arXiv subjects

Ariel Amir

Publications and source records attributed to Ariel Amir.

At least 19 recordsLinked to original sources

arXiv2026

Essential Role of Extrinsic Noise in Models of E. coli Division Control

Our understanding of cell division control in bacteria still relies largely on interpreting correlations between phenomenological variables, with limited connection to the underlying molecular mechanisms. Here, we analytically solve a stochastic threshold-accumulation model in which a size-dependent divisor protein triggers division upon reaching a noisy, autocorrelated threshold, quantifying within a unified framework the combined effects of intrinsic and extrinsic noise and key mechanistic parameters such as protein reset and threshold memory. We show that incorporating these elements yields behavior far richer than the commonly assumed adder, spanning a continuum of division strategies from timer to sizer while modulating size fluctuations in a nontrivial fashion. Comparison with single-cell E. coli data shows that extrinsic noise and additional mechanistic ingredients are required to account for the observed size fluctuations. The adder emerges when threshold correlations balance protein reset, generalizing the hypothesis that full reset is necessary to maintain adder control. Our results establish a unified analytical framework linking stochastic molecular processes to emergent division laws, to be used in more complex bacterial cell-cycle models.

q-bio.CB↗

arXiv2026

Air Drag Controls the Finite-Time Singularity of Euler's Disk

The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we study the dynamics of disks with varying mass and radius on different surfaces. We show that the late-time motion near the singularity is governed by viscous air-drag arising from shear in the boundary layer beneath the disk, as evidenced by the mass dependence of the dynamics, measurements in a partial vacuum, and a geometric control using a steel ring. At earlier times, dissipation is dominated by rolling friction, which on glass exhibits an unexpected sublinear scaling with disk mass, suggesting an adhesion-based rolling resistance. These results clarify the dissipation mechanisms underlying the singularity of Euler's disk and have broader implications for rolling-contact systems operating under low loads on smooth surfaces.

cond-mat.soft↗

arXiv2025

Extremal events dictate population growth rate inference

Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite data, which introduces systematic errors. A comprehensive understanding of these errors in the context of finite data remains elusive. To address this gap, we study the error in growth rate estimates across different models. We show that under the usual bias-variance decomposition, the bias can be decomposed into a finite-time bias and nonlinear averaging bias. We demonstrate that finite-time bias, which dominates at short times, can be mitigated by fitting its monotonic behavior. In contrast, at longer times, nonlinear averaging bias becomes the predominant source of error, leading to a phase transition. This transition can be understood through the Random Energy Model, a mean-field model of disordered systems, where a few lineages dominate the estimator. Applying these methods to experimental data demonstrates that correcting for biases in lineage-based approaches yields consistent results for the long-term growth rate across multiple methods and enables the reverse-engineering of dynamic models. This new framework provides a quantitative understanding of growth rate estimators, clarifies the conditions under which they can be effectively applied to finite data, and introduces model-free approaches for studying the connections between physiology and cell growth.

cond-mat.stat-mech↗

arXiv2024

Mechanics and wrinkling patterns of pressurized bent tubes

Take a drinking straw and bend it from its ends. After sufficient bending, the tube buckles forming a kink, where the curvature is localized in a very small area. This instability, known generally as the Brazier effect, is inherent to thin-walled cylindrical shells, which are particularly ubiquitous in living systems, such as rod-shaped bacteria. However, tubular biological structures are often pressurized, and the knowledge of the mechanical response upon bending in this scenario is limited. In this work, we use a computational model to study the mechanical response and the deformations as a result of bending pressurized tubes. In addition, we employ tension-field theory to describe the mechanical behaviour before and after the wrinkling transition. Furthermore, we investigate the development and evolution of wrinkle patterns beyond the instability, showing different wrinkled configurations. We discover the existence of a multi-wavelength mode following the purely sinusoidal wrinkles and anticipating the kinked configuration of the tube.

cond-mat.soft↗

arXiv2024

Connecting cooperative transport by ants with the physics of self-propelled particles

Paratrechina longicornis ants are known for their ability to cooperatively transport large food items. Previous studies have focused on the behavioral rules of individual ants and explained the efficient coordination using the coupled-carrier model. In contrast to this microscopic description, we instead treat the transported object as a single self-propelled particle characterized by its velocity magnitude and angle. We experimentally observe P. longicornis ants cooperatively transporting loads of varying radii. By analyzing the statistical features of the load's movement, we show that its salient properties are well captured by a set of Langevin equations describing a self-propelled particle. We relate the parameters of our macroscopic model to microscopic properties of the system. While the autocorrelation time of the velocity direction increases with group size, the autocorrelation time of the speed has a maximum at an intermediate group size. This corresponds to the critical slowdown close to the phase transition identified in the coupled-carrier model. Our findings illustrate that a self-propelled particle model can effectively characterize a system of interacting individuals.

