BIOCOMPUTATION: some history and prospects.

At first glance, biology and computer science are diametrically opposed sciences. Biology deals with carbon based life forms shaped by evolution and natural selection. Computer Science deals with electronic machines designed by engineers and guided by mathematical algorithms. In this brief paper, we review biologically inspired computing. We discuss several models of computation which have arisen from various biological studies. We show what these have in common, and conjecture how biology can still suggest answers and models for the next generation of computing problems. We discuss computation and argue that these biologically inspired models do not extend the theoretical limits on computation. We suggest that, in practice, biological models may give more succinct representations of various problems, and we mention a few cases in which biological models have proved useful. We also discuss the reciprocal impact of computer science on biology and cite a few significant contributions to biological science.

The mathematical biophysics of Nicolas Rashevsky.

N. Rashevsky (1899-1972) was one of the pioneers in the application of mathematics to biology. With the slogan: mathematical biophysics : biology :: mathematical physics ; physics, he proposed the creation of a quantitative theoretical biology. Here, we will give a brief biography, and consider Rashevsky's contributions to mathematical biology including neural nets and relational biology. We conclude that Rashevsky was an important figure in the introduction of quantitative models and methods into biology.

Population models: stability in one dimension.

Some of the simplest models of population growth are one dimensional nonlinear difference equations. While such models can display wild behavior including chaos, the standard biological models have the interesting property that they display global stability if they display local stability. Various researchers have sought a simple explanation for this agreement of local and global stability. Here, we show that enveloping by a linear fractional function is sufficient for global stability. We also show that for seven standard biological models local stability implies enveloping and hence global stability. We derive two methods to demonstrate enveloping and show that these methods can easily be applied to the seven example models. Although enveloping by a linear fractional is a sufficient for global stability, we show by example that such enveloping is not necessary. We extend our results by showing that enveloping implies global stability even when f(x) is a discontinuous multi-function which might be a more reasonable description of real bilogical data. We show that our techniques can be applied to situations which are not population models. Finally, we give examples of population models which have local stability but not global stability.

Walking tree heuristics for comparative genomic alignments.

Genomic sequence data is available for an ever-increasing number of organisms, but the full meaning of this data remains an enigma. String alignment is one approach for deciphering the information contained in genetic strings. Sequences which are conserved across species will help identify genes and other important structures. Similarity between species can be scored by measuring how well their sequences align. The walking tree method is an approximate string alignment method that can handle insertions, deletions, substitutions, translocations, and more than one level of inversion. We will describe this method and recent improvements which allow fast alignment of megabase strings. We will show examples in which the method located or discovered genes. We show how the method can be used to construct phylogenetic trees. We also show that the method can be used to identify essential regions for protein function.