@article {1533988,
title = {Non-genetic variability: survival strategy or nuisance?},
year = {2020},
abstract = {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.},
url = {https://arxiv.org/abs/2010.05672},
author = {Levien, Ethan and Jiseon Min and Kondev, Jane and Amir, Ariel}
}
@article {1528054,
title = {Disentangling intrinsic and extrinsic gene expression noise in growing cells},
year = {2020},
abstract = {Gene expression is a stochastic process. Despite the increase of protein numbers in growing cells, the protein concentrations are often found to be confined within small ranges throughout the cell cycle. Considering the time trajectory of protein concentration as a random walker in the concentration space, an effective restoring force (with a corresponding "spring constant") must exist to prevent the divergence of concentration due to random fluctuations. In this work, we prove that the magnitude of the effective spring constant is directly related to the fraction of intrinsic noise in the total protein concentration noise. We show that one can infer the magnitude of intrinsic, extrinsic, and measurement noises of gene expression solely based on time-resolved data of protein concentration, without any a priori knowledge of the underlying gene expression dynamics. We apply this method to experimental data of single-cell bacterial gene expression. The results allow us to estimate the average protein number and the translation burst parameter.},
url = {https://www.biorxiv.org/content/10.1101/2020.08.26.268722v1},
author = {Lin, Jie and Amir, Ariel}
}
@article {1512219,
title = {Stability of gene regulatory networks},
year = {2020},
abstract = {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 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.},
url = {https://arxiv.org/pdf/2006.00018.pdf},
author = {Guo, Yipei and Amir, Ariel}
}
@article {1491152,
title = {Thermal conductance of one-dimensional disordered harmonic chains},
journal = {Physical Review B},
volume = {101},
number = {12},
year = {2020},
abstract = {We study heat conduction mediated by longitudinal phonons in one-dimensional disordered harmonic chains. Using scaling properties of the phonon density of states and localization in disordered systems, we find nontrivial scaling of the thermal conductance with the system size. Our findings are corroborated by extensive numerical analysis. We show that, suprisingly, the thermal conductance of a system with strong disorder, characterized by a {\textquotedblleft}heavy-tailed{\textquotedblright} probability distribution, and with large impedance mismatch between the bath and the system, scales normally with the system size, i.e., in a manner consistent with Fourier{\textquoteright}s law. We identify a dimensionless scaling parameter, related to the temperature scale and the localization length of the phonons, through which the thermal conductance for different models of disorder and different temperatures follows a universal behavior.},
url = {https://link.aps.org/doi/10.1103/PhysRevB.101.121403},
author = {Biswarup Ash and Amir, Ariel and Yohai Bar-Sinai and Oreg, Yuval and Imry, Yoseph}
}
@article {1484156,
title = {Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations},
journal = {Physical Review Letters},
volume = {125},
number = {4},
year = {2020},
abstract = {In exponentially proliferating populations of microbes, the population doubles at a rate less than the average doubling time of a single-cell due to variability at the single-cell level. It is known that the distribution of generation times obtained from a single lineage is, in general, insufficient to determine a population{\textquoteright}s growth rate. Is there an\ explicit\ relationship between observables obtained from a single lineage and the population growth rate? We show that a population{\textquoteright}s growth rate can be represented in terms of averages over isolated lineages. This lineage representation is related to a large deviation principle that is a generic feature of exponentially proliferating populations. Due to the large deviation structure of growing populations, the number of lineages needed to obtain an accurate estimate of the growth rate depends exponentially on the duration of the lineages, leading to a nonmonotonic convergence of the estimate, which we verify in both synthetic and experimental data sets.},
url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.048102},
author = {Levien, Ethan and Trevor GrandPre and Amir, Ariel}
}
@article {1483083,
title = {An elementary renormalization-group approach to the generalized central limit theorem and extreme value distributions},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
volume = {2020},
year = {2020},
abstract = {The generalized central limit theorem is a remarkable generalization of the central limit theorem, showing that the sum of a large number of independent, identically-distributed (i.i.d) random variables with infinite variance may converge under appropriate scaling to a distribution belonging to a special family known as L{\'e}vy stable distributions. Similarly, the\ maximum\ of i.i.d. variables may converge to a distribution belonging to one of three universality classes (Gumbel, Weibull and Fr{\'e}chet). Here, we rederive these known results following a mathematically non-rigorous yet highly transparent renormalization-group-inspired approach that captures both of these universal results following a nearly identical procedure.},
url = {https://iopscience.iop.org/article/10.1088/1742-5468/ab5b8c/pdf},
author = {Amir, Ariel}
}
@article {1481816,
title = {Cell-size regulation in budding yeast does not depend on linear accumulation of Whi5},
journal = {PNAS},
year = {2020},
abstract = {Cells must couple cell-cycle progress to their growth rate to restrict the spread of cell sizes present throughout a population. Linear, rather than exponential, accumulation of Whi5, was proposed to provide this coordination by causing a higher Whi5 concentration in cells born at a smaller size. We tested this model using the inducible\ GAL1\ promoter to make the Whi5 concentration independent of cell size. At an expression level that equalizes the mean cell size with that of wild-type cells, the size distributions of cells with galactose-induced Whi5 expression and wild-type cells are indistinguishable. Fluorescence microscopy confirms that the endogenous and\ GAL1\ promoters produce different relationships between Whi5 concentration and cell volume without diminishing size control in the G1 phase. We also expressed Cln3 from the GAL1 promoter, finding that the spread in cell sizes for an asynchronous population is unaffected by this perturbation. Our findings indicate that size control in budding yeast does not fundamentally originate from the linear accumulation of Whi5, contradicting a previous claim and demonstrating the need for further models of cell-cycle regulation to explain how cell size controls passage through Start.},
url = {https://www.pnas.org/content/early/2020/06/08/2001255117/tab-article-info},
author = {Felix Barber and Amir, Ariel and Andrew W. Murray}
}
@article {1480111,
title = {From single-cell variability to population growth},
journal = {Physical Review E},
volume = {101},
number = {1},
year = {2020},
pages = {012401},
abstract = {Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more general and biologically relevant model in which cells grow exponentially and generation times are correlated in a manner which controls cell size. In addition to the fluctuating generation times, we also allow the single-cell growth rates to fluctuate and account for their correlations across the lineage tree. Surprisingly, we find that the population growth rate only depends on the distribution of single-cell growth rates and their correlations.},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.101.012401},
author = {Lin, Jie and Amir, Ariel}
}
@article {1468351,
title = {Evolution of microbial growth traits under serial dilution},
journal = {Genetics},
volume = {215},
number = {2},
year = {2020},
abstract = {Selection of mutants in a microbial population depends on multiple cellular traits. In serial-dilution evolution experiments, three key traits are the lag time when transitioning from starvation to growth, the exponential growth rate, and the yield (number of cells per unit resource). Here we investigate how these traits evolve in laboratory evolution experiments using a minimal model of population dynamics, where the only interaction between cells is competition for a single limiting resource. We find that the fixation probability of a beneficial mutation depends on a linear combination of its growth rate and lag time relative to its immediate ancestor, even under clonal interference. The relative selective pressure on growth rate and lag time is set by the dilution factor; a larger dilution factor favors the adaptation of growth rate over the adaptation of lag time. The model shows that yield, however, is under no direct selection. We also show how the adaptation speeds of growth and lag depend on experimental parameters and the underlying supply of mutations. Finally, we investigate the evolution of covariation between these traits across populations, which reveals that the population growth rate and lag time can evolve a nonzero correlation even if mutations have uncorrelated effects on the two traits. Altogether these results provide useful guidance to future experiments on microbial evolution.},
url = {https://www.genetics.org/content/early/2020/05/04/genetics.120.303149},
author = {Lin, Jie and Michael Manhart and Amir, Ariel}
}
@article {1462822,
title = {A Mechanistic Model of the Regulation of Division Timing by the Circadian Clock in Cyanobacteria},
journal = {Biophysical Journal},
volume = {118},
number = {12},
year = {2020},
pages = {2905-2913},
abstract = {The cyanobacterium\ Synechococcus elongatus\ possesses a circadian clock in the form of a group of proteins whose concentrations and phosphorylation states oscillate with daily periodicity under constant conditions. The circadian clock regulates the cell cycle such that the timing of the cell divisions is biased toward certain times during the circadian period, but the mechanism underlying this phenomenon remains unclear. Here, we propose a mechanism in which a protein limiting for division accumulates at a rate proportional to the cell volume growth and is modulated by the clock. This {\textquotedblleft}modulated rate{\textquotedblright} model, in which the clock signal is integrated over time to affect division timing, differs fundamentally from the previously proposed {\textquotedblleft}gating{\textquotedblright} concept, in which the clock is assumed to suppress divisions during a specific time window. We found that although both models can capture the single-cell statistics of division timing in\ S.\ elongatus, only the modulated rate model robustly places divisions away from darkness during changes in the environment. Moreover, within the framework of the modulated rate model, existing experiments on\ S.\ elongatus\ are consistent with the simple mechanism that division timing is regulated by the accumulation of a division limiting protein in a phase with genes whose activity peaks at dusk.},
url = {https://www.sciencedirect.com/science/article/abs/pii/S0006349520304124},
author = {Ho, Po-Yi and Bruno M.C. Martins and Amir, Ariel}
}
@article {1445318,
title = {The interplay of phenotypic variability and fitness in finite microbial populations},
journal = {Journal of the Royal Society Interface},
volume = {17},
number = {166},
year = {2020},
abstract = {
In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler{\textendash}Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler{\textendash}Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.
