Gavin E. Crooks

News

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. ...

2008-07-03: Preprint: Far-from-Equilibrium Measurements of Thermodynamic Length

E. H. Feng, G.E. Crooks, 0807.0621
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 single molecule 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 mean force, as well as the thermodynamic length, in single molecule experiments.

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

2007-09-07: Published: Measuring thermodynamic length

G.E. Crooks, Phys. Rev. Lett. 99 100602 (2007)
doi:10.1103/PhysRevLett.99.100602

Research highlight: Nature Physics

Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information, and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out of equilibrium. In this Letter, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length. .

2007-08-14: Technical Note 003: The Amoroso Distribution

The Amoroso distribution is a continuous, univariate, unimodal probability distribution with a semi-infinite range. A surprisingly large menagerie of interesting, univariate probability distributions are special cases or limiting forms of the Amoroso distribution.

2007-07-03: Preprint: 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, arXiv:0707.0089 The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium 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 previously been considered. Here, we present a Bayesian formalism for estimating free-energy changes from non-equilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise, and therefore provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with AFM, optical, and magnetic tweezers.

2007-06-27: Preprint: Quantum operation time reversal

G.E. Crooks, arXiv:0706.3749 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 towards 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.

2007-06-13 Preprint: On the Quantum Jarzynski Identity

G.E. Crooks, arXiv:0706.1994 In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the system, and instead measure the heat flow from the environment. We represent the measurement of heat flow with Hermitian map superoperators that act on the system density matrix. Hermitian maps provide a convenient and compact representation of sequential measurement and correlation functions.

2007-06-04: Preprint: Measuring thermodynamic length

G.E. Crooks, arXiv:0706.0559 Thermodynamic length is a metric distance between equilibrium thermodynamic states. Among other interesting properties, this metric asymptotically bounds the dissipation induced by a finite time transformation of a thermodynamic system. It is also connected to the Jensen-Shannon divergence, Fisher information and Rao's entropy differential metric. Therefore, thermodynamic length is of central interest in understanding matter out-of-equilibrium. In this paper, we will consider how to define thermodynamic length for a small system described by equilibrium statistical mechanics and how to measure thermodynamic length within a computer simulation. Surprisingly, Bennett's classic acceptance ratio method for measuring free energy differences also measures thermodynamic length.

2007-05-20: Technical Notes

002 Approximate convolution of a logistic function with a Gaussian distribution G. E. Crooks [Full Text]

001 Estimating probabilities from counts with a prior of uncertain reliability G. E. Crooks [Full Text]

2007-04-27: Published: Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium

G.E. Crooks, Phys. Rev. E 75, 041119 (2007) What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium? Here, we argue the most appropriate additional parameter is the nonequilibrium entropy of the system. Moreover, we should not attempt to estimate the probability distribution of the system directly, but rather the metaprobability (or hyperensemble) that the system is described by a particular probability distribution. The result is an entropic distribution with two parameters, one a nonequilibrium temperature, and the other a measure of distance from equilibrium. This dispersion parameter smoothly interpolates between certainty of a canonical distribution at equilibrium and great uncertainty as to the probability distribution as we move away from equilibrium. We deduce that, in general, large, rare fluctuations become far more common as we move away from equilibrium.

2007-04-09: Gratuitous Link: David Crooks

Bohemian artist / Bohemian scientist.

2007-04-01: Random Quotes

Life is short and the alphabet shorter.
C.T.J. Dobson

In this context the real numbers are called scalars. The only reason for not calling them just "numbers", which would adequately distinguish them from vectors, is that for historical reasons nobody else does, and in mathematics, as in other languages, the idea is to be understood.
C.T.J. Dobson

Substitute damn every time you're inclined to write very; your editor will delete it and the writing will be just as it should be.
Mark Twain

2007-02-04: Published: Work distribution for the adiabatic compression of a dilute and interacting classical gas

G.E. Crooks, C. Jarzynski. Phys. Rev. E 75, 021116 (2007) We consider a simple, physically motivated model of a dilute classical gas of interacting particles, initially equilibrated with a heat bath, undergoing adiabatic and quasistatic compression or expansion. This provides an example of a thermodynamic process for which non-Gaussian work fluctuations can be computed exactly from microscopic principles. We find that the work performed during this process is described statistically by a gamma distribution, and we use this result to show that the model satisfies the nonequilibrium work and fluctuation theorems, but not a prediction based on linear response theory.

