Colin P. Please

Light-off behavior of catalytic converters

This paper studies a system of partial differential equations modeling the behavior of an automotive catalytic converter. The particular phenomenon considered in detail is light-off, when the temperature of the converter changes dramatically from cold to hot somewhere within the converter. The initial position of light-off and the subsequent movement of this steep jump in temperature toward the inlet of the converter are analyzed. The method of matched asymptotic expansions is used to study light-off and to derive approximate formulas that determine its behavior in the limits of small heat diffusion and large activation energy. Numerical calculations are presented and are used to compare with the analytical formulas. These calculations reveal that the asymptotic results for small diffusion are quantitatively accurate, while those for small diffusion and large activation energy give the qualitative behavior of the solution but give poor quantitative predictions for the range of parameters encountered in pr...

Combining mechanical and chemical effects in the deformation and failure of a cylindrical electrode particle in a Li-ion battery

A general framework to study the mechanical behaviour of a cylindrical silicon anode particle in a lithium ion battery as it undergoes lithiation is presented. The two-way coupling between stress and concentration of lithium in silicon, including the possibility of plastic deformation, is taken into account and two particular cases are considered. First, the cylindrical particle is assumed to be free of surface traction and second, the axial deformation of the cylinder is prevented. In both cases plastic stretches develop through the entire cylinder and not just near the surface as is commonly found in spherical anode particles. It is shown that the stress evolution depends both on the lithiation rate and the external constraints. Furthermore, as the cylinder expands during lithiation it can develop a compressive axial stress large enough to induce buckling, which in turn may lead to mechanical failure. An explicit criterion for swelling-induced buckling obtained as a modification of the classical Euler buckling criterion shows the competition between the stabilising effect of radius increase and the destabilising effect of axial stress.

Review: Modelling placental amino acid transfer--from transporters to placental function.

Amino acid transfer to the fetus is dependent on several different factors. While these factors can be understood in isolation, it is still not possible to predict the function of the system as a whole. In order to do this an integrated approach is required which incorporates the interactions between the different determinants of amino acid transfer. Computational modelling of amino acid transfer in the term human placenta provides a mechanism by which this integrated approach can be delivered. Such a model would be invaluable for understanding amino acid transfer in both normal and pathological pregnancies. In order to develop a computational model it is necessary to determine all the biological factors which are important contributors to net amino acid transfer and the ways in which they interact. For instance, how different classes of amino acid transporter must interact to transfer amino acids across the placenta. Mathematically, the kinetics of each type of transporter can be represented by separate equations that describe their transfer rate as a non-linear function of amino acid concentrations. These equations can then be combined in the model to predict the overall system behaviour. Testing these predictions experimentally will demonstrate the strengths and weaknesses of the model, which can then be refined with increasing complexity and retested in an iterative fashion. In this way we hope to develop a functional computational model which will allow exploration of the factors that determine amino acid transfer across the placenta. This model may also allow the development of strategies to optimise placental transfer in pathologies associated with impaired amino acid transfer such as fetal growth restriction.

Computational modelling of amino acid exchange and facilitated transport in placental membrane vesicles

Placental amino acid transport is required for fetal development and impaired transport has been associated with poor fetal growth. It is well known that placental amino acid transport is mediated by a broad array of specific membrane transporters with overlapping substrate specificity. However, it is not fully understood how these transporters function, both individually and as an integrated system. We propose that mathematical modelling could help in further elucidating the underlying mechanisms of how these transporters mediate placental amino acid transport. The aim of this work is to model the sodium independent transport of serine, which has been assumed to follow an obligatory exchange mechanism. However, previous amino acid uptake experiments in human placental microvillous plasma membrane vesicles have persistently produced results that are seemingly incompatible with such a mechanism; i.e. transport has been observed under zero-trans conditions, in the absence of internal substrates inside the vesicles to drive exchange. This observation raises two alternative hypotheses; (i) either exchange is not fully obligatory, or (ii) exchange is indeed obligatory, but an unforeseen initial concentration of amino acid substrate is present within the vesicle which could drive exchange. To investigate these possibilities, a mathematical model for tracer uptake was developed based on carrier mediated transport, which can represent either facilitated diffusion or obligatory exchange (also referred to as uniport and antiport mechanisms, respectively). In vitro measurements of serine uptake by placental microvillous membrane vesicles were carried out and the model applied to interpret the results based on the measured apparent Michaelis–Menten parameters Km and Vmax. In addition, based on model predictions, a new time series experiment was implemented to distinguish the hypothesised transporter mechanisms. Analysis of the results indicated the presence of a facilitated transport component, while based on the model no evidence for substantial levels of endogenous amino acids within the vesicle was found.

Computational modelling of placental amino acid transfer as an integrated system

Placental amino acid transfer is essential for fetal development and its impairment is associated with poor fetal growth. Amino acid transfer is mediated by a broad array of specific plasma membrane transporters with overlapping substrate specificity. However, it is not fully understood how these different transporters work together to mediate net flux across the placenta. Therefore the aim of this study was to develop a new computational model to describe how human placental amino acid transfer functions as an integrated system. Amino acid transfer from mother to fetus requires transport across the two plasma membranes of the placental syncytiotrophoblast, each of which contains a distinct complement of transporter proteins. A compartmental modelling approach was combined with a carrier based modelling framework to represent the kinetics of the individual accumulative, exchange and facilitative classes of transporters on each plasma membrane. The model successfully captured the principal features of transplacental transfer. Modelling results clearly demonstrate how modulating transporter activity and conditions such as phenylketonuria, can increase the transfer of certain groups of amino acids, but that this comes at the cost of decreasing the transfer of others, which has implications for developing clinical treatment options in the placenta and other transporting epithelia.