},
url = {https://royalsocietypublishing.org/doi/full/10.1098/rsif.2019.0827?casa_token=xJqU2Cx74DAAAAAA\%3AI5ACrQSmiE1W4PKeKhZNbpgKtQ3hhmcrLpwskaFmhqg9RmM5nYYRxrP2oAQIVf5hpwxS6IEnyP6E},
author = {Levien, Ethan and Kondev, Jane and Amir, Ariel}
}
@article {1478101,
title = {Dynamics of diffusive cell signaling relays},
year = {2019},
abstract = {Cells can communicate with each other by emitting diffusible signaling molecules into the surrounding environment. However, simple diffusion is slow. Even small molecules take hours to diffuse millimeters away from their source, making it difficult for thousands of cells to coordinate their activity over millimeters, as happens routinely during development and immune response. Moreover, simple diffusion creates shallow, Gaussian-tailed concentration profiles. Attempting to move up or down such shallow gradients - to chemotax - is a difficult task for cells, as they see only small spatial and temporal concentration changes. Here, we demonstrate that cells utilizing diffusive relays, in which the presence of one type of diffusible signaling molecule triggers participation in the emission of the same type of molecule, can propagate fast-traveling diffusive waves that give rise to steep chemical gradients. Our methods are general and capture the effects of dimensionality, cell density, signaling molecule degradation, pulsed emission, and cellular chemotaxis on the diffusive wave dynamics. We show that system dimensionality - the size and shape of the extracellular medium and the distribution of the cells within it - can have a particularly dramatic effect on wave initiation and asymptotic propagation, and that these dynamics are insensitive to the details of cellular activation. As an example, we show that neutrophil swarming experiments exhibit dynamical signatures consistent with the proposed signaling motif. Interpreted in the context of these experiments, our results provide insight into the utility of signaling relays in immune response.},
url = {https://www.biorxiv.org/content/10.1101/2019.12.27.887273v1},
author = {Paul Dieterle and Jiseon Min and Irimia, Daniel and Amir, Ariel}
}
@article {1468355,
title = {Length regulation of multiple flagella that self-assemble from a shared pool of components},
journal = {eLife},
volume = {8},
year = {2019},
abstract = {The single-celled green algae\ Chlamydomonas reinhardtii\ with its two flagella - microtubule-based structures of equal and constant lengths - is the canonical model organism for studying size control of organelles. Experiments have identified motor-driven transport of tubulin to the flagella tips as a key component of their length control. Here we consider a class of models whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that the limiting-pool assumption is insufficient to describe the results of severing experiments, in which a flagellum is regenerated after it has been severed. Next, we consider an extension of the limiting-pool model that incorporates proteins that depolymerize microtubules. We show that this {\textquoteright}active disassembly{\textquoteright} model of flagellar length control explains in quantitative detail the results of severing experiments and use it to make predictions that can be tested in experiments.},
author = {Thomas G Fai and Mohapatra, Lishibanya and Prathitha Kar and Kondev, Jane and Amir, Ariel}
}
@article {1453446,
title = {Stochastic tunneling across fitness valleys can give rise to a logarithmic long-term fitness trajectory},
journal = {Science Advances},
volume = {5},
number = {7},
year = {2019},
abstract = {Adaptation, where a population evolves increasing fitness in a fixed environment, is typically thought of as a hill-climbing process on a fitness landscape. With a finite genome, such a process eventually leads the population to a fitness peak, at which point fitness can no longer increase through individual beneficial mutations. Instead, the ruggedness of typical landscapes due to epistasis between genes or DNA sites suggests that the accumulation of multiple mutations (via a process known as stochastic tunneling) can allow a population to continue increasing in fitness. However, it is not clear how such a phenomenon would affect long-term fitness evolution. By using a spin-glass type model for the fitness function that takes into account microscopic epistasis, we find that hopping between metastable states can mechanistically and robustly give rise to a slow, logarithmic average fitness trajectory.},
url = {https://advances.sciencemag.org/content/advances/5/7/eaav3842.full.pdf},
author = {Guo, Yipei and Marija Vucelja and Amir, Ariel}
}
@article {1423481,
title = {Mechanics and dynamics of translocating MreB filaments on curved membranes},
journal = {eLife},
volume = {8},
year = {2019},
pages = {e40472},
abstract = {MreB is an actin homolog that is essential for coordinating the cell wall synthesis required for the rod shape of many bacteria. Previously we have shown that filaments of MreB bind to the curved membranes of bacteria and translocate in directions determined by principal membrane curvatures to create and reinforce the rod shape (Hussain et al., 2018). Here, in order to understand how MreB filament dynamics affects their cellular distribution, we model how MreB filaments bind and translocate on membranes with different geometries. We find that it is both energetically favorable and robust for filaments to bind and orient along directions of largest membrane curvature. Furthermore, significant localization to different membrane regions results from processive MreB motion in various geometries. These results demonstrate that the\ in vivo\ localization of MreB observed in many different experiments, including those examining negative Gaussian curvature, can arise from translocation dynamics alone.},
url = {https://elifesciences.org/articles/40472},
author = {Felix Wong and Ethan C. Garner and Amir, Ariel}
}
@article {1365182,
title = {Quantum Diffusion in the Strong Tunneling Regime},
journal = {Physical Review B},
volume = {100},
number = {2},
year = {2019},
abstract = {We study the spread of a quantum-mechanical wave packet in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations between different level-crossing events can be neglected, we use the solution of the Landau-Zener problem to find how the diffusion constant depends on the noise. We also show that when an electric field or external disordered potential is applied to the system, the diffusion constant is suppressed with no drift term arising. The results are relevant to various quantum systems, including exciton diffusion in photosynthesis and electronic transport in solid-state physics.},
url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.024110},
author = {Nisarga Paul and Amir, Ariel}
}
@article {1315424,
title = {Mechanics and Dynamics of Bacterial Cell Lysis},
journal = {Biophysical Journal},
volume = {116},
number = {12},
year = {2019},
pages = {2378-2389},
abstract = {Membrane lysis, or rupture, is a cell death pathway in bacteria frequently caused by cell wall-targeting antibiotics. Although previous studies have clarified the biochemical mechanisms of antibiotic action, a physical understanding of the processes leading to lysis remains lacking. Here, we analyze the dynamics of membrane bulging and lysis in\ Escherichia coli, in which the formation of an initial, partially subtended spherical bulge ({\textquotedblleft}bulging{\textquotedblright}) after cell wall digestion occurs on a characteristic timescale of 1\ s and the growth of the bulge ({\textquotedblleft}swelling{\textquotedblright}) occurs on a slower characteristic timescale of 100 s. We show that bulging can be energetically favorable due to the relaxation of the entropic and stretching energies of the inner membrane, cell wall, and outer membrane and that the experimentally observed timescales are consistent with model predictions. We then show that swelling is mediated by the enlargement of wall defects, after which cell lysis is consistent with both the inner and outer membranes exceeding characteristic estimates of the yield areal strains of biological membranes. These results contrast biological membrane physics and the physics of thin, rigid shells. They also have implications for cellular morphogenesis and antibiotic discovery across different species of bacteria.},
url = {https://www.sciencedirect.com/science/article/pii/S0006349519304126?dgcid=author},
author = {Felix Wong and Amir, Ariel}
}
@article {1309584,
title = {Optimal segregation of proteins: phase transitions and symmetry breaking},
journal = {Physical Review Letters},
volume = {122},
year = {2019},
pages = {068101},
abstract = {Asymmetric segregation of key proteins at cell division{\textemdash}be it a beneficial or deleterious protein{\textemdash}is ubiquitous in unicellular organisms and often considered as an evolved trait to increase fitness in a stressed environment. Here, we provide a general framework to describe the evolutionary origin of this asymmetric segregation. We compute the population fitness as a function of the protein segregation asymmetry\ a, and show that the value of\ a\ which optimizes the population growth manifests a phase transition between symmetric and asymmetric partitioning phases. Surprisingly, the nature of phase transition is different for the case of beneficial proteins as opposed to deleterious proteins: a smooth (second order) transition from purely symmetric to asymmetric segregation is found in the former, while a sharp transition occurs in the latter. Our study elucidates the optimization problem faced by evolution in the context of protein segregation, and motivates further investigation of asymmetric protein segregation in biological systems.},
