arXiv subjects

Nash Rochman

Publications and source records attributed to Nash Rochman.

4 recordsLinked to original sources

arXiv2018

Erg(r)odicity: Hidden Bias and the Growthrate Gain

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the "von Foerster equation" for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, "a single individual observed over many generations recapitulates the behavior of the entire ensemble" is implied by the other, "the probability of observing any state is conserved across time and over all individuals" in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the "growth rate gain" - the phenomenon that variations in the cell cycle duration lead to an improved population-level growth rate - in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

q-bio.QM↗

arXiv2017

Inertia and Prediction in the Response to External Perturbation of Noisy Variables

For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation Dissipation Theorem (FDT). In a previous paper, we proposed a phenomenological model for the response of the cell cycle duration distribution to environmental changes which correlated the width of this distribution to response efficiency when FDT was not applicable. Here we emphasize how that model may be used to illustrate this general principle, that the stochasticity of a variable while inversely proportional to stability is often directly proportional to lability. Comparisons are made between this discrete-time model and the simple harmonic oscillator. We then consider a simple continuous dynamical system, the 'Active Oscillator', which illustrates this principle in another fashion.

physics.gen-ph↗

arXiv2016

"Inchworm Filaments": Motility and Pattern Formation

In a previous paper, we examined a class of possible conformations for helically patterned filaments in contact with a bonding surface. In particular, we investigated geometries where contact between the pattern and the surface was improved through a periodic twisting and lifting of the filament. A consequence of this lifting is that the total length of the filament projected onto the surface decreases after bonding. When the bonding character of the surface is actuated, this phenomenon can lead to both lifelike "inchworm" behavior of the filaments and ensemble movement. We illustrate, through simulation, how pattern formation may be achieved through this mechanism.

q-bio.SC↗

arXiv2016

To Grow is Not Enough: Impact of Noise on Cell Environmental Response and Fitness

Quantitative single cell measurements have shown that cell cycle duration (the time between cell divisions) for diverse cell types is a noisy variable. The underlying distribution is mean scalable with a universal shape for many cell types in a variety of environments. Here we show through both experiment and theory that increasing the amount of noise in the regulation of the cell cycle negatively impacts the growth rate but positively correlates with improved cellular response to fluctuating environments. Our findings suggest that even non-cooperative cells in exponential growth phase do not optimize fitness through growth rate alone, but also optimize adaptability to changing conditions. In a manner similar to genetic evolution, increasing the noise in biochemical processes correlates with improved response of the system to environmental changes.

q-bio.CB↗