Biomedical subjects

N F Britton

Publications and source records attributed to N F Britton.

At least 19 recordsLinked to original sources

PubMed2005

Pollen limitation or mate search need not induce an Allee effect.

When a process modelling the availability of gametes is included explicitly in population models a critical depensation or Allee effect usually results. Non-spatial models cannot describe clumping and so small populations must be assumed very diffuse. Consequently individuals in small populations experience low contact rates and so reproduction is limited. In Nature invasions into new territory are unlikely to be as diffuse as those described by non-spatial models. We develop pair approximations to a probabilistic cellular automata model with independent pollination and seed setting processes (equivalently mate search and reproduction processes). Each process can be either global (population-wide) or local (within a small neighbourhood) or a mixture of the two. When either process is global the resulting model recaptures the Allee effect found in non-spatial models. However, if both processes are at least partially local we obtain a model in which Allee effects can be avoided altogether if individuals are suitably strong pollinators and colonisers. The Allee effect disappears because small populations are dramatically more clumped when colonisation is local and less wasteful of pollen when pollination is local.

Algorithms↗

PubMed2005

Space mediates coexistence of females and hermaphrodites.

In gynodioecious populations of flowering plants females and hermaphrodites coexist. Gynodioecy is widespread and occurs in both asexual and sexual species but does not admit a satisfactory explanation from classical sex ratio theory. In sexual populations male fertility restoring genes have evolved to counter non-nuclear male sterility mutations. In pseudogamous asexual populations pollen retention and increased self-fertilization can make male sterility costly. Both of these mechanisms can promote coexistence. However, it remains unclear how either of these mechanisms could evolve if coexistence was not initially possible. In the absence of these adaptations non-spatial models predict that females either fail to invade hermaphrodite populations or else displace them until pollen shortage drives the population to extinction. We develop a pair approximation to a probabilistic cellular automata model in which females and hermaphrodites interact on a regular lattice. The model features independent pollination and colonization processes which take place on different timescales. The timescale separation is exploited to obtain, with perturbation methods, a more manageable aggregated pair approximation. We present both the mean field model which recreates the classical non-spatial predictions and the pair approximation, which strikingly predicts different invasion criteria and coexistence under a wide range of parameters. The pair approximation is shown to correspond well qualitatively with simulation behaviour.

Models, Biological↗

PubMed2004

Endosperm triploidy has a selective advantage during ongoing parental conflict by imprinting.

The endosperm of the flowering plant mediates the supply of maternal resources for embryogenesis. An endosperm formed in sexual reproduction between diploid parents is typically triploid, with a 2 : 1 ratio of maternal genetic material (denoted as 2m : 1p). Variation from this ratio affects endosperm size, indicating parent-specific expression of genes involved in endosperm growth and development. The presence of paternally or maternally imprinted genes can be explained by parental conflict over the transfer of nutrients from maternal to offspring tissue. Genomic imprinting can, for example, provide the male parent of an embryo in a mixed-paternity seed pod, with an opportunity for expressing its preference for a disproportionate allocation of resources to its embryo. It has been argued that a diploid 1m : 1p endosperm was ancestral and the 2m : 1p endosperm evolved after parental conflict, to improve maternal control over seed provisioning. We present a population genetic model, which instead places the origin of triploidy early in the parental conflict over resource allocation. We find that there is an advantage to having a triploid endosperm as the parental conflict continues. This advantage can help to explain why the 2m : 1p endosperm prevails among flowering plants.

Genetics, Population↗

PubMed2004

The effects of spatial movement and group interactions on disease dynamics of social animals.

The effects of spatial movements of infected and susceptible individuals on disease dynamics is not well understood. Empirical studies on the spatial spread of disease and behaviour of infected individuals are few and theoretical studies may be useful to explore different scenarios. Hence due to lack of detail in empirical studies, theoretical models have become necessary tools in investigating the disease influence in host-pathogen systems. In this paper we developed and analysed a spatially explicit model of two interacting social groups of animals of the same species. We investigated how the movement scenarios of susceptible and infected individuals together with the between-group contact parameter affect the survival rate of susceptible individuals in each group. This work can easily be applied to various host-pathogen systems. We define bounds on the number of susceptibles which avoid infection once the disease has died out as a function of the initial conditions and other model parameters. For example, once disease has passed through the populations, a larger diffusion coefficient for each group can result in higher population levels when there is no between-group interaction but in lower levels when there is between-group interaction. Numerical simulations are used to demonstrate these bounds and behaviours and to describe the different outcomes in ecological terms.

Animals↗

PubMed2002

Modelling natural burst firing in nigral dopamine neurons.

