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Yunxin Zhang

Publications and source records attributed to Yunxin Zhang.

At least 37 records · Page 2Linked to original sources
arXiv2021

Biochemical pathways of forward/backward steps of motor protein kinesin-1

Kinesin-1 is an ATP-driven, two-headed motor protein that transports intracellular cargoes along microtubule. Based on recent experimental observations, we formulate a mechanochemical model for it, in which forward/backward/futile cycle of kinesin-1 can be realized through multiple biochemical pathways. Our results show that both forward and futile cycles consist of two biochemical pathways, while backward cycle may be realized through six possible pathways. Backward motion of kinesin-1 is mainly through backward sliding along microtubule when it is in semi-detach state, and usually coupled with ATP hydrolysis. Under low external load, about 80\% of ATP is wasted by kinesin-1, and this proportion of waste is almost independent of ATP concentration. At high ATP concentration or under high external load, both heads of kinesin are always in ATP or ADP$\cdot$Pi binding state and bind to microtubule tightly. But at low ATP concentration and low load, kinesin mainly stays at the one head bound state. In contrast to mean run length, the mean run time of kinesin-1 along microtubule decreases with ATP concentration. Unless external load is near the stall force, the motion of kinesin-1 is almost deterministic, not as predicted by usual Browian ratchet models.

physics.bio-ph↗
arXiv2021

Entropy production related properties of first passage process

With nontrivial entropy production, first passage process is one of the most common nonequilibrium process in stochastic thermodynamics. Using one dimensional birth and death precess as a model framework, approximated expressions of mean first passage time (FPT), mean total number of jumps (TNJ), and their coefficients of variation (CV), are obtained for the case far from equilibrium. Consequently, uncertainty relations for FPT and TNJ are presented. Generally, mean FPT decreases exponentially with entropy production, while mean TNJ decreases exponentially first and then tends to a starting site dependent limit. For forward biased process, the CV of TNJ decreases exponentially with entropy production, while that of FPT decreases exponentially first and then tends to a starting site dependent limit. For backward biased process, both CVs of FPT and TNJ tend to one for large absolute values of entropy production. Related properties about the case of equilibrium are also addressed briefly for comparison.

cond-mat.stat-mech↗
arXiv2020

Motility and Energetics of Randomly Flashing Ratchets

We consider a randomly flashing ratchet, where the potential acting can be switched to another at random. Using coupled Fokker-Planck equations, we formulate the expressions of quantities measuring dynamics and thermodynamics. Extended numerical calculations present how the potential landscapes and the transitions affect the motility and energetics. Load-dependent velocity and energetic efficiency of motor proteins, kinesin and dynein, further exemplify the randomly flashing ratchet model. We also discuss the system with two shifted sawtooth potentials.

cond-mat.stat-mech↗
arXiv2020

Optimization of a class of heat engines with explicit solution

A specific class of stochastic heat engines driven cyclically by time-dependent potential, which is defined in the half-line ($0<x<+\infty$), is analysed. For such engines, most of their physical quantities can be obtained explicitly, including the entropy and internal energy of the heat engine, as well as output work (power) and heat exchange with the environment during a finite time interval. The optimisation method based on the external potential to reduce {\it irreversible} work and increase energy efficiency is presented. With this optimised potential, efficiency $η^*$ and its particular value at maximum power $η^*_{\rm EMP}$ are calculated and discussed briefly.

cond-mat.stat-mech↗
arXiv2020

Optimization of stochastic thermodynamic machines

The study of stochastic thermodynamic machines is one of the main topics in nonequilibrium thermodynamics. In this study, within the framework of Fokker-Planck equation, and using the method of characteristics of partial differential equation as well as the variational method, performance of stochastic thermodynamic machines is optimized according to the external potential, with the irreversible work $W_{irr}$, or the total entropy production $ΔS_{\rm tot}$ equivalently, reaching its lower bound. Properties of the optimal thermodynamic machines are discussed, with explicit expressions of upper bounds of work output $W$, power $P$, and energy efficiency $η$ are presented. To illustrate the results obtained, typical examples with optimal protocols (external potentials) are also presented.

cond-mat.stat-mech↗
arXiv2020

Work needed to drive a thermodynamic system between two distributions

In this study, the minimum amount of work needed to drive a thermodynamic system from one initial distribution to another in a given time duration is discussed. Equivalently, for given amount of work, the minimum time duration required to complete such a transition is obtained. Results show that the minimum amount of work is used to achieve the following three objectives, to increase the internal energy of the system, to decrease the system entropy, to change the mean position of the system, and with other nonzero part dissipated into environment. To illustrate the results, an example with explicit solutions is presented.

cond-mat.stat-mech↗
arXiv2019

Comment on "Fluctuation Theorem Uncertainty Relation" and "Thermodynamic Uncertainty Relations from Exchange Fluctuation Theorems"

