Adhesion-induced phase separation of multiple species of membrane junctions

A theory is presented for the membrane junction separation induced by the adhesion between two biomimetic membranes that contain two different types of anchored junctions (receptor/ligand complexes). The analysis shows that several mechanisms contribute to the membrane junction separation. These mechanisms include (i) the height difference between type-1 and type-2 junctions is the main factor which drives the junction separation, (ii) when type-1 and type-2 junctions have different rigidities against stretch and compression, the ``softer'' junctions are the ``favored'' species, and the aggregation of the softer junction can occur, (iii) the elasticity of the membranes mediates a non-local interaction between the junctions, (iv) the thermally activated shape fluctuations of the membranes also contribute to the junction separation by inducing another non-local interaction between the junctions and renormalizing the binding energy of the junctions. The combined effect of these mechanisms is that when junction separation occurs, the system separates into two domains with different relative and total junction densities.Comment: 23 pages, 6 figure

Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies

Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon graded regular elements of arbitrary Heisenberg subalgebras are considered. We show that, in the case of the nontwisted loop algebra $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ considered by DS. The methods of DS are utilized throughout the analysis, but formulating the reduction entirely within the Hamiltonian framework provided by the classical r-matrix approach leads to some simplifications even for $p=1$.Comment: 43 page

T-Cell activation: a queuing theory analysis at low agonist density

We analyze a simple linear triggering model of the T-cell receptor (TCR) within the framework of queuing theory, in which TCRs enter the queue upon full activation and exit by downregulation. We fit our model to four experimentally characterized threshold activation criteria and analyze their specificity and sensitivity: the initial calcium spike, cytotoxicity, immunological synapse formation, and cytokine secretion. Specificity characteristics improve as the time window for detection increases, saturating for time periods on the timescale of downregulation; thus, the calcium spike (30 s) has low specificity but a sensitivity to single-peptide MHC ligands, while the cytokine threshold (1 h) can distinguish ligands with a 30% variation in the complex lifetime. However, a robustness analysis shows that these properties are degraded when the queue parameters are subject to variation—for example, under stochasticity in the ligand number in the cell-cell interface and population variation in the cellular threshold. A time integration of the queue over a period of hours is shown to be able to control parameter noise efficiently for realistic parameter values when integrated over sufficiently long time periods (hours), the discrimination characteristics being determined by the TCR signal cascade kinetics (a kinetic proofreading scheme). Therefore, through a combination of thresholds and signal integration, a T cell can be responsive to low ligand density and specific to agonist quality. We suggest that multiple threshold mechanisms are employed to establish the conditions for efficient signal integration, i.e., coordinate the formation of a stable contact interface

Extensions of the matrix Gelfand-Dickey hierarchy from generalized Drinfeld-Sokolov reduction

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra $\widehat{gl}_{pr}\otimes {\Complex}[\lambda, \lambda^{-1}]$. Here a series of extensions of this matrix Gelfand-Dickey system is derived by means of a generalized Drinfeld-Sokolov reduction defined for the Lie algebra $\widehat{gl}_{pr+s}\otimes {\Complex}[\lambda,\lambda^{-1}]$ using the natural embedding $gl_{pr}\subset gl_{pr+s}$ for $s$ any positive integer. The hierarchies obtained admit a description in terms of a $p\times p$ matrix pseudo-differential operator comprising an $r$-KdV type positive part and a non-trivial negative part. This system has been investigated previously in the $p=1$ case as a constrained KP system. In this paper the previous results are considerably extended and a systematic study is presented on the basis of the Drinfeld-Sokolov approach that has the advantage that it leads to local Poisson brackets and makes clear the conformal ($\cal W$-algebra) structures related to the KdV type hierarchies. Discrete reductions and modified versions of the extended $r$-KdV hierarchies are also discussed.Comment: 60 pages, plain TE

