X.-M. Zhu

Calculating biological behaviors of epigenetic states in the phage λ life cycle

The biology and behavior of bacteriophage λ regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage λ life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of OR. We also predict the desired robustness for the λ genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage λ regulatory network, one of the simplest and most well-studied regulatory systems.

GENERIC ENZYMATIC RATE EQUATION UNDER LIVING CONDITIONS

Based on our experience in kinetic modeling of coupled multiple metabolic pathways, we propose a generic rate equation for the dynamical modeling of metabolic kinetics. It is symmetric for forward and backward reactions. Its Michaelis-Menten-King-Altman form makes the kinetic parameters (or functions) easy to relate to experimental values in the database and to use in computation. In addition, such a uniform form is ready to arbitrary number of substrates and products with different stiochiometry. We explicitly show how to obtain such rate equations rigorously for three well-known binding mechanisms. Hence, the proposed rate equation is formally exact under the quasi-steady state condition. Various features of this generic rate equation are discussed. In particular, for irreversible reactions, the product inhibition which directly arises from enzymatic reaction is eliminated in a natural way. We also discuss how to include the effects of modifiers and cooperativity.

Electric resistance of single-walled carbon nanotubes under hydrostatic pressure

The electric resistance of single-walled nanotube mats has been studied systematically under both ambient and high hydrostatic pressures up to 1.5 GPa. Both the temperature dependence of the resistance and the magnetoresistance indicate that electrical transport occurs by variable range hopping, apparently in 2D. We suggest that this unexpected dimensionality arises from a fractal network of tubes and bundles. Under hydrostatic pressure (HP) the resistance still shows 2D variable range hopping and decreases with increasing HP. An irreversible increase in localization length and DOS is induced below 0.5 GPa. The behavior is reversible and due to strong interaction of tubes from 0.5 GPa up to 1.05 GPa. These results indicate that 2D variable range hopping occurs within bundles.

LIMIT CYCLE AND CONSERVED DYNAMICS

We demonstrate here that the potential can coexist with limit cycle in nonlinear dissipative dynamics, where the potential plays the driving role for dynamics and determines the final steady state distribution in a manner similar to other situations in physics. First, we show the existence of limit cycle from a typical physics setting by an explicit construction: the potential is of the Mexican-hat shape, the strength of the magnetic field scales with that of the potential gradient near the limit cycle, and the friction goes to zero faster than that of potential gradient when approaching to the limit cycle. The dynamics at the limit cycle is conserved in this limit. The diffusion matrix is nevertheless finite at the limit cycle. Second, based on the physics knowledge, we construct the potential in the dynamics with limit cycle in a typical dynamical systems setting. Third, we argue that such a construction can be, in principle, carried out in a general situation combined with a novel method. Our present result may be useful in many applications, such as in the discussion of metastability of limit cycle and in the construction of Hopfield potential in the neural network computation.

Semimetallic and semiconductor properties of some superhard and ultrahard fullerites in the range 300-2 K

Electrical resistivity and magnetoresistance were measured on samples with disordered structures synthesized from pure C60 and C70 at pressures in the range 8–12.5 GPa and temperatures of 900–1500 ...

Towards predictive stochastic dynamical modeling of cancer genesis and progression

Based on an innovative endogenous network hypothesis on cancer genesis and progression we have been working towards a quantitative cancer theory along the systems biology perspective. Here we give a brief report on our progress and illustrate that combing ideas from evolutionary and molecular biology, mathematics, engineering, and physics, such quantitative approach is feasible.

MICROSCOPIC THEORY OF VORTEX DYNAMICS IN HOMOGENEOUS SUPERCONDUCTORS

Vortex dynamics in fermionic superfluids is carefully considered from the microscopic point of view. Finite temperatures, as well as impurities, are explicitly incorporated. To enable readers understand the physical implications, macroscopic demonstrations based on thermodynamics and fluctuations- dissipation theorems are constructed. For the first time a clear summary and a critical review of previous results are given.

Vortex dynamics within the BCS theory

Abstract Based on the BCS theory we outline a conventional path integral derivation of the transverse force and the friction for a vortex in a superconductor. The derivation is valid in both clean and dirty limits at both zero and finite temperatures. The transverse force is found to be precisely as what has been obtained by Ao and Thouless using the Berrys phase method. The friction is essentially the same as the Bardeen and Stephens result.

Effects of Geometric Phases in Josephson Junction Arrays.

We show that the en route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect in the classical limit. However, geometric phases due to the finite superfluid density at superconductor grains have a profound influence on the quantum dynamics of vortices. Subsequently we find rich and complex Hall behaviors analogous to the Thouless-Kohmoto-Nightingale-den Nijs effect in the quantum regime.

Mechanical measurement of the transverse force on the moving vortices in superconductors

We have designed a mechanical experiment to measure the total transverse force on moving vortices in a type H superconductor. The transverse force is measured by monitoring the motion of the superconductor while the vortices are driven into motion by a moving magnet. The advantage of this direct force measurement is that it is free from complications due to vortex interactions.