physics.bio-ph↗

arXiv2024

Criticality in the Luria-Delbrück model with an arbitrary mutation rate

The Luria-Delbrück model is a classic model of population dynamics with random mutations, that has been used historically to prove that random mutations drive evolution. In typical scenarios, the relevant mutation rate is exceedingly small, and mutants are counted only at the final time point. Here, inspired by recent experiments on DNA repair, we study a mathematical model that is formally equivalent to the Luria-Delbrück setup, with the repair rate $p$ playing the role of mutation rate, albeit taking on large values, of order unity per cell division. We find that although at large times the fraction of repaired cells approaches one, the variance of the number of repaired cells undergoes a phase transition: when $p>1/2$ the variance decreases with time, but, intriguingly, for $p<1/2$ even though the fraction of repaired cells approaches 1, the variance in number of repaired cells increases with time. Analyzing DNA-repair experiments, we find that in order to explain the data the model should also take into account the probability of a successful repair process once it is initiated. Taken together, our work shows how the study of variability can lead to surprising phase-transitions as well as provide biological insights into the process of DNA-repair.

physics.bio-ph↗

arXiv2023

Gene expression in growing cells: A biophysical primer

Cell growth and gene expression, essential elements of all living systems, have long been the focus of biophysical interrogation. Advances in single-cell methods have invigorated theoretical studies into these processes. However, until recently, there was little dialog between the two areas of study. Most theoretical models for gene regulation assumed gene activity to be oblivious to the progression of the cell cycle between birth and division. But there are numerous ways in which the periodic character of all cellular observables can modulate gene expression. The molecular factors required for transcription and translation increase in number during the cell cycle, but are also diluted due to the continuous increase in cell volume. The replication of the genome changes the dosage of those same cellular players but also provides competing targets for regulatory binding. Finally, cell division reduces their number again, and so forth. Stochasticity is inherent to all these biological processes, manifested in fluctuations in the synthesis and degradation of new cellular components as well as the random partitioning of molecules at each cell division. The notion of gene expression as stationary is thus hard to justify. In this review, we survey the emerging paradigm of cell-cycle regulated gene expression, with an emphasis on the global expression patterns rather than gene-specific regulation. We discuss recent experimental reports where cell growth and gene expression were simultaneously measured in individual cells, providing first glimpses into the coupling between the two. While the experimental findings, not surprisingly, differ among genes and organisms, several theoretical models have emerged that attempt to reconcile these differences and form a unifying framework for understanding gene expression in growing cells.

q-bio.SC↗

arXiv2023

Design principles of transcription factors with intrinsically disordered regions

Transcription Factors (TFs) are proteins crucial for regulating gene expression. Effective regulation requires the TFs to rapidly bind to their correct target, enabling the cell to respond efficiently to stimuli such as nutrient availability or the presence of toxins. However, the search process is hindered by slow diffusive movement and the presence of `false' targets --DNA segments that are similar to the true target. In eukaryotic cells, most TFs contain an Intrinsically Disordered Region (IDR), which is commonly assumed to behave as a long, flexible polymeric tail composed of hundreds of amino acids. Recent experimental findings indicate that the IDR of certain TFs plays a pivotal role in the search process. However, the principles underlying the IDR's role remain unclear. Here, we reveal key design principles of the IDR related to TF binding affinity and search time. Our results demonstrate that the IDR significantly enhances both of these aspects. Furthermore, our model shows good agreement with experimental results, and we propose further experiments to validate the model's predictions.

physics.bio-ph↗

arXiv2023

Pressure-induced Shape-shifting of Helical Bacteria

Many bacterial species are helical in form, including the widespread pathogen H. pylori. Motivated by recent experiments on H. pylori showing that cell wall synthesis is not uniform, we investigate the possible formation of helical cell shape induced by elastic heterogeneity. We show, experimentally and theoretically, that helical morphogenesis can be produced by pressurizing an elastic cylindrical vessel with helical reinforced lines. The properties of the pressurized helix are highly dependent on the initial helical angle of the reinforced region. We find that steep angles result in crooked helices with, surprisingly, reduced end-to-end distance upon pressurization. This work helps to explain the possible mechanisms for the generation of helical cell morphologies and may inspire the design of novel pressure-controlled helical actuators.

cond-mat.soft↗

arXiv2022

Conditional Probability as Found in Nature: Facilitated Diffusion

Transcription Factors (TFs) are proteins that regulate gene expression. The regulation mechanism is via the binding of a TF to a specific part of the gene associated with it, the TF's target. The target of a specific TF corresponds to a vanishingly small part of the entire DNA, where at the same time the search must end in a matter of tens of seconds at most for its biological purpose to be fulfilled - this makes the search a problem of high interest. Facilitated Diffusion is a mechanism used in nature for a robust and efficient search process. This mechanism combines 1D diffusion along the DNA and "excursions" of diffusion in 3D that help the TF to quickly arrive at distant parts of the DNA. In this paper we provide a derivation concerning this mechanism that links this search process to fundamental concepts in probability theory (conditional probability).

