Homogeneous and Spatio-temporal Chaos in Biochemical Reactions With Feedback Inhibition

Biochemical reactions are occurring constantly in cells, converting starting substances to different products, usually with the help of enzymes that speed the reactions. Without enzymes, it would take far too long for most reactions to occur to be useful to the cell!

Allosteric regulation of enzymes occurs when the binding of an effector molecule to a site that is different from the active site causes a change in the enzymatic activity. This alternate site is called an allosteric site, and an enzyme can contain more than one of these sites. Allosteric regulation can either be positive or negative, resulting in an increase or decrease in enzyme activity. Most enzymes that display allosteric regulation are metabolic enzymes involved in the degradation or...

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...

Allosteric regulation of enzymes occurs when the binding of an effector molecule to a site that is different from the active site causes a change in the enzymatic activity. This alternate site is called an allosteric site, and an enzyme can contain more than one of these sites. Allosteric regulation can either be positive or negative, resulting in an increase or decrease in enzyme activity. Most enzymes that display allosteric regulation are metabolic enzymes involved in the degradation or...

An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both directions, releasing energy into their environment in one direction, and absorbing it from the environment in the other direction. The same is true for the chemical reactions involved in cell metabolism, such as the breaking down and building up of proteins into and from individual amino acids, respectively. Reactants within a closed system...

Feedback in control systems plays a critical role in shaping various operational parameters, extending beyond simple error reduction to influence stability, bandwidth, gain, impedance, and sensitivity. Understanding these effects requires examining a basic feedback system characterized by defined input, output, error, and feedback signals.
Feedback significantly modifies the gain of a control system. The gain of a system without feedback is altered by a factor of one plus GH, where G represents...