The Second Law and Biophysics

author: Kenneth Dill, University of California
published: July 24, 2013,   recorded: October 2007,   views: 2700

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“Biology is messy,” says Kenneth Dill, and it’s “heavily about entropy.” Just look at how biological systems repeat entropy at every possible turn: a parent cell making two daughter cells, sending one DNA molecule to each; and the process of biochemical reactions, with water getting stripped off the molecules. Dill is convinced that the “language of biology in the future will be nonequilibrium statistical mechanics.” He’s engaged in experiments that explore how dynamical laws apply to very small biological systems, such as those inside cells.

Traditional macro-scale dynamics, explains Dill, have laws where concentration gradients or temperature gradients drive flux. But inside cells, there are elements that sometimes contain five molecules, and then in the next instant, 500 molecules. The question is how to think about these highly fluctuating quantities in terms of dynamics. To that end, researchers have been devising experiments to describe the dynamics of micro systems.

Dill’s colleagues have built a microfluidics apparatus that plots the diffusion of microscopic particles over time, their probable routes and rates. To help frame this work, and make predictions about comparable systems, they use an analogy to entropy, described as caliber. Just as there can be maximum entropy, there can be maximum caliber -- “an extremum principle that predicts the dynamical laws, just as maximum entropy predicts equilibrium,” says Dill. This way of modeling fluxes deals with the likely trajectories and speeds traveled by particles within a certain time period.

Dill also describes how statistical mechanics applies in the “dog-flea model.” Scientists calculate the probabilities of fleas jumping from one dog to another, and of going up against a concentration gradient. Dill says this model can be used “to argue in the simplest way how diffusion works,” to predict flux distribution.

Scientists have also worked out an experiment to model two-state kinetic processes, such as single ion channels opening and closing. Colloidal particles wiggling in adjacent laser traps can jump over barriers from one trap to the other, depending on the height of the barrier and the depth of the well. This allows researchers to count trajectories, and to measure “the full dynamical distribution functions.” The value of the maximum caliber approach, Dill says, is that you get data about the first moment of the system in state “and from them you can predict everything else.” Says Dill, “One of the great things about having an extremum principle and partition-based approach is it turns out all kinds of analogies with normal thermodynamics.” So far, researchers have only taken the earliest steps to illustrate this new tack. “The potential power of caliber hasn’t been tested yet,” believes Dill.

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