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In living cells, intrinsically disordered proteins (IDPs), such as FUS and DDX4, undergo phase separation, forming biomolecular condensates. Using molecular dynamics simulations, we investigate their behavior in their respective homogenous droplets. We find that the proteins exhibit transient subdiffusion due to the viscoelastic nature and confinement effects in the droplets. The conformation and the instantaneous diffusivity of the proteins significantly vary between the interior and the interface of the droplet, resulting in non-Gaussianity in the displacement distributions. This study highlights key aspects of IDP behavior in biomolecular condensates.

Dimensions and molecular structure play pivotal roles in the principle of heat conduction. The dimensional characteristics of solution within nanoscale systems depend on the degrees of confinement. However, the influence of such variations on heat transfer remains inadequately understood. Here, we perform quasi-one-dimensional non-equilibrium molecular dynamics simulations to calculate the thermal conductivity of water molecules confined in carbon nanotubes. The structure of water molecules is determined depending on the nanotube radius, forming a single-file, a single-layer, and a double-layer structure, corresponding to an increasing radius order. We reveal that the thermal conductivity of liquid water has a sublinear dependency on nanotube length exclusively when water molecules form a single file. Stronger confinement leads to behavioral and structural characteristics closely resembling a one-dimensional nature. Moreover, single-layer-structured water molecules exhibit enhanced thermal conductivity. We elucidate that this is due to the increase in the local water density and the absence of transitions to another layer, which typically occurs in systems with double-layer water structures within relatively large radius nanotubes.

Aquaporins (AQPs) are recognized as transmembrane water channels that facilitate selective water permeation through their monomeric pores. Among the AQP family, AQP6 has a unique characteristic as an anion channel, which is allosterically controlled by pH conditions and is eliminated by a single amino acid mutation. However, the molecular mechanism of anion permeation through AQP6 remains unclear. Using molecular dynamics simulations in the presence of a transmembrane voltage utilizing an ion concentration gradient, we show that chloride ions permeate through the pore corresponding to the central axis of the AQP6 homotetramer. Under low pH conditions, a subtle opening of the hydrophobic selective filter (SF), located near the extracellular part of the central pore, becomes wetted and enables anion permeation. Our simulations also indicate that a single mutation (N63G) in human AQP6, located at the central pore, significantly reduces anion conduction, consistent with experimental data. Moreover, we demonstrate the pH-sensing mechanism in which the protonation of H184 and H189 under low pH conditions allosterically triggers the gating of the SF region. These results suggest a unique pH-dependent allosteric anion permeation mechanism in AQP6 and could clarify the role of the central pore in some of the AQP tetramers.

Complex systems such as protein conformational fluctuations and supercooled liquids exhibit a long relaxation time and are considered to posses multiple relaxation times. We analytically obtain the exact correlation function for stochastic processes with multiple relaxation times. We show that the time-averaged correlation function calculated by a trajectory whose length is shorter than the longest relaxation time exhibits an apparent aging behavior. We propose a method to extract relaxation times from a single trajectory. This method successfully extracts relaxation times of a stochastic process with multiple states when a state can be characterized by the values of the trajectory. As an application of this method, we estimate several relaxation times smaller than the longest relaxation time in conformational fluctuations of a small protein., Comment: 10 pages, 4 figures

Cell membranes phase separate into ordered ${\rm L_o}$ and disordered ${\rm L_d}$ domains depending on their compositions. This membrane compartmentalization is heterogeneous and regulates the localization of specific proteins related to cell signaling and trafficking. However, it is unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in ${\rm L_o}$ and ${\rm L_d}$ domains. Here, using Langevin dynamics simulations coupled with the phase-field (LDPF) method, we investigate several tens of milliseconds-scale diffusion and localization of proteins in heterogeneous biological membrane models showing phase separation into ${\rm L_o}$ and ${\rm L_d}$ domains. The diffusivity of proteins exhibits temporal fluctuations depending on the field composition. Increases in molecular concentrations and domain preference of the molecule induce subdiffusive behavior due to molecular collisions by crowding and confinement effects, respectively. Moreover, we quantitatively demonstrate that the protein partitioning into the ${\rm L_o}$ domain is determined by the difference in molecular diffusivity between domains, molecular preference of domain, and molecular concentration. These results pave the way for understanding how biological reactions caused by molecular partitioning may be controlled in heterogeneous media. Moreover, the methodology proposed here is applicable not only to biological membrane systems but also to the study of diffusion and localization phenomena of molecules in various heterogeneous systems.

