Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

Memory systems in the brain and localization of a memory

It is now clear that there are a number of different forms or aspects of learning and memory that involve different brain systems. Broadly, memory phenomena have been categorized as explicit or implicit. Thus, explicit memories for experience involve the hippocampus–medial temporal lobe system and implicit basic associative learning and memory involves the cerebellum, amygdala, and other systems. Under normal conditions, however, many of these brain–memory systems are engaged to some degree in learning situations. But each of these brain systems is learning something different about the situation. The cerebellum is necessary for classical conditioning of discrete behavioral responses (eyeblink, limb flexion) under all conditions; however, in the “trace” procedure where a period of no stimuli intervenes between the conditioned stimulus and the unconditioned stimulus the hippocampus plays a critical role. Trace conditioning appears to provide a simple model of explicit memory where analysis of brain substrates is feasible. Analysis of the role of the cerebellum in basic delay conditioning (stimuli overlap) indicates that the memories are formed and stored in the cerebellum. The phenomenon of cerebellar long-term depression is considered as a putative mechanism of memory storage.

Simple neural networks for the amplification and utilization of small changes in neuron firing rates

I describe physiologically plausible “voter-coincidence” neural networks such that secondary “coincidence” neurons fire on the simultaneous receipt of sufficiently large sets of input pulses from primary sets of neurons. The networks operate such that the firing rate of the secondary, output neurons increases (or decreases) sharply when the mean firing rate of primary neurons increases (or decreases) to a much smaller degree. In certain sensory systems, signals that are generally smaller than the noise levels of individual primary detectors, are manifest in very small increases in the firing rates of sets of afferent neurons. For such systems, this kind of network can act to generate relatively large changes in the firing rate of secondary “coincidence” neurons. These differential amplification systems can be cascaded to generate sharp, “yes–no” spike signals that can direct behavioral responses.

Complex dynamics of multilocus systems subjected to cyclical selection.

Earlier we have shown that oscillations with a long period ("supercycles") may arise in two-locus systems experiencing cyclical selection with a short period. However, this mode of complex limiting behavior appeared to be possible for narrow ranges of parameters. Here we demonstrate that a multilocus system subjected to stabilizing selection with cyclically moving optimum can generate ubiquitous complex limiting behavior including supercycles, T-cycles, and chaotic-like phenomena. This mode of multilocus dynamics far exceeds the potential attainable under ordinary selection models resulting in simple behavior. It may represent a novel evolutionary mechanism increasing genetic diversity over long-term time periods.