Synaptic Vesicle Dynamics: A Simple Model of Phasic Release

We present a simple model of phasic neurotransmitter release whichreproduces the salient features of chemical neurotransmission. The synapticvesicle cycle has been modelled as a set of biochemical reactionsrepresented by a system of coupled differential equations. These equationshave been solved analytically to obtain the time dependent behaviour of thesystem on perturbation from the steady state. The scheme of the synapticvesicle network has been emphasized and its role in determining some of themajor experimentally observed properties of synaptic transmission has beendiscussed, which includes the biphasic decay of the rate neurotransmitterrelease even under sustained stimulation. Another interesting outcome ofthis theoretical exercise is the saturation of total release with thecalcium dependent rate constant. The theoretically calculated values oftotal release fit very well into a sigmoidal saturating function with afourth order cooperativity exponent similar to the empiricalDodge–Rahamimoff equation. It appears that the synaptic vesiclenetwork itself is responsible for some of the major properties associatedwith chemical neurotransmission.     

A Novel Implicit Solvent Model for Simulating the Molecular Dynamics of RNA

Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin–Debye model and the Poisson–Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.     

Model Studies of the Dynamics of Bacterial Flagellar Motors

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.     

Dynamics of Hepatitis C Virus (HCV) RNA-dependent RNA Polymerase NS5B in Complex with RNA

The hepatitis C virus (HCV) non-structural protein 5B (NS5B) is an RNA-dependent RNA polymerase that is essentially required for viral replication. Although previous studies revealed important properties of static NS5B-RNA complexes, the nature and relevance of dynamic interactions have yet to be elucidated. Here, we devised a single molecule Förster Resonance Energy Transfer (SM-FRET) assay to monitor temporal changes upon binding of NS5B to surface immobilized RNA templates. The data show enzyme association-dissociation events that occur within the time resolution of our setup as well as FRET-fluctuations in association with stable binary complexes that extend over prolonged periods of time. Fluctuations are shown to be dependent on the length of the RNA substrate, and enzyme concentration. Mutations in close proximity to the template entrance (K98E, K100E), and in the center of the RNA binding channel (R394E), reduce both the population of RNA-bound enzyme and the fluctuations associated to the binary complex. Similar observations are reported with an allosteric nonnucleoside NS5B inhibitor. Our assay enables for the first time the visualization of association-dissociation events of HCV-NS5B with RNA, and also the direct monitoring of the interaction between HCV NS5B, its RNA template, and finger loop inhibitors. We observe both a remarkably low dissociation rate for wild type HCV NS5B, and a highly dynamic enzyme-RNA binary complex. These results provide a plausible mechanism for formation of a productive binary NS5B-RNA complex, here NS5B slides along the RNA template facilitating positioning of its 3′ terminus at the enzyme active site.     

A Mathematical Model for Bacterial Chemotaxis

A differential equation describing the chemotactic migration of a bacterial population in a fixed exponential gradient of attractant has been integrated using the appropriate boundary conditions. The solution predicts an initial bacterial accumulation at the concentration “knee” with the final distribution of bacteria approaching a time-independent state. Specific additional experiments to obtain further data for a rigorous test of the theory are suggested.