We propose a water pump that actively transports water molecules through nanochannels. Spatially asymmetric thermal fluctuations imposed on the channel radius cause unidirectional water flow without osmotic pressure, which can be attributed to hysteresis in the cyclic transition between the wetting/drying states. We show that the water transport depends on fluctuations, such as white, Brownian, and pink noises. Because of the high-frequency components in white noise, fast switching of open and close states inhibits channel wetting. Conversely, pink and Brownian noises generate high-pass filtered net flow. Brownian fluctuation leads to a faster water transport rate, whereas pink noise has a higher capability to overcome osmotic pressure in the opposite direction. A trade-off relationship exists between the resonant frequency of the fluctuation and the flow amplification. The proposed pump can be considered as an analogy for the reversed Carnot cycle, which is the upper limit on the energy conversion efficiency.

Prediction of protein-ligand binding affinity is a major goal in drug discovery. Generally, free energy gap is calculated between two states (e.g., ligand binding and unbinding). The energy gap implicitly includes the effects of changes in protein dynamics induced by the binding ligand. However, the relationship between protein dynamics and binding affinity remains unclear. Here, we propose a novel method that represents protein behavioral change upon ligand binding with a simple feature that can be used to predict protein-ligand affinity. From unbiased molecular simulation data, an unsupervised deep learning method measures the differences in protein dynamics at a ligand-binding site depending on the bound ligands. A dimension-reduction method extracts a dynamic feature that is strongly correlated to the binding affinities. Moreover, the residues that play important roles in protein-ligand interactions are specified based on their contribution to the differences. These results indicate the potential for dynamics-based drug discovery.

Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity $D_I$. We find that the radius of gyration $R_g$ of the proteins exhibits $1/f$ fluctuations, that are synchronous with the fluctuations of $D_I$. Our analysis demonstrates the validity of the local Stokes-Einstein type relation $D_I\propto1/(R_g + R_0)$, where $R_0\sim0.3$ nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations the validity of the Stokes-Einstein type relation appears to be a general property.

Decision making based on behavioral and neural observations of living systems has been extensively studied in brain science, psychology, and other disciplines. Decision-making mechanisms have also been experimentally implemented in physical processes, such as single photons and chaotic lasers. The findings of these experiments suggest that there is a certain common basis in describing decision making, regardless of its physical realizations. In this study, we propose a local reservoir model to account for choice-based learning (CBL). CBL describes decision consistency as a phenomenon where making a certain decision increases the possibility of making that same decision again later, which has been intensively investigated in neuroscience, psychology, etc. Our proposed model is inspired by the viewpoint that a decision is affected by its local environment, which is referred to as a local reservoir. If the size of the local reservoir is large enough, consecutive decision making will not be affected by previous decisions, thus showing lower degrees of decision consistency in CBL. In contrast, if the size of the local reservoir decreases, a biased distribution occurs within it, which leads to higher degrees of decision consistency in CBL. In this study, an analytical approach on local reservoirs is presented, as well as several numerical demonstrations. Furthermore, a physical architecture for CBL based on single photons is discussed, and the effects of local reservoirs is numerically demonstrated. Decision consistency in human decision-making tasks and in recruiting empirical data are evaluated based on local reservoir. In summary, the proposed local reservoir model paves a path toward establishing a foundation for computational mechanisms and the systematic analysis of decision making on different levels.