url = {https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.068101},
author = {Lin, Jie and Jiseon Min and Amir, Ariel}
}
@article {1316181,
title = {Homeostasis of protein and mRNA concentrations in growing cells},
journal = {Nature Communications},
volume = {9},
number = {4496},
year = {2018},
abstract = {Many experiments show that the numbers of mRNA and protein are proportional to the cell volume in growing cells. However, models of stochastic gene expression often assume constant transcription rate per gene and constant translation rate per mRNA, which are incompatible with these experiments. Here, we construct a minimal gene expression model to fill this gap. Assuming ribosomes and RNA polymerases are limiting in gene expression, we show that the numbers of proteins and mRNAs both grow exponentially during the cell cycle and that the concentrations of all mRNAs and proteins achieve cellular homeostasis; the competition between genes for the RNA polymerases makes the transcription rate independent of the genome number. Furthermore, by extending the model to situations in which DNA (mRNA) can be saturated by RNA polymerases (ribosomes) and becomes limiting, we predict a transition from exponential to linear growth of cell volume as the protein-to-DNA ratio increases.},
url = {https://www.nature.com/articles/s41467-018-06714-z},
author = {Lin, Jie and Amir, Ariel}
}
@article {1306299,
title = {Learning from Noise: How Observing Stochasticity May Aid Microbiology},
journal = {Trends in Microbiology},
volume = {26},
year = {2018},
pages = {374-385},
abstract = {For many decades, the wedding of quantitative data with mathematical modeling has been fruitful, leading to important biological insights. Here, we review some of the ongoing efforts to gain insights into problems in microbiology {\textendash} and, in particular, cell-cycle progression and its regulation {\textendash} through observation and quantitative analysis of the natural fluctuations in the system. We first illustrate this idea by reviewing a classic example in microbiology {\textendash} the Luria{\textendash}Delbr{\"u}ck experiment {\textendash} and discussing how, in that case, useful information was obtained by looking beyond the\ mean\ outcome of the experiment, but instead paying attention to the variability between replicates of the experiment. We then switch gears to the contemporary problem of cell cycle progression and discuss in more detail how insights into cell size regulation and, when relevant, coupling between the cell cycle and the circadian clock, can be gained by studying the natural fluctuations in the system and their statistical properties. We end with a more general discussion of how (in this context) the correct level of phenomenological model should be chosen, as well as some of the pitfalls associated with this type of analysis. Throughout this review the emphasis is\ not\ on providing details of the experimental setups or technical details of the models used, but rather, in fleshing out the conceptual structure of this particular approach to the problem. For this reason, we choose to illustrate the framework on a rather broad range of problems, and on organisms from all domains of life, to emphasize the commonality of the ideas and analysis used (as well as their differences).},
url = {http://www.cell.com/trends/microbiology/fulltext/S0966-842X(18)30026-X},
author = {Amir, Ariel and Nathalie Q. Balaban}
}
@article {1297830,
title = {Thermal conductivity in 1d: disorder-induced transition from anomalous to normal scaling},
journal = {Europhysics Letters},
volume = {124},
number = {1},
year = {2018},
abstract = {It is well known that the contribution of harmonic phonons to the thermal conductivity of 1D systems diverges with the harmonic chain length\ L (explicitly, increases with\ L\ as a power-law with a positive power). Furthermore, within various one-dimensional models containing disorder it was shown that this divergence persists, with the thermal conductivity scaling as √L under certain boundary conditions, where\ L\ is the length of the harmonic chain. Here we show that when the chain is weakly coupled to the heat reservoirs and there is strong disorder this scaling can be violated. We find a weaker power-law dependence on\ L, and show that for sufficiently strong disorder the thermal conductivity stops being anomalous -- despite both density-of-states and the diverging localization length scaling anomalously. Surprisingly, in this strong disorder regime two anomalously scaling quantities cancel each other to recover Fourier{\textquoteright}s law of heat transport.},
url = {http://iopscience.iop.org/article/10.1209/0295-5075/124/16001},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {1297081,
title = {Disorder engineering: From structural coloration to acoustic filters},
journal = {Phys. Rev. Materials},
volume = {2},
year = {2018},
pages = {075201},
abstract = {We study localization of waves in a one-dimensional disordered metamaterial of bilayers composed of thin fixed length scatterers placed randomly along a homogenous medium. As an interplay between order and disorder, we identify a new regime of strong disorder where the localization length becomes independent of the amount of disorder but depends on the frequency of the wave excitation and on the properties of the fixed length scatterer. As an example of a naturally occurring nearly one-dimensional disordered bilayer, we calculate the wavelength-dependent reflection spectrum for Koi fish using the experimentally measured parameters and find that the main mechanisms for the emergence of their silver structural coloration can be explained through the phenomenon of localization of light in the regime of strong disorder discussed above. Finally, we show that, by tuning the thickness of the fixed length scatterer, the above design principles could be used to engineer disordered metamaterials which selectively allow harmonics of a fundamental frequency to be transmitted in an effect which is similar to the insertion of a half-wave cavity in a quarter-wavelength stack. However, in contrast to the Lorentzian resonant peak of a half-wave cavity, we find that our disordered layer has a Gaussian line shape whose width becomes narrower as the number of disordered layers is increased.},
url = {https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.2.075201},
author = {Nitin Upadhyaya and Amir, Ariel}
}
@article {1289166,
title = {Modeling cell size regulation: From single-cell level statistics to molecular mechanisms and population level effects},
journal = {Annual Review of Biophysics},
volume = {47},
year = {2018},
abstract = {Most microorganisms regulate their cell size. In this article, we review some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics that they generate. We review the biologically relevant insights obtained from these models. We then describe cell cycle regulation and its molecular implementations, protein number regulation, and population growth, all in relation to size regulation. Finally, we discuss several future directions for developing understanding beyond phenomenological models of cell size regulation.},
url = {https://www.annualreviews.org/doi/10.1146/annurev-biophys-070317-032955},
author = {Ho, Po-Yi and Lin, Jie and Amir, Ariel}
}
@article {Eun2017,
title = {Archaeal cells share common size control with bacteria despite noisier growth and division},
journal = {Nature Microbiology},
volume = {3},
year = {2018},
pages = {148-154},
abstract = {In nature, microorganisms exhibit different volumes spanning six orders of magnitude 1 . Despite their capability to create different sizes, a clonal population in a given environment maintains a uniform size across individual cells. Recent studies in eukaryotic and bacterial organisms showed that this homogeneity in cell size can be accomplished by growing a constant size between two cell cycle events (that is, the adder model 2-6 ). Demonstration of the adder model led to the hypothesis that this phenomenon is a consequence of convergent evolution. Given that archaeal cells share characteristics with both bacteria and eukaryotes, we investigated whether and how archaeal cells exhibit control over cell size. To this end, we developed a soft-lithography method of growing the archaeal cells to enable quantitative time-lapse imaging and single-cell analysis, which would be useful for other microorganisms. Using this method, we demonstrated that Halobacterium salinarum, a hypersaline-adapted archaeal organism, grows exponentially at the single-cell level and maintains a narrow-size distribution by adding a constant length between cell division events. Interestingly, the archaeal cells exhibited greater variability in cell division placement and exponential growth rate across individual cells in a population relative to those observed in Escherichia coli 6-9 . Here, we present a theoretical framework that explains how these larger fluctuations in archaeal cell cycle events contribute to cell size variability and control.},
