Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Solvent dependence of dynamic transitions in protein solutions

A transition as a function of increasing temperature from harmonic to anharmonic dynamics has been observed in globular proteins by using spectroscopic, scattering, and computer simulation techniques. We present here results of a dynamic neutron scattering analysis of the solvent dependence of the picosecond-time scale dynamic transition behavior of solutions of a simple single-subunit enzyme, xylanase. The protein is examined in powder form, in D2O, and in four two-component perdeuterated single-phase cryosolvents in which it is active and stable. The scattering profiles of the mixed solvent systems in the absence of protein are also determined. The general features of the dynamic transition behavior of the protein solutions follow those of the solvents. The dynamic transition in all of the mixed cryosolvent–protein systems is much more gradual than in pure D2O, consistent with a distribution of energy barriers. The differences between the dynamic behaviors of the various cryosolvent protein solutions themselves are remarkably small. The results are consistent with a picture in which the picosecond-time scale atomic dynamics respond strongly to melting of pure water solvent but are relatively invariant in cryosolvents of differing compositions and melting points.

Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli, as well as for two different mutant strains.

Dynamic modeling of gene expression data

We describe the time evolution of gene expression levels by using a time translational matrix to predict future expression levels of genes based on their expression levels at some initial time. We deduce the time translational matrix for previously published DNA microarray gene expression data sets by modeling them within a linear framework by using the characteristic modes obtained by singular value decomposition. The resulting time translation matrix provides a measure of the relationships among the modes and governs their time evolution. We show that a truncated matrix linking just a few modes is a good approximation of the full time translation matrix. This finding suggests that the number of essential connections among the genes is small.

Creating a dynamic picture of the sliding clamp during T4 DNA polymerase holoenzyme assembly by using fluorescence resonance energy transfer

The coordinated assembly of the DNA polymerase (gp43), the sliding clamp (gp45), and the clamp loader (gp44/62) to form the bacteriophage T4 DNA polymerase holoenzyme is a multistep process. A partially opened toroid-shaped gp45 is loaded around DNA by gp44/62 in an ATP-dependent manner. Gp43 binds to this complex to generate the holoenzyme in which gp45 acts to topologically link gp43 to DNA, effectively increasing the processivity of DNA replication. Stopped-flow fluorescence resonance energy transfer was used to investigate the opening and closing of the gp45 ring during holoenzyme assembly. By using two site-specific mutants of gp45 along with a previously characterized gp45 mutant, we tracked changes in distances across the gp45 subunit interface through seven conformational changes associated with holoenzyme assembly. Initially, gp45 is partially open within the plane of the ring at one of the three subunit interfaces. On addition of gp44/62 and ATP, this interface of gp45 opens further in-plane through the hydrolysis of ATP. Addition of DNA and hydrolysis of ATP close gp45 in an out-of-plane conformation. The final holoenzyme is formed by the addition of gp43, which causes gp45 to close further in plane, leaving the subunit interface open slightly. This open interface of gp45 in the final holoenzyme state is proposed to interact with the C-terminal tail of gp43, providing a point of contact between gp45 and gp43. This study further defines the dynamic process of bacteriophage T4 polymerase holoenzyme assembly.

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.