tension is well approximated by the macroscopic definition given by CNT. However, when the free energy barrier is within $\sim 10~\rm kT$, the transition state is somewhere between a stalk-like structure and a thinned membrane leading to a hole that is partially exposed to solvents. These molecular rearrangements involved in the formation of a pore are not captured by CNT.   

Capturing electrostatic interactions explicitly with the 3SPN model for DNA

The ``Three Sites Per Nucleotide'' (3SPN) model for nucleic acid simulation provides a powerful tool for computational studies of biological phenomena. Previously, this model has relied on an implicit representation of the surrounding ionic environment at the level of Debye-H\"{u}ckel theory. In this work, we eliminate this limitation and implement an explicit representation of ions, both monovalent and divalent. The coarse-grain ion-ion and ion-phosphate$_{DNA}$ potential is adapted after the model of Lenart \textit{et al.} and parameterized to reproduce the key features in the local structure and organization of ions in the bulk and in the presence of DNA. The parameters of the previous generation of 3SPN (3SPN.1) have been modified to reproduce melting temperatures observed experimentally employing a biased parallel tempering scheme. The resulting model is capable of reproducing the local structure observed in fully detailed atomistic simulations as well as the melting temperature of DNA reported experimentally for a range of DNA oligonucleotide lengths, CG-content, Na$^{+}$ concentration and Mg$^{2+}$ concentration. The usefulness of the model is demonstrated in the context of confinement of dsDNA within a viral capsid and the exploration of pathways between dehybridized and hybridized DNA.   

Intrinsic noise in stochastic models of gene expression with molecular memory and bursting

Regulation of intrinsic noise in gene expression is essential for many cellular functions. Correspondingly, there is considerable interest in understanding how different molecular mechanisms of gene expression impact variations in protein levels across a population of cells. In this work, we analyze a stochastic model of bursty gene expression which considers general waiting-time distributions governing arrival and decay of proteins. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. The derived results extend previous work by including the effects of arbitrary probability distributions representing the effects of molecular memory and bursting. The analytical expressions obtained provide insight into the role of transcriptional, post-transcriptional and post-translational mechanisms in controlling the noise in gene expression.   

First-Principles Study of Muon Trapping in Singlet and Triplet States of Oxyhemoglobin

Observation of muon spin-lattice relaxation effects in Oxyhemoglobin by the muon-spin rotation ($\mu $SR) technique [1] has sparked current interest in the possibility of magnetic character in Oxyhemoglobin (OxyHb). First-Principles variational Hartree-Fock Many Body Perturbation Theory (VHFMBPT) technique investigations on the singlet and triplet states of pure (OxyHb) have shown [2] that the triplet state is considerably higher than the singlet state ruling out magnetic character. However the charge distribution obtained by the VHFMBPT procedure in both states show a number of sites that have negative charges where the trapping of muon is being investigated to examine if the energy gap in the ordering of singlet and triplet states can be reduced or reversed leading to magnetic effects. Other possible sources of magnetism in Oxyhemoglobin will also be discussed. [1] K. Nagamine et al. Proc. Japan. Acad. B-Physics 83, 120 (2007); [2] S.R. Badu et al. Reported at Third Joint HFI-NQI International Conference, CERN, Geneva, September 2010.   

Binding-rebinding dynamics of proteins interacting non-specifically with a long DNA molecule

Protein interactions with DNA chains and/or fibers regulate a large number of cell functions, and are also important in the understanding of experiments that reveal biochemical and physical cell processes. In order to determine the time range and length range of interactions between proteins and DNA, we analyze the adsorption and de-sorption of units (proteins) that bind reversibly to linear chains (DNA fibers) via non specific interactions through Monte Carlo simulations. We assume the particles are random walkers and that bind reversibly to stretched DNA fiber. In particular we determine the number of re-bindings events. We find that the number of protein re-bindings have a logarithmic dependence on DNA fiber length.   

Regulation of gene expression by small RNAs via coupled stoichiometric degradation: a variational approach

Regulatory genes called small RNAs (sRNAs) are known to play critical roles in cellular responses to changing environments. For several bacterial sRNAs, regulation is effected by coupled stoichiometric degradation with messenger RNAs (mRNAs). The nonlinearity inherent in this regulatory scheme implies that exact analytical solutions for the corresponding stochastic models are intractable. Based on the mapping of the master equation to a quantum evolution equation, we use the variational method (introduced by Eyink) to analyze a well-studied stochastic model for regulation by sRNAs. Results from the variational ansatz are in excellent agreement with stochastic simulations for a wide range of parameters, including regions of parameter space where mean-field approaches break down. The results derived provide new insights into sRNA-based regulation and will serve as useful inputs for future studies focusing on the interplay of stochastic gene expression and regulation by sRNAs.   

Spatial gradients of Ran-GTP-importin-$\beta$ complex around chromosomes in a cell of spheroidal shape

The concept of signaling gradients of a diffusible and slowly degraded chemical plays an important role in the description of cell signal transduction. It has been suggested that the generation of spatial gradients around chromosomes of the complex, Ran-GTP-importin-$\beta$, promotes microtubule nucleation and growth of the mitotic-spindle in Xenopus egg extracts. Here we solved the appropriate reaction-diffusion equation in spheroidal coordinates, and use measured values of the diffusion coefficients and activities to find out how the magnitude of the gradients depend upon the shape and geometry of the chromatin and cytoplasm. We found that the greater the eccentricity the smaller the magnitude of the stationary gradient. When the chromatin becomes spherical the magnitude of the gradient of the complex appears to be optimized.   

Kinetic simulations of tension-induced DNA strand-unpeeling transition

Sequence- and salt- dependent kinetic simulation assuming strand-unpeeling from B-DNA using the Gellispie's stochastic kinetics simulation algorism was performed for DNA fragments of a few hundred base pairs. Similar to DNA unzipping experiments, sequence-dependent energy barriers resulted stepwise extension changes were observed during the transition. The simulations were compared with recent single-molecule studies of overstretching transition of the same DNAs occurring at around 65 pN. The results quantitatively reproduced the dynamics of overstretching transition of the same DNAs under conditions when overstretching led to strand separation, and were distinct from that when the transition led to a double-stranded overstretched DNA called ``S-DNA'' through the B-S transition pathway. We conclude that the strand separation transition pathway was a strand-unpeeling transition from the two free ends of DNA. Further, our results suggest that the B-S transition pathway does not involve base-pair separation.   

Determination of NMR chemical shifts for cholesterol crystals from first-principles

Solid State Nuclear Magnetic Resonance (NMR) is a powerful tool in crystallography when combined with theoretical predictions. So far, empirical calculations of spectra have been employed for an unambiguous identification. However, many complex systems are outside the scope of these methods. Our implementation of ultrasoft and projector augmented wave pseudopotentials within \textit{ab initio} gauge including projector augmented plane wave (GIPAW) method in Quantum Espresso simulation package allows affordable calculations of NMR spectra for systems of thousands of electrons. We report here the first \textit{ab initio} determination of NMR spectra for several crystal structures of cholesterol. Cholesterol crystals, the main component of human gallstones, are of interest to medical research as their structural properties can shed light on the pathologies of gallbladder. With our application we show that \textit{ab initio} calculations can be employed to aid NMR crystallography.