issn = {2058-5276},
doi = {10.1038/s41564-017-0082-6},
url = {https://www.nature.com/articles/s41564-017-0082-6},
author = {Eun, Ye-Jin and Ho, Po-Yi and Kim, Minjeong and LaRussa, Salvatore and Lydia Robert and Lars D. Renner and Schmid, Amy and Garner, Ethan and Amir, Ariel}
}
@article {1213091,
title = {Energy-speed-accuracy relation in complex networks for biological discrimination},
journal = {Phys. Rev. E Stat Nonlin. Soft Matter Phys.},
volume = {98},
year = {2018},
pages = {012420},
abstract = {Discriminating between correct and incorrect substrates is a core process in biology but how is energy apportioned between the conflicting demands of accuracy (μ), speed (σ) and total entropy production rate (P)? Previous studies have focussed on biochemical networks with simple structure or relied on simplifying kinetic assumptions. Here, we use the linear framework for timescale separation to analytically examine steady-state probabilities away from thermodynamic equilibrium for networks of arbitrary complexity. We also introduce a method of scaling parameters that is inspired by Hopfield{\textquoteright}s treatment of kinetic proofreading. Scaling allows asymptotic exploration of high-dimensional parameter spaces. We identify in this way a broad class of complex networks and scalings for which the quantity\ σ*ln(μ)/P\ remains asymptotically finite whenever accuracy improves from equilibrium, so that\ μ_eq/μ{\textrightarrow}0. Scalings exist, however, even for Hopfield{\textquoteright}s original network, for which\ σ*ln(μ)/P\ is asymptotically infinite, illustrating the parametric complexity. Outside the asymptotic regime, numerical calculations suggest that, under more restrictive parametric assumptions, networks satisfy the bound,\ σ*ln(μ/μ_eq)/P\<1, and we discuss the biological implications for discrimination by ribosomes and DNA polymerase. The methods introduced here may be more broadly useful for analysing complex networks that implement other forms of cellular information processing.},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.012420},
author = {Felix Wong and Amir, Ariel and Gunawardena, Jeremy}
}
@article {Hussain197475,
title = {MreB filaments align along greatest principal membrane curvature to orient cell wall synthesis},
journal = {eLife},
volume = {7},
year = {2018},
pages = {e32471},
publisher = {Cold Spring Harbor Laboratory},
abstract = {MreB is essential for rod shape in many bacteria. Membrane-associated MreB filaments move around the rod circumference, helping to insert cell wall in the radial direction to reinforce rod shape. To understand how oriented MreB motion arises, we altered the shape of\ Bacillus subtilis. MreB motion is isotropic in round cells, and orientation is restored when rod shape is externally imposed. Stationary filaments orient within protoplasts, and purified MreB tubulates liposomes\ in vitro, orienting within tubes. Together, this demonstrates MreB orients along the greatest principal membrane curvature, a conclusion supported with biophysical modeling. We observed that spherical cells regenerate into rods in a local, self-reinforcing manner: rapidly propagating rods emerge from small bulges, exhibiting oriented MreB motion. We propose that the coupling of MreB filament alignment to shape-reinforcing peptidoglycan synthesis creates a locally-acting, self-organizing mechanism allowing the rapid establishment and stable maintenance of emergent rod shape.},
doi = {10.1101/197475},
url = {https://elifesciences.org/articles/32471},
author = {Hussain, Saman and Wivagg, Carl N and Szwedziak, Piotr and Felix Wong and Schaefer, Kaitlin and Izor{\'e}, Thierry and Renner, Lars D and Holmes, Matthew J and Sun, Yingjie and Bisson-Filho, Alexandre W and Walker, Suzanne and Amir, Ariel and L{\"o}we, Jan and GARNER, ETHAN C}
}
@article {1227791,
title = {A Parallel Adder Coordinates Mycobacterial Cell-Cycle Progression and Cell-Size Homeostasis in the Context of Asymmetric Growth and Organization},
journal = {Current Biology},
year = {2017},
abstract = {In model bacteria, such as\ E.\ coli\ and\ B.\ subtilis, regulation of cell-cycle progression and cellular organization achieves consistency in cell size, replication dynamics, and chromosome positioning [ 1{\textendash}3 ]. Mycobacteria elongate and divide asymmetrically, giving rise to significant variation in cell size and elongation rate among closely related cells [ 4, 5 ]. Given the physical asymmetry of mycobacteria, the models that describe coordination of cellular organization and cell-cycle progression in model bacteria are not directly translatable [ 1, 2, 6{\textendash}8 ]. Here, we used time-lapse microscopy and fluorescent reporters of DNA replication and chromosome positioning to examine the coordination of growth, division, and chromosome dynamics at a single-cell level in\ Mycobacterium smegmatis\ (M.\ smegmatis) and\ Mycobacterium bovis\ Bacillus Calmette-Gu{\'e}rin (BCG). By analyzing chromosome and replisome localization, we demonstrated that chromosome positioning is asymmetric and proportional to cell size. Furthermore, we found that cellular asymmetry is maintained throughout the cell cycle and is not established at division. Using measurements and stochastic modeling of mycobacterial cell size and cell-cycle timing in both slow and fast growth conditions, we found that well-studied models of cell-size control are insufficient to explain the mycobacterial cell cycle. Instead, we showed that mycobacterial cell-cycle progression is regulated by an unprecedented mechanism involving parallel adders (i.e., constant growth increments) that start at replication initiation. Together, these adders enable mycobacterial populations to regulate cell size, growth, and heterogeneity in the face of varying environments.},
url = {http://www.cell.com/current-biology/fulltext/S0960-9822(17)31244-7},
author = {Michelle M. Logsdon and Ho, Po-Yi and Kadamba Papavinasasundaram and Kirill Richardson and Murat Cokol and Christopher M. Sassetti and Amir, Ariel and Bree B. Aldridge}
}
@article {1214571,
title = {Details Matter: noise and model structure set the relationship between cell size and cell cycle timing},
journal = {Front. Cell Dev. Biol.},
volume = {5},
year = {2017},
pages = {92},
abstract = {Organisms across all domains of life regulate the size of their cells. However, the means by which this is done is poorly understood. We study two abstracted "molecular" models for size regulation: inhibitor dilution and initiator accumulation. We apply the models to two settings: bacteria like Escherichia coli, that grow fully before they set a division plane and divide into two equally sized cells, and cells that form a bud early in the cell division cycle, confine new growth to that bud, and divide at the connection between that bud and the mother cell, like the budding yeast Saccharomyces cerevisiae. In budding cells, delaying cell division until buds reach the same size as their mother leads to very weak size control, with average cell size and standard deviation of cell size increasing over time and saturating up to 100-fold higher than those values for cells that divide when the bud is still substantially smaller than its mother. In budding yeast, both inhibitor dilution or initiator accumulation models are consistent with the observation that the daughters of diploid cells add a constant volume before they divide. This adder behavior has also been observed in bacteria. We find that in bacteria an inhibitor dilution model produces adder correlations that are not robust to noise in the timing of DNA replication initiation or in the timing from initiation of DNA replication to cell division (the C + D period). In contrast, in bacteria an initiator accumulation model yields robust adder correlations in the regime where noise in the timing of DNA replication initiation is much greater than noise in the C + D period, as reported previously [1]. In bacteria, division into two equally sized cells does not broaden the size distribution.},
url = {https://www.frontiersin.org/articles/10.3389/fcell.2017.00092/full?\&utm_source=Email_to_authors_\&utm_medium=Email\&utm_content=T1_11.5e1_author\&utm_campaign=Email_publication\&field=\&journalName=Frontiers_in_Cell_and_Developmental_Biology\&id=286522},
author = {Felix Barber and Ho, Po-Yi and Andrew W. Murray and Amir, Ariel}
}
@article {1198136,
title = {The Effects of Stochasticity at the Single-Cell Level and Cell Size Control on the Population Growth},
journal = {Cell Systems},
year = {2017},
abstract = {Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the experimentally observed correlations between mother-daughter generation times that are unavoidable when cell size is controlled for, which is essentially always the case. Here, we study population-level growth in the presence of cell size control and corroborate our theory using experimental measurements of single-cell growth rates. We derive a closed formula for the population growth rate and demonstrate that it only depends on the single-cell growth rate variability, not other sources of stochasticity. Our work provides an evolutionary rationale for the narrow growth rate distributions often observed in nature: when single-cell growth rates are less variable but have a fixed mean, the population will exhibit an enhanced population growth rate as long as the correlations between the mother and daughter cells{\textquoteright} growth rates are not too strong.},