In recent letter [Phys.~Rev.~Lett {\bf 123}, 110602 (2019)], Y.~Hasegawa and T.~V.~Vu derived a thermodynamic uncertainty relation. But the bound of their relation is loose. In this comment, through minor changes, an improved bound is obtained. This improved bound is the same as the one obtained in [Phys.~Rev.~Lett {\bf 123}, 090604 (2019)] by A.~M.~Timpanaro {\it et. al.}, but the derivation here is straightforward.

cond-mat.stat-mech↗
arXiv2019

Mean velocity and effective diffusion constant for translocation of biopolymer chains across membrane

Chaperone-assisted translocation through a nanopore embedded in membrane holds a prominent role in the transport of biopolymers. Inspired by classical Brownian ratchet, we develop a theoretical framework characterizing such translocation process through a master equation approach. In this framework, the polymer chain, provided with reversible binding of chaperones, undergoes forward/backward diffusion, which is rectified by chaperones. We drop the assumption of timescale separation and keep the length of a polymer chain finite, both of which happen to be the key points in most of the previous studies. Our framework makes it accessible to derive analytical expressions for mean translocation velocity and effective diffusion constant in stationary state, which is the basis of a comprehensive understanding towards the dynamics of such process. Generally, the translocation of polymer chain across membrane consists of three subprocesses: initiation, termination, and translocation of the main body part of a polymer chain, where the translocation of the main body part depends on the binding/unbinding kinetics of chaperones. That is the main concern of this study. Our results show that the increase of forward/backward diffusion rate of a polymer chain and the binding/unbinding ratio of chaperones both raise the mean translocation velocity of a polymer chain, and roughly speaking, the dependence of effective diffusion constant on these two factors achieves similar behavior.

physics.bio-ph↗
arXiv2018

Comment on "Speed Limit for Classical Stochastic Processes"

In recent letter [Phys. Rev. Lett {\bf 121}, 070601 (2018), arXiv:1802.06554], the speed limit for classical stochastic Markov processes is considered, and a trade-off inequality between the speed of the state transformation and the entropy production is given. In this comment, a more accurate inequality will be presented.

cond-mat.stat-mech↗
arXiv2018

Theoretical model of transcription based on torsional mechanics of DNA template

Transcription is the first step of gene expression, in which a particular segment of DNA is copied to RNA by the enzyme RNA polymerase (RNAP). Despite many details of the complex interactions between DNA and RNA synthesis disclosed experimentally, much of physical behavior of transcription remains largely unknown. Understanding torsional mechanics of DNA and RNAP together with its nascent RNA and RNA-bound proteins in transcription maybe the first step towards deciphering the mechanism of gene expression. In this study, based on the balance between viscous drag on RNA synthesis and torque resulted from untranscribed supercoiled DNA template, a simple model is presented to describe mechanical properties of transcription. With this model, the rotation and supercoiling density of the untranscribed DNA template are discussed in detail. Two particular cases of transcription are considered, transcription with constant velocity and transcription with torque dependent velocity. Our results show that, during the initial stage of transcription, rotation originated from the transcribed part of DNA template is mainly released by the rotation of RNAP synthesis. During the intermediate stage, the rotation is usually released by both the supercoiling of the untranscribed part of DNA template and the rotation of RNAP synthesis, with proportion depending on the friction coefficient in environment and the length of nascent RNA. However, with the approaching to the upper limit of twisting of the untranscribed DNA template, the rotation resulted from transcription will then be mainly released by the rotation of RNAP synthesis.

physics.bio-ph↗
arXiv2016

Mechanism of helicase translocation along nucleic acid

In cells, helicase translocation along nucleic acid is essential for many biological processes. However, so far, the mechanism of this translocation is not fully understood. Recent studies show that helicase might translocate through two processes, active process and passive process, with different translocation rate. In this study, a model including such two processes is presented. In which, each of these two processes consists of two sub-processes, chemical sub-process in which needed translocation factors are attached, and mechanochemical sub-process in which helicase makes a forward translocation step. Helicase can switch stochastically between these two processes with external force dependent rates. By this model, ribosome translocation along message RNA is detailed discussed. We found that, with the increase of external force, the mean translocation rate of ribosome increases from one lower limit to one upper limit, and both of these two limits increase with concentrations of the translocation factors. Under high external force, ribosome translocates mainly through active process. At saturating concentrations of translocation factors, the translocation is governed by mechanochemical sub-processes.

q-bio.BM↗
arXiv2016

How does a protein reach its binding locus: sliding along DNA chain or not?

