Engineering - Molecular Theory of the Living Cell - page 142

entails specifying the behavior of the smallest unit of life, the cell. The cell behavior
is depicted as a curvy line denoted as R (from “river,” the symbol of life) in
Fig. 5.10 . The genetic program responsible for the cell behavior is indicated as
the projection R g of R onto the internal coordinate (or genetic information) space
(see the vertical plane on the left in Fig. 5.10 ). The projection of R onto the
spacetime plane produces its spacetime trajectory denoted as R s .
The trajectory R is postulated to be composed of N sub-trajectories called
“streams,” where N is the number of biopolymers inside the cell. Each stream
represents the behavior of one biopolymer inside the cell. The uncertainty about the
behavior about the cell cannot be less than the uncertainty about the behavior of one
of the N biopolymers. The uncertainty about the behavior of a biopolymer inside the
cell can be estimated as follows:

1. There is a finite amount of uncertainty that is associated with the determination
of the Gibbs free energy change underlying a given intracellular process
catalyzed by a biopolymer. This uncertainty is designated as D G. Since driving
any net biological process necessitates dissipating Gibbs free energy at least as
large as thermal energies, kT, it would follow that the smallest uncertainty about
the measurement of the Gibbs free energy change attending a biopolymer-
catalyzed process inside the cell can be estimated to be

D G kT kcal = mol (5.49)

2. Due to D G, the cross section of the behavior trajectory R of the biopolymer
possesses a finite size. This leads to an uncertainty about the internal coordinate
(i.e., the genetic information) of the biopolymer, since there are at least two
internal coordinates that can be accommodated within the cross section of R (see
1, 1', and 1” and their projections, not shown, onto the information space).
Therefore, the uncertainty concerning the genetic information associated with
the biopolymer behavior is at least one bit:

D I 1 bit (5.50)

3. Inequalities 5.49 and 5.50 can be combined by multiplication to obtain what was
referred to as the Cellular Uncertainty Principle in (Ji 1991, pp. 119-122):

ðD G ÞðD I Þ kT bit kcal = mol (5.51)

The three uncertainty principles discussed above are given in the first rows of
Tables 5.6 , 5.7 , and 5.8 , the first two of which are the modified forms of Tables 2.9
and 2.10 in Sect. 2.3 . The two forms of the HUP are reproduced in the first row of
Table 5.6 , that is, Inequalities 2.38 and 2.39 . These inequalities are displayed in the
table as the horizontal and vertical margins, respectively. As pointed out in
Sect. 2.3.5 , the uncertainty relations are located on the margins of the table and
the complementary relations such as the kinematics-dynamics duality are located in
the diagonal boxes (or the interior) of the table , suggesting that the uncertainty