url = {http://www.cell.com/cell-systems/fulltext/S2405-4712(17)30387-3},
author = {Lin, Jie and Amir, Ariel}
}
@article {1122471,
title = {Mechanical strain sensing implicated in cell shape recovery in Escherichia coli},
journal = {Nature Microbiology},
volume = {2},
year = {2017},
pages = {17115},
abstract = {The shapes of most bacteria are imparted by the structures of their peptidoglycan cell walls, which are determined by many dynamic processes that can be described on various length scales ranging from short-range glycan insertions to cellular-scale elasticity. Understanding the mechanisms that maintain stable, rod-like morphologies in certain bacteria has proved to be challenging due to an incomplete understanding of the feedback between growth and the elastic and geometric properties of the cell wall. Here, we probe the effects of mechanical strain on cell shape by modelling the mechanical strains caused by bending and differential growth of the cell wall. We show that the spatial coupling of growth to regions of high mechanical strain can explain the plastic response of cells to bending and quantitatively predict the rate at which bent cells straighten. By growing filamentous\ Escherichia coli\ cells in doughnut-shaped microchambers, we find that the cells recovered their straight, native rod-shaped morphologies when released from captivity at a rate consistent with the theoretical prediction. We then measure the localization of MreB, an actin homologue crucial to cell wall synthesis, inside confinement and during the straightening process, and find that it cannot explain the plastic response to bending or the observed straightening rate. Our results implicate mechanical strain sensing, implemented by components of the elongasome yet to be fully characterized, as an important component of robust shape regulation in\ E. coli.},
url = {http://rdcu.be/urfw},
author = {Felix Wong and Lars D. Renner and Gizem {\"O}zbaykal and Paulose, Jayson and Douglas B. Weibel and van Teeffelen, Sven and Amir, Ariel}
}
@article {1058176,
title = {Effect of interactions and disorder on the relaxation of two-level systems in amorphous solids},
journal = {Physical Review B},
volume = {95},
year = {2017},
pages = {144207},
abstract = {At low temperatures the dynamical degrees of freedom in amorphous solids are tunneling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a {\textquotedblleft}TLS glass,{\textquotedblright} 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\ et al.,\ Phys. Rev. B\ 77, 165207 (2008)]. Similarly to the electron glass, we find a\ 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.},
url = {https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.144207},
author = {Ofek Asban and Amir, Ariel and Imry, Yoseph and Moshe Schechter}
}
@article {973711,
title = {Point of view: Is cell size a spandrel?},
journal = {eLife},
volume = {6},
year = {2017},
pages = {e22186},
abstract = {All organisms control the size of their cells. We focus here on the question of size regulation in bacteria, and suggest that the quantitative laws governing cell size and its dependence on growth rate may arise as byproducts of a regulatory mechanism which evolved to support multiple DNA replication forks. In particular, we show that the increase of bacterial cell size during Lenski{\textquoteright}s long-term evolution experiments is a natural outcome of this proposal. This suggests that, in the context of evolution, cell size may be a {\textquoteright}spandrel{\textquoteright}},
url = {https://elifesciences.org/content/6/e22186},
author = {Amir, Ariel}
}
@article {827556,
title = {Non-Monotonic Aging and Memory Retention in Disordered Mechanical Systems},
journal = {Physical Review Letters},
volume = {118},
year = {2017},
pages = {085501},
abstract = {We observe nonmonotonic aging and memory effects, two hallmarks of glassy dynamics, in two disordered mechanical systems: crumpled thin sheets and elastic foams. Under fixed compression, both systems exhibit monotonic nonexponential relaxation. However, when after a certain waiting time the compression is partially reduced, both systems exhibit a nonmonotonic response: the normal force first increases over many minutes or even hours until reaching a peak value, and only then is relaxation resumed. The peak time scales linearly with the waiting time, indicating that these systems retain long-lasting memory of previous conditions. Our results and the measured scaling relations are in good agreement with a theoretical model recently used to describe observations of monotonic aging in several glassy systems, suggesting that the nonmonotonic behavior may be generic and that athermal systems can show genuine glassy behavior.},
url = {http://physics.aps.org/articles/v10/18},
author = {Lahini, Yoav and Gottesman, Omer and Amir, Ariel and Shmuel Rubinstein}
}
@article {955951,
title = {Interrogating the Escherichia coli cell cycle by cell dimension perturbations},
journal = {Proc. Natl. Acad. Sci. USA},
year = {2016},
abstract = {Bacteria tightly regulate and coordinate the various events in their cell cycles to duplicate themselves accurately and to control their cell sizes. Growth of Escherichia coli, in particular, follows a relation known as Schaechter{\textquoteright}s growth law. This law says that the average cell volume scales exponentially with growth rate, with a scaling exponent equal to the time from initiation of a round of DNA replication to the cell division at which the corresponding sister chromosomes segregate. Here, we sought to test the robustness of the growth law to systematic perturbations in cell dimensions achieved by varying the expression levels of mreB and ftsZ. We found that decreasing the mreB level resulted in increased cell width, with little change in cell length, whereas decreasing the ftsZ level resulted in increased cell length. Furthermore, the time from replication termination to cell division increased with the perturbed dimension in both cases. Moreover, the growth law remained valid over a range of growth conditions and dimension perturbations. The growth law can be quantitatively interpreted as a consequence of a tight coupling of cell division to replication initiation. Thus, its robustness to perturbations in cell dimensions strongly supports models in which the timing of replication initiation governs that of cell division, and cell volume is the key phenomenological variable governing the timing of replication initiation. These conclusions are discussed in the context of our recently proposed {\textquotedblleft}adder-per-origin{\textquotedblright} model, in which cells add a constant volume per origin between initiations and divide a constant time after initiation.},
url = {http://www.pnas.org/content/early/2016/12/08/1617932114.full.pdf},
author = {Hai Zheng and Ho, Po-Yi and Meiling Jiang and Bin Tang and Weirong Liu and Dengjin Li and Xuefeng Yu and Nancy E. Kleckner and Amir, Ariel and Liu, Chenli}
}
@article {908041,
title = {Glassy Dynamics in Disordered Electronic Systems Reveal Striking Thermal Memory Effects},
journal = {Physical Review Letters},
volume = {117},
year = {2016},
pages = {116601},
abstract = {Memory is one of the unique qualities of a glassy system. The relaxation of a glass to equilibrium contains information on the sample{\textquoteright}s excitation history, an effect often refer to as {\textquotedblleft}aging.{\textquotedblright} We demonstrate that under the right conditions a glass can also possess a different type of memory. We study the conductance relaxation of electron glasses that are fabricated at low temperatures. Remarkably, the dynamics are found to depend not only on the ambient measurement temperature but also on the maximum temperature to which the system was exposed. Hence the system {\textquotedblleft}remembers{\textquotedblright} its highest temperature. This effect may be qualitatively understood in terms of energy barriers and local minima in configuration space and therefore may be a general property of the glass state.},
author = {A. Eisenbach and T. Havdala and J. Delahaye and T. Grenet and A. Amir and A. Frydman}
}
@article {877776,
title = {Chirped photonic crystals: a natural strategy for broadband reflectance},
journal = {Optica},
volume = {3},
year = {2016},
pages = {1436-1439},
abstract = {
One-dimensional photonic crystals with slowly varying, i.e. "chirped", lattice period are responsible for broadband light reflectance in many diverse biological contexts, ranging from the shiny coatings of various beetles to the eyes of certain butterflies. We present a quantum scattering analogy for light reflection from these adiabatically chirped photonic crystals (ACPCs) and apply a WKB-type approximation to obtain a closed-form expression for the reflectance. From this expression we infer several design principles, including a differential equation for the chirp pattern required to elicit a given reflectance spectrum and the minimal number of bilayers required to exceed a desired reflectance threshold. Comparison of the number of bilayers found in ACPCs throughout nature and our predicted minimal required number also gives a quantitative measure of the optimality of chirped biological reflectors. Together these results elucidate the design principles of chirped reflectors in nature and their possible application to future optical technologies.
