Biomedical Engineering Reference
In-Depth Information
correspondingly weaker. However, it remains a fascinating question to pose: to
what extent do human institutions represent instances of mechanisms for bio-
logical robustness? In the non-reductive (gene-independent) example of medical
care and hospitals the case is obvious. There are indications, though, that behav-
ioral rules, such as reciprocity and sharing, are to some extent causally related to
the actions of our genes (8).
Modeling in this area tends to be either game theoretical (39) or some vari-
ant of population genetics to allow for both vertical and horizontal transmission.
This is a nascent field for theory.
4.
CASE STUDIES OF ROBUST PRINCIPLES
In the remainder of this chapter I have chosen case studies to illustrate the
application of theory in the study of biological robustness. I have done so be-
cause as of yet there is no unified theory of biological robustness, only collec-
tions of illustrative models. These models vary in the degree to which they deal
with robustness explicitly, and yet all them bear on the question in some funda-
mental way.
4.1. Redundancy in Genetic Networks
Wagner (60) has studied dynamical models for evolution of transcription
regulation circuits. Gene duplication is thought of as a mutational event neces-
sary to establish the genetic diversity for subsequent diversity in spatiotemporal
patterning during development. Wagner poses this question: what is the average
proportion of genes likely to be involved in a duplication event, such that the
initial effect on the phenotype of duplication is minimized? In other words, what
fraction of genes is capable of performing redundantly? This question can be
inverted by asking how many genes from a portion of genome made up from
duplicate sets can be deleted and made to preserve the same phenotype. In the
first case the perturbation involves adding genes, and in the second eliminating
genes. Wagner models the gene expression dynamics in much the same way
connectionist modelers describe neural networks. The activity of gene
i
is de-
noted by
S
i
. The magnitude of transcriptional activation between gene
i
and gene
j
is given by weight matrix entry
w
ij
. The dynamics of gene expression in dis-
crete time are
¯
N
¡
°
St
(
+=
UT
)
wS t
( )
=
T
[
ht
( )]
.
[1]
¡
°
i
ij
j
i
¢
±
i
