Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Systemic inflammatory responses to maximal versus submaximal lengthening contractions of the elbow flexors

We compared changes in markers of muscle damage and systemic inflammation after submaximal and maximal lengthening muscle contractions of the elbow flexors. Using a cross-over design, 10 healthy young men not involved in resistance training completed a submaximal trial (10 sets of 60 lengthening contractions at 10% maximum isometric strength, 1 min rest between sets), followed by a maximal trial (10 sets of three lengthening contractions at 100% maximum isometric strength, 3 min rest between sets). Lengthening contractions were performed on an isokinetic dynamometer. Opposite arms were used for the submaximal and maximal trials, and the trials were separated by a minimum of two weeks. Blood was sampled before, immediately after, 1 h, 3 h, and 1-4 d after each trial. Total leukocyte and neutrophil numbers, and the serum concentration of soluble tumor necrosis factor-alpha receptor 1 were elevated after both trials (P < 0.01), but there were no differences between the trials. Serum IL-6 concentration was elevated 3 h after the submaximal contractions (P < 0.01). The concentrations of serum tumor necrosis factor-alpha, IL-1 receptor antagonist, IL-10, granulocyte-colony stimulating factor and plasma C-reactive protein remained unchanged following both trials. Maximum isometric strength and range of motion decreased significantly (P < 0.001) after both trials, and were lower from 1-4 days after the maximal contractions compared to the submaximal contractions. Plasma myoglobin concentration and creatine kinase activity, muscle soreness and upper arm circumference all increased after both trials (P < 0.01), but were not significantly different between the trials. Therefore, there were no differences in markers of systemic inflammation, despite evidence of greater muscle damage following maximal versus submaximal lengthening contractions of the elbow flexors.

The mixed anion mineral parnauite Cu9[(OH)10|SO4|(AsO4)2]•7H2O – a Raman spectroscopic study

The mixed anion mineral parnauite Cu9[(OH)10|SO4|(AsO4)2].7H2O from two localities namely Cap Garonne Mine, Le Pradet, France and Majuba Hill mine, Pershing County, Nevada, USA has been studied by Raman spectroscopy. The Raman spectrum of the French sample is dominated by an intense band at 975 cm-1 assigned to the ν1 (SO4)2- symmetric stretching mode and Raman bands at 1077 and 1097 cm-1 may be attributed to the ν3 (SO4)2- antisymmetric stretching mode. Two Raman bands 1107 and 1126 cm-1 are assigned to carbonate CO32- symmetric stretching bands and confirms the presence of carbonate in the structure of parnauite. The comparatively sharp band for the Pershing County mineral at 976 cm-1 is assigned to the ν1 (SO4)2- symmetric stretching mode and a broad spectral profile centered upon 1097 cm-1 is attributed to the ν3 (SO4)2- antisymmetric stretching mode. Two intense bands for the Pershing County mineral at 851 and 810 cm-1 are assigned to the ν1 (AsO4)3- symmetric stretching and ν3 (AsO4)3- antisymmetric stretching modes. Two Raman bands for the French mineral observed at 725 and 777 cm-1 are attributed to the ν3 (AsO4)3- antisymmetric stretching mode. For the French mineral, a low intensity Raman band is observed at 869 cm-1 and is assigned to the ν1 (AsO4)3- symmetric stretching vibration. Chemical composition of parnauite remains open and the question may be raised is parnauite a solid solution of two or more minerals such as a copper hydroxy-arsenate and a copper hydroxy sulphate.

Poly[aqua([mu]3-2-hydroxy-5-nitrobenzoato-[kappa]3O1:O1':O2)rubidium]

In the structure of title compound [Rb2(C7H4NO2)2(H2O)2]n the centrosymmetric cyclic dimeric repeating unit comprises two irregular RbO4 complex centres bridged by the carboxylate groups of the 5-nitrosalicylate ligands. The coordination about each Rb is completed by a monodentate water molecule and a phenolic O donor which gives a bridging extension [Rb-O range 3.116(7)-3.135(5)A]. The two-dimensional polymeric structure is stabilized by intermolecular water O-H...O(carboxyl) hydrogen bonds and weak inter-ring pi--pi interactions [minimum ring centroid separation, 3.620(4)A].

