Supplementary Materials1_si_001. any pairs of receptors. pattern during the acknowledgement of membrane bound antigens.7-10 A lot of recent experimental and theoretical attempts have been devoted to elucidate the mechanisms of such pattern formation for the case of membrane-bound antigens.8-16 In contrast, little is known KW-6002 inhibitor about the mechanism of B cell receptor (BCR) clustering during the recognition of soluble antigens. It is known that B cell receptors cluster in the form of a at one pole of a cell during the acknowledgement of soluble antigens.17 It has also been shown that B cell receptors 1st micro-cluster upon cross-linking by soluble antigens and then at a later stage those micro-clusters coalesce into a large macroscopic cluster in the form of a cap.11 Membrane domains (or rafts) that are enriched in sphingolipids and cholesterol have been implicated in such receptor capping.18 Lack of a large number of experimental studies on B cell receptor clustering, during the recognition of soluble antigens, makes its mechanistic exploration challenging. In this article we study a model of BCR clustering that is mediated by mutual attraction between BCR molecules. Such mutual receptor-receptor attraction can arise due to antigen cross-linking, improved raft association of BCRs upon antigen binding, or by some other biophysical mechanisms. 11, 19-21 We use an energy-function centered Monte Carlo algorithm to study receptor clustering due to mutual attraction between receptors. We vary the strength of the Rabbit polyclonal to CUL5 attractive interaction as well as the denseness of molecules in our simulations. Nearest neighbor attraction among receptors placed on a square lattice is definitely shown to be enough for receptor micro-clustering. Very high denseness of receptors also prospects to receptor macro-clustering but such high receptor denseness may not be physiological. We simulate a mechanism of directed diffusion where BCR molecules move towards the largest micro-cluster having a diffusion bias. Such biased diffusion readily macro-cluster B cells receptors as seen in cap formation. Based on the spatial corporation of receptors networks within the cell surface we develop some quantitative criteria to characterize different types of B cell receptor clustering. We 1st consider the average pair smart range among all the receptors, which shows some simple functional relationship with the number of receptors for the extreme cases of receptor random distribution and receptor macro-clustering. An alternative metric, which is based on the total quantity of nearest neighbor receptor pairs, also shows simple scaling with the total quantity of receptors. Our Monte Carlo simulations verify the receptor network centered quantitative relations, which are derived using simple geometrical arguments. METHODS We carry out energy-based Monte Carlo simulations to model mutual receptor-receptor attraction on B cell surface. The total energy (Hamiltonian) of the system is definitely given by math xmlns:mml=”http://www.w3.org/1998/Math/MathML” display=”block” id=”M1″ overflow=”scroll” mrow mi H /mi mo = /mo mo ? /mo mi K /mi munder mo /mo mrow mi i /mi mo , /mo mi j /mi /mrow /munder msub mi S /mi mi KW-6002 inhibitor i /mi /msub msub mi S /mi mi j /mi /msub /mrow /math S can take two ideals 0 (no receptor) and 1 (receptor occupied). (i,j) are nearest neighbor sites for which mutual receptor sights are considered. The constant parameter K in the energy function represents the strength of an attractive connection that is assorted in our simulations. A total of four/eight neighboring sites are included in evaluating the energy.3 Initially the cell receptor molecules are placed randomly on a cell surface. We pick up a molecule randomly within the cell surface and attempt KW-6002 inhibitor a diffuse move to any of the four neighboring sites. In each Monte Carlo move, neighboring sites of a molecule are chosen with equal probability and a diffusion move can be made only when the chosen site is not KW-6002 inhibitor already occupied by another molecule. Finally, the diffusion move KW-6002 inhibitor to a new neighboring site is definitely approved with an energy-based criterion (as depicted in Number 1). One Monte Carlo time step consists of N repeated solitary molecule techniques where N is the total number of molecules. Open in a separate window Number 1 Flow chart depicting the used Monte Carlo algorithm When a receptor is definitely moved to a new.