arXiv subjects

Yunxin Zhang

Publications and source records attributed to Yunxin Zhang.

At least 55 records · Page 3Linked to original sources

arXiv2015

Translation with frameshifting of ribosome along mRNA transcript

Translation is an important process for prokaryotic and eukaryotic cells to produce necessary proteins for cell growth. Numerious experiments have been performed to explore the translational properties. Diverse models have also been developed to determine the biochemical mechanism of translation. However, to simplify the majority of the existing models, the frameshifting of ribosome along the mRNA transcript is neglected, which actually occurs in real cells and has been extensively experimentally studied. The frameshifting of ribosome evidently influences the efficiency and speed of translation, considering that the peptide chains synthesized by shifted ribosomes will not fold into functional proteins and will degrade rapidly. In this study, a theoretical model is presented to describe the translational process based on the model for totally asymmetric simple exclusion process. In this model, the frameshifting of the ribosome along the mRNA transcript and the attachment/detachment of the ribosome to/from the main body of mRNA codons during translation elongation process, are explicitly included. The results show that, with ribosome frameshifing, the speed of correctly synthesized peptide chains may increase first and then decrease with both the translation initiation rate $α$ and the ribosome detachment rate $ω_d$. This results indicates that regulating the translation process to reach maximal synthesized speed of proteins is theoretically feasible. Traffic-related problems of ribosome motion along the mRNA transcript are also addressed theoretically. Depending on parameter values, shock wave (or domain wall) may exist for ribosome probabilities along the mRNA.

physics.bio-ph↗

arXiv2014

Admissible pairs of Hermitian symmetric spaces in the perspective of the theory of varieties of minimal rational tangents

We study a pair (\mathcal{S}_0,\mathcal{S}) of irreducible Hermitian Symmetric Spaces of compact type (cHSS) in this paper, with the first aim being classifying all the admissible pairs (\mathcal{S}_0,\mathcal{S})). This notion is a natural generalization of the pairs of sub-diagram type originated by Jaehyun Hong and Ngaiming Mok ([HoM 10]). Based on this classification, we partially solve the rigidity problem for the admissible pairs (\mathcal{S}_0,\mathcal{S}) which was raised by Mok and Zhang (2014) ([MoZ 14]), culminating in determining a sufficient condition for the pairs being non-rigid and proving that special pairs, which show up in the classification procedure, are algebraic, as a weaker result than being rigid. However, whether special pairs are rigid or not remains unknown and needs further investigation in the framework of VMRT theory.

math.DG↗

arXiv2014

Relationship between promoter sequence and its strength in gene expression

In this study, through various tests one theoretical model is presented to describe the relationship between promoter strength and its nucleotide sequence. Our analysis shows that, promoter strength is greatly influenced by nucleotide groups with three adjacent nucleotides in its sequence. Meanwhile, nucleotides in different regions of promoter sequence have different effects on promoter strength. Based on experimental data for {\it E. coli} promoters, our calculations indicate, nucleotides in -10 region, -35 region, and the discriminator region of promoter sequence are more important than those in spacing region for determining promoter strength. With model parameter values obtained by fitting to experimental data, four promoter libraries are theoretically built for the corresponding experimental environments under which data for promoter strength in gene expression has been measured previously.

q-bio.MN↗

arXiv2013

Properties of sodium-driven bacterial flagellar motor: A two-state model approach

Bacterial flagellar motor (BFM) is one of the ion-driven molecular machines, which drives the rotation of flagellar filaments and enable bacteria to swim in viscous solutions. Understanding its mechanism is one challenge in biophysics. Based on previous models and inspired by the idea used in description of motor proteins, in this study one two-state model is provided. Meanwhile, according to corresponding experimental data, mathematical relationship between BFM membrane voltage and pH value of the environment, and relationship between internal and external sodium concentrations are given. Therefore, with model parameter values obtained by fitting theoretical results of torque-speed relation to recent experimental data, many biophysical properties of bacterial flagellar motor can be obtained for any pH values and any external sodium concentrations. Including the rotation speed, stall torque (i.e. the torque generated by BFM), rotation dispersion, and rotation randomness. In this study, the single-stator BFM will be firstly analyzed, and then properties of multiple-stator BFM are addressed briefly.

physics.bio-ph↗

arXiv2013

Improvement of risk estimate on wind turbine tower buckled by hurricane

Wind is one of the important reasonable resources. However, wind turbine towers are sure to be threatened by hurricanes. In this paper, method to estimate the number of wind turbine towers that would be buckled by hurricanes is discussed. Monte Carlo simulations show that our method is much better than the previous one. Since in our method, the probability density function of the buckling probability of a single turbine tower in a single hurricane is obtained accurately but not from one approximated expression. The result in this paper may be useful to the design and maintenance of wind farms.

