A Note on Vestigial Osmotic Pressure.

Recent experiments have indicated that at least a part of the osmotic pressure across the giant unilamellar vesicle (GUV) membrane was balanced by the rapid formation of the monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Therefore, we investigated a possible osmotic role played by these daughter vesicles for the maintenance of osmotic regulation in the GUVs and, by extension, in living cells. We highlighted a mechanism whereby the daughter vesicles acted as osmotically active solutes (osmoticants), contributing an extra vestigial osmotic pressure component across the membrane of the parent vesicle, and we showed that the consequences were consistent with experimental observations. Our results highlight the significance of osmotic regulation in cellular processes, such as fission/fusion, endocytosis, and exocytosis.

Kinetic assays of DNA polymerase fidelity: A theoretical perspective beyond Michaelis-Menten kinetics.

The high fidelity of DNA polymerase (DNAP) is critical for the faithful replication of DNA. There are several quantitative approaches to measure DNAP fidelity. Directly counting the error frequency in the replication products gives the true fidelity but it turns out very hard to implement in practice. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using kinetic theories combined with the measured apparent kinetic rates. However, whether it is equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies using these assays to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. In this paper, we make a comprehensive examination on the theoretical foundation of the two kinetic assays, based on the theory of DNAP fidelity recently proposed by us. Our studies show that while the conventional kinetic assays are generally valid to quantify the discrimination efficiency of DNAP, they are valid to quantify the proofreading efficiency of DNAP only when the kinetic parameters satisfy some constraints which will be given explicitly in this paper. These results may inspire more carefully-designed experiments to quantify DNAP fidelity.

Spontaneous Freezing of Water between 233 and 235 K Is Not Due to Homogeneous Nucleation.

The spontaneous freezing of microdroplets around 233 K has long been regarded as the occurrence of homogeneous ice nucleation. The corresponding temperature has been directly regarded as the homogeneous ice nucleation temperature, which is an intrinsic character of water. However, many recent investigations indicate that the spontaneous freezing may be still induced by surfaces of the water microdroplets or the residual impurities inside. Therefore, it is highly desired to reveal with solid evidence the exact origin of the spontaneous freezing. Here we show with no ambiguity that the spontaneous freezing between 233 and 235 K is actually triggered by the surface of microdroplets, as the nucleation rate is found to be proportional to the surface area of droplets, via systematically investigating the freezing of water droplets with varying sizes under various cooling rates followed by a new approach in data analysis. The conclusion is further consolidated by published experimental data from other groups when using our data analysis approach. This study is critical for understanding the sources of "no-man's land" and features of homogeneous nucleation, as well as studying the structure and properties of deeply supercooled liquid water.

Template-specific fidelity of DNA replication with high-order neighbor effects: A first-passage approach.

DNA replication fidelity is a critical issue in molecular biology. Biochemical experiments have provided key insights on the mechanism of fidelity control by DNA polymerases in the past decades, whereas systematic theoretical studies on this issue began only recently. Because of the underlying difficulties of mathematical treatment, comprehensive surveys on the template-specific replication kinetics are still rare. Here we propose a first-passage approach to address this problem, in particular the positional fidelity, for complicated processes with high-order neighbor effects. Under biologically relevant conditions, we derived approximate analytical expressions of the positional fidelity which show intuitively how some key kinetic pathways are coordinated to guarantee the high fidelity, as well as the high velocity, of the replication processes. It is also shown that the fidelity at any template position is dominantly determined by the nearest-neighbor template sequences, which is consistent with the idea that replication mutations are randomly distributed in the genome.

Behaviors of Glioblastoma Cells in in Vitro Microenvironments.

Glioblastoma (GBM) is the most malignant and highly aggressive brain tumor. In this study, four types of typical GBM cell lines (LN229, SNB19, U87, U251) were cultured in a microfabricated 3-D model to study their in vitro behaviors. The 3-D in vitro model provides hollow micro-chamber arrays containing a natural collagen interface and thus allows the GBM cells to grow in the 3-D chambers. The GBM cells in this model showed specific properties on the aspects of cell morphology, proliferation, migration, and invasion, some of which were rarely observed before. Furthermore, how the cells invaded into the surrounding ECM and the corresponding specific invasion patterns were observed in details, implying that the four types of cells have different features during their development in cancer. This complex in vitro model, if applied to patient derived cells, possesses the potential of becoming a clinically relevant predictive model.

Proofreading of DNA polymerase: a new kinetic model with higher-order terminal effects.