cond-mat.stat-mech↗

arXiv2022

Universal catastrophe time distributions of dynamically unstable polymers

Dynamic instability -- the growth, catastrophe, and shrinkage of quasi-one-dimensional filaments -- has been observed in multiple biopolymers. Scientists have long understood the catastrophic cessation of growth and subsequent depolymerization as arising from the interplay of hydrolysis and polymerization at the tip of the polymer. Here, we show that for a broad class of catastrophe models, the expected catastrophe time distribution is exponential. We show that the distribution shape is insensitive to noise, but that depletion of monomers from a finite pool can dramatically change the distribution shape by reducing the polymerization rate. We derive a form for this finite-pool catastrophe time distribution and show that finite-pool effects can be important even when the depletion of monomers does not greatly alter the polymerization rate.

cond-mat.soft↗

arXiv2021

Bending Instability of Rod-shaped Bacteria

A thin-walled tube, e.g., a drinking straw, manifests an instability when bent by localizing the curvature change in a small region. This instability has been extensively studied since the seminal work of Brazier nearly a century ago. However, the scenario of pressurized tubes has received much less attention. Motivated by rod-shaped bacteria such as E. coli, whose cell walls are much thinner than their radius and are subject to a substantial internal pressure, we study, theoretically, how this instability is affected by this internal pressure. In the parameter range relevant to the bacteria, we find that the internal pressure significantly postpones the onset of the instability, while the bending stiffness of the cell wall has almost no influence. This study suggests a new method to infer turgor pressure in rod-shaped bacteria from bending experiments.

cond-mat.soft↗

arXiv2021

Temporal Evolution of Flow in Pore-Networks: From Homogenization to Instability

We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.

physics.flu-dyn↗

arXiv2021

A transport approach to relate asymmetric protein segregation and population growth

Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry $a$ = 1) and when the asymmetry is small ($0 \leq a \ll 1$). We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter ($a_{\rm eff}$). We discuss the biological implication of our models and compare with other theoretical models.

q-bio.PE↗

arXiv2021

Diffusive wave dynamics beyond the continuum limit

Scientists have observed and studied diffusive waves in contexts as disparate as population genetics and cell signaling. Often, these waves are propagated by discrete entities or agents, such as individual cells in the case of cell signaling. For a broad class of diffusive waves, we characterize the transition between the collective propagation of diffusive waves -- in which the wave speed is well-described by continuum theory -- and the propagation of diffusive waves by individual agents. We show that this transition depends heavily on the dimensionality of the system in which the wave propagates and that disordered systems yield dynamics largely consistent with lattice systems. In some system dimensionalities, the intuition that closely packed sources more accurately mimic a continuum can be grossly violated.

nlin.PS↗

arXiv2020

Stability of gene regulatory networks

Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as transcription factors (TFs), the full set of proteins within the cell constitutes a large system of interacting components. Here, we explore factors affecting the stability of this system by coupling the dynamics of mRNAs and protein concentrations in a growing cell. We find that it is possible for protein concentrations to become unstable if the regulation strengths or system size becomes too large, and that other global structural features of the networks can dramatically enhance the stability of the system. In particular, given the same number of proteins, TFs, number of interactions, and regulation strengths, a network that resembles a bipartite graph with a lower fraction of interactions that target TFs has a higher chance of being stable. By scrambling the $\textit{E. coli.}$ transcription network, we find that the randomized network with the same number of regulatory interactions is much more likely to be unstable than the real network. These findings suggest that constraints imposed by system stability could have played a role in shaping the existing regulatory network during the evolutionary process. We also find that contrary to what one might expect from random matrix theory and what has been argued in the literature, the degradation rate of mRNA does not affect whether the system is stable.

physics.bio-ph↗

arXiv2020

Non-genetic variability: survival strategy or nuisance?

The observation that phenotypic variability is ubiquitous in isogenic populations has led to a multitude of experimental and theoretical studies seeking to probe the causes and consequences of this variability. Whether it be in the context of antibiotic treatments or exponential growth in constant environments, non-genetic variability has shown to have significant effects on population dynamics. Here, we review research that elucidates the relationship between cell-to-cell variability and population dynamics. After summarizing the relevant experimental observations, we discuss models of bet-hedging and phenotypic switching. In the context of these models, we discuss how switching between phenotypes at the single-cell level can help populations survive in uncertain environments. Next, we review more fine-grained models of phenotypic variability where the relationship between single-cell growth rates, generation times and cell sizes is explicitly considered. Variability in these traits can have significant effects on the population dynamics, even in a constant environment. We show how these effects can be highly sensitive to the underlying model assumptions. We close by discussing a number of open questions, such as how environmental and intrinsic variability interact and what the role of non-genetic variability in evolutionary dynamics is.

q-bio.PE↗

arXiv2020

The effect of interactions and disorder on the relaxation of two-level systems in amorphous solids

At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass", described by the random field Ising model with random $1/r^3$ interactions. In this paper we perform a self consistent mean field calculation, previously used to study the electron-glass (EG) model [A.~Amir {\it et al.}, Phys. Rev. B {\bf 77}, 165207, (2008)]. Similar to the electron-glass, we find $\frac{1}λ$ distribution of relaxation rates $λ$, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLS glass model shows faster dynamics. This suggests that given system specific properties, glass dynamics can be slowed down or sped up by the interactions.

cond-mat.dis-nn↗