The biexponential distributions of open times are observed in various types of ion channels. In this paper, by discussing a simple channel model, we show that there are two different schemes to understand the biexponential distribution of open times. One scheme is mathematically strict based on generator matrix theory, while the other one has a clear physical explanation according to an approximation process with numerical simulation of Markovian channel dynamics. Our comparison results suggest that even for biologically complex channels, in addition to carrying out a stochastic simulation, the strict theoretical analysis should be considered to understand the multiple exponential distributions of open times.

Nanostructures self-assembled by cross-β peptides with ordered structures and advantageous mechanical properties have many potential applications in biomaterials and nanotechnologies. Quantifying the intra-and inter-molecular driving forces for peptide self-assembly at the atomistic level is essential for understanding the formation mechanism and nanomechanics of various morphologies of self-assembled peptides. We investigate the thermodynamics of the intra-and inter-sheet structure formations in the self-assembly process of cross-β peptide KⅢIK by means of steered molecular dynamics simulation combined with umbrella sampling. It is found that the mechanical properties of the intra-and inter-sheet structures are highly anisotropic with their intermolecular bond stiffness at the temperature of 300 K being 5.58 N/m and 0.32 N/m, respectively. This mechanical anisotropy comes from the fact that the intra-sheet structure is stabilized by enthalpy but the inter-sheet structure is stabilized by entropy. Moreover, the formation process of KⅢIK intra-sheet structure is cooperatively driven by the van der Waals (VDW) interaction between the hydrophobic side chains and the electrostatic interaction between the hydrophilic backbones, but that of the inter-sheet structure is primarily driven by the VDW interaction between the hydrophobic side chains. Although only peptide KⅢIK is studied, the qualitative conclusions on the formation mechanism should also apply to other cross-β peptides.

Cyclin-dependent kinases (CDKs) are critical to the cell cycle and many other biological processes, and as such, are considered as one of the promising targets for therapy against cancer and other diseases. Most pan-CDK inhibitors bind to the highly conserved catalytic ATP-binding pocket and therefore lack the specificity to prevent side effects. It is desirable to develop drugs targeting non-catalytic pockets for specificity towards individual CDKs. Here we performed a systematic analysis of non-catalytic pockets on CDKs and identified a region underneath the T-loop, which we term TL pocket, for potential inhibitor development. Specifically, we compared the TL pockets of human CDK2 and CDK7-homolog Pfmrk of Plasmodium falciparum, a malaria-causing parasite. Molecular dynamics simulations of several short peptides revealed that this less conserved TL pocket could be used to design potentially specific inhibitors against malaria disease.

We present an extended analytical model including the depletion effect and the dimension of ligand-receptor complex, aiming to elucidate their influences on endocytosis of spherocylindrical nanoparticles (NPs). It is found that the dimension of ligand-receptor complex (δ) and the depletion effect interrelatedly govern the optimal conditions of NP endocytosis. The endocytosis phase diagram constructed in the space of NP radius and relative aspect ratio indicates that the endocytosis of NP is enhanced evidently by reducing the optimal radius and the threshold radius of endocytosed NP. Meanwhile, through thermodynamic and kinetic analysis of the diffusion of receptors, the dependence of diffusion length on depletion effect and the dimension of ligand-receptor complex can be identified in great detail. For small aspect ratio, diffusion length decreases with increasing concentration c of small bioparticles in cellular environment. Endocytosis speed corresponding to large radius R and high concentration c of small bioparticles strongly depends on the increasing (2r-δ). These results may show some highlights into the conscious design of NPs for diagnostic agents and therapeutic drug delivery applications.

Cell migration plays an essential role in a wide variety of physiological and pathological processes. In this paper we numerically discuss the properties of an anisotropic persistent random walk (APRW) model, in which two different and independent persistent times are assumed for cell migrations in the x-and y-axis directions. An intrinsic orthogonal coordinates with the primary and non-primary directions can be defined for each migration trajectory based on the singular vector decomposition method. Our simulation results show that the decay time of single exponential distribution of velocity auto-correlation function (VACF) in the primary direction is actually the large persistent time of the APRW model, and the small decay time of double exponential VACF in the non-primary direction equals the small persistent time of the APRW model. Thus, we propose that the two persistent times of anisotropic migration of cells can be properly estimated by discussing the VACFs of trajectory projected to the primary and non-primary directions.

Research on protein-membrane interactions has been undeveloped due to the lack of proper techniques to detect the position of proteins at membranes because membranes are usually only about 4-nm thick. We have recently developed a new method named surface-induced fluorescence attenuation (SIFA) to track both vertical and lateral kinetics of a single labelling dye in supported lipid bilayers. It takes advantage of strong interaction between a light-emitting dye and a partially reflecting surface. By applying the technique to membrane proteins being fluorescently labelled at different residues, here we show that SIFA can measure not only the insertion depth of a dye inside a lipid bilayer, but also the position of a dye in solution near the surface. SIFA can therefore be used to study membrane proteins of various types.

