arXiv subjects

Jinzhi Lei

Publications and source records attributed to Jinzhi Lei.

40 records · Page 3Linked to original sources

arXiv2009

Rosette Central Configurations, Degenerate central configurations and bifurcations

In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another $n$-gon concentric with the first, but rotated of an angle $π/n$, and an additional particle of mass $m_0$ lies at the center of mass of the system. This system admits two mass parameters $μ=m_0/m_1$ and $\ep=m_2/m_1$. We show that, as $μ$ varies, if $n> 3$, there is a degenerate central configuration and a bifurcation for every $\ep>0$, while if $n=3$ there is a bifurcations only for some values of $ε$.

math-ph↗

arXiv2007

Scaling Law for Radius of Gyration and Its Dependence on Hydrophobicity

Scaling law for geometrical and dynamical quantities of biological molecules is an interesting topic. According to Flory's theory, a power law between radius of gyration and the length of homopolymer chain is found, with exponent 3/5 for good solvent and 1/3 for poor solvent. For protein in physiological condition, a solvent condition in between, a power law with exponent ~2/5 is obtained. In this paper, we present a unified formula to cover all above cases. It shows that the scaling exponents are generally correlated with fractal dimension of a chain under certain solvent condition. While applying our formula to protein, the fractal dimension is found to depend on its hydrophobicity. By turning a physical process-varying hydrophobicity of a chain by amino acid mutation, to an equivalent chemical process-varying polarity of solvent by adding polar or nonpolar molecules, we successfully deprive this relation, with reasonable agreement to statistical data. And it will be helpful for protein structure prediction. Our results indicate that the protein may share the same basic principle with homopolymer, despite its specificity as a heteropolymer.

physics.bio-ph↗

arXiv2007

Dynamics of Alpha-Helix Formation in the CSAW Model

We study the folding dynamics of polyalanine (Ala$_{20}$), a protein fragment with 20 residues whose native state is a single alpha helix. We use the CSAW model (conditioned self-avoiding walk), which treats the protein molecule as a chain in Brownian motion, with interactions that include hydrophobic forces and internal hydrogen bonding. We find that large scale structures form before small scale structures, and obtain the relevant relaxation times. We find that helix nucleation occurs at two separate points on the protein chain. The evolution of small and large scale structures involve different mechanisms. While the former can be describe by rate equations governing the growth of helical content, the latter is akin to the relaxation of an elastic solid.

cond-mat.soft↗

arXiv2006

Sequential recruitment and combinatorial assembling of multiprotein complexes in transcriptional activation

In human cells, estrogenic signals induce cyclical association and dissociation of specific proteins with the DNA in order to activate transcription of estrogen-responsive genes. These oscillations can be modeled by assuming a large number of sequential reactions represented by linear kinetics with random kinetic rates. Application of the model to experimental data predicts robust binding sequences in which proteins associate with the DNA at several different phases of the oscillation. Our methods circumvent the need to derive detailed kinetic graphs, and are applicable to other oscillatory biological processes involving a large number of sequential steps.

q-bio.CB↗