The fidelity of DNA replication by DNA polymerase (DNAP) has long been an important issue in biology. While numerous experiments have revealed details of the molecular structure and working mechanism of DNAP which consists of both a polymerase site and an exonuclease (proofreading) site, there were quite a few theoretical studies on the fidelity issue. The first model which explicitly considered both sites was proposed in the 1970s and the basic idea was widely accepted by later models. However, all these models did not systematically investigate the dominant factor on DNAP fidelity, i.e. the higher-order terminal effects through which the polymerization pathway and the proofreading pathway coordinate to achieve high fidelity. In this paper, we propose a new and comprehensive kinetic model of DNAP based on some recent experimental observations, which includes previous models as special cases. We present a rigorous and unified treatment of the corresponding steady-state kinetic equations of any-order terminal effects, and derive analytical expressions for fidelity in terms of kinetic parameters under bio-relevant conditions. These expressions offer new insights on how the higher-order terminal effects contribute substantially to the fidelity in an order-by-order way, and also show that the polymerization-and-proofreading mechanism is dominated only by very few key parameters. We then apply these results to calculate the fidelity of some real DNAPs, which are in good agreements with previous intuitive estimates given by experimentalists.

A general theory of kinetics and thermodynamics of steady-state copolymerization.

Kinetics of steady-state copolymerization has been investigated since the 1940s. Irreversible terminal and penultimate models were successfully applied to a number of comonomer systems, but failed for systems where depropagation is significant. Although a general mathematical treatment of the terminal model with depropagation was established in the 1980s, a penultimate model and higher-order terminal models with depropagation have not been systematically studied, since depropagation leads to hierarchically-coupled and unclosed kinetic equations which are hard to solve analytically. In this work, we propose a truncation method to solve the steady-state kinetic equations of any-order terminal models with depropagation in a unified way, by reducing them into closed steady-state equations which give the exact solution of the original kinetic equations. Based on the steady-state equations, we also derive a general thermodynamic equality in which the Shannon entropy of the copolymer sequence is explicitly introduced as part of the free energy dissipation of the whole copolymerization system.

Effect of side-chain length on structural and dynamic properties of ionic liquids with hydroxyl cationic tails.

The recent study has revealed that ionic liquids (ILs) with hydroxyl cationic tails are polar liquids without tightly aggregated nonpolar tail domains. Nevertheless, the influence of varying side-chain length on their microscopic structure and dynamics is still unclear. By performing all-atom molecular dynamics simulations for 1-(n-hydroxyalkyl)-3-methylimidazolium nitrate, where n varies from 2 to 12, we found that, with increasing side-chain length, both the nonpolar region and the flexibility of cationic tails increase. The larger nonpolar region pushes both the charged groups (heads and anions) and nonpolar groups (methylene groups on the side chains) to become more organized, while the increasing tail flexibility allows the hydroxyl terminals to retain a relatively uniform distribution. The increase of side-chain length does not apparently alter the polar nature of the ILs with hydroxyl tails, and has little effect on the total number of formed hydrogen bonds, but slows down the dynamics of ILs.

Controlling the morphology of membranes by excess surface charge in cat-anionic fluorinated surfactant mixtures.

The segregation and phase sequence of semifluorinated cat-anionic surfactant membranes at different excess surface charges was investigated by freeze-fracture transmission electron microscope (FF-TEM), X-ray diffraction (XRD), and nuclear magnetic resonance (NMR). The thermal behavior of the membranes was evaluated by conductivity, rheology, and deuterium nuclear magnetic resonance ((2)H NMR). The experimental results show that the cat-anionic fluorinated surfactant mixtures can form faceted vesicles and punctured lamellar phase when there is excess surface charge. The cationic and anionic fluorinated surfactants are stiff in the membranes, like phospholipids in the frozen "crystalline" or "gel" phase. For the system with excess cationic surface charge, the gel-like faceted vesicles and punctured lamellae can transform into smooth-shaped vesicles at 65 °C. However, for the system with no excess charge or with excess anionic surface charge, no phase transformation occurs even at 90 °C. A model was established to demonstrate the mechanism of the formation and transition of the aggregates with different morphologies. The segregation-crystallization mechanism works well with other cosmotropic counterions from the Hofmeister series. The observations provide a better understanding of how to control the membrane morphology of the aqueous solutions of cat-anionic surfactant mixtures.

Master equation approach for a cross-bridge power-stroke model with a finite number of motors.

