78 research outputs found
Numerical comparison of two approaches for the study of phase transitions in small systems
We compare two recently proposed methods for the characterization of phase
transitions in small systems. The validity and usefulness of these approaches
are studied for the case of the q=4 and q=5 Potts model, i.e. systems where a
thermodynamic limit and exact results exist. Guided by this analysis we discuss
then the helix-coil transition in polyalanine, an example of structural
transitions in biological molecules.Comment: 16 pages and 7 figure
Knowledge-based energy functions for computational studies of proteins
This chapter discusses theoretical framework and methods for developing
knowledge-based potential functions essential for protein structure prediction,
protein-protein interaction, and protein sequence design. We discuss in some
details about the Miyazawa-Jernigan contact statistical potential,
distance-dependent statistical potentials, as well as geometric statistical
potentials. We also describe a geometric model for developing both linear and
non-linear potential functions by optimization. Applications of knowledge-based
potential functions in protein-decoy discrimination, in protein-protein
interactions, and in protein design are then described. Several issues of
knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe
Are biological systems poised at criticality?
Many of life's most fascinating phenomena emerge from interactions among many
elements--many amino acids determine the structure of a single protein, many
genes determine the fate of a cell, many neurons are involved in shaping our
thoughts and memories. Physicists have long hoped that these collective
behaviors could be described using the ideas and methods of statistical
mechanics. In the past few years, new, larger scale experiments have made it
possible to construct statistical mechanics models of biological systems
directly from real data. We review the surprising successes of this "inverse"
approach, using examples form families of proteins, networks of neurons, and
flocks of birds. Remarkably, in all these cases the models that emerge from the
data are poised at a very special point in their parameter space--a critical
point. This suggests there may be some deeper theoretical principle behind the
behavior of these diverse systems.Comment: 21 page
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