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A nonlinear kinetic chemotaxis model with internal dynamics incorporatingsignal transduction and adaptation is considered. This paper is concerned with:(i) the global solution for this model, and, (ii) its fast adaptation limit toOthmer-Dunbar-Alt type model. This limit gives some insight to the molecularorigin of the chemotaxis behaviour.  First, by using the Schauder fixed point theorem, the global existence ofweak solution is proved based on detailed a priori estimates, under some quitegeneral assumptions on the model and the initial data. However, the Schauderfixed point theorem does not provide uniqueness. Therefore, additional analysisis required to be developed to obtain uniqueness.  Next, the fast adaptation limit of this model is derived by extracting a weakconvergence subsequence in measure space. For this limit, the first difficultyis to show the concentration effect on the internal state. When the smallparameter {\epsilon}, the adaptation time scale, goes to zero, we prove thatthe solution converges to a Dirac mass in the internal state variable. Anotherdifficulty is the strong compactness argument on the chemical potential, whichis essential for passing the nonlinear kinetic equation to the weak limit.

Global solution for a kinetic chemotaxis model with internal dynamics and its fast adaptation limit