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<p style="margin-top:0;margin-bottom:0"><span style="font-size: 12pt;">Hi FISers,</span><br>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif">(<b>1</b>) In 1997 [9], I defined </span><span style="font-family:"Times New Roman",Times,serif">the
<i>cell language</i> as follows:</span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">"</span><b style="font-family:"Times New Roman",Times,serif; font-size:12pt">Cell language is a self-organizing system of molecules, some of
which </b><br>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"><b><span style="font-family:"Times New Roman",Times,serif">encode, act as signs for, or trigger, gene-directed cell processes."</span></b></span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif">So defined the cell language shares many
<b>qualitative </b>similarities or principles with the human language as summarized in
<b>Tables 2</b> and </span><span style="font-family:"Times New Roman",Times,serif"><b>6-3</b> in my 11/27/2017 post to this list. In contrast,
<b>Table 3</b> in the same post provides <b>quantitative </b>similarities between the two languages, since </span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif">(i) PDE, y = (A/(x + B)^5)/(Exp (C/(x + B)) -1) derived from physics and MAL, </span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">y
= (Ax^-B)</span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">/Exp (Cx), </span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">derived from linguistics [15] have a similar mathematical form in that they are
both the products of a <i>power function</i> and an <i>exponential function</i>, and </span></p>
<p class="x_MsoNormal" style="font-size:12pt"><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">(</span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">ii</span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">)
PDE and MAL are equivalent as far as their ability to fit </span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">long-tailed histograms regardless of whether they </span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">came from </span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">physics
or linguistics. </span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-size:12pt; font-family:"Times New Roman",Times,serif">These findings strongly indicate </span><span style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-0.25in">that there are
structural features of cell and human languages that are similar in terms of their </span><i style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-0.25in">functions </i><span style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-0.25in">as
inferred in </span><b style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-0.25in">Table 4</b><span style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-0.25in">. 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]:</span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif"> </span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif">1<sup>st</sup> articulation = words forming sentences</span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif">2<sup>nd</sup> articulation = letters forming words<br>
<span style="color:red">3<sup>rd</sup> articulation = sentences forming texts</span>. </span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif"> </span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><b><span style="font-size:12pt; font-family:"Times New Roman",serif">Table 4. </span></b><span style="font-size:12pt; font-family:"Times New Roman",serif">Isomorphism between cell and
human languages deduced from a qualitative comparison between linguistics and cell biology [1, 2, 3, 4].</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><b><span style="font-size:12pt; font-family:"Times New Roman",serif">Cell Language</span></b></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><b><span style="font-size:12pt; font-family:"Times New Roman",serif">Human Language</span></b></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><b><span style="font-size:12pt; font-family:"Times New Roman",serif">Function</span></b></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Alphabet</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">A, C, G, T/U</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Elementary signs [5]</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Words</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Gene/mRNA/protein</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Denotation</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Sentences</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Metabolic pathways</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif">Decision making</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif; color:red">Texts</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif; color:red">Functionally related sets of metabolic pathways (FRMPs)</span></p>
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<p class="x_MsoNormal" style="margin-bottom:0.0001pt; line-height:normal"><span style="font-size:12pt; font-family:"Times New Roman",serif; color:red">Logical reasoning or computing</span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif"> </span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif">(<b>2</b>)
<b>What is the Planckian-Shannon plot (PSP) or the Planckian-Shannon space (PSS) ?</b></span></p>
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<span style="font-size:12pt; line-height:17.12px">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 <i>non-randomness</i>, <i>order, </i>
or<i> information</i> encoded in PDE [11]. There are two ways of quantifying the information content of PDE:</span></p>
