Gavin E. Crooks

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2009-06-23: Published: Self-Organization of the Escherichia coli Chemotaxis Network Imaged with Super-Resolution Light Microscopy

Derek Greenfield, Ann L. McEvoy, Hari Shroff, Gavin E. Crooks, Ned S. Wingreen, Eric Betzig, Jan Liphardt Plos Biol. 7:e1000137 (2009) doi:10.1371/journal.pbio.1000137
The Escherichia coli chemotaxis network is a model system for biological signal processing. In E. coli, transmembrane receptors responsible for signal transduction assemble into large clusters containing several thousand proteins. These sensory clusters have been observed at cell poles and future division sites. Despite extensive study, it remains unclear how chemotaxis clusters form, what controls cluster size and density, and how the cellular location of clusters is robustly maintained in growing and dividing cells. Here, we use photoactivated localization microscopy (PALM) to map the cellular locations of three proteins central to bacterial chemotaxis (the Tar receptor, CheY, and CheW) with a precision of 15 nm. We find that cluster sizes are approximately exponentially distributed, with no characteristic cluster size. One-third of Tar receptors are part of smaller lateral clusters and not of the large polar clusters. Analysis of the relative cellular locations of 1.1 million individual proteins (from 326 cells) suggests that clusters form via stochastic self-assembly. The super-resolution PALM maps of E. coli receptors support the notion that stochastic self-assembly can create and maintain approximately periodic structures in biological membranes, without direct cytoskeletal involvement or active transport.

2009-02-17: Invited talk "Length of time's arrow" @BioStruct09 Firenze, February 16-18, 2009

• Slides: Length of time's arrow
• Further reading: E. H. Feng, G.E. Crooks Phys. Rev. Lett. 101 090602 (2008)

2009-01-29: Published: Far-from-equilibrium measurements of thermodynamic length

E. H. Feng, G.E. Crooks Phys. Rev. E 79, 012104 (2009) 10.1103/PhysRevE.79.012104
Thermodynamic length is a path function that generalizes the notion of length to the surface of thermodynamic states. Here, we show how to measure thermodynamic length in far-from-equilibrium experiments using the work fluctuation relations. For these microscopic systems, it proves necessary to define the thermodynamic length in terms of the Fisher information. Consequently, the thermodynamic length can be directly related to the magnitude of fluctuations about equilibrium. The work fluctuation relations link the work and the free-energy change during an external perturbation on a system. We use this result to determine equilibrium averages at intermediate points of the protocol in which the system is out of equilibrium. This allows us to extend Bennett's method to determine the potential of the mean force, as well as the thermodynamic length, in single-molecule experiments.

2009-01-11: Invited talk "Length of time's arrow" @ 2009 Berkeley Mini Stat. Mech. Meeting

• Slides: Length of time's arrow
• Further reading: E. H. Feng, G.E. Crooks Phys. Rev. Lett. 101 090602 (2008)

2008-12-01: FQXi 2008 Essay Contest on The Nature of Time: Whither Time's Arrow?

In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous.

Until mid-December you can vote on your favorite essay here.

2008-10-31 Published: On the Jarzynski relation for dissipative quantum dynamics

G.E. Crooks J. Stat. Mech.: Theor. Exp. P10023 (9pp) (2008) In this paper, we will discuss how to compactly express the Jarzynski identity for an open quantum system with dissipative dynamics. In quantum dynamics we must avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the state of the system, and instead measure the heat flow from the environment. These measurements can be concisely represented with Hermitian map superoperators, which provide convenient and compact representations of correlation functions and sequential measurements of quantum systems.

2008-10-14: WebLogo: Release 3.0.0

A major update with many new features and improved graphics.

2008-09-05: Press: Physicists investigate how time moves forward

PhysOrg.com: "As humans, we have a very intuitive concept of time, and of the differences between the past, present, and future. But, as scientists Edward Feng of the University of California, Berkeley, and Gavin Crooks of the Lawrence Berkeley National Laboratory point out, science does not provide a clear definition of time." By Lisa Zyga

2008-08-29: Published: The Length of Time's Arrow

E. H. Feng, G.E. Crooks Phys. Rev. Lett. 101 090602 (2008)
An unresolved problem in physics is how the thermodynamic arrow of time arises from an underlying time reversible dynamics. We contribute to this issue by developing a measure of time-symmetry breaking, and by using the work fluctuation relations, we determine the time asymmetry of recent single molecule RNA unfolding experiments. We define time asymmetry as the Jensen-Shannon divergence between trajectory probability distributions of an experiment and its time-reversed conjugate. Among other interesting properties, the length of time's arrow bounds the average dissipation and determines the difficulty of accurately estimating free energy differences in nonequilibrium experiments.

2008-07-08: Published: Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise

Paul Maragakis, Felix Ritort, Carlos Bustamante, Martin Karplus, Gavin E. Crooks, J. Chem. Phys. 129 024102 (2008)
The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to nonequilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not been considered previously. Here, we present a Bayesian formalism for estimating free energy changes from nonequilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. ...

2008-04-28: Cumulative Errata

A memorandum of miscellaneous minor mistakes.

2008-04-24: Lectures: Non-Equilibrium Fluctuation Theorems, from Jarzynski's identity and beyond

April 24, 29 and May 1, 433 Latimer, 2-3:30 PM Reading list:

• G. E. Crooks, Excursions in Statistical Mechanics (UC Berkeley PhD Thesis, 1999).
• G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. USA 98, 3658-3661(2001)
• C. Bustamante, J. Liphardt and F. Ritort, "The non-equilibrium thermodynamics of small systems," Physics Today 58, 43-48(2005).

2008-04-14: Technical Note 004: Inequalities between the Jenson-Shannon and Jeffreys divergences

Jeffreys' J-divergence and the Jensen-Shannon divergence are shown to be related by an inequality that involves a transcendental function of the Jeffreys divergence.

2008-03-27: Published: Quantum operation time reversal

G.E. Crooks, G.E. Crooks, Phys. Rev. A 77 034101(4) (2008) doi:10.1103/PhysRevA.77.034101 The dynamics of an open quantum system can be described by a quantum operation: A linear, complete positive map of operators. Here, I exhibit a compact expression for the time reversal of a quantum operation, which is closely analogous to the time reversal of a classical Markov transition matrix. Since open quantum dynamics are stochastic, and not, in general, deterministic, the time reversal is not, in general, an inversion of the dynamics. Rather, the system relaxes toward equilibrium in both the forward and reverse time directions. The probability of a quantum trajectory and the conjugate, time reversed trajectory are related by the heat exchanged with the environment.

2008-03-27: Word of the Day: Super-duper-operator (n)

An operator is a linear map that acts on a vector space. A superoperator is an operator of an operator, an operator that acts on a vector space of operators. A super-duper-operator is an operator of an operator of an operator, an operator that acts on a vector space of superoperators.

2008-02-14: Technical Note 003v2: The Amoroso Distribution

The Amoroso distribution is the natural unification of the generalized gamma and generalized extreme value families of distributions. At least 40 distinct, named distributions (and as many synonyms) occur as special cases or limiting forms. Consequentially, this single simple functional form encapsulates and systematizes an extensive menagerie of interesting and common probability distributions.

2007-12-10: Office Translocation

New Office address: 260K Stanley Hall

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