Computational modelling of TNFα related pathways regulated by neuroinflammation, oxidative stress and insulin resistance in neurodegeneration

Computational and mathematical modelling towards understanding the structure and dynamics of biological systems has significantly impacted on translational neuroscience to face novel approaches toward neurological disorders such as Alzheimer’s (AD) and Parkinson’s disease (PD). In this study, a computational model of AD and PD have been modelled using biochemical systems theory, and shows how Tumour Necrosis Factor alpha (TNF훼) regulated neuroinflammation, oxidative stress and insulin pathways can dysregulate its downstream signalling cascade that lead to neurodegeneration observed in AD and PD. The experimental data for initial conditions for this model and validation of the model was based on data reported in literature. In simulations, elevations in the aggregations of major proteins involved in the pathology of AD and PD including amyloid beta, alpha synuclein, tau have been modelled. Abnormal aggregation of these proteins and hyperphosphorylation of tau were observed in the model. This aggregation may lead to developing Lewy bodies, fibrils, plaques and tangles inside neurons that trigger apoptosis. An increase in the concentrations of TNF훼 and glutamate during diseased conditions was noted in the model. Accumulation of these proteins may be related to the feedback mechanism of TNF훼 that initiates its own release and the production of excess glutamate. This could lead to the prolonged activation of microglia that result in death of surrounding neurons. With the elevation in reactive oxygen species, oxidative stress also increased. Simulations suggest insulin may be an important factor identifying neurodegeneration in AD and PD, through its action along with the neuroinflammation and oxidative stress. Low insulin level was noticed in the diseased condition due to abnormal protein aggregation that leads to TNFα release. Given the role towards better design of real experiments, accumulation of oligomers of mutated proteins in AD and PD activating microglia and secreting TNFα along with other cytokines map to oxidative stress that led to cell death.

Piecewise synergetic systems and applications in biochemical systems theory

We study piecewise synergetic systems originating from Biochemical Systems Theory. In the first part of the paper, the emphasis is put on practical calculations with such systems. We consider four examples: calculation of trajectories and steady states, solution of an optimization problem and a method of estimation of parameters (kinetic orders), all examples being biologically motivated. In the second part of the paper, we study convergence of solutions, in particularly, steady states, of a sequence of piecewise synergetic systems approximating an arbitrary compartment model. This convergence analysis is then applied to the optimization problem and the method of estimating sensitivities (kinetic orders) in a generic compartment model. In this paper we put forward arguments for the importance of the theoretical and numerical analysis of piecewise synergetic systems.