Theoretical biophysics: evolutionary dynamics, self-organization, and control


     Intro and goals


Since the early days of evolutionary theory, the origin of the remarkable organization in the biological world has evinced a mixture of awe and wonder. One of the most seminal moments in the history of science was the discovery in the late 19th century that this order is not created by design, but rather originates due to .
The question as to whether additional -physical- organizing principles are involved in the generation of order, or whether natural selection alone is sufficent, has remained, and has been notoriously difficult to prove.
This debate originated in the differing views of Alfred Russell Wallace and Charles Darwin. Wallace ascribed

Wallace appeared to have envisioned natural selection as a kind of feedback mechanism keeping species and varieties adapted to their environment.[73] They point to a largely overlooked passage of Wallace's famous 1858 paper:

In a well-known speech before the Linnean Society, on ...., Wallace stated:
"The action of this [evolutionary selection] principle is exactly
like that of the centrifugal governor of the steam engine, which
checks and corrects any irregularities almost before they become
evident; and in like manner no unbalanced deficiency in the animal
kingdom can ever reach any conspicuous magnitude, because it would
make itself felt at the very first step, by rendering existence
difficult and extinction almost sure soon to follow."

In the latter half of the 20th century and into the 21st, more quantitative techniques have been deployed in order to answer this question.

Dennett, e.g., contends that the algorithm of natural selection, without additional self-organizing principles, are sufficient for generating
all the complexity in the living world around us. Many notable evolutionary biologists, including Steven J. Gould, have contested this claim,

Stuart Kauffman, in particular, has been a major proponent of the thesis that self-organizing principles based on statistical mechanics are essential for the origin and refinement of life.

Fitness measure overarching all:


The key to our approach is that it remains fully consistent with evolutionary theory while pointing to the ability of natural selection to exploit
powerful organizing steering principles that maximize evolutionary fitness. "Modern synthesis"

     Mutagenic evidence for the optimal control of evolutionary dynamics

     Evidence for the impact of self-organizing principles of control and systems theory to biological evolution has been virtually nonexistent
     since the time of Wallace and Darwin.

     1.  R. Chakrabarti, H. Rabitz, S. Springs, and G. L. McLendon, Phys. Rev. Lett.  (2008)

    2.   R. Chakrabarti, H. Rabitz, and G. L. McLendon. Optimal control of evolutionary dynamics       .   eprint arXiv:0805.---- [quant-bio]  

(extended version w/ statistical analysis) post it here before arxiv
    
     We propose  a new evolutionary theory, based on experimental data, which extends the standard Darwinian model of
      fitness maximization.


     Computational prediction of native protein-ligand binding and enzyme active site sequences

    3.   R. Chakrabarti, A. M. Klibanov, and R. A. Friesner, Proc. Natl. Acad. Sci. USA 102: 10153-10158 (2005).  free access
      Supporting info (combine with main text and post?)

      We show for the f


In the following paper, we use microscopic models of protein biophysics to show that the evolution of functional protein catalysts,
which lie at the heart of the biological machinery, display hierarchical self-organization that facilitates the refinement of functional activity
through random mutation and selection.


     Sequence optimization and designability of enzyme active sites

      4.  R. Chakrabarti, A. M. Klibanov, and R. A. Friesner, Proc. Natl. Acad. Sci. USA 102, 12035-12040 (2005).
      Supporting info

     The first quantitative physical investigation of the fitness measures underlying the natural evolution of biocatalysts.



Next steps:

engineering apps - pcr optimization    
computational enzyme design

Some of the most interesting evolutionary dynamics processes (e.g., those implicated in the origin of life or other discontinuities in evolutionary history) occur when finite population size effects cannot be ignored. As discussed on the --stochastic control--- pages, there exists a well-developed theory for estimation and control of stochastic dynamical systems. My next step will be to develop stochastic optimal control theory, as well as closed loop feedback control theory, for finite-sized, self-replicating DNA or RNA populations. What are the limits of control possible with external (e.g.. temperature) fields? This is tied in to the experimental goal of implementing such control systems in microelectronic hardware described on the -biomolecular reaction engineering-- page.

stochastic control of evolutionary dynamics - implications for early life; what can be done with external fields?
pcr as model system

Links to: PED