Browsing by Author "Zhu, Fangqiang"
Now showing 1 - 10 of 11
Results Per Page
Sort Options
Item Biophysical studies of cholesterol in unsaturated phospholipid model membranes(2013) Williams, Justin A.; Wassall, Stephen R.; Decca, Ricardo; Petrache, Horia; Zhu, Fangqiang; Todd, Brian A.Cellular membranes contain a staggering diversity of lipids. The lipids are heterogeneously distr ibuted to create regions, or domains, whose physical properties differ from the bulk membrane and play an essential role in modulating the function of resident proteins. Many basic questions pertaining to the formation of these lateral assemblies remain. T his research employs model membranes of well - defined composition to focus on the potential role of polyunsaturated fatty acids (PUFAs) and their interaction with cholesterol (chol) in restructuring the membrane environment. Omega - 3 (n - 3) PUFAs are the main bioactive components of fish oil, whose consumption alleviates a variety of health problems by a molecular mechanism that is unclear. We hypothesize that the incorporation of PUFAs into membrane lipids and the effect they have on molecular organization may be, in part, responsible. Chol is a major constituent in the plasma membrane of mammals. It determines the arrangement and collective properties of neighboring lipids, driving the formation of domains via differential affinity for different lipids . T he m olecular organization of 1 -[ 2 H 31 ]palmitoyl -2- eicosapentaenoylphosphatidylcholine (PEPC - d 31 ) and 1 -[ 2 H 31 ]palmitoyl -2- docosahexaenoylphosphatidylcholine (PDPC -d 31 ) in membran es with sphingomyelin (SM) and chol (1:1:1 mol) was compared by solid - state 2 H NMR spectroscopy. Eicosapentaenoic (EPA) and docosahexaenoic (DHA) acids are the two major n - 3 PUFAs found in fish oil, while PEPC -d 31 and PDPC -d 31 are phospholipids containing the respective PUFAs at the sn - 2 position and a perdeuterated palmitic acid a t the sn - 1 position . Analysis of s pectra recorded as a function of temperature indicate s that in both cases, formation of PUFA - rich (less ordered) and SM - rich (more ordered) domains occurred. A surprisingly substantial proportion of PUFA was found to infil trate the more ordered domain. There was almost twice as much DHA (65%) as EPA (30%) . The implication is that n - 3 PUFA s can incorporate into lipid rafts, which are domains enriched in SM and chol in the plasma membrane, and potentially disrupt the activity of signaling proteins that reside therein. DHA, furthermore, may be the more potent component of fish oil. PUFA - chol interactions were also examined through affinity measurements. A novel method utilizing electron paramagnetic resonance (EPR) was develope d, to monitor the partitioning of a spin - labeled analog of chol , 3β - doxyl - 5α - cholestane (chlstn), between large unilamellar vesicles (LUVs) and met hyl - β - cyclodextrin (mβCD). The EPR spectra for chlstn in the two environments are distinguishable due to the substantial differences in tumbling rates , allowing the population distribution ratio to be determined by spectral simulation. Advantages of this approach include speed of implementation and a vo idance of potential artifact s associated with physical separation of LUV and mβCD . Additionally, in a check of the method, t he relative partition coefficients between lipids measured for the spin label analog agree with values obtained for chol by isothermal titration calorimetry (ITC). Results from LUV with different composition confirmed a hierarchy of decreased sterol affinity for phospholipids with increasing acyl chain unsaturation , PDPC possessing half the affinity of the corresponding monounsaturated phospholipid. Taken together, the results of these studies on model membranes demonstrate the potential for PUFA - driven alteration of the architecture of biomembranes, a mechanism through which human health may be impacted.Item Calculating Single-Channel Permeability and Conductance from Transition Paths(ACM, 2019-02) Zhou, Xiaoyan; Zhu, Fangqiang; Physics, School of SciencePermeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.Item Calculating transition rates from durations of transition paths(AIP, 2017-03) Zhu, Fangqiang; Physics, School of ScienceCalculating the kinetic rates for rare transitions is an important objective for molecular simulations. Here I prove equalities that relate the transition rates to the equilibrium free energy and the statistics of the transition paths. In particular, the durations of the transition paths within given intervals of the reaction coordinate provide the kinetic pre-factor in the rate formula. Based on the available free energy, the transition rates can further be rigorously calculated by initiating forward and backward simulations and evaluating the duration of each transition path. Validation on a model system confirms that the approach correctly predicts the transition rates from the simulations and demonstrates that whereas the relations here are general