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<span style="font-size:12pt; line-height:17.12px"><br>
Plankian information of the first kind: I<sub>PF</sub> = log<sub>2 </sub>[AUC (PDE)/AUC (GLE)] (1)<br>
<br>
Plankian </span><span style="font-size:12pt">information of the second kind: I</span><sub>PS</sub><span style="font-size:12pt"> = - log</span><sub>2 </sub><span style="font-size:12pt">[(\mu – mode)/(\sigma)] (2) </span></p>
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<span style="font-size:12pt; line-height:17.12px"><br>
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<br>
<br>
</span></p>
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<span style="font-size:12pt; line-height:17.12px">H = - \Sigma (p<sub>i </sub>log<sub>2</sub> p<sub>i</sub>) (3)<br>
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</span></p>
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<span style="font-size:12pt; line-height:17.12px">wh where \Sigma is the sum over i from 1 to n, the number of data points, and p<sub>i</sub> is the probability of the occurrence of the i<sup>th</sup> data point. <br>
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]. </span><span style="font-size: 12pt;">These data sets all produced long-tailed histograms
</span><span style="font-size: 12pt;">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 “</span><b style="font-size: 12pt;">Plank-Shannon
space</b><span style="font-size: 12pt;">”, a linear correlation (called the </span>
<b style="font-size: 12pt;">Planck-Shannon plot</b><span style="font-size: 12pt;">) was found with the R^2 value of 0.686(see the upper panel of </span><b style="font-size: 12pt;">Figure 1</b><span style="font-size: 12pt;">). 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 </span><b style="font-size: 12pt;">Figure 1</b><span style="font-size: 12pt;">). </span></p>
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<img naturalheight="599" naturalwidth="479" size="34247" id="x_img425154" tabindex="0" style="max-width: 99.9%; user-select: none;" src="cid:a3e6c6be-7963-4aff-860c-4f025c88cd7b"><br>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif""> (<b>3</b>) <span style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif">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 </span><i style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif">Planck-Shannon
plots</i><span style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif"> as exemplified in </span><span style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif"><b>Figure 1.
</b>In other words, <b>w</b></span><span style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif">hen two sets of metabolic pathways are chosen that have 30 or more mRNA molecules in each pathway <span style="font-family:"Times New Roman",serif; font-size:16px; text-indent:-24px">(so
that a decent histogram can be obtained)</span>, 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 I</span><sub style="text-indent:-0.25in; font-family:"Times New Roman",serif">PS</sub><span style="font-size:12pt; text-indent:-0.25in; font-family:"Times New Roman",serif"> vs. H plot) is capable of distinguishing sets of metabolic pathways that are
<i>functionally related</i> from those having <i>no functional relations</i>.</span></span></p>
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<p class="x_MsoListParagraphCxSpLast" style="font-size:16px; font-family:Calibri,Helvetica,sans-serif,EmojiFont,"Apple Color Emoji","Segoe UI Emoji",NotoColorEmoji,"Segoe UI Symbol","Android Emoji",EmojiSymbols; text-indent:-0.25in">
<b><span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif">(5)<span style="font-weight:normal; font-size:7pt; line-height:normal; font-family:"Times New Roman""> </span></span></b><span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif">If
this interpretation of the Planck-Shannon plots is correct, the isomorphism between the structures of the human and cell languages as described in <b>Table 4</b> above may be said to have been proven, at least in principle. <span style="color:red">That is,
we may have finally decoded the <i>cell language</i> (also called the <i>DNA language</i> by Trifonov in [13]). </span>I am tempted to suggest that the discovery of
<i>PDE</i> in 2008 and that of its derivative, the Planck-Shannon space in 2017, may be comparable to the discovery of the
<i>DNA double helix</i> in 1953 [14].</span></p>
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<span style="font-size:12pt; line-height:17.12px; font-family:"Times New Roman",serif"><br>
<span style="font-size: 12pt;">Any questions or comments are welcome.</span><br>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"">Sung</span></p>
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<b><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"">(3)<span style="font-weight:normal; font-size:7pt; line-height:normal; font-family:"Times New Roman"">
</span></span></b><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif""> </span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><b><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"">References:</span></b></p>
<p class="x_MsoNormal" style="font-size:12pt"><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif""> [1] Ji, S. (2017).
<i>Planck-Shannon space</i>: A novel quantitative method to identify functionally related metabolic pathways in cell biology. A short talk to be presented at the
<i>118<sup>th</sup> Statistical Mechanics Conference, </i>Hill Center<i>, </i>Rutgers University, 12/17-19/2017.<br>
<span style="color:#222222"> [2] Ji, S. (1997). Isomorphism between cell and human languages: molecular biological, bioinformatic and linguistic implications. <i>BioSystems</i> <b>44</b>: 17-39.
