scholarly journals Power-law tail in lag time distribution underlies bacterial persistence

2019 ◽  
Vol 116 (36) ◽  
pp. 17635-17640 ◽  
Author(s):  
Emrah Şimşek ◽  
Minsu Kim
Keyword(s):  
Population Dynamics ◽  
Antibiotic Treatment ◽  
Rate Constant ◽  
Exponential Decay ◽  
Power Law ◽  
Time Distribution ◽  
Molecular Mechanisms ◽  
Lag Time ◽  
Phenotypic Heterogeneity ◽  
Power Law Decay

Genetically identical microbial cells respond to stress heterogeneously, and this phenotypic heterogeneity contributes to population survival. Quantitative analysis of phenotypic heterogeneity can reveal dynamic features of stochastic mechanisms that generate heterogeneity. Additionally, it can enable a priori prediction of population dynamics, elucidating microbial survival strategies. Here, we quantitatively analyzed the persistence of an Escherichia coli population. When a population is confronted with antibiotics, a majority of cells is killed but a subpopulation called persisters survives the treatment. Previous studies have found that persisters survive antibiotic treatment by maintaining a long period of lag phase. When we quantified the lag time distribution of E. coli cells in a large dynamic range, we found that normal cells rejuvenated with a lag time distribution that is well captured by an exponential decay [exp(−kt)], agreeing with previous studies. This exponential decay indicates that their rejuvenation is governed by a single rate constant kinetics (i.e., k is constant). Interestingly, the lag time distribution of persisters exhibited a long tail captured by a power-law decay. Using a simple quantitative argument, we demonstrated that this power-law decay can be explained by a wide variation of the rate constant k. Additionally, by developing a mathematical model based on this biphasic lag time distribution, we quantitatively explained the complex population dynamics of persistence without any ad hoc parameters. The quantitative features of persistence demonstrated in our work shed insights into molecular mechanisms of persistence and advance our knowledge of how a microbial population evades antibiotic treatment.

The Encounter Probability for Random Walkers in a Confined Space

2005 ◽  
Vol 899 ◽  
Author(s):  
James P. Lavine
Keyword(s):  
Survival Time ◽  
Exponential Decay ◽  
Power Law ◽  
Time Distribution ◽  
Model Space ◽  
Confined Space ◽  
Encounter Probability ◽  
Random Walkers ◽  
Initial Separation ◽  
Spatial Dimensions

AbstractParticles diffusing in a confined space should encounter one another with a probability that depends on the size and dimension of the space. The present work uses pairs of random walkers on a lattice to investigate the encounter probability in one, two, and three spatial dimensions. There is an initial rapid decay of the survival-time distribution that is followed by an exponential decay in time. The characteristic time for this latter decay is strongly dependent on the model space size and scales as a power law in the size. The exponent of the power law depends on the number of spatial dimensions. For a fixed L, the exponential tail of the survival-time distribution has a similar slope when the initial separation of the two walkers is varied. The spacing between the exponential decay curves scales with the initial separation in 1-D, but not in 2-D or 3-D. In addition, the mapping of two random walkers to an equivalent single walker is explored.

scholarly journals Wide lag time distributions break a trade-off between reproduction and survival in bacteria

2020 ◽  
Vol 117 (31) ◽  
pp. 18729-18736 ◽  
Author(s):  
Stefany Moreno-Gámez ◽  
Daniel J. Kiviet ◽  
Clément Vulin ◽  
Susan Schlegel ◽  
Kim Schlegel ◽  
...  
Keyword(s):  
Population Dynamics ◽  
Population Growth ◽  
Rapid Growth ◽  
Evolutionary Model ◽  
Lag Time ◽  
Substantial Effect ◽  
Phenotypic Heterogeneity ◽  
Trade Off ◽  
Extreme Phenotypes ◽  
Lag Times

Many microorganisms face a fundamental trade-off between reproduction and survival: Rapid growth boosts population size but makes microorganisms sensitive to external stressors. Here, we show that starved bacteria encountering new resources can break this trade-off by evolving phenotypic heterogeneity in lag time. We quantify the distribution of single-cell lag times of populations of starvedEscherichia coliand show that population growth after starvation is primarily determined by the cells with shortest lag due to the exponential nature of bacterial population dynamics. As a consequence, cells with long lag times have no substantial effect on population growth resumption. However, we observe that these cells provide tolerance to stressors such as antibiotics. This allows an isogenic population to break the trade-off between reproduction and survival. We support this argument with an evolutionary model which shows that bacteria evolve wide lag time distributions when both rapid growth resumption and survival under stressful conditions are under selection. Our results can explain the prevalence of antibiotic tolerance by lag and demonstrate that the benefits of phenotypic heterogeneity in fluctuating environments are particularly high when minorities with extreme phenotypes dominate population dynamics.

