Chao-Kun Cheng

A cellular automata model of enzyme kinetics

We have developed a cellular automata model of an enzyme reaction with a substrate in water. The model produces Michaelis-Menten kinetics with good Lineweaver-Burk plots. The variation in affinity parameters predicts that, in general, hydrophobic substrates are more reactive with enzymes, this attribute being more important than the relationship between enzyme and substrate. The ease of generation and the illustrative value of the model lead us to believe that cellular automata models have a useful role in the study of dynamic phenomena such as enzyme kinetics.

Cellular automata models of biochemical phenomena

Abstract This paper describes the use of kinematic, asynchronous, stochastic cellular automata to model water and solution phenomena encountered in complex biological systems. These in silico experiments are designed to assess the ability of the dynamic simulations to model some physical properties observed in solutions. Several experiments are described with significant relationship to physical reality. These include solution behavior, dissolution, immiscible systems, micelle formation, diffusion, membrane passage, enzyme activity and acid dissociation. From the confidence developed in these models, it is possible to consider cellular automata as an exploratory method for the discovery and understanding of new, unexpected phenomena.

A Cellular Automata Model of the Hydrophobia Effect

Dynamic simulations of solute molecules in water are made using cellular automata. By varying the parameter governing the breaking probability of water-solute tesselated pairs, sets of configurations were modeled of solutions ranging from polar to non-polar solutes. The emergent behavior of the non-polar solute models leads us to believe that this is a possible model of the hydrophobic effect.

Cellular automata models of kinetically and thermodynamically controlled reactions

Cellular automata simulations of the competition between kinetically controlled and thermodynamically controlled products of a reaction are described. The simulations are based on a stochastic first-order cellular automata model described previously (20) and dem- onstrate an alternative to the traditional approach to such problems that relies on solution of a set of coupled differential rate equations. Unlike the traditional approach, the cellular automata models are applicable to finite numbers of elements and yield statistical information on the fluctuations to be expected in such finite cases. The usual deterministic solutions appear as limiting cases involving either very large numbers of reacting ingredients or a large number of trials for smaller sets of ingredients. 2000 John Wiley & Sons, Inc. Int J Chem Kinet 32: 529- 534, 2000

A cellular automata model of acid dissociation

A dynamic cellular automata model that simulates the dissociation of an organic acid in solution is described. In the model, acids are represented by a novel cell type in which one face corresponds to the dissociating carboxylic acid group and the remaining faces represent the anionic portion of the acid. Simulations are described that analyze the effects of variable acid strength, changes of solvent temperature, and environmental influences, such as the presence of cosolutes and other acids. Several general features of acid dissociation in solution are replicated by the model and some additional aspects are examined. As a rule, additional solutes depress acid dissociation, the effect being greatest when the added cosolute is lipophilic, as might occur, for example, in a biological system. In mixtures of two different acids, the dissociation of each is suppressed, the weaker acid experiencing the greater suppression.

A CELLULAR AUTOMATA MODEL OF THE PERCOLATION PROCESS

A cellular automata model of a dynamic system has been created which predicts the concentration of onset and 50% probability of a spanning cluster existing which coincides with the percolation phenomenon. The valences of the cells at each concentration were monitored revealing patterns of diversity influenced by the joining and breaking rules of the simulation. The diversity of these cell valence types was quantified using the Shannon information content. The Shannon index curve versus the concentration of cells coincided almost exactly with the curve reflecting the fraction of the divalent cells at the same concentration. The simulation offers a useful solution to the difficult analysis of mobile or dynamic percolation characteristics.

A cellular automata model of an anticipatory system

An anticipatory system has been modeled using the dynamic characteristics of cellular automata. Rules governing the steps in an enzymatic conversion of substrates to products are operative in the system. A concentration of an intermediate product influences the creation of a supplemental enzyme that enhances the competence of an enzyme down stream. This anticipation of the future event creates a condition in which the concentration of a later substrate is suppressed, a property characteristic of the system. The model presents a useful opportunity to study a variety of aspects of this fascinating phenomena.

A cellular automata model of proton hopping down a channel.

Proton hopping is the process where a H‐atom on a hydronium ion forms a H‐bond with the O‐atom of a neighboring H2O molecule. There is then an exchange of bonding forces when that covalent bond of the H‐atom in the hydronium ion changes to a H‐bond, and the previous H‐bond changes to a covalent bond with the neighboring O‐atom. The neighboring molecule now becomes a hydronium (H3O+) ion. This process repeats itself very rapidly among neighboring hydronium and H2O molecules. There is a flow of protonic character through bulk H2O, referred to as proton hopping. This process carries information through living systems where H2O is present. A cellular automata model of proton hopping down a channel has been created and studied. Variations in the rate of proton entry into the channel and the effects of the polar character of the channel walls was studied using the model. The behavior of the models corresponds to experimental results.

Effect of initial temperature on water aggregation at a cold surface.

Cellular automata models of water at two initial temperatures were created. Each model was exposed to a freezing surface. The formation of fully bonded water cells, f4, was observed over time, beginning with a model of initially warm water and with initially cool water. The warm water formed more f4 cells earlier than the initially cool water. A high percentage of f4 cells is interpreted as the formation of ice. This is a model of the Mpemba effect. A description of the initial states for these two temperatures is offered in explanation of this effect.

A cellular automata model of chromatography

Dynamic models of the behavior of solvent and solute molecules can be made using cellular automata. A chromatographic column was represented by use of a cellular automata grid of 43 x 200 spaces. Solvent (mobile phase), solute and stationary phase cells were designated to simulate the chromatographic situation. The movements of solute and solvent cells down the grid were monitored for different numbers of iterations, different flow rates and different affinities of the solutes for the stationary phase and the solvent for itself. The cellular automata dynamics were successfully able to model expected chromatographic behavior except in a few cases where the number of cells was not large enough to provide an average value reflective of the molecular situation.