Introduction

1. Experimental Evidence for the Existence of the Cell Force and Cell Metabolic FieldDavid Yao and Sungchul Ji*Department of Pharmacology and Toxicology, Ernest Mario School of Pharmacy Rutgers University, Piscataway, N.J. *sji@rci.rutgers.edu We also conducted statistical analyses to test whether the differences in parameter ratios between different protein families before and after doxorubicin treatment were significant. This analysis produced mixed results: between protein families, the differences in parameter ratios were large enough to be statistically significant. However, comparing the parameter ratios before and after treatment within protein families yielded less clear results: the differences were only significant in 50% (5 out of 10) of the protein families studied, perhaps indicating that not all pathways contribute equally to tumor formation (Figure 6). Introduction The foundation of physics relies on the theory of fundamental forces that explain physical phenomena observed in the universe. Physicists have developed a framework of mathematical equations to describe these forces and their underlying fields at work in all natural processes. We propose the existence of similar concepts in the biological sciences, referred to here as the “cell force” [1] and “cell metabolic field” [2], based on experimental evidence obtained from analysis of human cancer cells. By developing a mathematical and theoretical framework for cell biology and pharmacology, we aim to further our understanding of biological processes and the deviations from these processes that result in disease. Using mRNA measurements before and after doxorubicin treatment, we constructed frequency histograms showing the distribution of mRNA levels for each protein family. These frequency histograms were divided into bin sizes such that the entire range of mRNA concentrations observed were partitioned into 50-60 bins of equal size. We then modeled each of these frequency histograms with the so-called Blackbody Radiation-Like Equation (BRE) which is given below: where a, b, A, and B represent specific numerical constants [5]. The BRE was previously found to fit the single-molecule turnover times of cholesterol oxidase enzymes suggesting that the Gibbs free energy levels of enzymes are quantized [5]. Our application of the BRE to mRNA data from human cancer cells was based on the hypothesis that this energy quantization would be observable in all enzymes in living cells, including human breast cancer cells. After modeling the frequency distributions of each protein family with BRE, we obtained specific parameter values (a, b, A, B) for each family before and after doxorubicin treatment: After our initial analysis, we noticed that we could obtain an optimal BRE fit to the mRNA data with multiple sets of parameter values. To further investigate this finding, we calculated parameter ratios for each BRE fit to see whether these ratios changed along with the parameter values. Interestingly, the parameter ratios stayed constant even as the parameter values themselves changed. This phenomena remained true for every protein family analyzed before and after doxorubicin treatment. Discussion & Conclusions To explain the inconsistency in statistical significance of parameter ratios before and after doxorubicin treatment within the same protein family, we turn to the principle that averaging leads to loss of information. Because individual patients have varying responses to chemotherapy [4], reflected in the dramatic variation of mRNA concentrations before and after doxorubicin treatment, these responses may in effect be “averaged” when looking at an aggregate analysis of patients as was done in our experiment. Therefore, the observed statistical insignificance may not be an indicator of actual insignificance, but rather the loss of individual patient information as a result of averaging the results over all 20 patient data sets. Further analysis of BRE parameter ratios for individual patient data sets may lead to a better characterization of changes in individual mRNA concentrations due to chemotherapy. The discovery of set parameter values within the BRE models of mRNA levels supports the notion that the Gibbs free energy levels of enzymes are quantized [5], similar to the energy quantization of electrons in atoms as demanded by the blackbody radiation equation discovered by Max Planck in 1900. Since mRNA leveles are determined by cellular enzyme activity, the BRE parameters that model mRNA levels indicate specific Gibbs free energy levels that enzymes operate at, consistent with the conformon hypothesis of enzyme catalysis [1, 5]. The invariance of BRE parameter ratios suggests another interesting characteristic of these energy levels – namely, that the difference between these levels is invariant of their absolute value. This characteristic, known as a gauge invariance in physics, is analogous to the earth’s gravitational field, whereby the same amount of energy is needed to lift an object by a certain distance, regardless of the object’s starting position relative to a given