The tumor suppressor p53 mediates the cellular response to various stresses. It was experimentally shown that the concentration of p53 can show oscillations with short or long periods upon DNA damage. The underlying mechanism for this phenomenon is still not fully understood. Here, we construct a network model comprising the ATM-p53-Wip1 and p53-Mdm2 negative feedback loops and ATM autoactivation. We recapitulate the typical features of p53 oscillations including p53 birhythmicity. We show the dependence of p53 birhythmicity on various factors such as the phosphorylation status of ATM. We also perform stochastic simulation and find the noise-induced transitions between two modes of p53 oscillation, which increases the p53 variability in both the amplitude and period. These results suggest that p53 birhythmicity enhances the responsiveness of p53 network, which may facilitate its tumor suppressive function.

Nucleic acids are negatively charged biomolecules, and metal ions in solutions are important to their folding structures and thermodynamics, especially multivalent ions. However, it has been suggested that the binding of multivalent ions to nucleic acids cannot be quantitatively described by the well-established Poisson-Boltzmann (PB) theory. In this work, we made extensive calculations of ion distributions around various RNA-like macroions in divalent and trivalent salt solutions by PB theory and Monte Carlo (MC) simulations. Our calculations show that PB theory appears to underestimate multivalent ion distributions around RNA-like macroions while can reliably predict monovalent ion distributions. Our extensive comparisons between PB theory and MC simulations indicate that when an RNA-like macroion gets ion neutralization beyond a “critical” value, the multivalent ion distribution around that macroion can be approximately described by PB theory. Furthermore, an empirical formula was obtained to approximately quantify the critical ion neutralization for various RNA-like macroions in multivalent salt solutions, and this empirical formula was shown to work well for various real nucleic acids including RNAs and DNAs.

To extract the dynamic parameters from single molecule manipulation experiments, usually lots of data at different forces need to be recorded. But the measuring time of a single molecule is limited due to breakage of the tether or degradation of the molecule. Here we propose a data analysis method based on probability maximization of the recorded time trace to extract the dynamic parameters from a single measurement. The feasibility of this method was verified by dealing with the simulation data of a two-state system. We also applied this method to estimate the parameters of DNA hairpin folding and unfolding dynamics measured by a magnetic tweezers experiment.

An understanding of protein folding/unfolding processes has important implications for all biological processes, including protein degradation, protein translocation, aging, and diseases. All-atom molecular dynamics (MD) simulations are uniquely suitable for it because of their atomic level resolution and accuracy. However, limited by computational capabilities, nowadays even for small and fast-folding proteins, all-atom MD simulations of protein folding still presents a great challenge. An alternative way is to study unfolding process using MD simulations at high temperature. High temperature provides more energy to overcome energetic barriers to unfolding, and information obtained from studying unfolding can shed light on the mechanism of folding. In the present study, a 1000-ns MD simulation at high temperature (500 K) was performed to investigate the unfolding process of a small protein, chicken villin headpiece (HP-35). To infer the folding mechanism, a Markov state model was also built from our simulation, which maps out six macrostates during the folding/unfolding process as well as critical transitions between them, revealing the folding mechanism unambiguously.

Capillary filling in small length scale is an important process in nanotechnology and microfabrication. When one end of the tube or channel is sealed, it is important to consider the escape of the trapped gas. We develop a dynamic model on capillary filling in closed-end tubes, based on the diffusion-convection equation and Henry's law of gas dissolution. We systematically investigate the filling dynamics for various sets of parameters, and compare the results with a previous model which assumes a linear density profile of dissolved gas and neglect the convective term.

The radiation damage of adenine base was studied by B3LYP and MP2 methods in the presence of hydroxyl radicals to probe the reactivities of five possible sites of an isolated adenine molecule. Both methods predict that the C8 site is the more vulnerable than the other sites. For its bonding covalently with the hydroxyl radicals, B3LYP predicts a barrierless pathway, while MP2 finds a transition state with an energy of 106.1 kJ/mol. For the hydroxylation at the C2 site, the barrier was calculated to be 165.3 kJ/mol using MP2 method. For the dehydrogenation reactions at five sites of adenine, B3LYP method predicts that the free energy barrier decreases in the order of H8 > H2 > HN62 > HN61 > HN9.