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PDF at </span></span><a href="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" target="_blank" title="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
Ctrl+Click or tap to follow the link" tabindex="-1"><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"; color:#1155CC">http://www.conformon.net/wp-content/uploads/2012/05/Isomorphism1.pdf</span></a><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"; color:#222222">
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[3] Ji, S. (1999). The Linguistics of DNA: Words, Sentences, Grammar, Phonetics, and Semantics. <i>Ann. N. Y. Acad. Sci</i>. <b>870</b>:411-417. <br>
[4] Ji, S. (2017). <i>The Cell Language Theory; Connecting Mind and Matter. </i> World Scientific Publications, New Jersey.<br>
[5] Ji, S. (2017). </span><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"">The Quark Model of Peircean Signs, Section 6.6 in [4].<br>
[6] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications. Springer, New York. Section 6.1.2.</span></p>
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<span style="font-size:12pt; line-height:17.12px"><span style="color:rgb(32,32,32)">[3] [7] </span>Ji, S. (2015). </span><a href="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" target="_blank" title="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%"><span style="font-size:12pt; line-height:17.12px; color:black">Planckian
distributions </span><span class="x_m-679252801013745690xhighlight"><span style="font-size:12pt; line-height:17.12px; color:black">in</span></span><span style="font-size:12pt; line-height:17.12px; color:black"> molecular machines, living cells, and brains:
The wave-particle duality </span><span class="x_m-679252801013745690xhighlight"><span style="font-size:12pt; line-height:17.12px; color:black">in</span></span><span style="font-size:12pt; line-height:17.12px; color:black"> biomedical sciences.</span></a><span style="font-size:12pt; line-height:17.12px"> </span><span style="font-size:12pt; line-height:17.12px"> <span class="x_m-679252801013745690xhighlight">In</span>:
P<i>roceedings of the <span class="x_m-679252801013745690xhighlight">In</span>ternational Conference on Biology and Biomedical Engineering,</i> Vienna, March 15-17, 2015. Pp. 115-137. PDF at </span><a href="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" target="_blank" title="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%"><span style="font-size:12pt; line-height:17.12px">http://www.conformon.net/wp-content/uploads/2016/09</span></a><a href="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" target="_blank"><span style="font-size:12pt; line-height:17.12px; color:rgb(17,85,204)">/PDE_Vienna_2015.pdf</span></a><span style="font-size:12pt; line-height:17.12px"></span></p>
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<span style="font-size:12pt; line-height:17.12px; color:rgb(51,51,51)"> [4 [8] Ji, S. (2015</span><span style="font-size:12pt; line-height:17.12px">). </span><span style="font-size:12pt; line-height:17.12px">PLANCKIAN INFORMATION (IP): A NEW MEASURE OF ORDER
IN ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. <span style="color:rgb(51,51,51)">In: <em>Unified Field Mechanics: Natural Science beyond the Veil of Spacetime</em> (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<br>
[9] Ji, S. (2016). </span></span><a href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf" target="_blank"><span style="font-size:12pt; line-height:17.12px; color:black">WAVE-PARTICLE DUALITY IN PHYSICS AND BIOMEDICAL SCIENCES.</span></a><span style="font-size:12pt; line-height:17.12px"> </span><span style="font-size:12pt; line-height:17.12px; color:rgb(51,51,51)"> <em>Symmetry:
Science and Culture</em> <strong>27</strong> (2): 99-127 (2016). <br>
PDF at </span><span style="font-size:12pt; line-height:17.12px"><a href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf">http://www.conformon.net/wp-content/uploads/2016/09/PDE_SymmetryFestival_2016.pdf</a><br>
</span><span style="font-size:12pt; line-height:17.12px; color:rgb(51,51,51)"> [10] <span style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif; color:rgb(51,51,51)">Unpublished observations made in collaboration
with Pedro Marijuan of Zaragoza, Spain.</span><span style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif"> <br>
</span> [11] <span style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif; color:rgb(51,51,51)">Ji, S. (2015</span><span style="font-family:"Times New Roman",serif; font-size:12pt; text-indent:-24px; line-height:17.12px">). </span><span style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif">PLANCKIAN
INFORMATION (I_P): A NEW MEASURE OF ORDER IN ATOMS, ENZYMES, CELLS, BRAINS, HUMAN SOCIETIES, AND THE COSMOS. <span style="color:rgb(51,51,51)">In: <em>Unified Field Mechanics: Natural Science beyond the Veil of Spacetime</em> (Amoroso, R., Rowlands, P., and
Kauffman, L. eds.), World Scientific, New Jersey, 2015, pp. 579-589. PDF at <a href="http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf" class="x_OWAAutoLink" id="LPlnk961340" previewremoved="true">
http://www.conformon.net/wp-content/uploads/2016/09/PDE_Vigier9.pdf</a><br>
</span></span> [12] <span lang="ES-TRAD" style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif">Perou, C. M., Sorlie, T., Eisen, M. B.<i>, et al.</i> </span><span style="font-size:12pt; text-indent:-24px; line-height:17.12px; font-family:"Times New Roman",serif">(2000).
