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A symmetry-adapted version of the Maxwell rule appropriate to periodic bar-and-joint frameworks is obtained, and is further extended to body-and-joint systems. The treatment deals with bodies and forces that are replicated in every unit cell, and uses the point group isomorphic to the factor group of the space group of the framework. Explicit expressions are found for the numbers and symmetries of detectable mechanisms and states of self-stress in terms of the numbers and symmetries of framework components. This approach allows detection and characterization of mechanisms and states of self-stress in microscopic and macroscopic materials and meta-materials. Illustrative examples are described. The notion of local isostaticity of periodic frameworks is extended to include point-group symmetry.

Antibiotic resistance is hampering the efficacy of drugs in the treatment of several pathological infections. Dihydropteroate synthase (DHPS) has been targeted by sulphonamide inhibitors for the past 60 years and has developed different amino acid mutations to survive sulpha drug action. We couple homology modelling techniques and massively parallel molecular dynamics simulations to study both the drug-bound and apo forms of native and mutant DHPS. Simulations of the complex between sulphanilamide and Streptomyces pneumoniae, DHPS shows how sulphanilamide is able to position itself close to 6-hydroxymethyl-7, 8-dihydropteridine-phosphate in a suitable position for the enzymatic transformation whereas in the mutant complex the sulpha drug is expelled from the catalytic site. Our simulations, therefore, provide insight into the molecular basis for drug resistance with S. pneumoniae DHPS.

The calculation of binding free energies is important in many condensed matter problems. Although formally exact computational methods have the potential to complement, add to, and even compete with experimental approaches, they are difficult to use and extremely time consuming. We describe a Grid-based approach for the calculation of relative binding free energies, which we call Steered Thermodynamic Integration calculations using Molecular Dynamics (STIMD), and its application to Src homology 2 (SH2) protein cell signalling domains. We show that the time taken to compute free energy differences using thermodynamic integration can be significantly reduced: potentially from weeks or months to days of wall-clock time. To be able to perform such accelerated calculations requires the ability to both run concurrently and control in realtime several parallel simulations on a computational Grid. We describe how the RealityGrid computational steering system, in conjunction with a scalable classical MD code, can be used to dramatically reduce the time to achieve a result. This is necessary to improve the adoption of this technique and further allows more detailed investigations into the accuracy and precision of thermodynamic integration. Initial results for the Src SH2 system are presented and compared to a reported experimental value. Finally, we discuss the significance of our approach.