},
url = {https://www.osapublishing.org/optica/fulltext.cfm?uri=optica-3-12-1436\&id=355669},
author = {Caleb Q. Cook and Amir, Ariel}
}
@article {669406,
title = {Surprises in numerical expressions of physical constants},
journal = {American Mathematical Monthly},
volume = {123},
number = {6},
year = {2016},
pages = {609-612},
abstract = {
In science, as in life, "surprises"\ can be adequately appreciated only in the presence of a null model, what we expect a priori. In physics, theories sometimes express the values of dimensionless physical constants as combinations of mathematical constants like pi or e. The inverse problem also arises, whereby the measured value of a physical constant admits a "surprisingly"\ simple approximation in terms of well-known mathematical constants. Can we estimate the probability for this to be a mere coincidence, rather than an inkling of some theory? We answer the question in the most naive form.
},
author = {Amir, Ariel and Mikhail Lemeshko and Tadashi Tokieda}
}
@article {644081,
title = {Stochastic modeling of cell growth with symmetric or asymmetric division},
journal = {Phys. Rev. E Stat Nonlin. Soft Matter Phys.},
volume = {94},
year = {2016},
pages = {012405},
abstract = {We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the "master equation" describing how the resource distribution evolves over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendix, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.},
url = {https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.012405},
author = {Andrew Marantan and Amir, Ariel}
}
@article {635701,
title = {Non-Hermitian Localization in Biological Networks},
journal = {Phys. Rev. E (Editor{\textquoteright}s Choice)},
volume = {93},
year = {2016},
pages = {042310},
abstract = {We explore the spectra and localization properties of the\ N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately equal numbers of random excitatory and inhibitory connections lead to spatially localized eigenfunctions and an intricate eigenvalue spectrum in the complex plane that controls the spontaneous activity and induced response. A finite fraction of the eigenvalues condense onto the real or imaginary axes. For large\ N, the spectrum has remarkable symmetries not only with respect to reflections across the real and imaginary axes but also with respect to\ 90o\ rotations, with an unusual anisotropic divergence in the localization length near the origin. When chains with periodic boundary conditions become directed, with a systematic directional bias superimposed on the randomness, a hole centered on the origin opens up in the density-of-states in the complex plane. All states are extended on the rim of this hole, while the localized eigenvalues outside the hole are unchanged. The bias-dependent shape of this hole tracks the bias-independent contours of constant localization length. We treat the large-Nlimit by a combination of direct numerical diagonalization and using transfer matrices, an approach that allows us to exploit an electrostatic analogy connecting the {\textquotedblleft}charges{\textquotedblright} embodied in the eigenvalue distribution with the contours of constant localization length. We show that similar results are obtained for more realistic neural networks that obey {\textquotedblleft}Dale{\textquoteright}s law{\textquotedblright} (each site is purely excitatory or inhibitory) and conclude with perturbation theory results that describe the limit of large directional bias, when all states are extended. Related problems arise in random ecological networks and in chains of artificial cells with randomly coupled gene expression patterns.},
url = {http://arxiv.org/abs/1512.05478},
author = {Amir, Ariel and Naomichi Hatano and David R. Nelson}
}
@article {635706,
title = {An elementary derivation of first and last return times of 1D random walks},
journal = {Am. J. Phys.},
year = {2015},
abstract = {Random walks,\ and in particular, their first passage times, are ubiquitous in nature. Using direct enumeration of paths, we find the first-return-time distribution of a one-dimensional random walker, which is a heavy-tailed distribution with infinite mean. Using the same method, we find the last-return-time distribution, which follows the arcsine law. Both results have a broad range of applications in\ physics\ and other disciplines. The derivation presented here is readily accessible to\ physics\ undergraduates\ and provides an elementary introduction into\ random walks\ and their intriguing\ properties.},
author = {Sarah Kostinski and Amir, Ariel}
}
@article {635696,
title = {Single-Cell Analysis of Growth in Budding Yeast and Bacteria Reveals a Common Size Regulation Strategy},
journal = {Current Biology},
year = {2015},
url = {http://www.cell.com/current-biology/abstract/S0960-9822(15)01560-2},
author = {Ilya Soifer and Lydia Robert and Amir, Ariel}
}
@article {533041,
title = {Simultaneous regulation of cell size and chromosome replication in bacteria.},
journal = {Front Microbiol},
volume = {6},
year = {2015},
month = {2015},
pages = {662},
abstract = {Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the long-standing initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results.},
author = {Ho, Po-Yi and Amir, Ariel}
}
@article {533061,
title = {Anomalous symmetry breaking in two-dimensional diffusion of coherent atoms},
journal = {Physical Review A},
volume = {80},
number = {033807},
year = {2014},
abstract = {The electromagnetically induced transparency (EIT) spectrum of atoms diffusing in and out of a narrow beam is measured and shown to manifest the two-dimensional\ δ-function anomaly in a classical setting. In the limit of small-area beams, the EIT line shape is independent of power, and equal to the renormalized local density of states of a free particle Hamiltonian. The measured spectra for different powers and beam sizes collapses to a single universal curve with a characteristic logarithmic Van Hove singularity close to resonance.},
author = {Rami Pugatch and Dipankar Bhattacharyya and Amir, Ariel and Yoav Sagi and Nir Davidson}
}
@article {533051,
title = {Bending forces plastically deform growing bacterial cell walls.},
journal = {Proc Natl Acad Sci U S A},
volume = {111},
number = {16},
year = {2014},
month = {2014 Apr 22},
pages = {5778-83},
abstract = {Cell walls define a cell{\textquoteright}s shape in bacteria. The walls are rigid to resist large internal pressures, but remarkably plastic to adapt to a wide range of external forces and geometric constraints. Currently, it is unknown how bacteria maintain their shape. In this paper, we develop experimental and theoretical approaches and show that mechanical stresses regulate bacterial cell wall growth. By applying a precisely controllable hydrodynamic force to growing rod-shaped Escherichia coli and Bacillus subtilis cells, we demonstrate that the cells can exhibit two fundamentally different modes of deformation. The cells behave like elastic rods when subjected to transient forces, but deform plastically when significant cell wall synthesis occurs while the force is applied. The deformed cells always recover their shape. The experimental results are in quantitative agreement with the predictions of the theory of dislocation-mediated growth. In particular, we find that a single dimensionless parameter, which depends on a combination of independently measured physical properties of the cell, can describe the cell{\textquoteright}s responses under various experimental conditions. These findings provide insight into how living cells robustly maintain their shape under varying physical environments.},
keywords = {Anisotropy, Bacillus subtilis, Biomechanical Phenomena, Cell Wall, Escherichia coli, Stress, Mechanical},
author = {Amir, Ariel and Babaeipour, Farinaz and McIntosh, Dustin B and Nelson, David R. and Jun, Suckjoon}
}
@article {533056,
title = {Cell size regulation in bacteria},
journal = {Physical Review Letters},
volume = {112},
number = {208102},
year = {2014},
abstract = {Various bacteria such as the canonical gram negative\ Escherichia coli\ or the well-studied gram positive\ Bacillus subtilis\ divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically distributed over a narrow range. Here, we propose an analytically tractable model for cell size control, and calculate the cell size and interdivision time distributions, as well as the correlations between these variables. We suggest ways of extracting the model parameters from experimental data, and show that existing data for\ E.\ colisupports partial size control, and a particular explanation: a cell attempts to add a constant volume from the time of initiation of DNA replication to the next initiation event. This hypothesis accounts for the experimentally observed correlations between mother and daughter cells as well as the exponential dependence of size on growth rate.},
