Stochastic approach to molecular interactions and computational theory of metabolic and genetic regulations

Binding and unbinding of ligands to specific sites of a macromolecule are one of the most elementary molecular interactions inside the cell that embody the computational processes of biological regulations. The interaction between transcription factors and the operators of genes and that between ligands and binding sites of allosteric enzymes are typical examples of such molecular interactions. In order to obtain the general mathematical framework of biological regulations, we formulate these interactions as finite Markov processes and establish a computational theory of regulatory activities of macromolecules based mainly on graphical analysis of their state transition diagrams. The contribution is summarized as follows: (1) Stochastic interpretation of Michaelis-Menten equation is given. (2) Notion of \textit{probability flow} is introduced in relation to detailed balance. (3) A stochastic analogy of \textit{Wegscheider condition} is given in relation to loops in the state transition diagram. (4) A simple graphical method of computing the regulatory activity in terms of ligands' concentrations is obtained for Wegscheider cases.Comment: 20 pages, 13 figure

Compact boson stars in K field theories

We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.Comment: Latex, 45 pages, 25 figures, some references and comments adde

On membrane diffusion with near-equilibrium reaction

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32779/1/0000152.pd