Narendra S. Goel

The error catastrophe hypothesis with reference to aging and the evolution of the protein synthesizing machinery

A theory of the propagation of errors in the system of enzymes translating genetic information into proteins is presented. The formulation, which is non-statistical, makes it possible to determine the quantities of individual components of a system at any time. It is shown that depending on the initial conditions and on the effects of amino acid substitutions on enzymic activity, error catastrophe, stable states containing error, extinction of some amino acids, or evolution toward less ambiguous translation can occur. The results speak against the error catastrophe hypothesis of aging. The theory also provides a method to study the behavior of any self-replicating systems which might be surmised to have existed at earlier stages of the evolution of life.

Short range electrostatic interactions in dielectric media

The electrostatic theory for a dielectric sphere with arbitrary charge distribution within it is presented. The sphere is located in a dielectric medium which either contains another similar sphere or is separated from another dielectric medium by a planar interface. It is shown that the case of two dielectric spheres is simply related to that of a sphere near a planar interface. The cases of a point charge or a point dipole at the center of the sphere are analyzed in detail. For the point charge case, the numerical results for both the electrostatic potential energy and forces for a wide range of values of the ratio of dielectric constant of sphere to that of medium are given. In addition, approximate analytical expressions are given and constrasted with the exact numerical results. The asymptotic expression occasionally used is shown to provide a good approximation for equal and oppositely charged cavities embedded in a medium of very high dielectric constant. An analytical expression, similar in struct...