author = {Amir, Ariel}
}
@article {533046,
title = {Getting into shape: How do rod-like bacteria control their geometry?},
journal = {Syst Synth Biol},
volume = {8},
number = {3},
year = {2014},
month = {2014 Sep},
pages = {227-35},
abstract = {Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their near-perfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cell-wall geometry and mechanical stress play important roles in regulating cell shape in rod-like bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions which may help to shed light on this fundamental problem.},
author = {Amir, Ariel and van Teeffelen, Sven}
}
@article {533066,
title = {Universal frequency-dependent conduction of electron glasses},
journal = {EPL, },
volume = {107},
number = {47011},
year = {2014},
abstract = {Characterizing the frequency-dependent response of amorphous systems and glasses can provide important insights into their physics. Here, we study the response of an electron glass, where Coulomb interactions are important and have previously been shown to significantly modify the conductance and lead to memory effects and aging. We propose a model which allows us to take the interactions into account in a self-consistent way, and explore the frequency-dependent conduction at all frequencies. At low frequencies conduction occurs on the percolation backbone, and the model captures the variable-range-hopping behavior. At high frequencies conduction is dominated by localized clusters. Despite the difference in physical mechanisms at low and high frequency, we are able to approximately scale all numerical data onto a single curve, using two parameters: the DC conduction and the DC dielectric constant. The behavior follows the universal scaling that is experimentally observed for a large class of amorphous solids.},
url = {http://iopscience.iop.org/0295-5075/107/4/47011/pdf/0295-5075_107_4_47011.pdf},
author = {Amir, Ariel}
}
@article {533076,
title = {Elucidating the stop bands of structurally colored systems through recursion},
journal = {American Journal of Physics},
volume = {81},
number = {253},
year = {2013},
abstract = {Interference phenomena are the source of some of the spectacular colors of animals and plants in nature. In some of these systems, the physical structure consists of an ordered array of layers with alternating high and low refractive indices. This periodicity leads to an optical band structure that is analogous to the electronic band structure encountered in semiconductor physics; namely, specific bands of wavelengths (the stop bands) are perfectly reflected. Here, we present a minimal model for optical band structure in a periodic multilayer and solve it using recursion relations. We present experimental data for various beetles, whose optical structure resembles the proposed model. The stop bands emerge in the limit of an infinite number of layers by finding the fixed point of the recursive relations. In order for these to converge, an infinitesimal amount of absorption needs to be present, reminiscent of the regularization procedures commonly used in physics calculations. Thus, using only the phenomenon of interference and the idea of recursion, we are able to elucidate the concepts of band structure and regularization in the context of experimentally observed phenomena, such as the high reflectance and the iridescent color appearance of structurally colored beetles.},
author = {Amir, Ariel and Peter Vukusic}
}
@article {533081,
title = {Emergent percolation length and localization in random elastic networks},
journal = {Physical Review X},
volume = {3},
number = {021017},
year = {2013},
abstract = {We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency, and spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization-delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach, we calculate the speed of sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density and find good agreement of these predictions with numerical results using a recursive Green-function method that was adapted for this problem. The connection of our results to recent experiments on amorphous solids is discussed.},
author = {Amir, Ariel and Krich, Jacob and Vincenzo Vitelli and Oreg, Yuval and Imry, Yoseph}
}
@article {533071,
title = {Theory of interacting dislocations on cylinders.},
journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
volume = {87},
number = {4},
year = {2013},
month = {2013 Apr},
pages = {042314},
abstract = {We study the mechanics and statistical physics of dislocations interacting on cylinders, motivated by the elongation of rod-shaped bacterial cell walls and cylindrical assemblies of colloidal particles subject to external stresses. The interaction energy and forces between dislocations are solved analytically, and analyzed asymptotically. The results of continuum elastic theory agree well with numerical simulations on finite lattices even for relatively small systems. Isolated dislocations on a cylinder act like grain boundaries. With colloidal crystals in mind, we show that saddle points are created by a Peach-Koehler force on the dislocations in the circumferential direction, causing dislocation pairs to unbind. The thermal nucleation rate of dislocation unbinding is calculated, for an arbitrary mobility tensor and external stress, including the case of a twist-induced Peach-Koehler force along the cylinder axis. Surprisingly rich phenomena arise for dislocations on cylinders, despite their vanishing Gaussian curvature.},
keywords = {Bacteria, Biophysical Processes, Cell Wall, Models, Theoretical, Plant Leaves, Thermodynamics},
author = {Amir, Ariel and Paulose, Jayson and Nelson, David R.}
}
@article {533096,
title = {Defects on cylinders: superfluid helium films and bacterial cell walls},
journal = {Lectures given by D. R. Nelson at the Les Houches School on {\textquotedblright}Soft Interfaces,{\textquotedblright} July 2-27},
volume = {arxiv:1303.5896},
year = {2012},
author = {Nelson, David R. and Amir, Ariel}
}
@article {533091,
title = {On relaxations and aging of various glasses.},
journal = {Proc Natl Acad Sci U S A},
volume = {109},
number = {6},
year = {2012},
month = {2012 Feb 7},
pages = {1850-5},
abstract = {Slow relaxation occurs in many physical and biological systems. "Creep" is an example from everyday life. When stretching a rubber band, for example, the recovery to its equilibrium length is not, as one might think, exponential: The relaxation is slow, in many cases logarithmic, and can still be observed after many hours. The form of the relaxation also depends on the duration of the stretching, the "waiting time." This ubiquitous phenomenon is called aging, and is abundant both in natural and technological applications. Here, we suggest a general mechanism for slow relaxations and aging, which predicts logarithmic relaxations, and a particular aging dependence on the waiting time. We demonstrate the generality of the approach by comparing our predictions to experimental data on a diverse range of physical phenomena, from conductance in granular metals to disordered insulators and dirty semiconductors, to the low temperature dielectric properties of glasses.},
keywords = {Electrons, Glass, Indium, Models, Chemical, Physical Phenomena, Time Factors},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533086,
title = {Dislocation-mediated growth of bacterial cell walls.},
journal = {Proc Natl Acad Sci U S A},
volume = {109},
number = {25},
year = {2012},
month = {2012 Jun 19},
pages = {9833-8},
abstract = {Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference [Garner EC, et al., (2011) Science 333:222-225], [Dom{\'\i}nguez-Escobar J, et al. (2011) Science 333:225-228], [van Teeffelen S, et al. (2011) PNAS 108:15822-15827]. We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.},
keywords = {Bacteria, Cell Wall, Models, Theoretical},
author = {Amir, Ariel and Nelson, David R.}
}
@article {533106,
title = {Electron glass dynamics},
journal = {Annu. Rev. Condens. Matter Phys.},
volume = {2},
number = {235-62},
year = {2011},
abstract = {Examples of glasses are abundant, yet it remains one of the phases of matter whose understanding is very elusive. In recent years, remarkable experiments have been performed on the dynamical aspects of glasses. Electron glasses offer a particularly good example of the trademarks of glassy behavior, such as aging and slow relaxations. In this work we review the experimental literature on electron glasses, as well as the local mean-field theoretical framework put forward in recent years to understand some of these results. We also present novel theoretical results explaining the periodic aging experiment.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533101,
