• An Analysis of the Thermodynamics of Hydrophobic Solvation Based on Scaled Particle Theory

  • Adaptive Calcium Dynamics in Cardiomyocytes and Calcium-Induced Calcium Release
      An adaptive kinetic model for the calcium induced calcium release channel (also known as the ryanodine receptor) is studied. The model incorporates two characteristic calcium concentration dependencies indicated by experimental observations; namely, adaptive kinetic activation in a sub-micromolar range and equilibrium activation in a micromolar range. Following an equilibrium analysis, the kinetics of the model is cast in and analysed by a 3-state approximation, which yields an analytical solution. Temporal inactivation, as suggested by experimental measurements from skinned cardiac myocytes, naturally emerges from the single channel kinetics. The kinetic model of a single channel is then used to discuss the calcium induced calcium release in a cellular compartment. We show that the adaptive model for a single channel exhibits oscillatory calcium dynamics {\it in situ}. We conclude that temporal inactivation without concentration inhibition is sufficient as a negative control for rich calcium dynamics in cells.
  • Brownian Ratchet and Protein Polymerization Against Force
      The growth of filamentous proteins such as actin and microtubules can do work against molecular or cellular barriers that resist movement; hence it has been suggested that these filaments are partially responsible for the shape of various biological cells, and their dynamics are partially responsible for the extension of lamellipodia of motile cells (Cortese et al., 1989; Felder and Elson, 1990). To understand the physical principles behind this biochemical process, T.L. Hill has developed an elegant thermodynamic theory, for both equilibrium and nonequilibiurm, of polymerization against force (Hill, 1981, 1987). Recently, a more mechanistic model termed the {\it Brownian ratchet} (BR) has appeared (Peskin et al., 1993). A detailed mathematical analysis has revealed the crucial role of thermal fluctuations of both the filamental lengthening and the barrier; a true fluctuating molecular picture emerged. The model developed by Peskin et al. is essentially a theory for single filament; from their mathematical formalism it is not clear how to generalize the model to account for multiple filaments in a bundle, a situation which is biologically more realistic. The issue of how the multiple filaments grow as a bundle has important relevance in cell biology.
  • DNA Supercoiling and Nonlinear Elasticity
      It is well known that a large linking number induces an abrupt writhing of a circular rod with zero intrinsic curvature, i.e., the stress-free state of the rod is straight. We show here that for any rod with a uniform natural curvature, no matter how small the intrinsic curvature is, a twist will induce a continuous writhing from the circular configuration and the abrupt writhing is only the limiting case when the intrinsic curvature is absolutely zero. The implication of this result on elastic models of circular DNA is discussed.
  • Energy Balance and Purine Nucleotide Metabolism in Muscle
      Purine nucleotides are among the most important metabolites in cellular biochemistry. In addition to their well-known roles as precursors and intermediates of various biosynthesis and major players of cellular energetics, they are also involved in linking the energy balance of cells to the putative functional regulation of vasculature in cardiac and skeletal muscles. However, the precise mechanism(s) by which these regulations are carried out and in fact their significances {\it in vivo} remain to be a unsolved issue in both multi-cellular biochemistry and physiology (Schrader et al., 1998). These questions are particularly important in skeletal muscle cells and cardiac tissues where energy and its balance are the primary concerns of the cells. Under a normal physiological condition, the energetics inside these cells is balanced - the ATP synthesis and hydrolysis are well matched, and the level of total adenine nucleotide inside the cell is constant and dominated by ATP and ADP. The total concentration of AMP, adenosine, IMP, and their metabolites (inosine, hypoxanthine, etc.,) are low. When muscle cells undergo short normal exercise, the ATP-ADP dynamics are controlled by the action of creatine kinase, serving as a short-term buffer for cellular ATP (McFarland et al., 1994). In the present work, we develop a parallel model to study the energy balance in muscle and the purine metabolism. The model consists five components (Fig. 1B): ATP synthesis by oxidative phosphorylation, ATP hydrolysis, creatine kinase (CK), myokinase (MK), and purine nulceotide cycle (PNC). In contrast to the cardiac purine metabolism, this system is closed with respect to purine. The AMP deaminase irreversibly converts AMP to IMP, then the PNC regenerates AMP from IMP on a slower time scale. As we shall show, this temporary exclusion of purine, in the form of IMP, from the ATP-ADP dynamics has a similar effect as the open adenylate system but without a permanent lost of purine (Meyer and Terjung, 1980b). This model is a further development of the simple, three-component model for muscle energy balance recently proposed by Kushmerick (1998). Fig. 1B has two additional components: myokinase and purine nucleotide cycle.
  • Protein Folding Kinetics and Thermodynamics
      A simple energy landscape for protein folding (Bryngelson et al., 1995) is described. The model emphasizes the biased diffusive nature of protein folding (Levinthal, 1969) by utilizing the concept of dimensional reduction (Adam and Delbr\"{u}ck, 1968) which fits the recent observed folding intermediates in pulse-labeling hydrogen exchange experiments (Baldwin, 1993). The model has no enthalpic barriers between folded and unfolded protein. However an entropic barrier evidently gives rise to a two-state global folding kinetics. It is argued that the intermediate is in fact the transition state for the folding kinetics. The folding pathway should be understood as a sequence of events which selectively reduce the degrees of freedom of the peptide chain.
  • Stochastic Mechanics and Dynamics of Single Motor Proteins
      We carry out a theoretical analysis for the force generation of a single motor protein against an elastic load. The analysis is based on a previous work in which a simple kinetic framework for studying motor protein movement is developed (Qian, 1997). In particular, the kinetics of ATP hydrolysis and the stochastic movement of a motor protein along its track have been integrated into a coherent picture. We show that the stochastic motion (Svoboda et al., 1994; Meyh\"{o}fer and Howard, 1995) of the single motor protein is an inhomogeneous random walk in a harmonic potential. We further show that the dynamic force-velocity relationship obtained from the single motor measurements is equivalent to the isotonic velocity. The force-velocity relation is predicated to have curvature but appears to be linear in some parameter region. The transient relaxation time, the amplitude and correlation time of the stationary fluctuation under isometric condition can all be obtained. When considering the maximal force generated by the motor protein at both high and low ATP concentrations, the model fails to provide the [ATP] independent maximal force observed in experiments. Detailed analysis indicates that multiple kinetic cycles, some of them being futile, must be present in order to address the [ATP] dependence issue. Some suggestion for experimental work is provided.