A stochastic model for active transport

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (mean first passage time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

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A stochastic model for intracellular active transport

BIOMATH ◽

10.11145/j.biomath.2018.12.047 ◽

2018 ◽

Vol 7 (2) ◽

pp. 1812047

Author(s):

Raluca Purnichescu Purtan ◽

Irina Badralexi

Keyword(s):

Stochastic Model ◽

Active Transport ◽

Neurological Disorders ◽

Intracellular Transport ◽

Molecular Motor ◽

First Passage Time ◽

Passage Time ◽

Point Of View ◽

Biologically Relevant ◽

Time Required

We develop a stochastic model for an intracellular active transport problem. Our aims are to calculate the probability that a molecular motor reaches a hidden target, to study what influences this probability and to calculate the time required for the molecular motor to hit the target (Mean First Passage Time). We study different biologically relevant scenarios, which include the possibility of multiple hidden targets (which breed competition) and the presence of obstacles. The purpose of including obstacles is to illustrate actual disruptions of the intracellular transport (which can result, for example, in several neurological disorders. From a mathematical point of view, the intracellular active transport is modelled by two independent continuous-time, discrete space Markov chains: one for the dynamics of the molecular motor in the space intervals and one for the domain of target. The process is time homogeneous and independent of the position of the molecular motor.

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On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains

Mathematics ◽

10.3390/math9151745 ◽

2021 ◽

Vol 9 (15) ◽

pp. 1745

Author(s):

Andreas C. Georgiou ◽

Alexandra Papadopoulou ◽

Pavlos Kolias ◽

Haris Palikrousis ◽

Evanthia Farmakioti

Keyword(s):

Markov Chains ◽

Dna Sequences ◽

First Passage Time ◽

Passage Time ◽

Markov Modeling ◽

First Passage ◽

State Duration ◽

Time Required ◽

Semi Markov Processes ◽

Stochastic Phenomena

Semi-Markov processes generalize the Markov chains framework by utilizing abstract sojourn time distributions. They are widely known for offering enhanced accuracy in modeling stochastic phenomena. The aim of this paper is to provide closed analytic forms for three types of probabilities which describe attributes of considerable research interest in semi-Markov modeling: (a) the number of transitions to a state through time (Occupancy), (b) the number of transitions or the amount of time required to observe the first passage to a state (First passage time) and (c) the number of transitions or the amount of time required after a state is entered before the first real transition is made to another state (Duration). The non-homogeneous in time recursive relations of the above probabilities are developed and a description of the corresponding geometric transforms is produced. By applying appropriate properties, the closed analytic forms of the above probabilities are provided. Finally, data from human DNA sequences are used to illustrate the theoretical results of the paper.

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Variations on the Theme of Synaptic Filtering: A Comparison of Integrate-and-Express Models of Synaptic Plasticity for Memory Lifetimes

Neural Computation ◽

10.1162/neco_a_00889 ◽

2016 ◽

Vol 28 (11) ◽

pp. 2393-2460 ◽

Cited By ~ 5

Author(s):

Terry Elliott

Keyword(s):

Synaptic Plasticity ◽

Parameter Space ◽

Signal To Noise Ratio ◽

First Passage Time ◽

Passage Time ◽

Memory Storage ◽

Relevant Parameter ◽

Filter Model ◽

Biologically Relevant ◽

Consecutive Number

Integrate-and-express models of synaptic plasticity propose that synapses integrate plasticity induction signals before expressing synaptic plasticity. By discerning trends in their induction signals, synapses can control destabilizing fluctuations in synaptic strength. In a feedforward perceptron framework with binary-strength synapses for associative memory storage, we have previously shown that such a filter-based model outperforms other, nonintegrative, “cascade”-type models of memory storage in most regions of biologically relevant parameter space. Here, we consider some natural extensions of our earlier filter model, including one specifically tailored to binary-strength synapses and one that demands a fixed, consecutive number of same-type induction signals rather than merely an excess before expressing synaptic plasticity. With these extensions, we show that filter-based models outperform nonintegrative models in all regions of biologically relevant parameter space except for a small sliver in which all models encode memories only weakly. In this sliver, which model is superior depends on the metric used to gauge memory lifetimes (whether a signal-to-noise ratio or a mean first passage time). After comparing and contrasting these various filter models, we discuss the multiple mechanisms and timescales that underlie both synaptic plasticity and memory phenomena and suggest that multiple, different filtering mechanisms may operate at single synapses.

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Diffusion in liquids from a first-passage-time point of view

Physical Review E ◽

10.1103/physreve.47.4076 ◽

1993 ◽

Vol 47 (6) ◽

pp. 4076-4082 ◽

Cited By ~ 5

Author(s):

T. Munakata ◽

Y. Kaneko

Keyword(s):

First Passage Time ◽

Passage Time ◽

Point Of View ◽

First Passage ◽

Diffusion In Liquids ◽

Time Point

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First passage time for the state of exact chemical equilibrium

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19800777 ◽

1980 ◽

Vol 45 (3) ◽

pp. 777-782 ◽

Cited By ~ 1

Author(s):

Milan Šolc

Keyword(s):

Chemical Equilibrium ◽

First Passage Time ◽

Passage Time ◽

The State ◽

Recurrence Time ◽

First Passage ◽

First Order ◽

The Mean ◽

Passage Times ◽

Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

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