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.

On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

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.

Myosin Vb Is Associated with Plasma Membrane Recycling Systems

Myosin Va is associated with discrete vesicle populations in a number of cell types, but little is known of the function of myosin Vb. Yeast two-hybrid screening of a rabbit parietal cell cDNA library with dominant active Rab11a (Rab11aS20V) identified myosin Vb as an interacting protein for Rab11a, a marker for plasma membrane recycling systems. The isolated clone, corresponding to the carboxyl terminal 60 kDa of the myosin Vb tail, interacted with all members of the Rab11 family (Rab11a, Rab11b, and Rab25). GFP-myosin Vb and endogenous myosin Vb immunoreactivity codistributed with Rab11a in HeLa and Madin-Darby canine kidney (MDCK) cells. As with Rab11a in MDCK cells, the myosin Vb immunoreactivity was dispersed with nocodazole treatment and relocated to the apical corners of cells with taxol treatment. A green fluorescent protein (GFP)-myosin Vb tail chimera overexpressed in HeLa cells retarded transferrin recycling and caused accumulation of transferrin and the transferrin receptor in pericentrosomal vesicles. Expression of the myosin Vb tail chimera in polarized MDCK cells stably expressing the polymeric IgA receptor caused accumulation of basolaterally endocytosed polymeric IgA and the polymeric IgA receptor in the pericentrosomal region. The myosin Vb tail had no effects on transferrin trafficking in polarized MDCK cells. The GFP-myosin Va tail did not colocalize with Rab11a and had no effects on recycling system vesicle distribution in either HeLa or MDCK cells. The results indicate myosin Vb is associated with the plasma membrane recycling system in nonpolarized cells and the apical recycling system in polarized cells. The dominant negative effects of the myosin Vb tail chimera indicate that this unconventional myosin is required for transit out of plasma membrane recycling systems.

Frequency encoding in excitable systems with applications to calcium oscillations.

A number of excitable cell types respond to a constant hormonal stimulus with a periodic oscillation in intracellular calcium. The frequency of oscillation is often proportional to the hormonal stimulus, and one says that the stimulus is frequency encoded. Here we develop a theory of frequency encoding in excitable systems and apply it to intracellular calcium oscillations that results from increases in the intracellular level of inositol 1,4,5-triphosphate.