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Abstract: Binding affinities are useful measures of target interaction and have an important role in understanding biochemical reactions that involve binding mechanisms. Surface plasmon resonance (SPR) provides convenient real-time measurement of the reaction that enables subsequent estimation of the reaction constants necessary to determine binding affinity. Three models are considered for application to SPR experiments—the well-mixed Langmuir model and two models that represent the binding reaction in the presence of transport effects. One of these models, the effective rate constant approximation, can be derived from the other by applying a quasi-steady state assumption. Uniqueness of the reaction constants with respect to SPR measurements is considered via a structural identifiability analysis. It is shown that the models are structurally unidentifiable unless the sample concentration is known. The models are also considered for analytes with heterogeneity in the binding kinetics. This heterogeneity further confounds the identifiability of key parameters necessary for reliable estimation of the binding affinity. [Copyright &y& Elsevier]

Abstract: When any foreign object is found in the human body antibodies are generated that mark it for removal by the immune system. In most cases these are natural and healthy responses; however, when considering organ transplants the immune response to the implanted organ must be kept to a minimum to avoid host rejection. To reduce the host''s immune response to the implant, clinicians are able to manipulate the antibody dynamics through drug therapy, to minimise the antibody synthesis (immunosuppression), and by the removal of antibodies directly from the patients’ blood, a process known as apheresis. In this paper models are presented that describe the in vivo kinetics of three immune complexes which are routinely measured pre- and post-operatively in implant patients, namely IgA, IgG and IgM. These models are then used to analyse the effective clearance rates of different apheresis methods (plasmapheresis, plasma absorption or plasma exchange) and to quantify the impact immune-suppression drugs have on the underlying antibody synthesis. It is hoped that the simplicity of the mathematical models, and associated implementation, will allow the translation of knowledge gained of the process dynamics to positively impact future patient diagnosis and treatment. [Copyright &y& Elsevier]

Abstract: An important question in Systems Biology is the design of experiments that enable discrimination between two (or more) competing chemical pathway models or biological mechanisms. In this paper analysis is performed between two different models describing the kinetic mechanism of a three-substrate three-product reaction, namely the MurC reaction in the cytoplasmic phase of peptidoglycan biosynthesis. One model involves ordered substrate binding and ordered release of the three products; the competing model also assumes ordered substrate binding, but with fast release of the three products. The two versions are shown to be distinguishable; however, if standard quasi-steady-state assumptions are made distinguishability cannot be determined. Once model structure uniqueness is ensured the experimenter must determine if it is possible to successfully recover rate constant values given the experiment observations, a process known as structural identifiability. Structural identifiability analysis is carried out for both models to determine which of the unknown reaction parameters can be determined uniquely, or otherwise, from the ideal system outputs. This structural analysis forms an integrated step towards the modelling of the full pathway of the cytoplasmic phase of peptidoglycan biosynthesis. [Copyright &y& Elsevier]