arXiv subjects

Seong Jun Park

Publications and source records attributed to Seong Jun Park.

9 recordsLinked to original sources

arXiv2026

Viral population dynamics at the cellular level, considering the replication cycle

Viruses are microscopic infectious agents that require a host cell for replication. Viral replication occurs in several stages, and the completion time for each stage varies due to differences in the cellular environment. Thus, the time to complete each stage in viral replication is a random variable. However, no analytic expression exists for the viral population at the cellular level when the completion time for each process constituting viral replication is a random variable. This paper presents a simplified model of viral replication, treating each stage as a renewal process with independently and identically distributed completion times. Using the proposed model, we derive an analytical formula for viral populations at the cellular level, based on viewing viral replication as a birth-death process. The mean viral count is expressed via probability density functions representing the completion time for each step in the replication process. This work validates the results with stochastic simulations. This study provides a new quantitative framework for understanding viral infection dynamics.

q-bio.PE↗

arXiv2026

Infection dynamics for fluctuating infection or removal rates regarding the number of infected and susceptible individuals

In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR model, which categorizes individuals as susceptible, infectious, recovered or deceased. In this model, the infection rate, governing the transition from susceptible to infected individuals, is given by a linear function of both susceptible and infected populations. Similarly, the removal rate, representing the transition from infected to removed individuals, is a linear function of the number of infected individuals. While nonlinear infection and removal rates have been extensively studied in deterministic epidemiological models, analytic results for stochastic dynamics with general nonlinear rates remain limited. This work presents an analytic expression for the number of infected individuals considering nonlinear infection and removal rates. In particular, we examine how the number of infected individuals varies as cases emerge and obtain the expression accounting for the number of infected individuals at each moment. This work paves the way for new quantitative approaches to understanding infection dynamics.

q-bio.PE↗

arXiv2023

Relationship between event counting statistics and waiting time statistics in the steady state

There are two main quantities involved in the deviation of a stochastic process from a Poisson process: the squared coefficient of variation of the time intervals between adjacent events and the Fano factor of the number of reaction events. As well known, these two quantities are equal for renewal processes, while their relationship remains unexplored for non-renewal processes. In this paper, we establish an explicit relation between the two statistics that is applicable to non-renewal processes. The new relation, which reduces to the previously mentioned result for renewal processes, is confirmed to be accurate in several cases of non-renewal processes.

cond-mat.stat-mech↗

arXiv2023

Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes

Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every time birth or death occurs, which makes fluctuations in the rates inevitable. The differential-difference equation governing the time evolution of such a birth-death process is well established, but it resists solving for a non-asymptotic solution. In this work, we present the analytic solution of the differential-difference equation for birth-death processes without approximation. The time-dependent solution we obtain leads to an analytical expression for counting statistics of products (or customers). We further examine the relationship between the system size fluctuations and the birth and death rates, and find that statistical properties (variance subtracted by mean) of the system size are determined by the mean death rate as well as the covariance of the system size and the net growth rate (i.e., the birth rate minus the death rate). This work suggests a promising new direction for quantitative investigations into birth-death processes.

physics.soc-ph↗

arXiv2019

Product number counting statistics from stochastic bursting birth-death processes

Bursting and non-renewal processes are common phenomena in birth-death process, yet no theory can quantitatively describe a non-renewal birth process with bursting. Here, we present a theoretical model that yields the product number counting statistics of product creation occurring in bursts and of a non-renewal creation process. When product creation is a stationary process, our model confirms that product number fluctuation decreases with an increase in the product lifetime fluctuation, originating from the non-Poisson degradation dynamics, a result obtained in previous work. Our model additionally demonstrates that the dependence of product number fluctuation on product lifetime fluctuation varies with time, when product creation is a non-stationary process. We find that bursting increases product number fluctuation, compared to birth-processes without bursting. At time zero, in a burst-less birth process, product number fluctuation is unsurprisingly found to be zero, but we discover that, in a bulk creation process characterized by bursting, product number fluctuation is a finite value at time zero. The analytic expressions we obtain are applicable to many fields related to the study system population, such as queueing models and gene expression.