Molecular portraits of human breast Tumors. <i>Nature</i> <b>406</b>(6797):747-52.</span></span></p>
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<p class="x_MsoNormal" style="font-size:12pt"><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif""> [13]
</span><span style="font-size:8.5pt; line-height:107%; font-family:Verdana,sans-serif">Trifonov, E. N. (1993). DNA AS A LANGUAGE. Bioinformatics, Supercomputing and Complex Genome Analysis: pp. 103-110.</span><span style="font-size:12.0pt; line-height:107%; font-family:"Times New Roman","serif"">
</span><a href="https://doi.org/10.1142/9789814503655_0009" tabindex="-1"><span style="font-size:8.5pt; line-height:107%; font-family:Verdana,sans-serif; color:rgb(35,59,139)">https://doi.org/10.1142/9789814503655_0009</span></a><span style="font-size:8.5pt; line-height:107%; font-family:Verdana,sans-serif"> <br>
</span></p>
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<span style="font-size:12pt; font-family:"Times New Roman",serif"><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> [14] In introducing my 2012 book,
</span><i><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">Molecular Theory of the Living Cell</span></i><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">, on my web page at
</span></span><a href="http://www.conformon.net/2017/08/21/molecular-theory-of-the-living-cell-2/" tabindex="-1"><span style="font-size:12pt; font-family:"Times New Roman",Times,serif">http://www.conformon.net/2017/08/21/molecular-theory-of-the-living-cell-2/</span></a><span style="font-size:12pt; font-family:"Times New Roman",Times,serif">,
I wrote as follows (BRE is synonymous with PDE):</span></p>
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<span style="font-family:"Arial","sans-serif"; color:#333333; background:yellow"><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">“. . . One of the most surprising findings is that a mathematical equation, referred to as the </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">blackbody
radiation-like equation</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> (BRE), fits (i) protein folding Gibbs free energy data of the 4,300 proteins of </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">E.
coli</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> (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 </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">quantization of the energy of electrons</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> in atoms, it appears logical, by analogy, to
postulate that the </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">Gibbs free energy levels of enzymes</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> in living cells are also quantized.
The quantization of the energy levels of electrons in atoms accounted for the </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">structural regularities</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> of
matter embodied in the </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">periodic table. </span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">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 </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">functional regularities</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">of
living cells</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> and their higher-order structures including the human body. Just as the 1.25-page </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">Nature</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> 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 </span><em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt">Molecular Theory of the Living Cell</span></em><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> published
this year has found a secret of the living cell in the form of BRE (see Figure 1 and Table 1 below).”</span></span><span style="font-size:8.5pt; font-family:Verdana,sans-serif"></span></p>
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</span><span style="background-color:rgb(255,255,255); font-family:"Times New Roman",Times,serif; font-size:12pt"> </span><span style="font-family:"Times New Roman",Times,serif">[15] Menzerath-Altmann law. </span><a href="https://en.wikipedia.org/wiki/Menzerath%27s_law" class="x_OWAAutoLink" id="LPlnk507543" previewremoved="true"><span style="font-family:"Times New Roman",Times,serif">https://en.wikipedia.org/wiki/Menzerath%27s_law</span></a><br>
<span style="font-family:"Times New Roman",Times,serif; font-size:12pt"> </span></span><span style="font-family:"Times New Roman",Times,serif; font-size:12pt"></span></p>
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