In heterogeneous environments, the diffusivity is not constant but changes with time. It is important to detect changes in the diffusivity from single-particle-tracking trajectories in experiments. Here, we devise a novel method for detecting the transition times of the diffusivity from trajectory data. A key idea of this method is the introduction of a characteristic time scale of the diffusive states, which is obtained by a fluctuation analysis of the time-averaged mean square displacements. We test our method in silico by using the Langevin equation with a fluctuating diffusivity. We show that our method can successfully detect the transition times of diffusive states and obtain the diffusion coefficient as a function of time. This method will provide a quantitative description of the fluctuating diffusivity in heterogeneous environments and can be applied to time series with transitions of states., Comment: 11 pages, 4 figures

Local diffusion coefficients in disordered systems such as spin glass systems and living cells are highly heterogeneous and may change over time. Such a time-dependent and spatially heterogeneous environment results in irreproducibility of single-particle-tracking measurements. Irreproducibility of time-averaged observables has been theoretically studied in the context of weak ergodicity breaking in stochastic processes. Here, we provide rigorous descriptions of equilibrium and non-equilibrium diffusion processes for the annealed transit time model, which is a heterogeneous diffusion model in living cells. We give analytical solutions for the mean square displacement (MSD) and the relative standard deviation of the time-averaged MSD for equilibrium and non-equilibrium situations. We find that the time-averaged MSD grows linearly with time and that the diffusion coefficients are intrinsically random in non-equilibrium situations. Our findings pave the way for a theoretical understanding of distributional behavior of the diffusion coefficients in disordered systems., Comment: 13 pages, 5 figures

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a non-equilibrium ensemble, the ensemble-averaged mean square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time, and converges to a Gaussian distribution in a long time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion, and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterize the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized, and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool., Comment: 23 pages, 10 figures

We consider Langevin equation with dichotomously fluctuating diffusivity, where the diffusion coefficient changes dichotomously in time, in order to study fluctuations of time-averaged observables in temporary heterogeneous diffusion process. We find that occupation time statistics is a powerful tool for calculating the time-averaged mean square displacement in the model. We show that the time-averaged diffusion coefficients are intrinsically random when the mean sojourn time for one of the states diverges. Our model provides anomalous fluctuations of time-averaged diffusivity, which have relevance to large fluctuations of the diffusion coefficient in single-particle-tracking experiments., Comment: 6 pages, 3 figures

Water molecules on lipid membrane surfaces are known to contribute to membrane stability by connecting lipid molecules and acting as a water bridge. Although the number of water molecules near the membrane fluctuates dynamically, the hydration dynamics has been veiled. Here we investigate residence statistics of water molecules on the surface of a lipid membrane using all-atom molecular dynamics simulations. We show that hydration dynamics on the lipid membrane exhibit $1/f^\beta$ noise with two different power-law exponents, $\beta_l < 1$ and $\beta_h > 1$. By constructing a dichotomous process for the hydration dynamics, we find that the process can be regarded as a non-Markov renewal process. The result implies that the origin of the $1/f$ noise transition in hydration dynamics on the membrane surface is a combination of a power-law distribution with cutoff of interoccurrence times of switching events and a long-term correlation between the interoccurrence times., Comment: 5 pages, 4 figures

Water molecules play an important role in providing unique environments for biological reactions on cell membranes. It is widely believed that water molecules form bridges that connect lipid molecules and stabilize cell membranes. Using all-atom molecular dynamics simulations, we show that translational and rotational diffusion of water molecules on lipid membrane surfaces exhibit subdiffusion. Moreover, we provide evidence that both divergent mean trapping time (continuous-time random walk) and long-correlated noise (fractional Brownian motion) contribute to this subdiffusion. These results suggest that subdiffusion on cell membranes causes the water retardation, an enhancement of cell membrane stability, and a higher reaction efficiency., Comment: 6 pages, 4 figures