2006-05-01: Press: WebLogo: Data visualization for everyone

The Scientist, Volume 20, Issue 5, Page 67

2006-03-07: Preprint: Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium

G.E. Crooks. cond-mat/0603120 (2006) What is the best description that we can construct of a thermodynamic system that is not in equilibrium, given only one, or a few, extra parameters over and above those needed for a description of the same system at equilibrium?...

2006-03-07: Preprint: On the work distribution for the adiabatic compression of a dilute classical gas

G.E. Crooks, C. Jarzynski. cond-mat/0603116 (2006) We consider the adiabatic and quasi-static compression of a dilute classical gas, confined in a piston and initially equilibrated with a heat bath. We find that the work performed during this process is described statistically by a gamma distribution. We use this result to show ...

2006-01-10: Published: A high level interface to SCOP and ASTRAL implemented in Python

J.A. Casbon, G.E. Crooks, M.A.S. Saqi, BMC Bioinformatics 7:10 (2006) Benchmarking algorithms in structural bioinformatics often involves the construction of datasets of proteins with given sequence and structural properties. The SCOP database is a manually curated structural classification which groups together proteins on the basis of structural similarity. The ASTRAL compendium provides ...

2005-12-01: Published (With Erratum): Statistical Evaluation of Pairwise Protein Sequence Comparison with the Bayesian Bootstrap

G.A. Price, G.E. Crooks, R.E. Brenner, S.E. Brenner, Bioinformatics 20:3824-3831 (2005) Erratum: Bioinformatics 21:4138 (2005) Protein sequence comparison methods are routinely used to infer the intricate network of evolutionary relationships found within the rapidly growing library of protein sequences, and thereby to predict the structure and function of uncharacterized proteins. Here, we detail an improved statistical benchmark of pairwise protein sequence comparison algorithms. ...

2005-10-10: Published: Pairwise alignment incorporating dipeptide covariation

G.E. Crooks, R.E. Brenner, S.E. Brenner, Bioinformatics 21:3704-3710 (2005) Standard algorithms for pairwise protein sequence alignment make the simplifying assumption that amino acid substitutions at neighboring sites are uncorrelated. This assumption allows implementation of fast algorithms for pairwise sequence alignment, but it ignores information that could conceivably increase the power of remote homolog detection. ...

2005-09-08: Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies Nature 437, 231-23 (2005)

2005-09-08: WebLogo: Release 2.8.2

A minor bug fix release. Made various improvements in handling malformed input; Fixed the fineprint checkbox option, which was stuck on; Renamed "Uniform Height Logo" option to a more descriptive "Frequency Plot", and removed deceptive y-axis; And fixed the specification of yellow, which looked orange.

2005-08-30: Published: Pairwise alignment incorporating dipeptide covariation

G.E. Crooks, R.E. Brenner, S.E. Brenner, Bioinformatics (2005) Standard algorithms for pairwise protein sequence alignment make the simplifying assumption that amino acid substitutions at neighboring sites are uncorrelated. This assumption allows implementation of fast algorithms for pairwise sequence alignment, but it ignores information that could conceivably increase the power of remote homolog detection. ...

2005-08-30: Published: Statistical Evaluation of Pairwise Protein Sequence Comparison with the Bayesian Bootstrap

G.A. Price, G.E. Crooks, R.E. Brenner, S.E. Brenner, Bioinformatics (2005) Protein sequence comparison methods are routinely used to infer the intricate network of evolutionary relationships found within the rapidly growing library of protein sequences, and thereby to predict the structure and function of uncharacterized proteins. Here, we detail an improved statistical benchmark of pairwise protein sequence comparison algorithms. ...