physics.ao-ph↗

arXiv2012

Cargo transportation by two species of motor protein

The cargo motion in living cells transported by two species of motor protein with different intrinsic directionality is discussed in this study. Similar to single motor movement, cargo steps forward and backward along microtubule stochastically. Recent experiments found that, cargo transportation by two motor species has a memory, it does not change its direction as frequently as expected, which means that its forward and backward step rates depends on its previous motion trajectory. By assuming cargo has only the least memory, i.e. its step direction depends only on the direction of its last step, two cases of cargo motion are detailed analyzed in this study: {\bf (I)} cargo motion under constant external load; and {\bf (II)} cargo motion in one fixed optical trap. Due to the existence of memory, for the first case, cargo can keep moving in the same direction for a long distance. For the second case, the cargo will oscillate in the trap. The oscillation period decreases and the oscillation amplitude increases with the motor forward step rates, but both of them decrease with the trap stiffness. The most likely location of cargo, where the probability of finding the oscillated cargo is maximum, may be the same as or may be different with the trap center, which depends on the step rates of the two motor species. Meanwhile, if motors are robust, i.e. their forward to backward step rate ratios are high, there may be two such most likely locations, located on the two sides of the trap center respectively. The probability of finding cargo in given location, the probability of cargo in forward/backward motion state, and various mean first passage times of cargo to give location or given state are also analyzed.

physics.bio-ph↗

arXiv2012

One-Dimensional Birth-Death Process and Delbrück-Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions

As a mathematical theory for the stochasstic, nonlinear dynamics of individuals within a population, Delbrück-Gillespie process (DGP) $n(t)\in\mathbb{Z}^N$, is a birth-death system with state-dependent rates which contain the system size $V$ as a natural parameter. For large $V$, it is intimately related to an autonomous, nonlinear ordinary differential equation as well as a diffusion process. For nonlinear dynamical systems with multiple attractors, the quasi-stationary and stationary behavior of such a birth-death process can be underestood in terms of a separation of time scales by a $T^*\sim e^{αV}$ $(α>0)$: a relatively fast, intra-basin diffusion for $t\ll T^*$ and a much slower inter-basin Markov jump process for $t\gg T^*$. In the present paper for one-dimensional systems, we study both stationary behavior ($t=\infty$) in terms of invariant distribution $p_n^{ss}(V)$, and finite time dynamics in terms of the mean first passsage time (MFPT) $T_{n_1\rightarrow n_2}(V)$. We obtain an asymptotic expression of MFPT in terms of the "stochastic potential" $Φ(x,V)=-(1/V)\ln p^{ss}_{xV}(V)$. We show in general no continuous diffusion process can provide asymptotically accurate representations for both the MFPT and the $p_n^{ss}(V)$ for a DGP. When $n_1$ and $n_2$ belong to two different basins of attraction, the MFPT yields the $T^*(V)$ in terms of $Φ(x,V)\approx ϕ_0(x)+(1/V)ϕ_1(x)$. For systems with a saddle-node bifurcation and catastrophe, discontinuous "phase transition" emerges, which can be characterized by $Φ(x,V)$ in the limit of $V\rightarrow\infty$. In terms of time scale separation, the relation between deterministic, local nonlinear bifurcations and stochastic global phase transition is discussed. The one-dimensional theory is a pedagogic first step toward a general theory of DGP.

math.DS↗

arXiv2012

Microtubule length dependence of motor traffic in cells

In living cells, motor proteins, such as kinesin and dynein can move processively along microtubule (MT), and also detach from or attach to MT stochastically. Experiments have found that, the traffic of motor might be jammed, and various theoretical models have been designed to understand this traffic jam phenomenon. But previous studies mainly focus on motor attachment/detachment rate dependent properties. Recent experiment of Leduc {\it et al.} found that the traffic jam formation of motor protein kinesin depends also on the length of MT [Proc. Natl. Acad. Sci. U.S.A. {\bf 109}, 6100-6105 (2012)]. In this study, the MT length dependent properties of motor traffic will be analyzed. We found that MT length has one {\it critical value} $N_c$, traffic jam occurs only when MT length $N>N_c$. The jammed length of MT increases with total MT length, while the non-jammed MT length might not change monotonically with the total MT length. The critical value $N_c$ increases with motor detachment rate from MT, but decreases with motor attachment rate to MT.