The cross-bridge power-stroke model has been widely used to describe the motion of large motor assemblies connected to a common rigid filament. In this paper, we go beyond the original velocity-ensemble approach and propose a master equation approach to account for the cooperative motion of a finite number of motors based on the cross-bridge model. By studying the force-velocity relationship for motors with strain-independent detachment rate, we show the convergence of our approach to the velocity-ensemble approach in the limit of large motor numbers. In the case that the detachment rate of motors is strain dependent, based on two assumptions for the strain distribution among motors, we show the occurrence of the bimodal distribution of the number of motors bound to the filament. This provides a new perspective to look at the instability of a multimotor system, which is essential for all the experimentally observed complex motions displayed by a group of motors, such as hysteresis, bidirectional motion, and spontaneous oscillation. By comparing the velocities calculated using the two assumptions with the stochastic simulation, it suggests that the coupling between motors via the common connection to the filament might facilitate the fast movement of filaments at small loading forces.

Concentration and temperature dependences of polyglutamine aggregation by multiscale coarse-graining molecular dynamics simulations.

The solvent-free multiscale coarse-graining model of polyglutamine was employed to study polyglutamine aggregation at different concentrations and temperatures by means of molecular dynamics simulation. The heterogeneity order parameter (HOP) was used to quantify the polyglutamine aggregation. Our simulation results demonstrate that polyglutamine aggregation is sensitive to concentration and temperature changes. In equilibrium states, polyglutamine molecules fluctuate between aggregating tightly and distributing uniformly. The degree of aggregation monotonically increases with decreasing temperature, but the fluctuation of HOP reaches its maximum at an intermediate temperature. With increasing concentration, the distribution of polyglutamines first changes from more uniform to more nonuniform and then changes back to be more uniform, and the HOP has the widest distribution at the turning point. Simulations with different system sizes indicate that the finite-size effect is trivial and do not change the conclusions drawn for the polyglutamine system. In addition, the composition of the potential energies has been analyzed to confirm that the nonbonded interactions dominate the aggregation of polyglutamines. These results can be thermodynamically understood by considering the competition between the system entropy and molecular interactions, and a statistical model based on HOP has been developed to explain the microscopic mechanism of polyglutamine aggregation.

The neck linker of kinesin 1 seems optimally designed to approach the largest stepping velocity: a simulation study of an ideal model.

The neck linker is widely believed to play a critical role in the hand-over-hand walking of conventional kinesin 1. Experiments have shown that change of the neck linker length will significantly change the stepping velocity of the motor. In this paper, we studied this length effect based on a highly simplified chemically powered ratchet model. In this model, we assume that the chemical steps (ATP hydrolysis, ADP and P(i) release, ATP binding, neck linker docking) are fast enough under conditions far from equilibrium and the mechanical steps (detachment, diffusional search and re-attachment of the free head) are rate-limiting in kinesin walking. According to this model, and regarding the neck linker as a worm-like-chain polypeptide, we can calculate the steady state stepping velocity of the motor for different neck linker lengths. Our results show, under the actual values of binding energy between kinesin head and microtubule (~15k(B)T) and the persistence length of neck linker (~0.5 nm), that there is an optimal neck linker length (~14-16 a.a.) corresponding to the maximal velocity, which implies that the length of the wild-type neck linker (~15 a.a.) might be optimally designed for kinesin 1 to approach the largest stepping velocity.

FoF1-ATPase, rotary motor and biosensor.

F(o)F(1)-ATPase is an amazing molecular rotary motor at the nanoscale. Single molecule technologies have contributed much to the understanding of the motor. For example, fluorescence imaging and spectroscopy revealed the physical rotation of isolated F(1) and F(o), or F(o)F(1) holoenzyme. Magnetic tweezers were employed to manipulate the ATP synthesis/hydrolysis in F(1), and proton translation in F(o). Here, we briefly review our recent works including a systematic kinetics study of the holoenzyme, the mechanochemical coupling mechanism, reconstituting the delta-free F(o)F(1)-ATPase, direct observation of F(o) rotation at single molecule level and activity regulation through external links on the stator.

Generalized integral fluctuation theorem for diffusion processes.

Using Feynman-Kac and Cameron-Martin-Girsanov formulas, we find a generalized integral fluctuation theorem (GIFT) for general diffusion processes by constructing a time-invariable integral. The existing integral fluctuation theorems can be derived as its specific cases. We interpret the origin of the GIFT in terms of time reversal of stochastic systems.

Temperature dependence of circular DNA topological states.

