Biology subjects

Ali, S. Y.

Publications and source records attributed to Ali, S. Y..

3 recordsLinked to original sources

bioRxiv2025

Fluctuations in first passage times and utility of resetting protocol in biochemical systems with two-state toggling

Interesting theoretical problems of target search or threshold crossing, formally known as first passage, often arise in both diffusive transport problems as well as problems of chemical reaction kinetics. We study three systems following different chemical kinetics, and are special as they toggle between two states: (i) a population dynamics of cells with auto-catalytic birth and intermittent toxic chemical-induced forced death, (ii) a bond cluster model representing membrane adhesion to extracellular matrix under a fluctuating load, and (iii) a model of gene transcription with a regulated promoter switching between active and inactive states. Each of these systems has a target state to attain, which defines a first passage problem - namely, population becoming extinct, complete membrane detachment, or mRNA count crossing a threshold. We study the fluctuations in first passage time and show that it is interestingly non-monotonic in all these cases, with increasing strength of bias towards the target. We also study suitable stochastic resetting protocols to expedite first passage for these systems, and show that there is a re-entrant transition of the efficacy of this protocol in all the three cases, as a function of the bias. The exact analytical condition for these transitions predicted in earlier literature is verified here through simulations.

biophysics↗

bioRxiv2025

Cyclo-stationary distributions of mRNA and Protein counts for random cell division times

There is a long history of using experimental and computational approaches to study noise in single-cell levels of mRNA and proteins. The noise originates from a myriad of factors: intrinsic processes of gene expression, partitioning errors during division, and extrinsic effects, such as, random cell-cycle times. Although theoretical methods are well developed to analytically understand full statistics of copy numbers for fixed or Erlang distributed cell cycle times, the general problem of random division times is still open. For any random (but uncorrelated) division time distribution, we present a method to address this challenging problem and obtain exact series representations of the copy number distributions in the cyclo-stationary state. We provide explicit cell age-specific and age-averaged results, and analyze the relative contribution to noise from intrinsic and extrinsic sources. Our analytical approach will aid the analysis of single-cell expression data and help in disentangling the impact of variability in division times.

systems biology↗

bioRxiv2024

Exact distributions of threshold crossing times of proteins under post-transcriptional regulation by small RNAs

The timings of several cellular events like cell lysis, cell division, or pore formation in endosomes are regulated by the time taken for the relevant proteins to cross a threshold in number or concentration. Since protein synthesis is stochastic, the threshold crossing time is a first passage problem. The exact distributions of these first passage processes have been obtained recently for unregulated and auto-regulated genes. Many proteins are however regulated by post-transcriptional regulation, controlled by small non-coding RNAs (sRNAs). Certain mathematical models of gene expression with post-transcriptional sRNA regulation have been recently exactly mapped to models without sRNA regulation. Utilizing this mapping and the exact distributions, we calculate exact results on fluctuations (full distribution, all cumulants, and characteristic times) of protein threshold crossing times in the presence of sRNA regulation. We derive two interesting predictions from these exact results. We show that the size of the fluctuation of the threshold crossing times have a non-monotonic U-shaped behavior as a function of the rates of binding and unbinding of the sRNA-mRNA complex. Thus there are optimal parameters that minimize noise. Furthermore, the fluctuations in models with sRNA regulation may be higher or lower compared to the model without regulation, depending on the mean protein burst size.

biophysics↗