Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Identification of Two Type V Myosins in Fission Yeast, One of Which Functions in Polarized Cell Growth and Moves Rapidly in the Cell

We characterized the novel Schizosaccharomyces pombe genes myo4+ and myo5+, both of which encode myosin-V heavy chains. Disruption of myo4 caused a defect in cell growth and led to an abnormal accumulation of secretory vesicles throughout the cytoplasm. The mutant cells were rounder than normal, although the sites for cell polarization were still established. Elongation of the cell ends and completion of septation required more time than in wild-type cells, indicating that Myo4 functions in polarized growth both at the cell ends and during septation. Consistent with this conclusion, Myo4 was localized around the growing cell ends, the medial F-actin ring, and the septum as a cluster of dot structures. In living cells, the dots of green fluorescent protein-tagged Myo4 moved rapidly around these regions. The localization and movement of Myo4 were dependent on both F-actin cables and its motor activity but seemed to be independent of microtubules. Moreover, the motor activity of Myo4 was essential for its function. These results suggest that Myo4 is involved in polarized cell growth by moving with a secretory vesicle along the F-actin cables around the sites for polarization. In contrast, the phenotype of myo5 null cells was indistinguishable from that of wild-type cells. This and other data suggest that Myo5 has a role distinct from that of Myo4.

How optimization of potential functions affects protein folding.

The relationship between the optimization of the potential function and the foldability of theoretical protein models is studied based on investigations of a 27-mer cubic-lattice protein model and a more realistic lattice model for the protein crambin. In both the simple and the more complicated systems, optimization of the energy parameters achieves significant improvements in the statistical-mechanical characteristics of the systems and leads to foldable protein models in simulation experiments. The foldability of the protein models is characterized by their statistical-mechanical properties--e.g., by the density of states and by Monte Carlo folding simulations of the models. With optimized energy parameters, a high level of consistency exists among different interactions in the native structures of the protein models, as revealed by a correlation function between the optimized energy parameters and the native structure of the model proteins. The results of this work are relevant to the design of a general potential function for folding proteins by theoretical simulations.

The underlying pathway structure of biochemical reaction networks

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.

In vivo functions of the Saccharomyces cerevisiae Hsp90 chaperone

In the highly concentrated environment of the cell, polypeptide chains are prone to aggregation during synthesis (as nascent chains await the emergence of the remainder of their folding domain), translocation, assembly, and exposure to stresses that cause previously folded proteins to unfold. A large and diverse group of proteins, known as chaperones, transiently associate with such folding intermediates to prevent aggregation, but in many cases the specific functions of individual chaperones are still not clear. In vivo, Hsp90 (heat shock protein 90) plays a role in the maturation of components of signal transduction pathways but also exhibits chaperone activity with diverse proteins in vitro, suggesting a more general function. We used a unique temperature-sensitive mutant of Hsp90 in Saccharomyces cerevisiae, which rapidly and completely loses activity on shift to high temperatures, to examine the breadth of Hsp90 functions in vivo. The data suggest that Hsp90 is not required for the de novo folding of most proteins, but it is required for a specific subset of proteins that have greater difficulty reaching their native conformations. Under conditions of stress, Hsp90 does not generally protect proteins from thermal inactivation but does enhance the rate at which a heat-damaged protein is reactivated. Thus, although Hsp90 is one of the most abundant chaperones in the cell, its in vivo functions are highly restricted.