Lymph node swelling combined with temporary effector T cell retention aids T cell response in a model of adaptive immunity

Swelling of lymph nodes (LNs) is commonly observed during the adaptive immune response, yet the impact on T cell (TC) trafficking and subsequent immune response is not well known. To better understand the effect of macro-scale alterations, we developed an agent-based model of the LN paracortex, describing the TC proliferative response to antigen-presenting dendritic cells alongside inflammation-driven and swelling-induced changes in TC recruitment and egress, while also incorporating regulation of the expression of egress-modulating TC receptor sphingosine-1-phosphate receptor-1. Analysis of the effector TC response under varying swelling conditions showed that swelling consistently aided TC activation. However, subsequent effector CD8⁺ TC production was reduced in scenarios where swelling occurred too early in the TC proliferative phase or when TC cognate frequency was low due to increased opportunity for TC exit. Temporarily extending retention of newly differentiated effector TCs, mediated by sphingosine-1-phosphate receptor-1 expression, mitigated any negative effects of swelling by allowing facilitation of activation to outweigh increased access to exit areas. These results suggest that targeting temporary effector TC retention and egress associated with swelling offers new ways to modulate effector TC responses in, for example, immuno-suppressed patients and to optimize of vaccine design.     

A mechanistic model for bromodeoxyuridine dilution naturally explains labelling data of self-renewing T cell populations

Bromodeoxyuridine (BrdU) is widely used in immunology to detect cell division, and several mathematical models have been proposed to estimate proliferation and death rates of lymphocytes from BrdU labelling and de-labelling curves. One problem in interpreting BrdU data is explaining the de-labelling curves. Because shortly after label withdrawal, BrdU⁺ cells are expected to divide into BrdU⁺ daughter cells, one would expect a flat down-slope. As for many cell types, the fraction of BrdU⁺ cells decreases during de-labelling, previous mathematical models had to make debatable assumptions to be able to account for the data. We develop a mechanistic model tracking the number of divisions that each cell has undergone in the presence and absence of BrdU, and allow cells to accumulate and dilute their BrdU content. From the same mechanistic model, one can naturally derive expressions for the mean BrdU content (MBC) of all cells, or the MBC of the BrdU⁺ subset, which is related to the mean fluorescence intensity of BrdU that can be measured in experiments. The model is extended to include subpopulations with different rates of division and death (i.e. kinetic heterogeneity). We fit the extended model to previously published BrdU data from memory T lymphocytes in simian immunodeficiency virus-infected and uninfected macaques, and find that the model describes the data with at least the same quality as previous models. Because the same model predicts a modest decline in the MBC of BrdU⁺ cells, which is consistent with experimental observations, BrdU dilution seems a natural explanation for the observed down-slopes in self-renewing populations.     

Experimental and mathematical modelling of magnetically labelled mesenchymal stromal cell delivery

A key challenge for stem cell therapies is the delivery of therapeutic cells to the repair site. Magnetic targeting has been proposed as a platform for defining clinical sites of delivery more effectively. In this paper, we use a combined in vitro experimental and mathematical modelling approach to explore the magnetic targeting of mesenchymal stromal cells (MSCs) labelled with magnetic nanoparticles using an external magnet. This study aims to (i) demonstrate the potential of magnetic tagging for MSC delivery, (ii) examine the effect of red blood cells (RBCs) on MSC capture efficacy and (iii) highlight how mathematical models can provide both insight into mechanics of therapy and predictions about cell targeting in vivo. In vitro MSCs are cultured with magnetic nanoparticles and circulated with RBCs over an external magnet. Cell capture efficacy is measured for varying magnetic field strengths and RBC percentages. We use a 2D continuum mathematical model to represent the flow of magnetically tagged MSCs with RBCs. Numerical simulations demonstrate qualitative agreement with experimental results showing better capture with stronger magnetic fields and lower levels of RBCs. We additionally exploit the mathematical model to make hypotheses about the role of extravasation and identify future in vitro experiments to quantify this effect.     

A dimensionless ordered pull-through model of the mammalian lens epithelium evidences scaling across species and explains the age-dependent changes in cell density in the human lens

We present a mathematical (ordered pull-through; OPT) model of the cell-density profile for the mammalian lens epithelium together with new experimental data. The model is based upon dimensionless parameters, an important criterion for inter-species comparisons where lens sizes can vary greatly (e.g. bovine (approx. 18 mm); mouse (approx. 2 mm)) and confirms that mammalian lenses scale with size. The validated model includes two parameters: β/α, which is the ratio of the proliferation rate in the peripheral and in the central region of the lens; and γ_GZ, a dimensionless pull-through parameter that accounts for the cell transition and exit from the epithelium into the lens body. Best-fit values were determined for mouse, rat, rabbit, bovine and human lens epithelia. The OPT model accounts for the peak in cell density at the periphery of the lens epithelium, a region where cell proliferation is concentrated and reaches a maximum coincident with the germinative zone. The β/α ratio correlates with the measured FGF-2 gradient, a morphogen critical to lens cell survival, proliferation and differentiation. As proliferation declines with age, the OPT model predicted age-dependent changes in cell-density profiles, which we observed in mouse and human lenses.     

