Calculating Single-Channel Permeability and Conductance from Transition Paths

Permeability 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

Calculating transition rates from durations of transition paths

Calculating 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

Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts

Spontaneous 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

Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter

Protein 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

Drying Transition in the Hydrophobic Gate of the GLIC Channel Blocks Ion Conduction

AbstractThe theoretical prediction of water drying transitions near nonpolar surfaces has stimulated an intensive search for biological processes exploiting this extreme form of hydrophobicity. Here we quantitatively demonstrate that drying of a hydrophobic constriction is the major determinant of ion conductance in the GLIC pentameric ion channel. Molecular-dynamics simulations show that in the closed state, the channel conductance is ∼12 orders-of-magnitude lower than in the open state. This large drop in conductance is remarkable because even in the functionally closed conformation the pore constriction remains wide enough for the passage of sodium ions, aided by a continuous bridge of ∼12 water molecules. However, we find that the free energy cost of hydrating the hydrophobic gate is large, accounting almost entirely for the energetic barrier blocking ion passage. The free energies of transferring a sodium ion into a prehydrated gate in functionally closed and open states differ by only 1.2 kcal/mol, compared to an 11 kcal/mol difference in the costs of hydrating the hydrophobic gate. Conversely, ion desolvation effects play only minor roles in GLIC ion channel gating. Our simulations help rationalize experiments probing the gating kinetics of the nicotinic acetylcholine receptor in response to mutations of pore-lining residues. The molecular character and phase behavior of water should thus be included in quantitative descriptions of ion channel gating

Parameter Optimization for Interaction between C-Terminal Domains of HIV-1 Capsid Protein

HIV-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

Kinetic mechanism for water in vibrating carbon nanotubes

Recent 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

milliFlow: Scene Flow Estimation on mmWave Radar Point Cloud for Human Motion Sensing

Approaching the era of ubiquitous computing, human motion sensing plays a crucial role in smart systems for decision making, user interaction, and personalized services. Extensive research has been conducted on human tracking, pose estimation, gesture recognition, and activity recognition, which are predominantly based on cameras in traditional methods. However, the intrusive nature of cameras limits their use in smart home applications. To address this, mmWave radars have gained popularity due to their privacy-friendly features. In this work, we propose \textit{milliFlow}, a novel deep learning method for scene flow estimation as a complementary motion information for mmWave point cloud, serving as an intermediate level of features and directly benefiting downstream human motion sensing tasks. Experimental results demonstrate the superior performance of our method with an average 3D endpoint error of 4.6cm, significantly surpassing the competing approaches. Furthermore, by incorporating scene flow information, we achieve remarkable improvements in human activity recognition, human parsing, and human body part tracking. To foster further research in this area, we provide our codebase and dataset for open access.Comment: 15 pages, 8 figure

RaTrack: Moving Object Detection and Tracking with 4D Radar Point Cloud

Mobile autonomy relies on the precise perception of dynamic environments. Robustly tracking moving objects in 3D world thus plays a pivotal role for applications like trajectory prediction, obstacle avoidance, and path planning. While most current methods utilize LiDARs or cameras for Multiple Object Tracking (MOT), the capabilities of 4D imaging radars remain largely unexplored. Recognizing the challenges posed by radar noise and point sparsity in 4D radar data, we introduce RaTrack, an innovative solution tailored for radar-based tracking. Bypassing the typical reliance on specific object types and 3D bounding boxes, our method focuses on motion segmentation and clustering, enriched by a motion estimation module. Evaluated on the View-of-Delft dataset, RaTrack showcases superior tracking precision of moving objects, largely surpassing the performance of the state of the art. We release our code and model at https://github.com/LJacksonPan/RaTrack.Comment: Accepted to ICRA 2024. 8 pages, 4 figures. Co-first authorship for Zhijun Pan, Fangqiang Ding and Hantao Zhong, listed randomly. See demo vide at: https://www.youtube.com/watch?v=_uSpbxOlLG