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.

Variations in frequencies of drug resistance in Plasmodium falciparum

Continual exposure of malarial parasite populations to different drugs may have selected not only for resistance to individual drugs but also for genetic traits that favor initiation of resistance to novel unrelated antimalarials. To test this hypothesis, different Plasmodium falciparum clones having varying numbers of preexisting resistance mechanisms were treated with two new antimalarial agents: 5-fluoroorotate and atovaquone. All parasite populations were equally susceptible in small numbers. However, when large populations of these clones were challenged with either of the two compounds, significant variations in frequencies of resistance became apparent. On one extreme, clone D6 from West Africa, which was sensitive to all traditional antimalarial agents, failed to develop resistance under simple nonmutagenic conditions in vitro. In sharp contrast, the Indochina clone W2, which was known to be resistant to all traditional antimalarial drugs, independently acquired resistance to both new compounds as much as a 1,000 times more frequently than D6. Additional clones that were resistant to some (but not all) traditional antimalarial agents acquired resistance to atovaquone at high frequency, but not to 5-fluoroorotate. These findings were unexpected and surprising based on current views of the evolution of drug resistance in P. falciparum populations. Such new phenotypes, named accelerated resistance to multiple drugs (ARMD), raise important questions about the genetic and biochemical mechanisms related to the initiation of drug resistance in malarial parasites. Some potential mechanisms underlying ARMD phenotypes have public health implications that are ominous.

Extension of the thermodynamics of small systems to open metastable states: An example

By using a simplified model of small open liquid-like clusters with surface effects, in the gas phase, it is shown how the statistical thermodynamics of small systems can be extended to include metastable supersaturated gaseous states not too far from the gas–liquid equilibrium transition point. To accomplish this, one has to distinguish between mathematical divergence and physical convergence of the open-system partition function.

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.

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.

High frequency of sex and equal frequencies of mating types in natural populations of the ciliate Tetrahymena thermophila.

In ciliate protists, sex involves the temporary joining of two cells of compatible mating type, followed by meiosis and exchange of gametic nuclei between conjugants. Reproduction is by asexual binary fission following conjugation. For the many ciliates with fixed multiple mating types, frequency-dependent sex-ratio theory predicts equal frequencies of mating types, if sex is common in nature. Here, we report that in natural populations of Tetrahymena thermophila sexually immature cells, indicative of recent conjugation, are found from spring through fall. In addition, the seven mating types occur in approximately equal frequencies, and these frequencies appear to be maintained by interaction between complex, multiple mat alleles and environmental conditions during conjugation. Such genotype-environment interaction determining mating type frequency is rare among ciliates.

Stability of Coulomb systems in a magnetic field.

I study N electrons and M protons in a magnetic field. It is shown that the total energy per particle is bounded below by a constant independent of M and N, provided the fine structure constant is small. Here, the total energy includes the energy of the magnetic field.