and valid for any chosen reaction coordinate, a good reaction coordinate will enable a more efficient sampling of the transition paths and thus a more reliable rate calculation.Item Conformational Changes in Two Inter-Helical Loops of Mhp1 Membrane Transporter(PLOS, 2015-07-17) Song, Hyun Deok; Zhu, Fangqiang; Department of Physics, School of ScienceMhp1 is a bacterial secondary transporter with high-resolution crystal structures available for both the outward- and inward-facing conformations. Through molecular dynamics simulations of the ligand-free Mhp1 as well as analysis of its crystal structures, here we show that two inter-helical loops, respectively located at the extra- and intracellular ends of the “hash motif” in the protein, play important roles in the conformational transition. In the outward- and inward-facing states of the protein, the loops adopt different secondary structures, either wrapped to the end of an alpha-helix, or unwrapped to extended conformations. In equilibrium simulations of 100 ns with Mhp1 in explicit lipids and water, the loop conformations remain largely stable. In targeted molecular dynamics simulations with the protein structure driven from one state to the other, the loops exhibit resistance and only undergo abrupt changes when other parts of the protein already approach the target conformation. Free energy calculations on the isolated loops further confirm that the wrapping/unwrapping transitions are associated with substantial energetic barriers, and consist of multiple sequential steps involving the rotation of certain backbone torsion angles. Furthermore, in simulations with the loops driven from one state to the other, a large part of the protein follows the loops to the target conformation. Taken together, our simulations suggest that changes of the loop secondary structures would be among the slow degrees of freedom in the conformational transition of the entire protein. Incorporation of detailed loop structures into the reaction coordinate, therefore, should improve the convergence and relevance of the resulting conformational free energy.Item Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter(ACS, 2017) Song, Hyun Deok; Zhu, Fangqiang; Physics, School of ScienceProtein conformational change is of central importance in molecular biology. Here we demonstrate a computational approach to characterize the transition between two metastable conformations in all-atom simulations. Our approach is based on the finite temperature string method, and the implementation is essentially a generalization of umbrella sampling simulations with Hamiltonian replica exchange. We represent the transition pathway by a curve in the conformational space, with the curve parameter taken as the reaction coordinate. Our approach can efficiently refine a transition pathway and compute a one-dimensional free energy as a function of the reaction coordinate. A diffusion model can then be used to calculate the forward and backward transition rates, the major kinetic quantities for the transition. We applied the approach on a local transition in the ligand-free Mhp1 transporter, between its outward-facing conformation and an intermediate conformation with the side chain of Phe305 flipped to the outside of the protein. Our simulations predict that the flipped-out position of this side chain has a free energy 6.5 kcal/mol higher than the original position in the crystal structure, and that the forward and backward transition rates are in the millisecond and submicrosecond time scales, respectively.Item How does Water Pass through a Sugar Transporter?(Elsevier B.V., 2014-03-18) Zhu, Fangqiang; Department of Physics, School of ScienceItem Kinetic mechanism for water in vibrating carbon nanotubes(APS, 2018-09) Zhou, Xiaoyan; Zhu, Fangqiang; Physics, School of ScienceRecent simulations revealed that, when an atom in a single-wall carbon nanotube was artificially driven to oscillate radially with the two ends of the nanotube fixed, water transport became highly unusual at some oscillation frequencies. Here we systematically investigate the underlying mechanism for such effects through a series of simulations and detailed analysis. We find that the pattern and magnitude for the vibration of the nanotube are sensitive to the driving frequency but largely independent of the presence of water. At certain resonance frequencies, some carbon atoms of the nanotube oscillate at much larger amplitudes than does the driving atom. Furthermore, a strongly vibrating nanotube tends to have a much-reduced water occupancy, which is mainly due to the heating effect rather than the induced deformation. Indeed, the water molecules inside the nanotube can be significantly heated and gain large kinetic energies due to the collisions with the vibrating carbon atoms. Consequently, the kinetic rate of water exchange through the nanotube could be enhanced even when the water occupancy is low. Our findings here may help understanding the physical mechanisms of similar