title = {Huge (but finite) time scales in slow relaxations: beyond simple aging.},
journal = {Phys Rev Lett},
volume = {107},
number = {18},
year = {2011},
month = {2011 Oct 28},
pages = {186407},
abstract = {Experiments performed in the last years demonstrated slow relaxations and aging in the conductance of a large variety of materials. Here, we present experimental and theoretical results for conductance relaxation and aging for the case-study example of porous silicon. The relaxations are experimentally observed even at room temperature over time scales of hours, and when a strong electric field is applied for a time tw, the ensuing relaxation depends on tw. We derive a theoretical curve and show that all experimental data collapse onto it with a single time scale as a fitting parameter. This time scale is found to be of the order of thousands of seconds at room temperature. The generic theory suggested is not fine-tuned to porous silicon, and thus we believe the results should be universal, and the presented method should be applicable for many other systems manifesting memory and other glassy effects.},
keywords = {Electric Conductivity, Porosity, Silicon, Time Factors},
author = {Amir, Ariel and Borini, Stefano and Oreg, Yuval and Imry, Yoseph}
}
@article {533111,
title = {Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach.},
journal = {Phys Rev Lett},
volume = {105},
number = {7},
year = {2010},
month = {2010 Aug 13},
pages = {070601},
abstract = {We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@inbook {533116,
title = {The localization transition at finite temperatures: electric and thermal transport},
booktitle = {50 Years of Anderson Localization},
year = {2010},
publisher = {World Scientific},
organization = {World Scientific},
address = {Singapore},
abstract = {The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.},
url = {http://arxiv.org/abs/1004.0966},
author = {Imry, Yoseph and Amir, Ariel},
editor = {E. Abrahams}
}
@proceedings {533131,
title = {1/f noise and slow relaxations in glasses},
journal = { TIDS conference},
volume = {18},
number = {12},
year = {2009},
pages = {836},
address = {Berlin},
abstract = {Recently we have shown that slow relaxations in the electron glass system can be understood in terms of the spectrum of a matrix describing the relaxation of the system close to a metastable state. The model focused on the electron glass system, but its generality was demonstrated on various other examples. Here, we study the noise spectrum in the same framework. We obtain a remarkable relation between the spectrum of relaxation rates\ λ\ described by the distribution function\ P(λ)\~{}1/λ\ and the\ 1/f\ noise in the fluctuating occupancies of the localized electronic sites. This noise can be observed using local capacitance measurements. We confirm our analytic results using numerics, and also show how the Onsager symmetry is fulfilled in the system.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533126,
title = {Classical diffusion of a quantum particle in a noisy environment.},
journal = {Phys Rev E Stat Nonlin Soft Matter Phys},
volume = {79},
number = {5 Pt 1},
year = {2009},
month = {2009 May},
pages = {050105},
abstract = {We study the spreading of a quantum-mechanical wave packet in a tight-binding model with a noisy potential and analyze the emergence of classical diffusion from the quantum dynamics due to decoherence. We consider a finite correlation time of the noisy environment and treat the system by utilizing the separation of fast (dephasing) and slow (diffusion) processes. We show that classical diffusive behavior emerges at long times and we calculate analytically the dependence of the classical diffusion coefficient on the noise magnitude and correlation time. This method provides a general solution to this problem for arbitrary conditions of the noisy environment. The calculation can be done in any dimension, but we demonstrate it in one dimension for clarity of representation. The results are relevant to a large variety of physical systems, from electronic transport in solid-state physics to light transmission in optical devices, diffusion of excitons, and quantum computation.},
author = {Amir, Ariel and Lahini, Yoav and Perets, Hagai B}
}
@article {533121,
title = {Slow relaxations and aging in the electron glass.},
journal = {Phys Rev Lett},
volume = {103},
number = {12},
year = {2009},
month = {2009 Sep 18},
pages = {126403},
abstract = {Glassy systems are ubiquitous in nature. They are characterized by slow relaxations to equilibrium without a typical time scale, aging, and memory effects. Understanding this has been a long-standing problem in physics. We study the aging of the electron glass, a system showing remarkable slow relaxations of the conductance. We find that the appropriate broad distribution of relaxation rates leads to a universal relaxation of the form log(1 + t_{w}/t) for the common aging protocol, where t_{w} is the length of time the perturbation driving the system out of equilibrium was on, and t the time of measurement. These results agree well with several experiments performed on different glassy systems, and examining different physical observables, for times ranging from seconds to several hours. The suggested theoretical framework appears to offer a paradigm for aging in a broad class of glassy materials.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533136,
title = {Variable range hopping in the Coulomb glass},
journal = {Physical Review B},
volume = {80},
number = {245214},
year = {2009},
abstract = {We use a local mean-field (Hartree-like) approach to study the conductance of a strongly localized electron system in two dimensions. We find a crossover between a regime where Coulomb interactions modify the conductance significantly to a regime where they are negligible. We show that under rather general conditions the conduction obeys a scaling relation which we verify using numerical simulations. The use of a local mean-field approach gives a clear physical picture, and removes the ambiguity of the use of single-particle tunneling density of states (DOS) in the calculation of the conductance. Furthermore, the theory contains interaction-induced correlations between the on site energy of the localized states and distances, as well as finite temperature corrections of the DOS.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533141,
title = {Decays in quantum hierarchical models},
journal = {Physical Review A},
volume = {77},
number = {050101(R)},
year = {2008},
abstract = {We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudocontinuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudocontinuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random, several cases are identified. For a pseudocontinuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For intermediate bandwidth one finds mesoscopic fluctuations in the probability with amplitude inversely proportional to the square root of the volume of the pseudocontinuum space. They last for a long time compared to the nonrandom case.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}
@article {533146,
title = {Mean-field model for electron-glass dynamics},
journal = {Physical Review B},
volume = {77},
number = {165207},
year = {2008},
abstract = {We study a microscopic mean-field model for the dynamics of the electron glass near a local equilibrium state. Phonon-induced tunneling processes are responsible for generating transitions between localized electronic sites, which eventually lead to the thermalization of the system. We find that the decay of an excited state to a locally stable state is far from being exponential in time and does not have a characteristic time scale. Working in a mean-field approximation, we write rate equations for the average occupation numbers\ ⟨ni⟩\ and describe the return to the locally stable state by using the eigenvalues of a rate matrix\ A\ describing the linearized time evolution of the occupation numbers. By analyzing the probability distribution\ P(λ)\ of the eigenvalues of\ A, we find that, under certain physically reasonable assumptions, it takes the form\ P(λ)\~{}1/|λ|, leading naturally to a logarithmic decay in time. While our derivation of the matrix\ A\ is specific for the chosen model, we expect that other glassy systems, with different microscopic characteristics, will be described by random rate matrices belonging to the same universality class of\ A. Namely, the rate matrix has elements with a very broad distribution, as in the case of exponentials of a variable with nearly uniform distribution.},
author = {Amir, Ariel and Oreg, Yuval and Imry, Yoseph}
}