Hi FISers,
(1) In 1997 [9], I defined the cell language as follows:
"Cell language is a self-organizing system of molecules, some of which
encode, act as signs for, or trigger, gene-directed cell processes."
So defined the cell language shares many qualitative similarities or principles
with the human language as summarized in Tables 2 and 6-3 in my 11/27/2017 post
to this list. In contrast, Table 3 in the same post provides quantitative
similarities between the two languages, since
(i) PDE, y = (A/(x + B)^5)/(Exp (C/(x + B)) -1) derived from physics and MAL, y
= (Ax^-B)/Exp (Cx), derived from linguistics [15] have a similar mathematical
form in that they are both the products of a power function and an exponential
function, and
(ii) PDE and MAL are equivalent as far as their ability to fit long-tailed
histograms regardless of whether they came from physics or linguistics.
These findings strongly indicate that there are structural features of cell and
human languages that are similar in terms of their functions as inferred in
Table 4. Please note that the first two terms in the following are well
established in linguistics and the third term was introduced in the cell
language theory in 2012 [6]:
1st articulation = words forming sentences
2nd articulation = letters forming words
3rd articulation = sentences forming texts.
Table 4. Isomorphism between cell and human languages deduced from a
qualitative comparison between linguistics and cell biology [1, 2, 3, 4].
Cell Language
Human Language
Function
Alphabet
A, C, G, T/U
Elementary signs [5]
Words
Gene/mRNA/protein
Denotation
Sentences
Metabolic pathways
Decision making
Texts
Functionally related sets of metabolic pathways (FRMPs)
Logical reasoning or computing
(2) What is the Planckian-Shannon plot (PSP) or the Planckian-Shannon space
(PSS) ?
E hAs pointed out earlier on this list, PDE has been found to fit almost all
long-tailed histograms we have analyzed so far that have been reported in the
fields of atomic physics, molecular biology, cell biology, neurophysiology,
psychology, glottometrics (also called quantitative linguistics), econometrics,
cosmology [7-9], and most recently social network science [10]. The deviation
of the asymmetric PDE from a symmetric curve such as the Gaussian distribution
function [4, Figure 8.7] can be used as a measure of non-randomness, order, or
information encoded in PDE [11]. There are two ways of quantifying the
information content of PDE:
Plankian information of the first kind: IPF = log2 [AUC (PDE)/AUC (GLE)]
(1)
Plankian information of the second kind: IPS = - log2 [(\mu – mode)/(\sigma)]
(2)
where AUC = Area Under the Curve; GLE = Gaussian-Like Equation whose rising
portion approximate closely the rising portion of PDE, and \mu and \sigma are,
respectively, the mean and the standard deviation of the data set that can be
represented as a long-tailed histogram fitting PDE. In addition PDE allows us
to calculate the associated Shannon entropy as
H = - \Sigma (pi log2 pi)
(3)
wh where \Sigma is the sum over i from 1 to n, the number of data points, and
pi is the probability of the occurrence of the ith data point.
We have analyzed the mRNA level data of the arbitrarily selected 10
metabolic pathways measured from human breast tissues using microarrays by
Perou et al. [12]. These data sets all produced long-tailed histograms that
fitted PDE, thus generating 10 pairs of the I_PS and H values. (We found that
I_PS values are more reproducible than I_PF.) When these 10 pairs of numbers
were plotted in the so-called “Plank-Shannon space”, a linear correlation
(called the Planck-Shannon plot) was found with the R^2 value of 0.686(see the
upper panel of Figure 1). Interestingly, when similarly sized 10 sets of the
mRNA levels were selected from the the human transcriptome that have no known
metabolic functions and plotted in the PSS, no correlation was found, the R^2
value being 0.213, far less than 0.7, the minimum threshold for a significant
correlation (see the lower panel of Figure 1).
[cid:a3e6c6be-7963-4aff-860c-4f025c88cd7b]
(3) Until just recently (fall, 2017), there has been no method to identify
FRMPs although they were predicted to exist by the cell language theory. It
now seems that we have such a method in the form of the Planck-Shannon plots as
exemplified in Figure 1. In other words, when two sets of metabolic pathways
are chosen that have 30 or more mRNA molecules in each pathway (so that a
decent histogram can be obtained), one set encoding functions while the other
set having no metabolic functions, we see the difference in the correlation
coefficients between their Planck-Shannon plots, indicating that the
Planck-Shannon space (or the IPS vs. H plot) is capable of distinguishing sets
of metabolic pathways that are functionally related from those having no
functional relations.
(5) If this interpretation of the Planck-Shannon plots is correct, the
isomorphism between the structures of the human and cell languages as described
in Table 4 above may be said to have been proven, at least in principle. That
is, we may have finally decoded the cell language (also called the DNA language
by Trifonov in [13]). I am tempted to suggest that the discovery of PDE in
2008 and that of its derivative, the Planck-Shannon space in 2017, may be
comparable to the discovery of the DNA double helix in 1953 [14].
Any questions or comments are welcome.
Sung
(3)
References:
[1] Ji, S. (2017). Planck-Shannon space: A novel quantitative method to
identify functionally related metabolic pathways in cell biology. A short talk
to be presented at the 118th Statistical Mechanics Conference, Hill Center,
Rutgers University, 12/17-19/2017.
[2] Ji, S. (1997). Isomorphism between cell and human languages: molecular
biological, bioinformatic and linguistic implications. BioSystems 44: 17-39.