Generalized turbulence space-correlation and wave-number spectrum-function pairs

1968 ◽  
Vol 46 (19) ◽  
pp. 2133-2153 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Correlation Function ◽  
Exponential Decay ◽  
Power Law ◽  
Computer Calculation ◽  
Wave Number ◽  
Large Wave ◽  
Space Correlation ◽  
Power Law Decay ◽  
Wave Numbers ◽  
Spectrum Function

A new generalized pair of space-correlation and wave-number spectrum functions, which has properties indicated by fluid dynamics and by intuition, is proposed. In contrast with previously used combinations, both are analytic functions and smooth and cover the complete range of their arguments. For example, the spectrum form can apply to all wave numbers rather than to any limited portion, such as the inertial range. Whenever convolution is necessary, it becomes a routine computer calculation. Furthermore, the correlation function has a zero first derivative and a negative second derivative at the origin, giving both an integral scale and a microscale for the turbulence. The spectrum function can have an inertial region with some power-law decay for intermediate wave numbers and has an exponential decay for very large wave numbers. There are three adjustable parameters, determined by experiment, namely, the spectral power-law decay index, the turnover point where this power law starts, and the turnover point where the power dependence changes to an exponential decay. A library of such spectrum functions is not required, since the single proposed function, with its adjustable parameters, can be made to fit most data. One can also allow any even power of wave number for the spectral dependence in the limit of zero wave number. Simple anisotropic functional forms can readily be incorporated. It is indicated that two inertial falloffs with different power laws can be provided and the resultant correlation function is derivable by convolution. The results are applied to simplified versions of plasma electron density fluctuations and to velocity fluctuations of the background fluid. Various scales of turbulence and the related pressure-correlation function are derived. Expressions of correlation functions of amplitude and phase over parallel-line-of-sight propagation paths are also deduced.The proposed pair of functions should only be considered as a generalized model of Tatarski's form, which allows easy conversion from the correlation to the spectrum function and vice versa. Perhaps even more realistic forms can be invented.

TRACER TIME DISTRIBUTION OF PARTICLES IN POROUS MEDIA

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 1075-1079
Author(s):  
MARIELA ARAUJO
Keyword(s):  
Porous Medium ◽  
Transit Time ◽  
Power Law ◽  
Time Distribution ◽  
Tracer Particle ◽  
Power Law Distribution ◽  
Low Velocity ◽  
Constant Flow Rate ◽  
Variable Permeability ◽  
Tracer Particles

We study the transit time distributions of tracer particles in a porous medium through which a constant flow rate is established. Our model assumes that non-Gaussian dispersion is due to the presence of low velocity zones or channels in parallel with a faster flow path. Each channel is represented as a trap and simulates the existence of variable permeability blocks inside the porous medium. The time the tracer particle spends inside each channel is related to the heterogeneity of the sample, and is assumed here to have a power-law distribution. We compare the transit time distribution of these particles for the case in which the traps are Poisson distributed with the one in which the trap distribution is a power-law function.

scholarly journals When an oscillating center in an open system undergoes power law decay

2018 ◽  
Vol 57 (3) ◽  
pp. 750-768 ◽  
Author(s):  
Sandip Saha ◽  
Gautam Gangopadhyay
Keyword(s):  
Power Law ◽  
Open System ◽  
Power Law Decay

scholarly journals EXPLORATION OF STYLIZED FACTS IN THE ARTIFICIAL LIFE SYSTEM AVIDA

2016 ◽  
Vol 4 ◽  
pp. 791-795
Author(s):  
Shinta Koyano ◽  
Lukáš Pichl
Keyword(s):  
Population Dynamics ◽  
Power Law ◽  
Artificial Life ◽  
Real Life ◽  
Central Processing Unit ◽  
Processing Unit ◽  
Full Width ◽  
Logic Function ◽  
Central Processing ◽  
Clique Graph

Population dynamics in the evolution, extinction, and re-evolution of various logic-function performing organisms is studied in the artificial life system, Avida. Following the work of Yedid (2009), we design an experiment involving two extinction regimes, pulse-extinction (corresponding to a random-kill event) and press-extinction (corresponding to a prolonged episode of rare resources). In addition, we study the effect of environmental topology (toroidal grid and clique graph). In the study of population dynamics, logarithmic returns are generally applied. The resulting distributions display a fat tail form of the power law: the more complex the logic function (in terms of NAND components), the broader the full width at half a maximum of the histogram. The power law exponents were in sound agreement with those of “real-life” populations and distributions. The distributions of evolutionary times, as well as post-extinction recovery periods, were very broad, and presumably had no standard deviations. Using 100 runs of 200,000 updates for each of the four cases (about 1 month of central processing unit time), we established the dynamics of the average population, with the effect of world topology.

scholarly journals Analysis of the buildup of spatiotemporal correlations and their bounds outside of the light cone

2018 ◽  
Vol 5 (5) ◽  
Author(s):  
Nils O. Abeling ◽  
Lorenzo Cevolani ◽  
Stefan Kehrein
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Light Cone ◽  
Relativistic Quantum ◽  
Initial State ◽  
Quantum Theories ◽  
Luttinger Model ◽  
Power Law Decay ◽  
Exactly Solvable ◽  
Exponentially Small

In non-relativistic quantum theories the Lieb-Robinson bound defines an effective light cone with exponentially small tails outside of it. In this work we use it to derive a bound for the correlation function of two local disjoint observables at different times if the initial state has a power-law decay. We show that the exponent of the power-law of the bound is identical to the initial (equilibrium) decay. We explicitly verify this result by studying the full dynamics of the susceptibilities and correlations in the exactly solvable Luttinger model after a sudden quench from the non-interacting to the interacting model.

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