In the present study, a fast chemical shift imaging (CSI) method has been used to dynamically monitor the formation of oil-water emulsions and the phase separation process of the emulsion phase from the excessive water or oil phase on the molecular level. With signals sampled from series of small voxels simultaneously within a few seconds, high-resolution one-dimensional (1D) ¹H nuclear magnetic resonance (NMR) spectra from different spatial positions for inhomogeneous emulsion systems induced by susceptibility differences among components can be obtained independently. On the basis of integrals from these ¹H NMR spectra, profiles obtained explicitly demonstrate the spatial and temporal variations of oil concentrations. Furthermore, the phase separation time and the length of the oil-water emulsion phase are determined. In addition, effects of oil types and proportions of the emulsifier on the emulsification states are also inspected. Experimental results indicate that 1D PHASICS (Partial Homogeneity Assisted Inhomogeneity Correction Spectroscopy) provides a helpful and promising alternative to research on dynamic processes or chemical reactions.

Docking of the kinesin's neck linker (NL) to the motor domain is the key force-generation process of the kinesin. In this process, NL's β 10 portion forms four backbone hydrogen bonds (HBs) with the motor domain. These backbone hydrogen bonds show big differences in their effective strength. The origins of these strength differences are still unclear. Using molecular dynamics method, we investigate the stability of the backbone HBs in explicit water environment. We find that the strength differences of these backbone HBs mainly arise from their relationships with water molecules which are controlled by arranging the surrounding residue sidechains. The arrangement of the residues in the C-terminal part of β 10 results in the existence of the water-attack channels around the backbone HBs in this region. Along these channels the water molecules can directly attack the backbone HBs and make these HBs relatively weak. In contrast, the backbone HB at the N-terminus of β 10 is protected by the surrounding hydrophobic and hydrophilic residues which cooperate positively with the central backbone HB and make this HB highly strong. The intimate relationship between the effective strength of protein backbone HB and water revealed here should be considered when performing mechanical analysis for protein conformational changes.

Cell migrations in the cell cultures are found to follow non-Gaussian statistics. We recorded long-term cell migration patterns with more than six hundred cells located in 28 mm². Our experimental data support the claim that an individual cell migration follows Gaussian statistics. Because the cell culture is inhomogeneous, the statistics of the cell culture exhibit a non-Gaussian distribution. We find that the normalized histogram of the diffusion velocity follows an exponential tail. A simple model is proposed based on the diffusional inhomogeneity to explain the exponential distribution of locomotion activity in this work. Using numerical calculation, we prove that our model is in great agreement with the experimental data.

Feed-forward gene transcriptional regulatory networks, as a set of common signal motifs, are widely distributed in the biological systems. In this paper, the noise characteristics and propagation mechanism of various feed-forward gene transcriptional regulatory loops are investigated, including (i) coherent feed-forward loops with AND-gate, (ii) coherent feed-forward loops with OR-gate logic, and (iii) incoherent feed-forward loops with AND-gate logic. By introducing logarithmic gain coefficient and using linear noise approximation, the theoretical formulas of noise decomposition are derived and the theoretical results are verified by Gillespie simulation. From the theoretical and numerical results of noise decomposition algorithm, three general characteristics about noise transmission in these different kinds of feed-forward loops are observed. i) The two-step noise propagation of upstream factor is negative in the incoherent feed-forward loops with AND-gate logic, that is, upstream factor can indirectly suppress the noise of downstream factors. ii) The one-step propagation noise of upstream factor is non-monotonic in the coherent feed-forward loops with OR-gate logic. iii) When the branch of the feed-forward loop is negatively controlled, the total noise of the downstream factor monotonically increases for each of all feed-forward loops. These findings are robust to variations of model parameters. These observations reveal the universal rules of noise propagation in the feed-forward loops, and may contribute to our understanding of design principle of gene circuits.

Knowledge-based scoring functions have been widely used for protein structure prediction, protein-small molecule, and protein-nucleic acid interactions, in which one critical step is to find an appropriate representation of protein structures. A key issue is to determine the minimal protein representations, which is important not only for developing of scoring functions but also for understanding the physics of protein folding. Despite significant progresses in simplifying residues into alphabets, few studies have been done to address the optimal number of atom types for proteins. Here, we have investigated the atom typing issue by classifying the 167 heavy atoms of proteins through 11 schemes with 1 to 20 atom types based on their physicochemical and functional environments. For each atom typing scheme, a statistical mechanics-based iterative method was used to extract atomic distance-dependent potentials from protein structures. The atomic distance-dependent pair potentials for different schemes were illustrated by several typical atom pairs with different physicochemical properties. The derived potentials were also evaluated on a high-resolution test set of 148 diverse proteins for native structure recognition. It was found that there was a crossover around the scheme of four atom types in terms of the success rate as a function of the number of atom types, which means that four atom types may be used when investigating the basic folding mechanism of proteins. However, it was revealed by a close examination of typical potentials that 14 atom types were needed to describe the protein interactions at atomic level. The present study will be beneficial for the development of protein related scoring functions and the understanding of folding mechanisms.

A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness h_f is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca^2/3 is found.