nanodevices.Item Monte Carlo Simulations of HIV Capsid Protein Homodimer(ACS, 2015-06) Zhu, Fangqiang; Chen, Bo; Department of Physics, School of ScienceCapsid protein (CA) is the building block of virus coats. To help understand how the HIV CA proteins self-organize into large assemblies of various shapes, we aim to computationally evaluate the binding affinity and interfaces in a CA homodimer. We model the N- and C-terminal domains (NTD and CTD) of the CA as rigid bodies and treat the five-residue loop between the two domains as a flexible linker. We adopt a transferrable residue-level coarse-grained energy function to describe the interactions between the protein domains. In seven extensive Monte Carlo simulations with different volumes, a large number of binding/unbinding transitions between the two CA proteins are observed, thus allowing a reliable estimation of the equilibrium probabilities for the dimeric vs monomeric forms. The obtained dissociation constant for the CA homodimer from our simulations, 20–25 μM, is in reasonable agreement with experimental measurement. A wide range of binding interfaces, primarily between the NTDs, are identified in the simulations. Although some observed bound structures here closely resemble the major binding interfaces in the capsid assembly, they are statistically insignificant in our simulation trajectories. Our results suggest that although the general purpose energy functions adopted here could reasonably reproduce the overall binding affinity for the CA homodimer, further adjustment would be needed to accurately represent the relative strength of individual binding interfaces.Item Parameter Optimization for Interaction between C-Terminal Domains of HIV-1 Capsid Protein(ACS, 2017-04) Sha, Hao; Zhu, Fangqiang; Physics, School of ScienceHIV-1 capsid proteins (CAs) assemble into a capsid that encloses the viral RNA. The binding between a pair of C-terminal domains (CTDs) constitutes a major interface in both the CA dimers and the large CA assemblies. Here, we attempt to use a general residue-level coarse-grained model to describe the interaction between two isolated CTDs in Monte Carlo simulations. With the standard parameters that depend only on the residue types, the model predicts a much weaker binding in comparison to the experiments. Detailed analysis reveals that some Lennard-Jones parameters are not compatible with the experimental CTD dimer structure, thus resulting in an unfavorable interaction energy. To improve the model for the CTD binding, we introduce ad hoc modifications to a small number of Lennard-Jones parameters for some specific pairs of residues at the binding interface. Through a series of extensive Monte Carlo simulations, we identify the optimal parameters for the CTD–CTD interactions. With the refined model parameters, both the binding affinity (with a dissociation constant of 13 ± 2 μM) and the binding mode are in good agreement with the experimental data. This study demonstrates that the general interaction model based on the Lennard-Jones potential, with some modest adjustment of the parameters for key residues, could correctly reproduce the reversible protein binding, thus potentially applicable for simulating the thermodynamics of the CA assemblies.Item Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts(ACS, 2017) Meshkin, Hamed; Zhu, Fangqiang; Physics, School of ScienceSpontaneous transitions between the native and non-native protein conformations are normally rare events that hardly take place in typical unbiased molecular dynamics simulations. It was recently demonstrated that such transitions can be well described by a reaction coordinate, Q, that represents the collective fraction of the native contacts between the protein atoms. Here we attempt to use this reaction coordinate to enhance the conformational sampling. We perform umbrella sampling simulations with biasing potentials on Q for two model proteins, Trp-Cage and BBA, using the CHARMM force field. Hamiltonian replica exchange is implemented in these simulations to further facilitate the sampling. The simulations appear to have reached satisfactory convergence, resulting in unbiased free energies as a function of Q. In addition to the native structure, multiple folded conformations are identified in the reconstructed equilibrium ensemble. Some conformations without any native contacts nonetheless have rather compact geometries and are stabilized by hydrogen bonds not present in the native structure. Whereas the enhanced sampling along Q reasonably reproduces the equilibrium conformational space, we also find that the folding of an α-helix in Trp-Cage is a slow degree of freedom orthogonal to Q and therefore cannot be accelerated by biasing the reaction coordinate. Overall, we conclude that whereas Q is an excellent parameter to analyze the simulations, it is not necessarily a perfect reaction coordinate for enhanced sampling, and better incorporation of other slow degrees of freedom may further improve this reaction coordinate.