Two-boundary first exit time of Gauss-Markov processes for stochastic modeling of acto-myosin dynamics.
We consider a stochastic differential equation in a strip, with coefficients suitably chosen to describe the acto-myosin interaction subject to time-varying forces. By simulating trajectories of the stochastic dynamics via an Euler discretization-based algorithm, we fit experimental data and determine the values of involved parameters. The steps of the myosin are represented by the exit events from the strip. Motivated by these results, we propose a specific stochastic model based on the corresponding time-inhomogeneous Gauss-Markov and diffusion process evolving between two absorbing boundaries. We specify the mean and covariance functions of the stochastic modeling process taking into account time-dependent forces including the effect of an external load. We accurately determine the probability density function (pdf) of the first exit time (FET) from the strip by solving a system of two non singular second-type Volterra integral equations via a numerical quadrature. We provide numerical estimations of the mean of FET as approximations of the dwell-time of the proteins dynamics. The percentage of backward steps is given in agreement to experimental data. Numerical and simulation results are compared and discussed.
Dipartimento di Matematica e Applicazioni, Univ. di Napoli FEDERICO II, Via Cintia, 80126, Napoli, Italy. giuseppe.donofrio@unina.it.
Giuseppe
G
D'Onofrio
Dipartimento di Matematica e Applicazioni, Univ. di Napoli FEDERICO II, Via Cintia, 80126, Napoli, Italy.
Enrica
E
Pirozzi
D000199:Actins / Q000737:chemistry / Q000502:physiology; D000205:Actomyosin / Q000737:chemistry* / Q000502:physiology*; D000255:Adenosine Triphosphate / Q000378:metabolism; D000818:Animals; D055592:Biophysical Phenomena; D003198:Computer Simulation; D008390:Markov Chains; D055641:Mathematical Concepts; D008954:Models, Biological; D009119:Muscle Contraction / Q000502:physiology; D009218:Myosins / Q000737:chemistry / Q000502:physiology; D016011:Normal Distribution; D054730:Protein Interaction Domains and Motifs; D013269:Stochastic Processes
D000199:Actins; D000255:Adenosine Triphosphate; D000205:Actomyosin; D009218:Myosins
Dwell-time; First passage time; Time-dependent tilting forces; Volterra integral equations
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 May;85(5 Pt 1):051110
23004706
Nature. 1985 Jul 25-31;316(6026):366-9
4022127
Biophys J. 2006 Feb 15;90(4):1295-307
16326899
Nature. 1995 Nov 9;378(6553):209-12
7477328
Nature. 1997 Jul 10;388(6638):186-90
9217160
Math Biosci. 2007 Jun;207(2):387-401
17360007
Adv Biophys. 1986;22:151-83
2882655
Nature. 1994 Mar 10;368(6467):113-9
8139653
Nature. 1999 Jan 14;397(6715):129-34
9923673
Physiol Rev. 1997 Jul;77(3):671-97
9234962
Biosystems. 2008 Sep;93(3):172-80
18479805
Biosystems. 2013 Sep;113(3):144-8
23791790
Nature. 2000 Dec 14;408(6814):764-6
11130692
Nature. 1994 Dec 8;372(6506):515-8
7990922
Genes Cells. 2000 Jan;5(1):9-16
10651901
Biosystems. 2005 Aug;81(2):165-77
15946790
Math Biosci Eng. 2016 Jun 1;13(3):495-507
27106180