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
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