Important biological events, such as cell fate during development and initiation of various immune responses, are determined by binary cell-cell interactions. Much attention has been directed toward understanding the exquisitely specific molecular scale receptor-ligand binding that is essential for intercellular recognition and signaling. In many instances, successful engagement of a receptor with a complementary ligand on the apposing cell is, by itself, insufficient for sustained intracellular signaling and the concomitant triggering of a specific biological function. For example, the definitive event governing a mature immune response when T lymphocyte or natural killer (NK) cells interact with target cells is the formation of an immunological synapse (e.g., refs. 1-10). Concerted reorganization of the spatial pattern of membrane proteins and cell shape occurs during this recognition process (1-3). The resulting synapse is a clearly organized pattern of protein complexes, several microns in diameter, that forms at the junction between the membranes of the two cells. The mechanisms that drive the formation of synaptic patterns in intercellular junctions are not as well understood as the individual receptor-ligand binding events.Here, we examine whether the observed characteristics of synaptic patterns (1-3) can emerge spontaneously during cooperative interaction between populations of receptors and ligands in two apposed membranes. We consider a fluctuating twodimensional membrane containing proteins that can interact with a flat two-dimensional membrane containing complementary protein ligands (Fig. 1). An analogous configuration has been used (e.g., refs. 2, 7, and 10) to visualize synapse formation between T cells and supported lipid membranes. We formulate and study a model for this situation that explicitly incorporates protein binding and dissociation, lateral motion of proteins in the cell membranes, membrane mechanics (bending rigidity and tension), and protein down regulation. The results show that natural coupling of the forces due to these phenomena can lead to spatio-temporal evolution of protein patterns and cell shape resembling that observed during synapse formation in living cells. In this paper, we focus primarily on applying this general model to study the specialized junction between T cells and antigen-presenting cells (APC).The formation of functional immunological synapses between T cells and supported bilayers reconstituted to mimic APCs has recently been observed (2). A combination of interference reflection microscopy, fluorescence imaging, and immunoradiometric assays has provided quantitative information on the spatial pattern of membrane protein concentrations and membrane topography during synapse formation. Detailed accounts of these measurements and those with T cells and APCs (which exhibit the same phenomenology) are available (1, 2). Abbreviations: NK, natural killer; APC, antigen-presenting cell; ICAM-1, intercellular adhesion molecule-1; TCR, T cell antigen receptor; LFA-1, ...

How T cells respond with extraordinary sensitivity to minute amounts of agonist peptide and major histocompatibility complex (pMHC) molecules on the surface of antigen-presenting cells bearing large numbers of endogenous pMHC molecules is not understood. Here we present evidence that CD4 affects the responsiveness of T helper cells by controlling spatial localization of the tyrosine kinase Lck in the synapse. This finding, as well as further in silico and in vitro experiments, led us to develop a molecular model in which endogenous and agonist pMHC molecules act cooperatively to amplify T cell receptor signaling. At the same time, activation due to endogenous pMHC molecules alone is inhibited. A key feature is that the binding of agonist pMHC molecules to the T cell receptor results in CD4-mediated spatial localization of Lck, which in turn enables endogenous pMHC molecules to trigger many T cell receptors. We also discuss broader implications for T cell biology, including thymic selection, diversity of the repertoire of self pMHC molecules and serial triggering.

We study the kinetics of order-disorder and order-order transitions in weakly segregated diblock copolymers using a time-dependent Ginzburg-Landau ͑TDGL͒ approach. In particular, we investigate the microstructural change as well as the order-parameter evolution after a sudden temperature jump from one phase to another. Direct numerical simulation of the TDGL equations shows that depending on the extent of the temperature jump, these transitions often occur in several stages and can involve nontrivial intermediate states. For example, we find that transition from the lamellar phase to the hexagonal cylinder phase goes through a perforated lamellar state within a certain temperature range. The numerical results are elucidated by a multimode analysis under the single-wave-number approximation. The analysis reveals that the geometric characteristics of the free energy surface, particularly saddle points and ridgelike features, are responsible for the nontrivial intermediate states on the kinetic pathways. On the basis of this analysis, a generalized kinetic ''phase diagram'' is constructed, which is able to account for all the different scenarios observed in the numerical simulation. Our results are discussed in connection with available experimental observations. In particular, we suggest the possibility that the perforated-modulated lamellar structures obtained by Bates and co-workers ͓I.

The kinetics of hexagonal to disordered and hexagonal to body-centered-cubic phase transitions in weakly segregated, microstructured systems (e.g., diblock copolymers) is studied using a time-dependent Ginzburg-Landau (TDGL) approach. Both computer simulation of the TDGL equation and analysis of a simplified two-mode model reveal nontrivial pathways during the transition.PACS numbers: 81.10. Aj, 81.30.Hd, 83.70.Hq A wide variety of chemical and physical systems, such as Langmuir films, ferrofluids, and diblock copolymers, exhibit ordered periodic domain structures [1]. Irrespective of differences in the systems, the domain structures have surprisingly similar appearance: stripes and circular droplets in two dimensions, and lamellae, hexagonal (HEX) cylinders, and body-centered-cubic (bcc) spheres in three dimensions. Although the specific origins may differ from system to system, the formation of spatially periodic patterns can be attributed to the competing shortrange and long-range interactions. Near the order-disorder transition, these systems can be phenomenologically described by an order parameter free energy functional of the formwhere c͑ r͒ is the order parameter, e.g., the local magnetization in magnetic systems, or the local density contrast between the two types of monomers in diblock copolymers. t is related to the distance from the order-disorder transition temperature, and the coefficients b, c, u, and y are phenomenological parameters which can be computed from more microscopic models. The last term in Eq.(1) represents the long-range repulsion, which penalizes longwavelength inhomogeneities. The equilibrium properties of systems described by Eq. (1) have been the subject of extensive experimental and theoretical studies [1,2]. In this Letter, we address the phenomenology of the kinetics of the various order-order and order-disorder transitions in weakly segregated, microstructured systems, using a time-dependent Ginzburg-Landau approach. Specifically we study the kinetic pathways of HEX to disordered and HEX to bcc phases after a sudden temperature jump. This study is motivated by the general intrinsic interest in understanding kinetics of phase transitions involving spatially modulated phases, in particular, by recent experiments on diblock copolymers [3][4][5][6][7]. To be concrete, we shall use diblock copolymers as the context; however, we believe the phenomenology is quite general for the class of systems described by the free energy Eq. (1), and will not limit our choice of parameters specifically to those for diblock copolymers [8].For conserved order parameters, as is appropriate for diblock copolymers, we may write the time-dependentHere M is a mobility coefficient, which we assume to be a constant; h͑ r, t͒ is a random force, which for a system in equilibrium at temperature T , satisfies the fluctuationdissipation relationAs a minimal model, we ignore any hydrodynamic effects and possible nonlocality in the mobility coefficient [10,11]. We will also ignore the noise term in subsequen...