Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

The strength of column-to-foundation joints in reinforced concrete

This thesis is concerned with the experimental and theoretical investigation into the compression bond of column longitudinal reinforcement in the transference of axial load from a reinforced concrete column to a base. Experimental work includes twelve tests with square twisted bars and twenty four tests with ribbed bars. The effects of bar size, anchorage length in the base, plan area of the base, provision of bae tensile reinforcement, links around the column bars in the base, plan area of column and concrete compressive strength were investigated in the tests. The tests indicated that the strength of the compression anchorage of deformed reinforcing steel in the concrete was primarily dependent on the concrete strength and the resistance to bursting, which may be available within the anchorage . It was shown in the tests without concreted columns that due to a large containment over the bars in the foundation, failure occurred due to the breakdown of bond followed by the slip of the column bars along the anchorage length. The experimental work showed that the bar size , the stress in the bar, the anchorage length, provision of the transverse steel and the concrete compressive strength significantly affect the bond stress at failure. The ultimate bond stress decreases as the anchorage length is increased, while the ultimate bond stress increases with increasing each of the remainder parameters. Tests with concreted columns also indicated that a section of the column contributed to the bond length in the foundation by acting as an extra anchorage length. The theoretical work is based on the Mindlin equation( 3), an analytical method used in conjunction with finite difference calculus. The theory is used to plot the distribution of bond stress in the elastic and the elastic-plastic stage of behaviour. The theory is also used to plot the load-vertical displacement relationship of the column bars in the anchorage length, and also to determine the theoretical failure load of foundation. The theoretical solutions are in good agreement with the experimental results and the distribution of bond stress is shown to be significantly influenced by the bar stiffness factor K. A comparison of the experimental results with the current codes shows that the bond stresses currently used are low and in particular, CPIlO(56) specifies very conservative design bond stresses .

The structure of the rare-earth phosphate glass(Sm2O3)0.205(P2O5)0.795 studied by anomalous dispersion neutron diffraction

The role of the Sm3+ ions in the structure of vitreous Sm2O3•4P2O5 has been investigated using the neutron diffraction anomalous dispersion technique, which employs the wavelength dependence of the real and imaginary parts of the neutron scattering length close to an absorption resonance. The data described here represent the first successful complete neutron anomalous dispersion study on an amorphous material. This experimental methodology permits one to determine exclusively the closest Sm• •• Sm separation. Knowledge of the R•••R (R = rare-earth) pairwise correlation is key to understanding the optical and magnetic properties of rare-earth phosphate glasses. The anomalous difference correlation function, ΔT''(r), shows a dominant feature pertaining to a Sm•••Sm separation, centred at 4.8 Å. The substantial width and marked asymmetry of this peak indicates that the minimum approach of Sm3+ ions could be as close as 4 Å. Information on other pairwise correlations is also revealed via analysis of T (r) and ΔT (r) correlation functions: Sm3+ ions display an average co-ordination number, n Sm(O), of 7, with a mean Sm–O bond length of 2.375(5) Å whilst the PO4 tetrahedra have a mean P–O bond length of 1.538(2) Å. Second- and third-neighbour correlations are also identified. These results corroborate previous findings. Such consistency lends support to the application of the anomalous dispersion technique to determine separations.

An XPS study of pulsed plasma polymerised allyl alcohol film growth on polyurethane

The growth of highly functionalised poly allyl alcohol films by pulsed plasma polymerisation of CH2 double bond; length as m-dashCHCH2OH on biomedical grade polyurethane has been followed by X-ray photoelectron spectroscopy (XPS) and contact angle measurements. Film thickness is observed to increase approximately linearly with plasma modification time, suggesting a layer-by-layer growth mode of poly allyl alcohol. Water contact angle measurements reveal the change in the surface free energy of wetting decreases linearly with plasma modification up to the monolayer point after which a constant limiting value of −24 mJ m−2 was attained. Films prepared at 20 W plasma power with a duty cycle of 10 μs:500 μs exhibit a high degree of hydroxyl (single bondOH) retention with minimal fragmentation of the monomer observed. Increasing the plasma power up to 125 W is found to improve single bondOH retention at the expense of ether formation generating films close to the monomer stoichiometry. Duty cycle plays an important role in controlling both film composition and thickness, with longer off times increasing single bondOH retention, while longer on times enhance allyl alcohol film growth.

Zirconium phosphate supported tungsten oxide solid acid catalysts for the esterification of palmitic acid

A series of zirconium phosphate supported WOx solid acid catalysts with W loadings from 1–25 wt% have been prepared on high surface area zirconium phosphate by a surface grafting method. Catalysts were characterized by N2 adsorption, FTIR, Raman, UV-Vis, 31P MAS NMR, pyridine TPD and X-ray methods. Spectroscopic measurements suggest a Keggin-type structure forms on the surface of zirconium phosphate as a ([triple bond, length as m-dash]ZrOH2+)(ZrPW11O405−) species. All catalysts show high activity in palmitic acid esterification with methanol. These materials can be readily separated from the reaction system for re-use, and are resistant to leaching of the active heteropolyacid, suggesting potential industrial applications in biodiesel synthesis. © The Royal Society of Chemistry 2006.

Contact time periods in immunological synapse

This paper resolves the long standing debate as to the proper time scale τ of the onset of the immunological synapse bond, the noncovalent chemical bond defining the immune pathways involving T cells and antigen presenting cells. Results from our model calculations show τ to be of the order of seconds instead of minutes. Close to the linearly stable regime, we show that in between the two critical spatial thresholds defined by the integrin:ligand pair (Δ2∼ 40-45 nm) and the T-cell receptor TCR:peptide-major-histocompatibility-complex pMHC bond (Δ1∼ 14-15 nm), τ grows monotonically with increasing coreceptor bond length separation δ (= Δ2-Δ1∼ 26-30 nm) while τ decays with Δ1 for fixed Δ2. The nonuniversal δ-dependent power-law structure of the probability density function further explains why only the TCR:pMHC bond is a likely candidate to form a stable synapse.