Simulation of coarsening of inter-lath cementite in a Q&T steel during tempering

A mathematical model, using the finite difference approach, was established to consider tempering in a low carbon low alloy quenched and tempered steel based on experimental observations, treating the coarsening of a larger particle and dissolution of a smaller particle as a continuous and simultaneous process for coupled inter-lath cementite systems. The diffusion of Mn was simplified as a 1D diffusion and occurred between the interface elements and their adjacent elements in the model. The mathematical model predicted the shortest dissolution times for smaller particles in coupled inter-lath cementite systems, which agreed well with experimental observations on tempering from 2 to 4?h. However, the larger particle coarsening was under predicted due to the simplification of considering two particle arrangements.     

Inelastic behaviour of collagen networks in cell–matrix interactions and mechanosensation

The mechanical properties of extracellular matrix proteins strongly influence cell-induced tension in the matrix, which in turn influences cell function. Despite progress on the impact of elastic behaviour of matrix proteins on cell–matrix interactions, little is known about the influence of inelastic behaviour, especially at the large and slow deformations that characterize cell-induced matrix remodelling. We found that collagen matrices exhibit deformation rate-dependent behaviour, which leads to a transition from pronounced elastic behaviour at fast deformations to substantially inelastic behaviour at slow deformations (1 μm min⁻¹, similar to cell-mediated deformation). With slow deformations, the inelastic behaviour of floating gels was sensitive to collagen concentration, whereas attached gels exhibited similar inelastic behaviour independent of collagen concentration. The presence of an underlying rigid support had a similar effect on cell–matrix interactions: cell-induced deformation and remodelling were similar on 1 or 3 mg ml⁻¹ attached collagen gels while deformations were two- to fourfold smaller in floating gels of high compared with low collagen concentration. In cross-linked collagen matrices, which did not exhibit inelastic behaviour, cells did not respond to the presence of the underlying rigid foundation. These data indicate that at the slow rates of collagen compaction generated by fibroblasts, the inelastic responses of collagen gels, which are influenced by collagen concentration and the presence of an underlying rigid foundation, are important determinants of cell–matrix interactions and mechanosensation.     

Mathematical simulation of the transformation of radiation formed by a plane resonator and an optical system in a paraxial approximation

A mathematical model of the transformation of radiation produced by a flat optical resonator, single lens, and a two-lens optical system with the use of the Kirchhoff scalar theory of diffraction is constructed and investigated. __________ Translated from Izmeritel’naya Tekhnika, No. 11, pp. 20–23, November, 2007.     

Electron structure and activation energy of hydrogen in α-Zr using nonlinear response theory

The electron structure of hydrogen in hcp Zr is calculated by using self-consistent nonlinear screening theory. The host-ion contribution is included through the spherical solid model potential (SSMP). The resulting charge density and scattering phase shifts are used to calculate the activation energy and residual resistivity of hydrogen in α-Zr matrix. The calculated activation energy 0·285 eV is found in reasonably good agreement with experimental value 0·3 eV. The estimated residual resistivity 0·53 μΩ cm/at% for Zr-H system using the scattering phase shifts agrees reasonably well with the observed value 0·27 μΩ cm/at%. The calculated configurational energy shows that hydrogen prefers tetrahedral(T)-sites over octahedral(O)-sites in α-Zr. The strong binding energy of electron-proton suggests that hydrogen forms zirconium hydride.     

A new belief Markov chain model and its application in inventory prediction

The Markov chain model is widely applied in many fields, especially the field of prediction. The discrete-time Markov chain (DTMC) is a common method for prediction. However, the classical DTMC model has some limitations when the system is complex with uncertain information or state space is not discrete. To address it, a new belief Markov chain (BMC) model combining Dempster-Shafer evidence theory and the DTMC is proposed. In our model, the uncertain data are allowed to be handled in the form of interval number, and the basic probability assignment is generated by an optimisation method based on the distance between interval numbers. The shortcoming of classical DTMC is overcome in the BMC model. Also, it has an efficient ability of dealing with uncertain information, including both the uncertainty of collected data and discerning states. Our model is applied to do the prediction of inventory demand and the result is close to the practical. Also, sensitivity analysis and some comparisons are accomplished to show the effectiveness and rationality of our proposed model.     