q-bio.MN↗

arXiv2019

Exploiting product molecule number to consider reaction rate fluctuation in elementary reactions

In many chemical reactions, reaction rate fluctuation is inevitable. Reaction rates are different whenever chemical reaction occurs due to their dependence on the number of reaction events or the product number. As such, understanding the impact of rate fluctuation on product number counting statistics is of the utmost importance when developing a quantitative explanation of chemical reactions. In this work, we present a master equation that describes reaction rates as a function of product number and time. Our equal reveals the relationship between the reaction rate and product number fluctuation. Product number counting statistics uncovers a stochastic property of the product number; product number directly manipulates the reaction rate. Specifically, we find that product number shows super-Poisson characteristics when the product number increases, inducing an increase in the reaction rate. While, on the other hand, when the product number shows sub-Poisson characteristics with an increase in the product number, this is induced by a decrease in the reaction rate. Furthermore, our analysis exploits reaction rate fluctuation, enabling the quantification of the deviation of an elementary reaction process from a renewal process.

q-bio.MN↗

arXiv2018

Frequency spectrum of biological noise: a probe of reaction dynamics in living cells

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular reactions creating these biomolecules. Although recent advances in single-cell experimental techniques enable the direct monitoring of the time-traces of the biological noise in each cell, the development of the theoretical tools needed to extract the information encoded in the stochastic dynamics of intracellular chemical fluctuation is still in its adolescence. Here, we present a simple and general equation that relates the power-spectrum of the product number fluctuation to the product lifetime and the reaction dynamics of the product creation process. By analyzing the time traces of the protein copy number using this theory, we can extract the power spectrum of the mRNA number, which cannot be directly measured by currently available experimental techniques. From the power spectrum of the mRNA number, we can further extract quantitative information about the transcriptional regulation dynamics. Our power spectrum analysis of gene expression noise is demonstrated for the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. Additionally, we investigate how the non-Poisson reaction dynamics and the cell-to-cell heterogeneity in transcription and translation affect the power-spectra of the mRNA and protein number.

physics.bio-ph↗

arXiv2018

Universal Transport Dynamics of Complex Fluids

Thermal motion in complex fluids is a complicated stochastic process but ubiquitously exhibits initial ballistic, intermediate sub-diffusive, and long-time non-Gaussian diffusive motion, unless interrupted. Despite its relevance to numerous dynamical processes of interest in modern science, a unified, quantitative understanding of thermal motion in complex fluids remains a long-standing problem. Here, we present a new transport equation and its solutions, which yield a unified quantitative explanation of the mean square displacement (MSD) and the non-Gaussian parameter (NGP) of various fluid systems. We find the environment-coupled diffusion kernel and its time correlation function are two essential quantities determining transport dynamics of complex fluids. From our analysis, we construct a general, explicit model of the complex fluid transport dynamics. This model quantitatively explains not only the MSD and NGP, but also the time-dependent relaxation of the displacement distribution for various systems. We introduce the concepts of intrinsic disorder and extrinsic disorder that have distinct effects on transport dynamics and different dependencies on temperature and density. This work presents a new paradigm for quantitative understanding of transport and transport-coupled processes in complex disordered media.

cond-mat.dis-nn↗

arXiv2017

Comments on Nonrenewal Statistics in the Catalytic Activity of Enzyme Molecules at Mesoscopic Concentrations

It is well known in enzyme kinetics that the Michaelis-Menten (MM) equation is applicable only to enzymes in the steady state. We show that the result obtained in the previous work [Phys. Rev. Lett. 107, 218301 (2011)] is inconsistent with the MM equation, not because the authors considered the enzyme system at mesoscopic concentrations but because they considered the enzyme system in the non-stationary state. The substrate concentration dependence of the mean turnover time is, in fact, consistent with the MM equation in the steady state, regardless of the number of enzymes in the system.

physics.bio-ph↗