In gene expression, various kinds of proteins need to bind to specific locus of DNA. It is still not clear how these proteins find their target locus. In this study, the mean first-passage time (FPT) of protein binding to its target locus on DNA chain is discussed by a chain-space coupled model. Our results show that the 1-dimensional diffusion constant has a critical value, with which the mean time spent by a protein to find its target locus is almost independent of the binding rate of protein to DNA chain and the detachment rate from DNA chain. Which implies that, the frequency of protein binding to DNA and the sliding time on DNA chain have little influence on the search efficiency, and therefore whether or not the 1-dimensional sliding on DNA chain increases the search efficiency depends on the 1-dimensional diffusion constant of the protein on DNA chain. This study also finds that only protein bindings to DNA loci which are close to the target locus help to increase the search efficiency, while bindings to those loci which are far from the target locus might delay the target binding process. As expected, the mean FPT increases with the distance between the initial position of protein in cell space and its target locus on DNA chain. The direct binding probability, which can be regarded as one index to describe if the 1-dimensional sliding along DNA chain is helpful to increase the search efficiency is calculated. Our results show that the influence of 1-dimensional sliding along DNA chain on the search process depends on both diffusion constants of protein in cell space and on the 1-dimensional DNA chain.

physics.bio-ph↗
arXiv2015

A weaker rigidity theorem for pairs of hyperquadrics and its application

In this short article, we establish a rigidity theorem for pairs of hyperquadrics in a weaker sense, i.e., we impose a condition that minimal rational curves are preserved, which is stronger than inheriting a sub-VMRT structure, a notion raised by Mok & Zhang (2014). This problem has its source in a theorem of Tsai (1993), and the main result of this article can be applied back to give a more intrinsic proof of Tsai's theorem.

math.DG↗
arXiv2015

Correlations between promoter activity and its nucleotide positions in spacing region

Transcription is one of the essential processes for cells to read genetic information encoded in genes, which is initiated by the binding of RNA polymerase to related promoter. Experiments have found that the nucleotide sequence of promoter has great influence on gene expression strength, or promoter activity. In synthetic biology, one interesting question is how we can synthesize a promoter with given activity, and which positions of promoter sequence are important for determining its activity. In this study, based on recent experimental data, correlations between promoter activity and its sequence positions are analyzed by various methods. Our results show that, except nucleotides in the two highly conserved regions, $-35$ box and $-10$ box, influences of nucleotides in other positions are also not neglectable. For example, modifications of nucleotides around position $-19$ in spacing region may change promoter activity in a large scale. The results of this study might be helpful to our understanding of biophysical mechanism of gene transcription, and may also be helpful to the design of synthetic cell factory.

q-bio.GN↗
arXiv2015

Comment on "Optimal Reaction Time for Surface-Mediated Diffusion"

In recent letter [Phys. Rev. Lett {\bf 105}, 150606 (2010)], the surface-mediated diffusion problem is theoretically discussed, and interesting results have been obtained. However, for more general cases, the ansatz of solutions of the diffusion equation, which is the starting point of their analysis, might not be appropriate. In this comment, suggested ansatz and corresponding methods will be presented.

math-ph↗
arXiv2015

Mean-field analysis of two-species TASEP with attachment and detachment

In cells, most of cargos are transported by motor proteins along microtubule. Biophysically, unidirectional motion of large number of motor proteins along a single track can be described by totally asymmetric simple exclusion process (TASEP). From which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high density and low density of motor protein along motion track) and boundary layers, can be obtained. However, it is biologically obvious that a single track may be occupied by different motor species. So previous studies based on TASEP of one particle species are not reasonable enough to find more detailed properties of the motion of motors along a single track. To address this problem, TASEP with two particle species is discussed in this study. Theoretical methods to get densities of each particle species are provided. Using these methods, phase transition related properties of particle densities are obtained. Our analysis show that domain wall and boundary layer of single species densities always appear simultaneously with those of the total particle density. The height of domain wall of total particle density is equal to the summation of those of single species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species.

q-bio.SC↗
arXiv2015

Theoretical analysis of transcription process with polymerase stalling

Experimental evidences show that in gene transcription, RNA polymerase has the possibility to be stalled at certain position of the transcription template. This may be due to the template damage, or protein barriers. Once stalled, polymerase may backtrack along the template to the previous nucleotide to wait for the repair of the damaged site, or simply bypass the barrier or damaged site and consequently synthesize an incorrect messenger RNA, or degrade and detach from the template. Thus, the {\it effective} transcription rate (the rate to synthesize correct product mRNA) and the transcription {\it effectiveness} (the ratio of the {\it effective} transcription rate to the {\it effective} transcription initiation rate) are both influenced by polymerase stalling events. This study shows that, Without backtracking, detachment of stalled polymerase can also help to increase the {\it effective} transcription rate and transcription {\it effectiveness}. Generally, the increase of bypass rate of the stalled polymerase will lead to the decrease of the {\it effective} transcription rate and transcription {\it effectiveness}. But when both detachment rate and backtracking rate of the stalled polymerase vanish, the {\it effective} transcription rate may also be increased by the bypass mechanism.

physics.bio-ph↗