Generalized Integrability and two-dimensional Gravitation

We review the construction of generalized integrable hierarchies of partial differential equations, associated to affine Kac-Moody algebras, that include those considered by Drinfel'd and Sokolov. These hierarchies can be used to construct new models of 2D quantum or topological gravity, as well as new $\cal W$-algebras.Comment: 24 pages, fixed broken tex sourc

The quantisation of Lie groups and Lie algebras

SIGLEAvailable from British Library Document Supply Centre- DSC:D061408 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Discriminating self from nonself with short peptides from large proteomes

We studied whether the peptides of nine amino acids (9-mers) that are typically used in MHC class I presentation are sufficiently unique for self:nonself discrimination. The human proteome contains 28,783 proteins, comprising 10(7) distinct 9-mers. Enumerating distinct 9-mers for a variety of microorganisms we found that the average overlap, i.e., the probability that a foreign peptide also occurs in the human self, is about 0.2%. This self:nonself overlap increased when shorter peptides were used, e.g., was 30% for 6-mers and 3% for 7-mers. Predicting all 9-mers that are expected to be cleaved by the immunoproteasome and to be translocated by TAP, we find that about 25% of the self and the nonself 9-mers are processed successfully. For the HLA-A*0201 and HLA-A*0204 alleles, we predicted which of the processed 9-mers from each proteome are expected to be presented on the MHC. Both alleles prefer to present processed 9-mers to nonprocessed 9-mers, and both have small preference to present foreign peptides. Because a number of amino acids from each 9-mer bind the MHC, and are therefore not exposed to the TCR, antigen presentation seems to involve a significant loss of information. Our results show that this is not the case because the HLA molecules are fairly specific. Removing the two anchor residues from each presented peptide, we find that the self:nonself overlap of these exposed 7-mers resembles that of 9-mers. Summarizing, the 9-mers used in MHC class I presentation tend to carry sufficient information to detect nonself peptides amongst self peptides

TCR dynamics on the surface of living T cells.

T lymphocyte activation by specific antigen requires prolonged TCR occupancy and sustained signaling. This is accomplished by the formation of a specialized signaling domain, the immunological synapse, at the T cell-antigen-presenting cell contact site. Surface receptors and signaling components are progressively recruited into this domain where they are organized in defined three-dimensional structures. To better understand how TCR are supplied to the signaling domain during the activation process, we measured (using confocal microscopy and photo-bleaching recovery techniques) lateral mobility of GFP-tagged TCR on living Jurkat cell surface. We show that: (i) surface-expressed TCR exhibit an intrinsic, actin cytoskeleton-independent, lateral mobility which allows them to passively diffuse over the entire T cell surface within approximately 60 min and (ii) non-stimulated TCR rapidly enter the signaling domain. Our results indicate that TCR lateral mobility per se is sufficient to ensure TCR supply to the immunological synapse in the course of sustained T cell activation

Autoimmunity arising from bystander proliferation of T cells in an immune response model

We study a mathematical model of immune response by T cells where the regulatory T cells (Treg) inhibit interleukin 2 secretion. The bystander proliferation to an immune response is modelled. We consider an asymmetry reflecting that the difference between the growth and death rates can be higher for the active T cells and Tregs than for the inactive. This asymmetry leads to a better understanding of the bystander proliferation. An exposure to a pathogen results in an increased proliferation rate of the bystander T cells. If the population of the bystander T cells becomes large enough, autoimmunity can arise, eventually after a long transient period. (C) 2010 Elsevier Ltd. All rights reserved

Immune response dynamics

The consequences of regulatory T cell (Treg) inhibition of interleukine 2 secretion are examined by mathematical modelling. We determine the analytic formula that describes the fine balance between Regulatory T cells and T cells at controlled and immune response equilibrium states. We demonstrate that cytokine dependent growth exhibits a quorum T cell population threshold that determines if immune responses develop on activation. We determine the analytic formulas of T cell proliferation thresholds that allow us to study the sensibility of the quorum growth thresholds controlling immune responses. (C) 2010 Elsevier Ltd. All rights reserved