Asymptotic solution of a model for bilayer organic diodes and solar cells

Organic diodes and solar cells are constructed by placing together two organic semiconducting materials with dissimilar electron affinities and ionization potentials. The electrical behavior of such devices has been successfully modeled numerically using conventional drift diffusion together with recombination (which is usually assumed to be bimolecular) and thermal generation. Here a particular model is considered and the dark current-voltage curve and the spatial structure of the solution across the device is extracted analytically using asymptotic methods. We concentrate on the case of Shockley--Read--Hall recombination but note the extension to other recombination mechanisms. We find that there are three regimes of behavior, dependent on the total current. For small currents---i.e., at reverse bias or moderate forward bias---the structure of the solution is independent of the total current. For large currents---i.e., at strong forward bias---the current varies linearly with the voltage and is primaril...

Stem Cell Differentiation as a Non-Markov Stochastic Process

Summary Pluripotent stem cells can self-renew in culture and differentiate along all somatic lineages in vivo. While much is known about the molecular basis of pluripotency, the mechanisms of differentiation remain unclear. Here, we profile individual mouse embryonic stem cells as they progress along the neuronal lineage. We observe that cells pass from the pluripotent state to the neuronal state via an intermediate epiblast-like state. However, analysis of the rate at which cells enter and exit these observed cell states using a hidden Markov model indicates the presence of a chain of unobserved molecular states that each cell transits through stochastically in sequence. This chain of hidden states allows individual cells to record their position on the differentiation trajectory, thereby encoding a simple form of cellular memory. We suggest a statistical mechanics interpretation of these results that distinguishes between functionally distinct cellular “macrostates” and functionally similar molecular “microstates” and propose a model of stem cell differentiation as a non-Markov stochastic process.

Extracellular Matrix Deposition in Engineered Micromass Cartilage Pellet Cultures: Measurements and Modelling.

This article explores possible mechanisms governing extracellular matrix deposition in engineered cartilaginous cell pellets. A theoretical investigation is carried out alongside an experimental study measuring proteoglycan and collagen volume fractions within murine chondrogenic (ATDC-5) cell pellets. The simple mathematical model, which adopts a nutrient-dependent proteoglycan production rate, successfully reproduces the periphery-dominated proteoglycan deposition, characteristic of the growth pattern observed experimentally within pellets after 21 days of culture. The results suggest that this inhomogeneous proteoglycan production is due to nutrient deficiencies at the pellet centre. Our model analysis further indicates that a spatially uniform distribution of proteoglycan matrix could be maintained by initiating the culture process with a smaller-sized pellet. Finally, possible extensions are put forward with an aim to improve the model predictions for the early behaviour, where different mechanisms appear to dominate the matrix production within the pellets.

Influence of constraints on axial growth reduction of cylindrical Li-ion battery electrode particles

Abstract Volumetric expansion of silicon anode particles in a lithium-ion battery during charging may lead to the generation of undesirable internal stresses. For a cylindrical particle such growth may also lead to failure by buckling if the expansion is constrained in the axial direction due to other particles or supporting structures. To mitigate this problem, the possibility of reducing axial growth is investigated theoretically by studying simple modifications of the solid cylinder geometry. First, an annular cylinder is considered with lithiation either from the inside or from the outside. In both cases, the reduction of axial growth is not found to be significant. Next, explicit physical constraints are studied by addition of a non-growing elasto-plastic material: first, an outer annular constraint on a solid silicon cylinder, and second a rod-like inner constraint for an annular silicon cylinder. In both cases, it is found that axial growth can be reduced if the yield stress of the constraining material is significantly higher than that of silicon and/or the thickness of the constraint is relatively high. Phase diagrams are presented for both the outer and the inner constraint cases to identify desirable operating zones. Finally, to interpret the phase diagrams and isolate the key physical principles two different simplified models are presented and are shown to recover important qualitative trends of the numerical simulation results.

Stem cell differentiation is a stochastic process with memory

Pluripotent stem cells are able to self-renew indefinitely in culture and differentiate into all somatic cell types in vivo. While much is known about the molecular basis of pluripotency, the molecular mechanisms of lineage commitment are complex and only partially understood. Here, using a combination of single cell profiling and mathematical modeling, we examine the differentiation dynamics of individual mouse embryonic stem cells (ESCs) as they progress from the ground state of pluripotency along the neuronal lineage. In accordance with previous reports we find that cells do not transit directly from the pluripotent state to the neuronal state, but rather first stochastically permeate an intermediate primed pluripotent state, similar to that found in the maturing epiblast in development. However, analysis of rate at which individual cells enter and exit this intermediate metastable state using a hidden Markov model reveals that the observed ESC and epiblast-like ‘macrostates’ conceal a chain of unobserved cellular ‘microstates’, which individual cells transit through stochastically in sequence. These hidden microstates ensure that individual cells spend well-defined periods of time in each functional macrostate and encode a simple form of epigenetic ‘memory’ that allows individual cells to record their position on the differentiation trajectory. To examine the generality of this model we also consider the differentiation of mouse hematopoietic stem cells along the myeloid lineage and observe remarkably similar dynamics, suggesting a general underlying process. Based upon these results we suggest a statistical mechanics view of cellular identities that distinguishes between functionally-distinct macrostates and the many functionally-similar molecular microstates associated with each macrostate. Taken together these results indicate that differentiation is a discrete stochastic process amenable to analysis using the tools of statistical mechanics.