Biology Reference
In-Depth Information
of the blackbody spectrum perfectly but underestimated the emission intensities at the
long-wavelength regions. It was in an attempt to remedy this shortcoming that Planck
was led to invoke the concept of “energy quanta,” which allowed him to derive his
radiation law, Eq.
11.26
. In effect, Planck demonstrated that the blackbody radiation
data are better explained in terms of the Bose-Einstein statistics than in terms of the
Boltzmann statistics.
Equation
11.27
consists of two terms, referred to as the “deterministic” and
“nondeterministic” terms. These could be equally well referred to as “synchronic”
and “diachronic” terms, respectively (for the definitions of “synchronic” versus
“diachronic” information, see Table
4.1
). The deterministic term is isomorphic with
Planck's radiation formula, Eq.
11.26
. It is important to point out that neither Lu
et al. (1998) nor Prakash and Marcus (2007) discussed the possibility of including
any
nondeterministic
(also called
diachronic
or
arbitrary
) term, X(w), in their
equations, probably because they assumed, as most biological theorists do, that
all biological data, including the waiting time distribution histogram, should fit
deterministic equations
as long as they are noise free. Under such an assumption,
any experimental data that do not fit deterministic equations such as Eqs.
11.25
and
11.26
would be
logically
regarded as noise and hence automatically excluded from
any theoretical considerations. In contrast, it is here assumed that:
(a) The nondeterministic (or
diachronic
or
arbitrary
) term, X(w), which is
defined by Eq.
11.27
as the difference between the measured and the
predicted values of w, is too large to be discounted as noise (as seems
evident in the lower panel of Fig.
11.24
).
(b) The nondeterministic term, X(w), in fact carries biological information (yet
to be determined and hence the symbol X), most likely encoded in the
evolutionarily conserved set of amino acid residues
constituting
conformons. By “evolutionarily conserved set of amino acid residues,” I
mean something similar to the “evolutionarily coevolving amino acid
residues” found in the WW domains by Lockless and Ranganathan (1999),
Suel et al (2003), Socolich et al. (2005), and Poole and Ranganathan (2006).
3. One possible mechanism by which the
evolutionary information
encoded in a
conformon can influence the probability of the occurrence of a given waiting
time w is described in Table
11.11
. This table is constructed on the basis of the
relations among
configurations
,
conformers
, and
conformons
described in
Fig.
11.21
. Waiting time, w, is postulated to be determined by
conformers
denoted as (
)
C
in Column (2), which is consistent with
the postulated mechanism of enzymic catalysis described in the right-hand panel
of Fig.
11.28
. Please note that three different conformers, A, B, and C, are
associated with three different waiting times, 51, 56, and 63 ms, as shown in
Column (2), and Column (4) lists the numerical value of the deterministic
component of the probability of the occurrence of w calculated from Eq.
11.27
with X(w) set to zero. Column (5) lists the numerical values of the nondetermin-
istic component of Eq.
11.27
calculated as the difference between the measured
probability value minus the deterministic component, and these differences are
attributed to the differences in (or the arbitrariness of) the
evolutionary
...
)
A,
(
...
)
B
, and (
...