4-Aminopyridinium cis-2-carboxycyclohexane-1-carboxylate

In the structure of the title compound, C5H7N2+ C8H11O4-, the cis-monoanions associate through short carboxylic acid-carboxyl O-H...O hydrogen bonds [graph set C(7)], forming zigzag chains which extend along c and are inter-linked through pyridinium and amine N-H...O(carboxyl) hydrogen bonds giving a three-dimensional network structure.

Ethane-1,2-diaminium 4,4'-sulfonyldibenzoate

In the title compound 2(C2H10N2+) C14H8O6S2-, both the ethylenediaminium cations and the 4,4'-sulfonyldibenzoate dianions have crystallographic two-fold rotational symmetry and are interlinked by aminium N-H...O(carboxyl) hydrogen-bonding associations giving sheets which extend along (101) and are further linked down b forming a three-dimensional structure.

Poly[tetra-mu-aqua-diaquatetrakis[mu-(E)-2-nitrocinnamato]tetrarubidium]

In the structure of the title compound [Rb4(C9H6NO4)4(H~2~O)6]n, the asymmetric unit comprises four rubidium complex cations, two of which have an RbO7 coordination polyhedron with a monocapped distorted octahedral stereochemistry and two of which have a distorted RbO6 octahedral coordination. The bonding about both the seven-coordinate centres is similar, comprising one monodentate water molecule together with three bridging water molecules and three carboxylate O-atom donors, two of which are bridging. The environments about the six-coordinate cations are also similar, comprising a monodentate nitro O-atom donor, a bridging water molecule and four bridging carboxylate O-atom donors [overall Rb-O range, 2.849(2)-3.190(2)A]. The coordination leads to a two-dimensional polymeric structure extending parallel to (001), which is stabilized by interlayer water O-H...O hydrogen-bonding associations to water, carboxyl and nitro O-atom acceptors, together with weak inter-ring pi--pi interactions [minimum ring centroid separation = 3.5319(19)A].

catena-Poly[[diaqualithium]-mu-[rac-cis-(2-carboxycyclohexane-1-carboxylato-kO1:O2]]

In the structure of the title compound, [C8H11LiO4(H2O)2]n the distorted tetrahadral LiO4 coordination sphere comprises two water molecules and two carboxyl O-donors from separate bridging cis-2-carboxycyclohexane-1-carboxylate monoanions [Li-O range, 1.887(4)-1.946(3)A], giving chain substructures which extend along (010). Water-water and water-carboxyl O-H...O hydrogen bonds stabilize these chain structures and provide inter-chain links, resulting in a two-dimensional layered structure extending across (011).

4-(4-Aminophenylsulfonyl)aniline-1,3-5-trinitrobenzene (1/2)

The asymmetric unit of the title co-crystalline 1:2 adduct C12H12N2O2 . 2(C6H3N3O6) contains two independent molecules of bis(4-aminophenyl)sulfone (the drug Dapsone) and four molecules of 1,3,5-trinitrobenzene and is extended into a two-dimensional hydrogen-bonded network structure through amino N-H...O hydrogen-bonding associations with nitro O- atom acceptors. In the two independent Dapsone molecules the inter-ring dihedral angles are 69.0(2) and 63.59(11)deg. Aromatic pi-pi interactions are also found between one of the Dapsone aromatic rings and a trinitrobenzene ring [minimum ring centroid separation 3.576(5)Ang.]. A 4-aminophenyl ring moiety of one of the Dapsone molecules and two nitro groups of a trinitrobenzene are disordered in a 50:50 ratio.

1,1,3,3-Tetraethylisoindolin-2-ium chloride

In the structure of the title compound C16H26N+ Cl-, the salt of a precursor in the synthesis of an isoindolin-2-yloxyl free-radical trapping agent, the cations and anions form discrete centrosymetric cyclic dimers through N---H...Cl hydrogen-bonding associations [graph set R2/4(8)].

rac-4-Carbamoylpiperidinium cis-2-carboxycyclohexane-1-carboxylate

In the title salt, racemic C6H12N2O+ C8H11O4- from the reaction of cis-cyclohexane-1,2-dicarboxylic anhydride with isonipecotamide, the cations are linked into duplex chain substructures through both centrosymmetric cyclic head-to-head 'amide motif' hydrogen-bonding associations [graph set R2/2(8)] and 'side-by-side' R2/2(14) associations. The anions are incorporated into the chains through cyclic R3/4(10) interactions involving amide and piperidinium N-H...O(carboxyl) hydrogen bonds which, together with inter-anion carboxylic acid O-H...O(carboxyl) hydrogen bonds, give a two-dimensional layered structure extending along (011).

