[...]... different types of T -cells The life-history of these cells is critically dependent on signals via their receptors expressed on the cell surface T-cell receptor (TCR) signals are involved in the positive and negative selection of immature T -cells in the thymus [77], and also in the survival, activation, differentiation, and cell cycle progression of mature circulating T -cells [63, 81] Understanding of immune... note 18 3 Micro-Agent and Stochastic Micro-Agent Models Fig 3.2 Micro-Agent model of the T-cell ; u(t) - event sequence; events: a - conjugate formation, b - conjugate dissociation; x - expression level of TCRs; x0 - initial expression level of TCRs, q0 - initial discrete state [54] that the T-cell hybrid system model (Figure 3.1) is a deterministic model Given an initial state (x0 , q0 ) and a time sequence... (t) T -Cells Dynamics Fig 3.4 T-cell population hybrid system model, where the Population Event Generator (PEG) is decomposed into several Micro-Agent Event Generators (MAEG) The serial connection of MAEG and Micro-Agents is named a ”Stochastic Micro-Agent” (SμA); ui - event sequence input to the ith T-cell, xi - the TCR expression level of the ith T-cell, i = 1, 2 N [54] 20 3 Micro-Agent and Stochastic... the study of large-size agent populations Our approach points at understanding how individual agent dynamical behavior propagates to the population dynamics The presented concepts and mathematical tools are general enough and provide results 1 Motility - ability to move spontaneously and independently [22] D Milutinovic and P Lima: Cells & Robots, STAR 32, pp 1–8, 2007 c Springer-Verlag Berlin Heidelberg... conjugate formation and conjugate dissociation of T -cells and APC This complex dynamics makes the difference between the TCR dynamics of a collection of separate T -cells and the TCR dynamics of a T-cell biological population (Figure 3.3) The conjugate f ormation and conjugate dissociation events, of T -cells in the population, are result of a complex dynamics which depends on the amount of the cells, their... conjugate formation and conjugate dissociation 2.1 Surface T-Cell Receptor Dynamics in a Mixture of Interacting Cells 11 Fig 2.2 T-cell receptor triggering: T-cell, T-cell receptor (TCR), antigen-presenting cell (APC), peptide-MHC complex The minimal biological system with the properties we are interested in is a homogeneous mixture of interacting T -cells and APCs which present TCRligands, depicted in... macro-dynamics, which results from the propagation of the individual cell dynamics, i.e., micro-dynamics Interaction between T-cell and APC starts when they become conjugated due to a random encounter Thus, considering single T-cell, the event conjugate formation, is a random event Similarly, T-cell and APC are also subject to the opposite process, dissociation, when the interaction between T-cell and. .. is an antigen-presenting cell (APC) and T -cells The APC expresses, on its surface, pieces of pathogen protein, so-called antigen, signaling the presence of pathogen, for example of virus or bacteria The contact of APCs and their interaction with T -cells is of vital importance for the start of the immune system response Without any infection, the T-cell moves randomly around the lymph node and scans APCs... dynamics of individual T-cell and the TCR average expression of the population, must be considered 12 2 Immune System and T-Cell Receptor Dynamics of a T-Cell Population conjugated not conjugated Legend: T-Cell APC not conjugated Fig 2.3 T-cell population surrounded by the APCs: T -cells can be conjugated or non conjugated to APC [53, 54, 56], c 2003 IEEE The models in [69] and [83] are tested against... whether dissociation is a random or deterministic process, we still can define event conjugate dissociation, which happens at the time point when the interaction between T-cell and APC ceases Based on this discussion, it is clear that the behavior of an individual T-cell can be described by a hybrid automaton with discrete states conjugated and free In D Milutinovic and P Lima: Cells & Robots, STAR 32, pp . 2007925208 ISSN print edition: 161 0-7 438 ISSN electronic edition: 161 0-7 42X ISBN-10 3-5 4 0-7 198 1-4 Springer Berlin Heidelberg New York ISBN-13 97 8-3 -5 4 0-7 198 1-6 Springer Berlin Heidelberg New York This. enough and provide results 1 Motility - ability to move spontaneously and independently [22]. D. Milutinovic and P. Lima: Cells & Robots, STAR 32, pp. 1–8, 2007. springerlink.com c  Springer-Verlag. a T-cell and of a T-cell population are introduced. The model of the T-cell motivates the formal definition of a Micro-Agent. We use the Micro-Agent model of an individual T-cell to build a T-cell