physics.bio-ph↗

arXiv2012

ATP binding to a multisubunit enzyme: statistical thermodynamics analysis

Due to inter-subunit communication, multisubunit enzymes usually hydrolyze ATP in a concerted fashion. However, so far the principle of this process remains poorly understood. In this study, from the viewpoint of statistical thermodynamics, a simple model is presented. In this model, we assume that the binding of ATP will change the potential of the corresponding enzyme subunit, and the degree of this change depends on the state of its adjacent subunits. The probability of enzyme in a given state satisfies the Boltzmann's distribution. Although it looks much simple, this model can fit the recent experimental data of chaperonin TRiC/CCT well. From this model, the dominant state of TRiC/CCT can be obtained. This study provided a new way to understand biophysical processes by statistical thermodynamics analysis.

math-ph↗

arXiv2011

Comment on "Length-dependent translation of messenger RNA by ribosomes"

In the recent paper of Valleriani {\it et al} [Phys. Rev. E {\bf 83}, 042903 (2011)], a simple model for describing the translation of messenger RNA (mRNA) by ribosomes is presented, and an expression of the translational ratio $r$, defined as the ratio of translation rate $ω_{\rm tl}$ of protein from mRNA to degradation rate $ω_p$ of protein, is obtained. The key point to get this ratio $r$ is to get the translation rate $ω_{\rm tl}$. In the study of Valleriani {\it et al}, $ω_{\rm tl}$ is assumed to be the mean value of measured translation rate, i.e. the mean value of ratio of the translation number of protein to the lifetime of mRNA. However, in experiments different methods might be used to get $ω_{\rm tl}$. Therefore, for the sake of future application of their model to more experimental data analysis, in this comment three methods to get the translation rate $ω_{\rm tl}$, and consequently the translational ratio $r$, are provided. Based on one of the methods which might be employed in most of the experiments, we find that the translational ratio $r$ decays exponentially with the length of mRNA in prokaryotic cells, and decays reciprocally with the length of mRNA in eukaryotic cells. This result is slight different from that obtained in Valleriani's study.

physics.bio-ph↗

arXiv2011

The mean velocity of two-state models of molecular motor

The motion of molecular motor is essential to the biophysical functioning of living cells. In principle, this motion can be regraded as a multiple chemical states process. In which, the molecular motor can jump between different chemical states, and in each chemical state, the motor moves forward or backward in a corresponding potential. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping models or by several coupled Fokker-Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest cases: in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, we find that the mean velocity of molecular motor might be nonzero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is energy input to the molecular motor. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two states, but also on the transition rates between the two chemical states.

physics.bio-ph↗

arXiv2011

Phenomenological analysis of ATP dependence of motor protein

In this study, through phenomenological comparison of the velocity-force data of processive motor proteins, including conventional kinesin, cytoplasmic dynein and myosin V, we found that, the ratio between motor velocities of two different ATP concentrations is almost invariant for any substall, superstall or negative external loads. Therefore, the velocity of motor can be well approximated by a Michaelis-Menten like formula $V=\atp k(F)L/(\atp +K_M)$, with $L$ the step size, and $k(F)$ the external load $F$ dependent rate of one mechanochemical cycle of motor motion in saturated ATP solution. The difference of Michaelis-Menten constant $K_M$ for substall, superstall and negative external load indicates, the ATP molecule affinity of motor head for these three cases are different, though the expression of $k(F)$ as a function of $F$ might be unchanged for any external load $F$. Verifications of this Michaelis-Menten like formula has also been done by fitting to the recent experimental data.

physics.bio-ph↗

arXiv2011

Growth and shortening of microtubules: a two-state model approach

In this study, a two-state mechanochemical model is presented to describe the dynamic instability of microtubules (MTs) in cells. The MTs switches between two states, assembly state and disassembly state. In assembly state, the growth of MTs includes two processes: free GTP-tubulin binding to the tip of protofilament (PF) and conformation change of PF, during which the first tubulin unit which curls outwards is rearranged into MT surface using the energy released from the hydrolysis of GTP in the penultimate tubulin unit. In disassembly state, the shortening of MTs includes also two processes, the release of GDP-tibulin from the tip of PF and one new tubulin unit curls out of the MT surface. Switches between these two states, which are usually called rescue and catastrophe, happen stochastically with external force dependent rates. Using this two-state model with parameters obtained by fitting the recent experimental data, detailed properties of MT growth are obtained, we find that MT is mainly in assembly state, its mean growth velocity increases with external force and GTP-tubulin concentration, MT will shorten in average without external force. To know more about the external force and GTP-tubulin concentration dependent properties of MT growth, and for the sake of the future experimental verification of this two-state model, eleven {\it critical forces} are defined and numerically discussed.