4-(4-Aminophenylsulfonyl)aniline-3,5-dinitrobenzoic acid (1/1)

In the title co-crystalline adduct of the drug Dapsone with 3,5-dinitrobenzoic acid, C~12~H~12~N~2~O~2~S . C~7~H~4~N~4~O~6~, the dihedral angle between the two aromatic rings of the Dapsone molecule is 75.4(2)deg. and those between these rings and that of the 3,5-dinitrobenzoic acid are 64.5(2) and 68.4(2)deg. A strong inter-species carboxylic acid O-H---N(amine) hydrogen-bond is found, which together with intermolecular amine N-H...O hydrogen-bonding associations with carboxyl, nitro and sulfone O-atom acceptors as well as weak pi-pi interactions between one of the Dapsone phenyl rings and the 3,5-dinitrobenzoic acid ring [minimum ring centroid separation 3.774(2)Ang.], give a two-dimensional network structure.

rac-3-exo-Ammonio-7-anti-carboxytricyclo-[2.2.10.2,6]heptane-3-endo-carboxylate

The racemic title compound, C9H11NO4 . H2O, a tricyclic rearranged aminonorbornane dicarboxylic acid is a conformationally rigid analogue of glutamic acid and exists as an ammonium-carboxylate zwitterion, with the bridghead carboxylic acid group anti-related. In the crystal, intermolecular N-H...O and O-H...O hydrogen-bonding interactions involving the ammonium, carboxylic acid and water donor groups with both water and carboxyl O-atom acceptors give a three-dimensional framework structure.

4-Amino-N-(4,6-dimethylpyrimidin-2-yl)benzenesulfonamide-4-nitrobenzoic acid

In the asymmetric unit of the title co-crystal, C12H14N4O2S . C7H5NO4 there are two independent but conformationally similar heterodimers, which are formed through intermolecular N-H...O(carboxy) and carboxyl O-H...N hydrogen-bond pairs, giving a cyclic motif [graph set R2/2(8)]. The dihedral angles between the rings in the sulfonamide molecules are 78.77(8) and 82.33(9)deg. while the dihedral angles between the ring and the CO2H group in the acids are 2.19(9) and 7.02(10)deg. A two-dimensional structure parallel to the ab plane is generated from the heterodimer units through hydrogen-bonding associations between NH2 and sulfone groups. Between neighbouring two-dimensional arrays there are two types of aromatic pi-pi stacking interactions involving either one of the pyrimidine rings and a 4-nitrobenzoic acid molecule [minimum ring centroid separation = 3.5886(9)A] or two acid molecules [minimum ring centroid separation = 3.7236(10)A].

Syntaxin 11 binds Vti1b and regulates late endosome to lysosome fusion in macrophages

Syntaxin 11 (Stx11) is a SNARE protein enriched in cells of the immune system. Loss or mutation of Stx11 results in familial hemophagocytic lymphohistiocytosis type-4 (FHL-4), an autosomal recessive disorder of immune dysregulation characterized by high levels of inflammatory cytokines along with defects in T-cell and natural killer cell function. We show here Stx11 is located on endosomalmembranes including late endosomes and lysosomes in macrophages. While Stx11 did not form a typical trans-SNARE complex, it did bind to the Q-SNARE Vti1b and was able to regulate the availability of Vti1b to form the Q-SNARE complexes Stx6/Stx7/Vtib and Stx7/Stx8/Vti1b. The mutant form of Stx11 sequestered Vti1b from forming the Q-SNARE complex that mediates late endosome to lysosome fusion. Depletion of Stx11 in activated macrophages leads to an accumulation of enlarged late endocytic compartments, increased trafficking to the cell surface and inhibition of late endosome to lysosome fusion. These phenotypes arerescued by the expression of an siRNA-resistant Stx11 construct in Stx11-depleted cells. Our results suggest that by regulating the availability of Vti1b, Stx11 regulates trafficking steps between late endosomes, lysosomes and the cell surface in macrophages.