Article: Scaling laws governing stochastic growth and division of single bacterial cells

Srividya Iyer-Biswas, Charles S. Wright, Jonathan T. Henry, Klevin Lo, Stanislav Burov, Yihan Lin, Gavin E. Crooks, Sean Crosson, Aaron R. Dinner, Norbert F. Scherer, Proc. Natl. Acad. Sci. U.S.A. (2014)

[ Full text | Journal | arXiv ]cell

This is the experimental paper that logically (but, alas, not chronologically) precedes the companion theory paper.

Abstract: Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

Article: Universality in Stochastic Exponential Growth

Srividya Iyer-Biswas, Gavin E. Crooks, Norbert F. Scherer, and Aaron R. Dinner, Phys. Rev. Lett., 113, 028101 (2014)

[ Full text | Journal ]cell

Abstract: Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. Continue reading

WebLogo 3.4 Released

WebLogo 3.4 web-server

WebLogo 3.4 code

3.4 (2014-06-03) [Gavin Crooks, Eric Talevich]

* Python 3
Weblogo now runs under python 2.6, 2.7, 3.2, 3.3 & 3.4 (Python2.5 is no longer
supported.) Note that the api for creating a logo has changed. See docs.
(Kudos: Eric Talevic)
* Fix bug with using Ghostscipt 9.10 (Issue 36)
(Kudos: Michael Imbeault, Estienne Swart, FiReaNG3L)
* Fix various bugs in transfac parsing.
(Kudos: Promita Bose, Christopher Lamantia)
* Fix –complement of gapped sequences, added –revcomp option
(Kudos: Jacob Engelbrecht))
* Miscellaneous minor bug fixes and refactoring.
(Kudos: Kamil Slowikowski, Jacob Engelbrecht)

Article: Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems

David A. Sivak, John D. Chodera, Gavin E. Crooks, arXiv:1301.3800

[ Full text | Journal | ArXiv]

Abstract: While the numerical integration of deterministic equations of motion for molecular systems now has a well-developed set of algorithms with commonly agreed-upon desirable properties, the simulation of stochastic equations of motion lacks algorithms with a similar degree of universal acceptance. Part of the difficulty is in determining which of many properties should be satisfied by such a discrete time integration scheme, with additional difficulties in satisfying many properties simultaneously with a single scheme. The desire to use these integration schemes for nonequilibrium simulations and in conjunction with recent nonequilibrium fluctuation theorems adds additional complications. Here, we compare a number of discrete time integration schemes for Langevin dynamics, Continue reading

Tech. Note: Survey of Simple, Continuous, Univariate Probability Distributions

Unimodal distributions

Version: 0.5 BETA

In a desperate attempt to preserve my own sanity, a survey of probability distributions used to describe a single, continuous, unimodal, univariate random variable.

Whats New: Added uniform product, half generalized Pearson VII, half exponential power distributions, GUD and q-Type distributions; Moved Pearson IV to own section; Fixed errors in Inverse Gaussian; Added random variate generation appendix. Fixed typos. Thanks to David Sivak, Dieter Grientschnig, Srividya Iyer-Biswas and Shervin Fatehi.

[ Full Text ]

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Article: Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics

David A. Sivak, John D. Chodera, Gavin E. Crooks, Phys. Rev. X 3, 011007 (2013)

[ Full text | Journal]

Abstract: Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite-time-step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that, even with a time-independent Hamiltonian, finite-time-step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate worklike quantity is defined – here called the shadow work – Continue reading


In science, as in life, it is extremely dangerous to fall in love with beautiful models.

Via Vijay Pande

Article: The geometry of thermodynamic control

Abstract: A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. Continue reading


♬ Hey I just met you, and this is crazy, but here’s my paper – so cite me maybe? ♬

Article: Thermodynamics of prediction

Susanne Still, David A. Sivak, Anthony J. Bell and Gavin E. Crooks, Phys. Rev. Lett., 109, 120604 (2012)

[ Full Text | Journal | Press | arXiv ]

Hat Trick! And Editors’ Suggestion. Also a Nature News item by Philip Ball.

This paper is a melding of ideas about machine learning from Susanne Still and Tony Bell, with ideas from David and I about nonequilibrium thermodynamics. For a molecular scale machine with information processing capabilities, there’s a tradeoff between thermodynamic efficiency, memory and prediction. A prodigious memory allows more accurate prediction of the future, which can be exploited to reduce dissipation. But the persistence of memory is a liability, since information erasure leads to increased dissipation. A thermodynamically optimal machine must balance memory versus prediction by minimizing its nostalgia, the useless information about the past.

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