The Diversity of Biochemical Time Patterns

Irreversible metabolic transitions: the glucose 6-phosphate metabolism in yeast cell-free extracts

The steady-state and dynamic behavior of a partial glycolytic reaction sequence are investigated in cell-free extracts of yeast. Pyruvate kinase, adenylate kinase and glucose 6-phosphate isomerase cooperate to a multienzyme system centered around the 6-phosphofructokinase (6-PFK) and fructose 1,6-bisphosphatase (FBPase) cycle. The reaction system operates under thermodynamically open conditions maintained by a continuous supply of substrates, i.e., glucose 6-phosphate (Glc6P), ATP and phosphoenolpyruvate (PPrv) in a flow-through reaction chamber. Appropriate conditions lead to the occurrence of (two) coexisting and markedly different time-independent states in the metabolite concentrations and fluxes. For particular experimental conditions, changes in the influx adenylic energy charge, [AEC]IN, may cause transitions between these alternative steady states which are either reversible as it occurs in classical hysteresis phenomena, or, more importantly, irreversible (irreversible transitions, IT) where the system is not able to switch back to its previous state even when the perturbation is reverted. The emergence of these irreversible transitions do not result from artificial or non-realistic experimental constraints, but are a potential intrinsic property of any non-linear dynamic system exhibiting bi- or multistability. These one-way transitions may well have important biological implications with respect to switching, adaptation and memory phenomena.

Irreversible transitions in the 6-phosphofructokinase/fructose 1,6-bisphosphatase cycle

The dynamics of the fructose 6-phosphate fructose-1,6-bisphosphate cycle operating in an open and homogeneous system reconstituted from purified enzymes was extensively studied. In addition to 6-phosphofructokinase and fructose-1,6-bisphosphatase, pyruvate kinase, adenylate kinae and glucose-6-phosphate isomerase were involved. In that multi-enzyme system, the main source of non-linearity is the reciprocal effect of AMP on the activities of 6-phosphofructokinase and fructose-1,6-bisphosphatase. Depending upon the experimental parameter values, stable attractors, various types of multiple states and sustained oscillations were shown to occur. In the present report we show that irreversible transitions are also likely to occur for realistic operating conditions. Two parameters of the system, that is the adenylate energy charge of the influx and the fructose-1,6-bisphosphatase maximal activity, are potential candidates to provoke such irreversible transitions from one steady state to the other: (a) when varying the maximal activity of fructose-1,6-bisphosphatase, the system can jump irreversibly from a low to a high stable steady state, and (b) when the adenylate energy charge of the influx is the changing parameter, irreversible transitions occur from a high stable steady state to a stable oscillatory state (limit cycle motion). This behavior can be predicted by constructing the loci of limit points and Hopf bifurcation points.

A hysteretic cycle in glucose 6-phosphate metabolism observed in a cell-free yeast extract

The dynamics of a partial glycolytic reaction sequence which converts glucose 6-phosphate to triose phosphates is described. The study was performed with cell-free extracts from baker's yeast harvested in the logarithmic and stationary growth phases. The experiments are based on a flow-through reactor supplied with the desalted cell-free extract as well as glucose 6-phosphate, ATP and phosphoenolpyruvate. In the reaction system the quasi-irreversible reactions catalyzed by 6-phosphofructo-1-kinase, pyruvate kinase, and fructose-1,6-bisphosphatase are involved. When substrate is supplied continuously, only stable stationary states can be observed. With transient perturbations of the substrate supply, multiple stationary states appear. Cyclic transitions between unique stable stationary states were induced by appropriate changes of the rate of substrate supply. A hysteretic cycle could then be demonstrated when, during reverse transitions, a parameter region of multistability was passed. The presence (in resting yeast) or absence (in growing yeast) of fructose-1,6-bisphosphatase did not significantly influence the dynamic capabilities of the investigated reaction sequence. The kinetic properties of the cell-free extracts fit mathematical models developed for in vitro systems reconstituted from purified enzymes.

A general theory of chemical cytotoxicity based on a molecular model of the living cell, the Bhopalator

To define the molecular processes underlying toxicological manifestations experimentally measured on the cellular level, it is essential to have available a molecular model of the living cell itself. The Bhopalator is a molecular model of the living cell formulated by integrating the three major branches of biology within a coherent theoretical framework - the Watson-Crick molecular genetics, the conformon theory of enzymic catalysis, and the theory of dissipative structures developed by I. Prigogine. According to this model, the living cell is a self-moving, self-thinking and self-reproducing machine (automaton) that receives information and energy from its environment, processes them according to the genetic programs stored in DNA, and generates output signals to environment in order to realize teleonomically designed functions. The Bhopalator suggests a set of general statements useful in toxicological research, and these statements have been utilized to provide possible answers to several fundamental questions raised by recent experimental findings on chemically-induced cell injury and death.

Chaos in biological systems

Chaos is a widespread and easily recognizable phenomenon that hardly anybody took notice of until recently. The reason may be that chaos has something profoundly counterintuitive about it. It will not fit easily into any familiar cause–effect frame. The best introduction to chaos is by the way of an example. Consider a leaking faucet (Shaw, 1984). When the weight of the accumulating drop exceeds the surface tension the drop falls and a new drop begins to form. If the leak is small and the pressure in the faucet is constant, the time taken for the drop to reach the critical weight is constant. The dripping is perfectly periodic, the period depending on the leak rate. If the leak is slightly increased, the period of dripping will decrease slightly and vice versa. However, somewhere beyond this point the leaking faucet becomes a nuisance. When the leak is increased beyond a certain point the dripping looses its regularity. The time interval between the drops will first alternate periodically between a short and a long time interval. After a further increase of the leak this double periodic pattern will become unstable and change into a new pattern where four different time intervals between the drops alternate periodically. As the leak is further increased the period will double again and again and finally the dripping becomes completely irregular without any repeating pattern. When this occurs we are observing chaos. At the same time we are posed with the problem of understanding how such a ridiculously simple system can show random behaviour.