| This dissertation analyzes the role of enzymes, which are nature’s catalysts and work in a complex manner, through kinetic Monte Carlo (MC) stochastic simulations. Previous studies have explored some of the questions related to catalytic properties of enzymes in single- and multi-step reactions occurring in nature, pointing out the effects of diffusion, enzyme fluctuations, cell size, colocalization of enzymes on the reaction rates. Except in special cases, the rate of a reaction is not well expressed by an Arrhenius rate expression, and the effective activation energy varies with temperature, as the rate limiting step shifts from reaction to diffusion. The effects of temperature depend on nature of the reaction, organization of the cell, cell topology, enzyme activity, rate constants, as well as diffusion coefficients and related variables. Therefore, it is challenging to determine the effective activation energy of a reaction because it may be loosely related to a potential energy barrier height.;We report MC simulations of temperature effects on single- and multi-step enzymatic reactions with varied rate constants and diffusion coefficients for reaction- and diffusion-limited reactions. For typical systems, in which the intrinsic reaction rate is more sensitive to temperature than diffusion, the overall reaction is rate-limited at low temperatures and diffusion-limited at high temperatures. The effective activation energy shifts to a much lower value as temperature is increased. Our results show, temperature dependence of enzyme-catalyzed reactions within a cell may be only loosely related to a potential energy barrier height. The effective activation energy may be strongly affected by coupling of reaction and diffusion. In the case of a single step enzymatic reaction with fixed diffusion coefficients and varied rate constants, the MC simulations show that as the temperature increases, the effective activation energy decreases. Furthermore, increasing the cell reaction volume by three orders of magnitude causes the effective activation energy to decrease approximately by a factor of four. Conversely, a different behavior is observed for reactions with fixed rate constants and varied diffusion coefficients. Irrespective of the reaction cell volume, as the temperature increases, the reaction rate remains unchanged and the reaction approaches the diffusion limit. However, the effective activation energy increases by approximately a factor of six when the cell reaction volume decreases by three orders of magnitude. The complexities increase for multi-step enzymatic reactions requiring colocalization of an enzyme pair in the same spatial vicinity and simultaneous or successive enzyme fluctuation activity for a successful reaction. Our MC simulations for multi-step enzymatic reactions highlight the subtle role of temperature for reactions with fixed rate constants and varied diffusion coefficients, where above a threshold temperature, the reaction is dominated by the intrinsic reaction rate and remains unaltered irrespective of the enzyme pair separation undergoing fluctuations with same frequency. Hence, these studies highlight the important effect of temperature in single- and multi-step enzymatic reactions and its role in determining the relationship between intrinsic and effective activation energy as the reaction shifts from reaction-limited to diffusion-limited behavior. Further, the cellular topological spatial variations are found to drastically affect the system behavior depicting “fractal-like kinetics”. Irrespective of the same fractional volume occupied by the cellular obstructions, the geometric pattern affects the reaction rates. Effective diffusivities are highly dependent on the diffusivities of the species in the various media, cellular topologies and temperature. The fractal effects are found to be largest for temperature driven diffusion-limited reactions. |
