Cell Language Theory, The: Connecting Mind And Matter

The Universality of the Planckian Distribution Equation 351

“6x9” b2861 The Cell Language Theory: Connecting Mind and Matter

V-genes, 2 D-genes, and 13 J-genes. These gene segments are recombined

via a series of stochastic recombination mechanisms catalyzed by appro-

priate enzymes to generate a large repertoire of CDR3 sequences. Each

CDR3 sequence can be viewed as the result of a generative event describ-

able by several random variables, including V-, D-, and J-gene choices.

From the set of observed CDR3 sequences, Murugan et al. [476] were

able to construct a mathematical equation called the generative probability

function that predicts the probability of generating CDR3 sequence s,

Pgen(s). Pgen(s) is the sum of the probabilities of all recombination events

involved in producing CDR3 sequence s. A typical example of the CDR3

sequence histogram predicted by Pgen(s) for one subject is given in Figure 8.6(f).

As evident in the histogram of Figure 8.6(f) (obtained by one of my pre-

med students at Rutgers, Vinay Valadi), the agreement between the Pgen(s)

distribution and the Planckian distribution is excellent. This despite the fact

that the histogram is left long-tailed (unlike most other histograms which

are right long-tailed) and the x-axis is logarithmic. Also we found that one

of the left long-tailed histograms (not shown) could not fit into the

3-parameter version of PDE, Eq. (8.3), but did fit the 4-parameter version,

Eq. (8.2). The fitting of the T-cell receptor variable region data to PDE

suggests that the SID–TEM–TOF mechanism may apply to the molecular

mechanisms of the generation of the T-cell receptor diversity, thus empha-

sizing the involvement of (a) Brownian motions, (b) the selection of a

subset of all possible choices by some triggering signals (yet to be identi-

fied), and (c) the function of the selected subsets, which is most likely the

accurate recognition of the epitope on the target antigen or antibody.

8.3.7 7-Mer Frequency Distribution in P. abyssi (Figure 8.6(g))

When DNA is fragmented into short segments, so-called n-mers are gen-

erated, where n is the number of nucleotides in them. The number of all

possible n-mers produced is 4n, since there are 4 different nucleotides in

cellular genomes, G, C, A, and T. When n = 7, 4n = 16,384. Zhou and

Mishra [480] studied the frequency distributions of the 7-mers of the P.

abyssi genome. The 7-mers were unevenly distributed — some (as distin-

guished by their nucleotide sequences) occurred only once and some did

not occur at all, while still others occurred more than one hundred times.

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