2005-04-01: Published: An Alternative Substitution Model of Amino Acid Replacement

G. E. Crooks, S. E. Brenner, Bioinformatics 21:975-980 (2005) We propose an alternative model of amino acid replacement during protein evolution. The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same background distribution of amino acids, an assumption that is incompatible with ...

2005-02-08: New Appointment: Divisional Fellow, Physical Biosciences, Lawrence Berkeley Natl. Lab

I have accepted a position as Divisonal Fellow, Physical Biosciences at Lawrence Berkeley National lab, where I will be continuing my research into in the fields of computational biology and nonequilibirum statistical mechanics.

2005-02-01: Preprint: Pairwise alignment incorporating dipeptide covariation

G. E. Crooks, R. E. Green, S. E. Brenner Submitted, (2005)

Motivation: Standard algorithms for pairwise protein sequence alignment make the simplifying assumption that amino acid substitutions at neighboring sites are uncorrelated. This assumption allows implementation of fast algorithms for pairwise sequence alignment, but it ignores information that could conceivably increase the power of remote homolog detection ...

2004-12-27: Published: A Generalized Affine Gap Model Significantly Improves Protein Sequence Alignment Accuracy

Marcus A. Zachariah, Gavin E. Crooks, Stephen R. Holbrook, and Steven E. Brenner, Proteins 58(2):329-338 (2005)

Sequence alignment underpins common tasks in molecular biology, including genome annotation, molecular phylogenetics, and homology modelling. Fundamental to sequence alignment is the placement of gaps, which represent character insertions or deletions. We assessed the ability of a generalized affine gap cost model ...

2004-12-01: Published: Measurements of protein sequence-structure correlations

Gavin E. Crooks, Jason Wolfe, Steven E. Brenner, Proteins 57(4):804-810 (2004)

Correlations between protein structures and amino acid sequences are widely used for protein structure prediction. For example, secondary structure predictors generally use correlations between a secondary structure sequence and corresponding primary structure sequence, whereas threading algorithms and similar tertiary structure predictors typically incorporate interresidue contact potentials. To investigate the relative importance of these sequence-structure interactions ...

2004-11-26: Published (Online): A Generalized Affine Gap Model Significantly Improves Protein Sequence Alignment Accuracy

Marcus A. Zachariah, Gavin E. Crooks, Stephen R. Holbrook, and Steven E. Brenner, Proteins(2004)

2004-11-05: Published (Online): An Alternative Substitution Model of Amino Acid Replacement

G. E. Crooks, S. E. Brenner, Bioinformatics In Press, (2005?) We propose an alternative model of amino acid replacement during protein evolution. The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same background distribution of amino acids, an assumption that is incompatible with ...

2004-10-24: In press: An Alternative Substitution Model of Amino Acid Replacement

G. E. Crooks, S. E. Brenner, Bioinformatics In Press, (2004) We propose an alternative model of amino acid replacement during protein evolution. The observed correlations between pairs of homologous protein sequences are typically explained in terms of a Markovian dynamic of amino acid substitution. This model assumes that every location on the protein sequence has the same background distribution of amino acids, an assumption that is incompatible with ...

2004-10-19: Published: Experimental test of Hatano and Sasas nonequilibrium steady-state equality

E. H. Trepagnier, C. Jarzynski, F. Ritort, G. E. Crooks, C. J. Bustamante, and J. Liphardt PNAS 101: 15038-15041 (2004)

Most natural processes occur far from equilibrium and cannot be treated within the framework of classical thermodynamics. In 1998, Oono and Paniconi proposed a general phenomenological framework, steady-state thermodynamics, encompassing nonequilibrium ...

2004-10-18: WebLogo: Release 2.8.1

Minor bug fix release. Made weblogo compatibly with ghostscript version 8.1x. This release is known to work with ghostscript version 7.05, 8.00 and 8.14

2004-10-08: In Press: Measurements of protein sequence-structure correlations

Gavin E. Crooks, Jason Wolfe, Steven E. Brenner, Proteins(2004)

2004-10-01: WebLogo: Release 2.8.0

Bug fixes: Fixed another form data parsing bug whose only apparent effect was to fill up the webserver's error log. Fixed an issue with using double slashes in weblogo's url.