Thermo-mechanical load interactions in foam cored axi-symmetric sandwich circular plates – High-order and FE models

This work presents analytical and finite element analysis (FEA) results of the thermo-mechanical non-linear response of an axi-symmetric circular sandwich plates with a compliant foam core. The study investigates the load–thermal interaction response of a sandwich panel where the properties of the core are temperature dependent and degrade as the temperatures are raised. It presents briefly the governing equations for a sandwich plate based on the principles of the high-order sandwich panel theory (HSAPT) which incorporates the effects of the vertical flexibility of the core material as well as the effects of temperature independent/dependent mechanical properties of the foam core. The effects of the thermal degradation of core material on the thermo-mechanical non-linear response of a simply supported circular sandwich plate are studied through the analytical and FE models. The difficulties involved in non-linear geometrical FE modeling of sandwich panels with a compliant “soft” core with temperature-dependent mechanical properties are discussed. The HSAPT model predictions are compared very well with FE result. An important conclusion of the study is that the interaction between mechanical loads, temperature induced deformations, and degradation of the mechanical properties due to elevated temperatures, may seriously affect the structural integrity of foam cored sandwich plates.     

Synergy of cell–cell repulsion and vacuolation in a computational model of lumen formation

A key step in blood vessel development (angiogenesis) is lumen formation: the hollowing of vessels for blood perfusion. Two alternative lumen formation mechanisms are suggested to function in different types of blood vessels. The vacuolation mechanism is suggested for lumen formation in small vessels by coalescence of intracellular vacuoles, a view that was extended to extracellular lumen formation by exocytosis of vacuoles. The cell–cell repulsion mechanism is suggested to initiate extracellular lumen formation in large vessels by active repulsion of adjacent cells, and active cell shape changes extend the lumen. We used an agent-based computer model, based on the cellular Potts model, to compare and study both mechanisms separately and combined. An extensive sensitivity analysis shows that each of the mechanisms on its own can produce lumens in a narrow region of parameter space. However, combining both mechanisms makes lumen formation much more robust to the values of the parameters, suggesting that the mechanisms may work synergistically and operate in parallel, rather than in different vessel types.     

Lexicographic fuzzy multi-objective model for minimisation of exceptional and void elements in manufacturing cell formation

This research proposes a lexicographic fuzzy multi-objective model based on perfect grouping for concurrent solving the part-family and machine-cell formation problems in a cellular manufacturing system. New simplified mathematical expressions of exceptional and void elements are proposed, opposing conventional quadratic and absolute functions. The main objectives of the proposed solution model, that is, the minimisation of both the number of exceptional elements and the number of void elements is defined by fuzzy goals as pre-emptive ordering. A lexicographic fuzzy goal model is developed to enhance cell performance and machine utilisation simultaneously. A satisfactory efficient solution can easily be obtained, and alternative solutions can also be generated by capturing flexibility of the proposed fuzzy multi-objective programming model. The formulated model can be solved by existing integer programming solvers. Finally, the evaluation of cell formation problems is briefly discussed to show the performance of the proposed model.     

pH-responsive dual-functional hydrogel integrating localized delivery and anti-cancer activities for highly effective therapy in PDX of OSCC

As one of the most promising localized drug delivery systems for enhancing therapeutic efficacy and reducing systemic toxicity, supramolecular hydrogels self-assembled from natural products have recently attracted tremendous attention. However, the intricate drug loading process, limited drug entrapment efficacy, and lack of stimulus responsiveness considerably impede their potential for biological applications and raise the need for advanced hydrogel-based delivery systems. Therefore, the development of updated materials that integrate localized delivery and drug activity into a single system is extremely desired and has great potential to overcome the aforementioned shortcomings. In this study, a pH-responsive dual-functional isoG-based supramolecular hydrogel with both localized delivery and anti-cancer activity in one molecule is successfully developed in one pot by following a simple and green procedure. The isoguanosine-phenylboronic-guanosine (isoGPBG) hydrogel exhibits exceptional stability (more than one year), outstanding pH-responsiveness and excellent sustained release capability. Both in vitro and in vivo experiments demonstrate that the isoGPBG hydrogel not only shows acceptable biocompatibility and biodegradability but also significantly inhibit tumor growth (approximately 60% inhibition of tumor growth) and improve overall survival, especially in preclinical patient-derived xenograft (PDX) model of oral squamous cell carcinoma (OSCC). Therefore, the isoGPBG hydrogel, to the best of our knowledge, is the first example of pH-responsive dual-functional isoG-based supramolecular hydrogel integrating localized delivery and anti-cancer activity in one molecule. It is implied that the isoGPBG hydrogel could act as a smart dual-functional localized delivery system in the future for clinical cancer therapy.