Wolfram Computation Meets Knowledge

Wolfram Summer School


Sungchul Ji

Summer School

Class of 2011


After getting a PhD degree in physical organic chemistry in 1970, I have been doing research in molecular biology and cell biology for the past several decades, the results of which are being written up into a book entitled Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications, to be published by Springer in New York in 2011–12. I have been teaching theoretical cell biology and theoretical pharmacology at Rutgers University since 1982.

In 1997, I published a paper characterizing a set of about 12 principles and laws that was found to be common to both human and cell languages [Isomorphism between cell and human languages: molecular biological, bioinformatics and linguistic implications, BioSystems 44: 17-39 (1997)]. My current research activities are focused on “decoding” the cell language, i.e. elucidating the molecular mechanisms that cells employ to communicate within themselves and with one another. Several pieces of recent evidence indicate to me that quantum mechanical principles play important roles in molecular and cell biology: (i) the distribution of single-molecule catalytic rate constants, (ii) distances between genome-wide RNA trajectories measured with microarrays in budding yeast undergoing metabolic perturbations, and (iii) the protein stability data all fit a mathematical equation that is similar in form to the blackbody radiation equation discovered by M. Planck in 1900, which led to the quantum revolution in physics in the 1920s. These findings suggest that the Gibbs free energy levels of enzymes (comparable to atoms) and enzyme complexes (comparable to quantum dots) may be quantized, not in the usual unit of the Planck constant, h, but most likely in the unit of the Boltzmann constant, k. It may be possible to test the validity of this hypothesis against relevant experimental data available on line using Mathematica and the NKS approach.

Project: Simulating the Single-Molecule Enzymic Activity of Cholesterol Oxidase Using Cellular Automata

In 1998, S. Xie and his group measured the turnover times (also called on times or waiting times) of a single molecule of cholesterol oxidase (CO) for the first time. The authors presented their measurements in the form of a histogram plotting the frequency (1–20) on the y-axis and the waiting time (10–250 ms) classes on the x-axis and proposed a double exponential function (DEF) to fit the histogram. In 2008, I found that the waiting time histogram of Xie et al. could also be fitted into a mathematical equation similar in structure to the blackbody radiation equation discovered by Planck in 1900 (hence referred to as the blackbody radiation-like equation or BRE). In fact, BRE fit the histogram better than DFE by a factor of about 2. The purpose of this research project is to use cellular automata to simulate the single-molecule enzymic activity of CO. The strategy to be employed in identifying the rules and the initial conditions for the cellular automata that faithfully reproduce the BRE behavior is summarized in Table 1.

Table 1. The strategy for simulating the mechanisms/process of single-molecule enzymic activity of cholesterol oxidase using cellular automata.

The initial conditions and rules of CA evolution are all motivated by the biological processes underlying the biological evolution and the mechanisms of action of CO. To simplify the problem, I will assume that there are only two different amino acids, black (0) and white (1), instead of the usual 20, and CO can be represented as a 10 amino acid polypeptide (deca peptides) represented as a string of 10 0s and 1s. The all possible polypeptides number 210=1024. The evolution of these dec apeptides will be constrained by two tables, one defining the binding affinity between the peptides and the substrate (having 4 points of contacts with CO) and the other characterizing the probability of the conformational transitions of a given decapeptide. Of all the possible conformers (i.e. conformational isomers), only those will be selected that produce the waiting time histogram that fit BRE. If this project is successful, it will support the mechanisms of enzymic action listed in the third column of Table 1.

Project-Related Demonstrations

Pivoting Polymer

View demonstration of Wolfram Demonstrations Project

Favorite Four-Color Totalistic Cellular Automaton

Rule 7052011