20 research outputs found
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
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case 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 .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 matrix version of the -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 . 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
using the natural
embedding for any positive integer. The
hierarchies obtained admit a description in terms of a matrix
pseudo-differential operator comprising an -KdV type positive part and a
non-trivial negative part. This system has been investigated previously in the
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 (-algebra) structures related to
the KdV type hierarchies. Discrete reductions and modified versions of the
extended -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 -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