Circular double-stranded DNA has different topological states which are defined by their linking numbers. Equilibrium distribution of linking numbers can be obtained by closing a linear DNA into a circle by ligase. Using Monte Carlo simulation, we predict the temperature dependence of the linking number distribution of small circular DNAs. Our predictions are based on flexible defect excitations that resulted from local melting or unstacking of DNA base pairs. We found that the reduced bending rigidity alone can lead to measurable changes of the variance of linking number distribution of short circular DNAs. If the defect is accompanied by local unwinding, the effect becomes much more prominent. The predictions can be easily investigated in experiments, providing a new method to study the micromechanics of sharply bent DNAs and the thermal stability of specific DNA sequences. Furthermore, the predictions are directly applicable to the studies of binding of DNA-distorting proteins that can locally reduce DNA rigidity, form DNA kinks, or introduce local unwinding.

Shear-induced domain deformation in a tilted lipid monolayer: from circle to ellipse and kinked stripe.

The shear-induced domain deformation in a lipid monolayer comprised of tilted molecules is studied as a mechanical balance between surface pressure, line tension, electrostatic energy due to the dipole-dipole interaction, hexatic-elastic stress, and viscous stress. It is found that a simple shear can deform a circular domain into an elliptic shape with the long axis inclined 45 degrees from the shear direction. The "ellipse" is elongated in the long axis as shear rate increases, and evolves to a straight or kinked stripe, which was observed as a "shear band" by Fuller's group [Science 274, 233 (1996)] and "avalanche-like fronts" by Schwaltz's group [Langmuir 17, 3017 (2001)], at a threshold shear rate. The propagation of stripe-shaped domains is discussed in the context of electrostatic energy. The dependence of the threshold shear rate on surface pressure is predicted in good agreement with observation and can be used to estimate surface viscosity. The shear-induced domain deformation is maintained by the effect of the lattice elastic stress when shear ceases.

Bayesian analysis of folding and unfolding time series of single-forced RNAs.

On the basis of a coarse-grain physical model of the folding and unfolding of single-forced RNAs conducted in light tweezer experiments, we theoretically investigate the feasibility of inferring the RNA's intrinsic kinetic parameters from the noisy time series of the molecule's extension. A Bayesian approach using Monte Carlo Markov Chain is proposed. We prove that this statistical approach is efficient and accurate in inferring the molecule's physical parameters, even if the experimental data are yielded under a narrow range of forces.

Two-pathway four-state kinetic model of thioredoxin-catalyzed reduction of single forced disulfide bonds.

Recent single-molecule experiments found that the thioredoxin-catalyzed reduction of individual disulfide bonds placed under a stretching mechanical force has distinct characteristics: the reduction rate of human thioredoxin monotonically decreases with the force, while the rate of E. coli thioredoxin first decreases and then increases as the force goes beyond a certain threshold. In this work, we present a force-dependent two-pathway four-state model to uniformly quantify these intriguing observations. Although our model is indistinguishable from the previous two-pathway three-state model in predicting the mean reduction rate, the distributions of dwell times of the two models are significantly distinctive. The very recent experiment favors our model.

Reversible transitions between peptide nanotubes and vesicle-like structures including theoretical modeling studies.

Peptide-based self-assembling systems are increasingly attractive because of their wide range of applications in different fields. Peptide nanostructures are flexible with changes in the ambient conditions. Herein, a reversible shape transition between self-assembled dipeptide nanotubes (DPNTs) and vesicle-like structures is observed upon a change in the peptide concentration. SEM, TEM, AFM, and CD spectroscopy were used to follow this transition process. We show that dilution of a peptide-nanotube dispersion solution results in the formation of vesicle-like structures, which can then be reassembled into the nanotubes by concentrating the solution. A theoretical model describing this shape-transition phenomenon is presented to propose ways to engineer assembling molecules in order to devise other systems in which the morphology can be tuned on demand.

A kinetic model of transcription initiation by RNA polymerase.

We establish a sequence-dependent kinetic model for the later stage of transcription initiation by RNA polymerase. We suggest that there are three reaction pathways, the abortive pathway, the scrunching pathway and the escape pathway, competitive with each other at each site during the transcription initiation. Using this three-pathway model, we mainly calculate the maximum sizes of the abortive transcripts, the abortive probabilities and the abortive/productive ratios for different promoters by Monte Carlo simulation and analytical methods. These results are quantitatively comparable with the experimental observations. In particular, our model can account for the unproductive initial transcribing complex and the nucleoside triphosphate concentration dependence of the transcription initiation, which have been found in the experiments and were hardly understood by the previous two-pathway kinetic competition model.