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The theory of multistate template-directed reversible copolymerization is developed by extending the method based on iterated function systems to matrices, taking into account the possibility of multiple activation states instead of a single one for the growth process. In this extended theory, the mean growth velocity is obtained with an iterated matrix function system and the probabilities of copolymer sequences are given by matrix products defined along the template. The theory allows us to understand the effects of template heterogeneity, which include a fractal distribution of local growth velocities far enough from equilibrium, and a regime of sublinear growth in time close to equilibrium.
Using large-scale DFT calculations (up to 1,476 atoms and 18,432 orbitals), we present the first detailed analysis on the unusual electronic properties of recently synthesized porphyrin nanotubes. We surprisingly observe extremely large oscillations
We propose a novel method for refining force-field parameters of protein systems. In this method, the agreement of the secondary-structure stability and instability between the protein conformations obtained by experiments and those obtained by molec
In this work, Flory-Huggins phase diagrams for correlated random copolymers with realistic chain lengths are calculated. This is achieved in two steps. At first we derive a distribution function of copolymer chains with respect to composition and blo
How does a cell self-organize so that its appendages attain specific lengths that are convenient for their respective functions? What kind of rulers does a cell use to measure the length of these appendages? How does a cell transport structure buildi
The availability of data from many different sources and fields of science has made it possible to map out an increasing number of networks of contacts and interactions. However, quantifying how reliable these data are remains an open problem. From B