framework of measurement. In this way, we can compare the gauge invariance of the gravitational field to that of the cell metabolic field. The corresponding force needed to achieve energy level transitions, termed gravitational force in describing objects falling in the gravitational field, would be the cell force, our proposed term to describe the Gibbs free energy changes necessary to maintain homeostasis in the cell. By further investigating and characterizing the cell force through mathematical analysis, we can perhaps better understand the disturbances in this force that result in catastrophic diseases such as cancer. BRE: Figure 1. The fundamental forces of nature and their mediators. The proposed cell force is also added, that is postulated to control cellular enzymes that catalyze chemical reactions and gene expressions. Figure 2. The atom-cell isomorphism postulate (ACIP). Two types of particles constitute the atom and the living cell. Hadrons are heavy particles such as protons and neutrons, and leptons are light particles including electrons and muons. Cytons, first invoked in [1] are the hypothetical physical entity operating inside the cell (analogous to bosons in physics) that mediate the interactions between equilibrons and dissipatons. Equilibrons are stable under normal conditions (e.g., DNA sequences), while dissipatons are unstable (e.g., membrane potentials), requiring continuous dissipation of free energy to be maintained. Figure 8. Averaging leads to loss of information, as shown when the averaging of individual pixel colors in the photo on the left results in a blank gray photo on the right when these colors are lost. Data, Analysis & Results Figure 3. A more detailed network representation of the atom-cell isomorphism postulate (ACIP). The claim of ACIP that the structures and functions of the atom and the cell share a common set of principles and features thought to be reflected in the symmetry between the topologies of the two networks: Although the labels of the nodes and edges are different, the two networks are topologically identical. It is interesting to note that, since Mattergy and Ergons are synonymous, the mattergy tree (i.e., atomic physics) is enfolded in the gnergy tree (i.e., cell biology) which makes the topology self-similar or recursive. Fitting of mRNA data to BRE in Figure 3 supports ACIP. Figure 5. The fitting to BRE of the CGI mRNA levles before (top) and after (bottom) doxorubicin treatment and associated parameter values and ratios. The BRE fitting of the data was performed by the Solver program in Excel. Methods The microarray data for 4,740 genes from 20 human breast cancer patients measured by Perou et al. [3] were analyzed in this study [4]. mRNA transcript levels were measured with microarrays in three different samples -- normal (N) human breast tissue culture, and the tumor biopsies taken before(BE) and after (AF) doxorubicin treatment: Patient X Biopsy Normal Tissue (N) Tumor Tissue Before Tumor Tissue After Drug Treatment (BE) Drug Treatment (AF) Figure 4. The preparation of the 3 samples for mRNA measurements. References[1] Ji, S. (1991). Manifolds, Fractals, Fiber Bundles, and Gauage fields: The Role of Genetic Information in the Theory of the Cell Force. Molecular Theories of Cell Life and Death. Rutgers University Press, New Brunswick. Pp. 90-122. PDF available at conformon.net under Publications <Proceedings and Abstract.[2] Smith, H. A. and Welch, G. R. (1991). Cytosociology: A Field-Theoretiic View of Cell Metabolism. In: Molecular Theories of Cell Life and Death (Ji, S., ed.), Rutgers University Press, New Brunswick. Pp. 282-323. PDF availabel at conformon.net under Liks < Biology. [3] Perou, C. M., Sorlie, T., Eisen, M. B., et al.(2000). Molecular portraits of human breast Tumors, Nature406(6797): 747-52. [4]Ji, S. , Cheng, L., Szafran, W. and Carmona, R. (2012). Proceedings of the 2012 IEEE International Conference on Bioinformatics and Biomedicine. Poster #180. [5]Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications, Springer, New York. See Sections 11 and 12. PDF available at conformon.net under Publications < Book chapters. Figure 6. Statistical analysis for parameter ratios obtained from BRE analysis of the CGI, MAPK, ZFP, CD, and ETF protein families before and after doxorubicin treatment. Figure 7. Demonstration of parameter ratio invariance vs. parameter value variance. Figures provided from CGI protein family analysis. We selected ten protein families of interest to analyze (Table 1). Each protein family was selected on the criteria of having at least 50 open reading frames (ORFs) included in the microarray data. Acknowledgment I gratefully acknowledge the guidance of Dr. Sungchul Ji and contributions of other students in the Theoretical and Computational Cell Biology Lab at the Ernest Mario School of Pharmacy at Rutgers University toward developing the methods described in this poster. Special acknowledgment goes to Kenneth So and Larry Cheng for first describing the method of fitting the BRE equation to mRNA concentrations measured in human breast cancer cells.