Steady-state phase or cooperative transitions between biochemical cycles

Repression of rearranged mu gene and translocated c-myc in mouse 3T3 cells X Burkitt lymphoma cell hybrids

The productively rearranged immunoglobulin mu chain gene and the translocated cellular oncogene c-myc are transcribed at high levels both in human Burkitt lymphoma cells carrying the t(8;14) chromosome translocation and in mouse plasmacytoma X Burkitt lymphoma cell hybrids. In the experiments reported here these genes were found to be repressed in mouse 3T3 fibroblast X Burkitt lymphoma cell hybrids. Such repression probably occurs at the transcriptional level since no human mu- and c-myc messenger RNA's are detectable in hybrid clones carrying the corresponding genes. It is therefore concluded that the ability to express these genes requires a differential B cell environment. The results suggest that the 3T3 cell assay may not be suitable to detect oncogenes directly involved in human B cell oncogenesis, since 3T3 cells apparently are incapable of transcribing an oncogene that is highly active in malignant B cells with specific chromosomal translocations.

The effects of modifiers on enzyme catalysis: a non-classical nearest neighbor approach

We present a nearest neighbor lattice model of the effects of modifiers on two-state enzyme catalysis of the reaction S in equilibrium with p. We do not in general make the assumptions of the classical approach to cooperative catalysis that yield (1) adsorption isotherms of the same form as those for the corresponding equilibrium system and (2) a rate of the catalyzed reaction proportional to the number of occupied catalytic sites. Closed form results are obtained for two approximations, the Bragg-Williams and the quasi-chemical. The latter requires (1), but is exact for several simple cases, including the concerted model, under this condition. Under (1) it is found that an interaction between modifier and catalytic sites, whether attractive or repulsive, increases the magnitudes of the slopes of the adsorption isotherms but that interactions between identical sites (catalytic or modifier) increase these magnitudes if attractive and decrease them if repulsive. Thus, the former interaction allows for phase transitions if sufficiently attractive or repulsive, but the latter only if sufficiently attractive. Herein also lies the explanation for why the concerted model displays only "positive cooperativity". It is further seen that it is not possible to classify a modifier as an activator or inhibitor of the catalyzed reaction solely on the basis of the sign of the interaction energy between catalytic and modifier sites. For a given energy, the rate of the reaction may increase or decrease in response to the modifier, or it may respond biphasically. Similarly, the rate may respond biphasically to the activities of s or p, leading to instabilities. Thus, possibilities of multiple nonequilibrium stationary states or spatio-temporal patterns are raised.

Theoretical models for cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin

Recent theoretical work on the cooperative equilibrium binding of myosin subfragment-1-ADP to regulated actin, as influenced by Ca2+, is extended here to the cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin. Exact solution of the general steady-state problem will require Monte Carlo calculations. Three interrelated special cases are discussed in some detail and sample computer (not Monte Carlo) solutions are given. The eventual objective is to apply these considerations to in vitro experimental data and to in vivo muscle models.

Subunit neighbor interactions in enzyme kinetics: half-of-the-sites reactivity in a dimer

We consider an isologous enzyme dimer in which the subunits, if operating independently, would obey Michaelis-Menten kinetics. However, because of neighbor interactions, the rate constants of the kinetic cycle in either subunit depend on the state (E or ES) of the other subunit. The steady-state behavior of this dimer system, with interactions, is investigated. In what is probably the most important special case, ES x ES is destabilized considerably by the neighbor interaction compared to E x ES. This leads to half-of-the-sites reactivity (one subunit is in state ES; the other subunit cycles between E and ES), negative cooperativity, and a considerable enhancement of enzyme activity relative to the activity of independent subunits.

Theoretical model for the cooperative equilibrium binding of myosin subfragment 1 to the actin-troponin-tropomyosin complex

Recent experimental data on the equilibrium binding of myosin subfragment 1 (S-1) to regulated actin filaments in the presence and in the absence of Ca(2+) are analyzed by using a linear Ising model. In the model, each tropomyosin-troponin unit (including seven sites on the actin filament) can be in one of two possible states, which have different intrinsic free energies and different binding constants for S-1. Bound S-1 molecules do not interact with each other. There are nearest-neighbor (pair) interactions between these units that depend on the state of each member of the pair and on the number of Ca(2+) bound to one member of the pair. There are two sources of positive cooperativity in this system: the fact that seven actin sites change state together as part of a single unit; and the existence of attractive nearest-neighbor interactions between units. Parameters in the model are evaluated by fitting the data, both in the presence and in the absence of Ca(2+). Several extensions of this model are discussed.

Approximate steady-state properties of lattices of interacting three-state enzyme molecules: a novel phase transition

Previous work on the cooperative behavior of lattices of interacting two-state enzyme molecules at steady state is extended here to interacting three-state enzyme molecules with a one-way cycle. The Bragg-Williams (mean field) approximation is used. A phase-transition example with a bifurcation point is discussed. Compared to conventional phase transitions (with a van der Waals loop), several new and complicated features appear. A second paper on this subject will contain a number of other examples of three-state systems.