237 research outputs found
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
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.Comment: 29 page
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.Comment: 9 page
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
Comment on "Efficiency of Isothermal Molecular Machines at Maximum Power"
Comment on "Efficiency of Isothermal Molecular Machines at Maximum Power"
(PRL 108, 210602 (2012), arXiv:1201.6396)Comment: So far, this manuscript has not been accepted for publication, and I
do not want to work on it now. So I want to withdraw it
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.Comment: So far, this manuscription has not been accepted for publication, and
I do not want to work on this topic no
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 , or the total entropy
production equivalently, reaching its lower bound.
Properties of the optimal thermodynamic machines are discussed, with explicit
expressions of upper bounds of work output , power , and energy
efficiency are presented. To illustrate the results obtained, typical
examples with optimal protocols (external potentials) are also presented
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
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
Totally asymmetric simple exclusion process with one or two shortcuts
In this paper, the operation of totally asymmetric simple exclusion process
with one or two shortcuts under open boundary conditions is discussed. Using
both mathematical analysis and numerical simulations, we have found that,
according to the method chosen by the particle at the bifurcation, the model
can be separated into two different situations which lead to different results.
The results obtained in this paper would be very useful in the road building,
especially at the bifurcation of the road
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