# American Institute of Mathematical Sciences

December  2020, 25(12): 4839-4852. doi: 10.3934/dcdsb.2020129

## A continuous-time stochastic model of cell motion in the presence of a chemoattractant

 Department of Mathematics, Brigham Young University, Provo, UT 84602-6539, USA

* Corresponding author

Received  October 2019 Revised  January 2020 Published  December 2020 Early access  April 2020

We consider a force-based model for cell motion which models cell forces using Hooke's law and a random outreach from the cell center. In previous work this model was simplified to track the centroid by setting the relaxation time to zero, and a formula for the expected velocity of the centroid was derived. Here we extend that formula to allow for chemotaxis of the cell by allowing the outreach distribution to depend on the spatial location of the centroid.

Citation: J. C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant. A continuous-time stochastic model of cell motion in the presence of a chemoattractant. Discrete & Continuous Dynamical Systems - B, 2020, 25 (12) : 4839-4852. doi: 10.3934/dcdsb.2020129
##### References:

show all references

##### References:
Panel a) and c) depicts the state space $\mathit{x_e}$ given as an example. The circle represents the cell centroid. The black "x"s represent attached I-sites (labeled 0 and 1) and the red "x" denotes the detached I-site (labeled 2). The sets $A$ and $B$ represent the example sets used in the measure for case 1 and case 2. Panels a) and b) are for case 1 where I-site 1 dettaches. Panel a) is the initial configuration and panel b) is the new state. Likewise, panels c), and d) are for cases 2 where I-site 2 attaches. The sets $\bar{A}$ and $\bar{B}$ are the sets $A$ and $B$ transformed by $S^{-1}\circ F^{-1}$. In panel a), $\bar{A} = A$ and $\bar{B} = B+(.5, .5)$. In panel c), $\bar{A} = A-(.5, .5)$ and $\bar{B} = 3B-(1.5, 1.5)$ and their intersection contains $\mathbf{ \pmb{\mathsf{ η}}} = (1, 0)$. In panel d), I-site 2 has attached at location $\mathbf {x}_2 = \mathbf{c}+\mathbf{ \pmb{\mathsf{ η}}} = (.5, .5)+(1, 0)$
 [1] Martin Friesen, Oleksandr Kutoviy. Stochastic Cucker-Smale flocking dynamics of jump-type. Kinetic & Related Models, 2020, 13 (2) : 211-247. doi: 10.3934/krm.2020008 [2] Deena Schmidt, Janet Best, Mark S. Blumberg. Random graph and stochastic process contributions to network dynamics. Conference Publications, 2011, 2011 (Special) : 1279-1288. doi: 10.3934/proc.2011.2011.1279 [3] Daoyi Xu, Yumei Huang, Zhiguo Yang. Existence theorems for periodic Markov process and stochastic functional differential equations. Discrete & Continuous Dynamical Systems, 2009, 24 (3) : 1005-1023. doi: 10.3934/dcds.2009.24.1005 [4] Michael C. Fu, Bingqing Li, Rongwen Wu, Tianqi Zhang. Option pricing under a discrete-time Markov switching stochastic volatility with co-jump model. Frontiers of Mathematical Finance, 2022, 1 (1) : 137-160. doi: 10.3934/fmf.2021005 [5] Xian Chen, Zhi-Ming Ma. A transformation of Markov jump processes and applications in genetic study. Discrete & Continuous Dynamical Systems, 2014, 34 (12) : 5061-5084. doi: 10.3934/dcds.2014.34.5061 [6] Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401 [7] Benoît Perthame, P. E. Souganidis. Front propagation for a jump process model arising in spacial ecology. Discrete & Continuous Dynamical Systems, 2005, 13 (5) : 1235-1246. doi: 10.3934/dcds.2005.13.1235 [8] Tan H. Cao, Boris S. Mordukhovich. Optimality conditions for a controlled sweeping process with applications to the crowd motion model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 267-306. doi: 10.3934/dcdsb.2017014 [9] Chandan Pal, Somnath Pradhan. Zero-sum games for pure jump processes with risk-sensitive discounted cost criteria. Journal of Dynamics & Games, 2021  doi: 10.3934/jdg.2021020 [10] H.Thomas Banks, Shuhua Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. Mathematical Biosciences & Engineering, 2012, 9 (1) : 1-25. doi: 10.3934/mbe.2012.9.1 [11] Fuke Wu, George Yin, Zhuo Jin. Kolmogorov-type systems with regime-switching jump diffusion perturbations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2293-2319. doi: 10.3934/dcdsb.2016048 [12] Felix X.-F. Ye, Yue Wang, Hong Qian. Stochastic dynamics: Markov chains and random transformations. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2337-2361. doi: 10.3934/dcdsb.2016050 [13] Isabelle Kuhwald, Ilya Pavlyukevich. Bistable behaviour of a jump-diffusion driven by a periodic stable-like additive process. Discrete & Continuous Dynamical Systems - B, 2016, 21 (9) : 3175-3190. doi: 10.3934/dcdsb.2016092 [14] Wuyuan Jiang. The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence. Discrete & Continuous Dynamical Systems - B, 2019, 24 (7) : 3037-3050. doi: 10.3934/dcdsb.2018298 [15] Donny Citra Lesmana, Song Wang. A numerical scheme for pricing American options with transaction costs under a jump diffusion process. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1793-1813. doi: 10.3934/jimo.2017019 [16] Yan Wang, Lei Wang, Yanxiang Zhao, Aimin Song, Yanping Ma. A stochastic model for microbial fermentation process under Gaussian white noise environment. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 381-392. doi: 10.3934/naco.2015.5.381 [17] Hongjun Gao, Fei Liang. On the stochastic beam equation driven by a Non-Gaussian Lévy process. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1027-1045. doi: 10.3934/dcdsb.2014.19.1027 [18] Linlin Tian, Xiaoyi Zhang, Yizhou Bai. Optimal dividend of compound poisson process under a stochastic interest rate. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2141-2157. doi: 10.3934/jimo.2019047 [19] Zhongming Chen, Liqun Qi. Circulant tensors with applications to spectral hypergraph theory and stochastic process. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1227-1247. doi: 10.3934/jimo.2016.12.1227 [20] Lin Xu, Rongming Wang, Dingjun Yao. Optimal stochastic investment games under Markov regime switching market. Journal of Industrial & Management Optimization, 2014, 10 (3) : 795-815. doi: 10.3934/jimo.2014.10.795

2020 Impact Factor: 1.327