physics.bio-ph↗

arXiv2011

Shock of three-state model for intracellular transport of kinesin KIF1A

Recently, a three-state model is presented to describe the intracellular traffic of unconventional (single-headed) kinesin KIF1A [Phys. Rev. Lett. {\bf 95}, 118101 (2005)], in which each motor can bind strongly or weakly to its microtubule track, and each binding site of the track might be empty or occupied by one motor. As the usual two-state model, i.e. the totally asymmetric simple exclusion process (TASEP) with motor detachment and attachment, in steady state of the system, this three-state model also exhibits shock (or domain wall separating the high-density and low density phases) and boundary layers. In this study, using mean-field analysis, the conditions of existence of shock and boundary layers are obtained theoretically. Combined with numerical calculations, the properties of shock are also studied. This study will be helpful to understand the biophysical properties of the collective transport of kinesin KIF1A.

physics.bio-ph↗

arXiv2011

Loose mechanochemical coupling of molecular motors

In living cells, molecular motors convert chemical energy into mechanical work. Its thermodynamic energy efficiency, i.e. the ratio of output mechanical work to input chemical energy, is usually high. However, using two-state models, we found the motion of molecular motors is loosely coupled to the chemical cycle. Only part of the input energy can be converted into mechanical work. Others is dissipated into environment during substeps without contributions to the macro scale unidirectional movement.

physics.bio-ph↗

arXiv2010

van't Hoff-Arrhenius Analysis of Mesoscopic and Macroscopic Dynamics of Simple Biochemical Systems: Stochastic vs. Nonlinear Bistabilities

Multistability of mesoscopic, driven biochemical reaction systems has implications to a wide range of cellular processes. Using several simple models, we show that one class of bistable chemical systems has a deterministic counterpart in the nonlinear dynamics based on the Law of Mass Action, while another class, widely known as noise-induced stochastic bistability, does not. Observing the system's volume ($V$) playing a similar role as the inverse temperature ($β$) in classical rate theory, an van't Hoff-Arrhenius like analysis is introduced. In one-dimensional systems, a transition rate between two states, represented in terms of a barrier in the landscape for the dynamics $Φ(x,V)$, $k\propto\exp\{-VΔΦ^‡(V)\}$, can be understood from a decomposition $ΔΦ^‡(V) \approxΔϕ_0^‡ Δϕ_1^‡/V$. Nonlinear bistability means $Δϕ_0^‡>0$ while stochastic bistability has $Δϕ_0^‡<0$ but $Δϕ_1^‡>0$. Stochastic bistabilities can be viewed as remants (or "ghosts) of nonlinear bifurcations or extinction phenomenon, and $Δϕ_0^‡$ and $Δϕ_1^‡$ as "enthalpic" and "entropic" barriers to a transition.

physics.chem-ph↗

arXiv2010

Simplification of the tug-of-war model for cellular transport in cells

The transport of organelles and vesicles in living cells can be well described by a kinetic tug-of-war model advanced by Müller, Klumpp and Lipowsky. In which, the cargo is attached by two motor species, kinesin and dynein, and the direction of motion is determined by the number of motors which bind to the track. In recent work [Phys. Rev. E 79, 061918 (2009)], this model was studied by mean field theory, and it was found that, usually the tug-of-war model has one, two, or three distinct stable stationary points. However, the results there are mostly obtained by numerical calculations, since it is hard to do detailed theoretical studies to a two-dimensional nonlinear system. In this paper, we will carry out further detailed analysis about this model, and try to find more properties theoretically. Firstly, the tug-of-war model is simplified to a one-dimensional equation. Then we claim that the stationary points of the tug-of-war model correspond to the roots of the simplified equation, and the stable stationary points correspond to the roots with positive derivative. Bifurcation occurs at the corresponding parameters, under which the simplified one-dimensional equation exists root with zero derivative. Using the simplified equation, not only more properties of the tug-of-war model can be obtained analytically, the related numerical calculations will become more accurate and more efficient. This simplification will be helpful to future studies of the tug-of-war model.

math-ph↗

arXiv2010

Properties of modified periodic one-dimensional hopping model

One-dimensional hopping model is useful to describe the motion of microscopic particle in thermal noise environment, such as motor proteins. Recent experiments about the new generation of light-driven rotary molecular motors found that, the motor in state i can jump forward to state i+1 or i+2, or backward to state i-1 or i-2 directly. In this paper, such modified periodic one-dimensional hopping model of arbitrary period N is studied mathematically. The mean velocity, effective diffusion constant, and mean dwell time in one single cycle are obtained. Corresponding results are illustrated and verified by being applied to a type of synthetic rotary molecular motors.

physics.chem-ph↗