PDF at
http://www.conformon.net/wp-content/uploads/2012/05/Isomorphism1.pdf<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.conformon.net%2Fwp-content%2Fuploads%2F2012%2F05%2FIsomorphism1.pdf&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C99b30733025745e6497308d530812baa%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C1%7C636468253742499909&sdata=d%2Brode7uE04ZWnUfzQeAW%2B2%2FeyyVgwkEXgzzIg9KzMs%3D&reserved=0>
[3] Ji, S. (1999). The Linguistics of DNA: Words, Sentences, Grammar,
Phonetics, and Semantics. Ann. N. Y. Acad. Sci. 870:411-417.
[4] Ji, S. (2017). The Cell Language Theory; Connecting Mind and Matter.
World Scientific Publications, New Jersey.
[5] Ji, S. (2017). The Quark Model of Peircean Signs, Section 6.6 in [4].
[6] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular
Mechanisms, and Biomedical Applications. Springer, New York. Section 6.1.2.
[3] [7] Ji, S. (2015). Planckian distributions in molecular machines,
living cells, and brains: The wave-particle duality in biomedical
sciences.<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.conformon.net%2Fwp-content%2Fuploads%2F2016%2F09%2FPDE_Vienna_2015.pdf&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C14ff9ca9cc074522748808d5300e95c4%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C1%7C636467761587775083&sdata=vfqYK%2F3Gg%2BM%2F5DXzMcSpFVN2AFlEUysLW9%2FK0ykxjwA%3D&reserved=0>
In: Proceedings of the International Conference on Biology and Biomedical
Engineering, Vienna, March 15-17, 2015. Pp. 115-137. PDF at
http://www.conformon.net/wp-content/uploads/2016/09<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.conformon.net%2Fwp-content%2Fuploads%2F2016%2F09%2FPDE_Vienna_2015.pdf&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C14ff9ca9cc074522748808d5300e95c4%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C1%7C636467761587775083&sdata=vfqYK%2F3Gg%2BM%2F5DXzMcSpFVN2AFlEUysLW9%2FK0ykxjwA%3D&reserved=0>/PDE_Vienna_2015.pdf<https://na01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.conformon.net%2Fwp-content%2Fuploads%2F2016%2F09%2FPDE_Vienna_2015.pdf&data=02%7C01%7Csji%40pharmacy.rutgers.edu%7C14ff9ca9cc074522748808d5300e95c4%7Cb92d2b234d35447093ff69aca6632ffe%7C1%7C1%7C636467761587775083&sdata=vfqYK%2F3Gg%2BM%2F5DXzMcSpFVN2AFlEUysLW9%2FK0ykxjwA%3D&reserved=0>
[4 [8] Ji, S. (2015). PLANCKIAN INFORMATION (IP): A NEW MEASURE OF ORDER IN
ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. In: Unified
Field Mechanics: Natural Science beyond the Veil of Spacetime (Amoroso, R.,
Rowlands, P., and Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp.
579-589. PDF at
http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf
[9] Ji, S. (2016). WAVE-PARTICLE DUALITY IN PHYSICS AND BIOMEDICAL
SCIENCES.<http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf>
Symmetry: Science and Culture 27 (2): 99-127 (2016).
PDF at
http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf
[10] Unpublished observations made in collaboration with Pedro Marijuan of
Zaragoza, Spain.
[11] Ji, S. (2015). PLANCKIAN INFORMATION (I_P): A NEW MEASURE OF ORDER IN
ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. In: Unified
Field Mechanics: Natural Science beyond the Veil of Spacetime (Amoroso, R.,
Rowlands, P., and Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp.
579-589. PDF at
http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf
[12] Perou, C. M., Sorlie, T., Eisen, M. B., et al. (2000). Molecular
portraits of human breast Tumors. Nature 406(6797):747-52.
[13] Trifonov, E. N. (1993). DNA AS A LANGUAGE. Bioinformatics,
Supercomputing and Complex Genome Analysis: pp. 103-110.
https://doi.org/10.1142/9789814503655_0009
[14] In introducing my 2012 book, Molecular Theory of the Living Cell, on my
web page at
http://www.conformon.net/2017/08/21/molecular-theory-of-the-living-cell-2/, I
wrote as follows (BRE is synonymous with PDE):
“. . . One of the most surprising findings is that a mathematical equation,
referred to as the blackbody radiation-like equation (BRE), fits (i) protein
folding Gibbs free energy data of the 4,300 proteins of E. coli (see the
right-hand panel of Figure 1 shown below), (ii) the single-molecule enzymic
activity of cholesterol oxidase (Section 11.3.3), and (iii) the whole-cell
transcription rate and transcript level data measured from budding yeast
undergoing glucose-galactose shift (Section 12.12). Because the mathematical
form of BRE is identical to that of the blackbody radiation equation discovered
by M. Planck in 1900 which later led to the quantization of the energy of
electrons in atoms, it appears logical, by analogy, to postulate that the Gibbs
free energy levels of enzymes in living cells are also quantized. The
quantization of the energy levels of electrons in atoms accounted for the
structural regularities of matter embodied in the periodic table. Similarly the
discovery of BRE and the consequent quantization of Gibbs free energy of
enzymes in living cells (Section 12.14) may account for the functional
regularities of living cells and their higher-order structures including the
human body. Just as the 1.25-page Nature article published by Watson and Crick
in 1953 found the secrets of life in the form of the DNA double helix, so it
may be that the 730-page Molecular Theory of the Living Cell published this
year has found a secret of the living cell in the form of BRE (see Figure 1 and
Table 1 below).”
[15] Menzerath-Altmann law.
https://en.wikipedia.org/wiki/Menzerath%27s_law
_______________________________________________
Fis mailing list
Fis@listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
