In this talk we examine two models used in the description of eukaryotic gradient sensing, from a systems perspective. The first is a so-called Local excitation global inhibition (LEGI) model which is used to describe signal transduction which incorporates both the feature of perfect adaptation (i.e. a response which returns to its basal pre-stimulus value) when subject to a spatially homogeneous input, as well as a persistent response in a steady gradient. The second is a model describing the regulation of a phosphoinositide lipid network in the membrane by enzymes PI3K and PTEN, both spatially and temporally.

In the first case, we examine the dynamic regulation of the LEGI module by the receptor from a dynamics/control perspective. We first analyze the nature of the transient response of the module to spatially homogeneous input, and obtain analytical expressions for the amplitude of the transient response in certain cases. We then examine the question of what kinds of oscillatory responses can and cannot be obtained as an output of this module. We then examine the extent to which the receptor can dynamically regulate the output of this module and obtain bounds on the output. Subsequently we analyze the regulation of the output by the receptor in the case of a linear gradient, and obtain bounds on the peak value of the response. We then turn to the analysis of the regulation of the lipid network by the enzymes PI3K and PTEN. We first consider the spatially homogeneous case and analyze the local accessibility of lipid regulation by the control input. We also construct a model for the experimentally observed output of the model, and analyze the observability question. We then analyze the extent to which the lipid concentrations can be varied in certain limiting cases. Finally we examine the question related to local accessibility and observability in a spatially discretized model of the PDEs. Overall the systems and control approaches contribute various insights which complement numerical simulation and other computational analysis.