Biology Reference
In-Depth Information
to state this law Heylighen and Joslyn (2001a, b) but the following definition
adopted from Ashby (1964) is suitable for application to molecular and cell
biology:
When a machine (also called a system or a network) is influenced by its environment in a
dominating manner (i.e., the environment can affect the machine but the machine cannot
influence its environment to any significant degree), the only way for the machine to reduce
the degree of the influence from its environment is to increase the variety of its internal
states. (5.62)
The complexity of biological systems (or bionetworks), from enzymes to protein
complexes to metabolic pathways and to genetic networks, is well known. One
way to rationalize the complexity of bionetworks is to invoke the Law of Requisite
Variety. We can express LRV quantitatively as shown in Eq.
5.63
. If we designate
the variety of the environment (e.g., the number of different environmental
conditions or inputs to the system) as V
E
and the variety of the internal states of the
machine as V
M
, then the variety of outputs of the machine, V
O
, can be expressed as
V
O
V
E
=
V
M
(5.63)
One interpretation of Eq.
5.63
is that, as the environmental conditions become
more and more complex (thus increasing V
E
), the variety of the internal states of the
machine, V
M
, must increase proportionately to maintain the number of outputs, V
O
,
constant (i.e., keep the system homeostatic). Another way to interpret this equation
is that, in order for a bionetwork to maintain its functional homeostasis (e.g., to keep
the numerical value of V
O
constant) under increasingly complexifying
environments (i.e., increasing V
E
), the bionetwork must increase its variety or
complexity, namely, V
M
.
The term “variety” appearing in LRV can be expressed in terms of either (1) the
number of distinct elements, or (2) the binary logarithm of that number. When
variety is measured in the binary logarithmic form, its unit is the bit. Taking the
binary logarithm to the base 2 of both sides of Inequality
5.63
leads to Inequalities
5.64
and
5.65
:
log V
O
log (V
E
=
V
M
Þ
or
(5.64)
log V
O
logV
E
logV
M
(5.65)
which is identical with the equation for LRV used by F. Heylighen and C. Joslyn
(2001), except that the buffering capacity of the machine, K, is assumed to be zero
here, that is, the machine under consideration is assumed to respond to all and every
environmental perturbations. Since logV
x
is defined as Shannon entropy H
x
(see
H
O
H
E
H
M
(5.66)
