Effect of the integration method on the accuracy and computational efficiency of free energy calculations using thermodynamic integration

Although calculations of free energy using molecular dynamics simulations have gained significant importance in the chemical and biochemical fields, they still remain quite computationally intensive. Furthermore, when using thermodynamic integration, numerical evaluation of the integral of the Hamiltonian with respect to the coupling parameter may introduce unwanted errors in the free energy. In this paper, we compare the performance of two numerical integration techniques-the trapezoidal and Simpson's rules and propose a new method, based on the analytic integration of physically based fitting functions that are able to accurately describe the behavior of the data. We develop and test our methodology by performing detailed studies on two prototype systems, hydrated methane and hydrated methanol, and treat Lennard-Jones and electrostatic contributions separately. We conclude that the widely used trapezoidal rule may introduce systematic errors in the calculation, but these errors are reduced if Simpson's rule is employed, at least for the electrostatic component. Furthermore, by fitting thermodynamic integration data, we are able to obtain precise free energy estimates using significantly fewer data points (5 intermediate states for the electrostatic component and 11 for the Lennard-Jones term), thus significantly decreasing the associated computational cost. Our method and improved protocol were successfully validated by computing the free energy of more complex systems hydration of 2-methylbutanol and of 4-nitrophenol-thus paving the way for widespread use in solvation free energy calculations of drug molecules

Early Spread of Scrapie from the Gastrointestinal Tract to the Central Nervous System Involves Autonomic Fibers of the Splanchnic and Vagus Nerves

Although the ultimate target of infection is the central nervous system (CNS), there is evidence that the enteric nervous system (ENS) and the peripheral nervous system (PNS) are involved in the pathogenesis of orally communicated transmissible spongiform encephalopathies. In several peripherally challenged rodent models of scrapie, spread of infectious agent to the brain and spinal cord shows a pattern consistent with propagation along nerves supplying the viscera. We used immunocytochemistry (ICC) and paraffin-embedded tissue (PET) blotting to identify the location and temporal sequence of pathological accumulation of a host protein, PrP, in the CNS, PNS, and ENS of hamsters orally infected with the 263K scrapie strain. Enteric ganglia and components of splanchnic and vagus nerve circuitry were examined along with the brain and spinal cord. Bioassays were carried out with selected PNS constituents. Deposition of pathological PrP detected by ICC was consistent with immunostaining of a partially protease-resistant form of PrP (PrP(Sc)) in PET blots. PrP(Sc) could be observed from approximately one-third of the way through the incubation period in enteric ganglia and autonomic ganglia of splanchnic or vagus circuitry prior to sensory ganglia. PrP(Sc) accumulated, in a defined temporal sequence, in sites that accurately reflected known autonomic and sensory relays. Scrapie agent infectivity was present in the PNS at low or moderate levels. The data suggest that, in this scrapie model, the infectious agent primarily uses synaptically linked autonomic ganglia and efferent fibers of the vagus and splanchnic nerves to invade initial target sites in the brain and spinal cord