The natural burst firing observed in vivo in mesolimbic dopamine neurons is of great significance regarding these neurons' involvement in response to sensory stimuli associated with primary reward. The cellular mechanisms underlying a natural burst have been experimentally characterized previously and hypothesized to be caused by a calcium-sensitive inactivation of a potassium channel. We present a mathematical model of a mesolimbic neuron that demonstrates how such a mechanism can produce realistic bursting patterns, but only when combined with an appropriately timed membrane depolarization from an external source.

Action Potentials↗

PubMed2002

Deciding on a new home: how do honeybees agree?

A swarm of honeybees (Apis mellifera) is capable of selecting one nest-site when faced with a choice of several. We adapt classical mathematical models of disease, information and competing beliefs to such decision-making processes. We show that the collective decision may be arrived at without the necessity for any bee to make any comparison between sites.

Animals↗

PubMed2001

Arms races and the evolution of big fierce societies.

The causes of biological gigantism have received much attention, but only for individual organisms. What selection pressures might favour the evolution of gigantic societies? Here we consider the largest single-queen insect societies, those of the Old World army ant Dorylus, single colonies of which can have 20 million workers. We propose that colony gigantism in Dorylus arises as a result of an arms race and test this prediction by developing a size-structured mathematical model. We use this model for exploring and potentially explaining differences in colony size, colony aggression and colony propagation strategies in populations of New World army ants Eciton and Old World army ants Dorylus. The model shows that, by determining evolutionarily stable strategies (ESSs), differences in the trophic levels at which these army ants live feed forwards into differences in their densities and collision rates and, hence, into different strategies of growth, aggression and propagation. The model predicts large colony size and the occurrence of battles and a colony-propagation strategy involving highly asymmetrical divisions in Dorylus and that Eciton colonies should be smaller, non-combative and exhibit equitable binary fission. These ESSs are in excellent agreement with field observations and demonstrate that gargantuan societies can arise through arms races.

Aggression↗

PubMed2000

The possible role of reaction-diffusion in leaf shape.

We consider mechanisms that may determine certain simple leaf shapes. Compared with other aspects of plant morphogenesis, such as phyllotaxis or spiral leaf arrangement, rather little is known about leaf-shape-determining mechanisms. We develop mathematical models for the gross pattern of leaf shape based on reaction diffusion systems. These models are consistent with what is known about factors that might determine leaf shape. They show that diverse leaf shapes may be obtained from a single reaction diffusion system. This has implications in terms of both convergent and divergent evolution. The models make predictions that can be tested experimentally. We predict the form of pre-patterns of growth promoters in leaf primordia of different sizes when the morphogens either diffuse into the primordia or are produced locally. We also predict the effects on leaf shape of removing parts of primordia at different times. The models can also predict the effects on leaf shape of the topical application of activators and inhibitors to leaf primordia.

Biological Evolution↗

PubMed1996

On the mathematical modelling of pain.

In this review a case is presented for the use of mathematical modelling in the study of pain. The philosophy of mathematical modelling is outlined and a recommendation is made for the use of modern nonlinear techniques and computational neuroscience in the modelling of pain. Classic and more recent examples of modelling in neurobiology in general and pain in particular, at three different levels-molecular, cellular and neural networks-are described and evaluated. Directions for further progress are indicated, particularly in plasticity and in modelling brain mechanisms. Major advantages of mathematical modelling are that it can handle extremely complex theories and it is non-invasive, and so is particularly valuable in the investigation of chronic pain.

Analgesia↗

PubMed1996

The role of N-methyl-D-aspartate (NMDA) receptors in wind-up: a mathematical model.

We present a mathematical model for the phenomenon of wind-up (Mendell, 1966, Exper. Neur. 16,316-22) which occurs in many neurons. We concentrate on its occurrence in the substantia gelatinosa of the dorsal horns of the spinal cord, where it is connected with certain pathological and nonpathological pain states. The model is a development of the model by Britton & Skevington (1989, J. Theor. Biol. 137, 91-105) for Melzack & Wall's gate control theory of pain (1965, Science, New York, 150, 971-9; 1982, The Challenge of Pain, Penguin: Harmondsworth), modified to take account of more recent information. Its variables are the electric potentials of various cells in the midbrain and the spinal cord. Britton & Skevington's original model simulated many of the phenomena observed in acute pain in humans, but not the wind-up mechanism. This is not surprising, since this model did not include the N-methyl-D-aspartate (NMDA) receptors that are now recognized as being crucial to the phenomenon. Here we rectify this omission, and obtain good agreement between the model and experimental data on wind-up. The positive feedback that NMDA receptors exhibit is shown to be the essential feature in producing wind-up. As an independent test of the model we simulate a completely different experimental set-up, and obtain good qualitative agreement with data there. Finally, we present a prediction of the model that has yet to be tested experimentally.

Animals↗

PubMed1993

A qualitative analysis of some models of tissue growth.

Using maximum principles for parabolic and elliptic operators, we examine, in a general way, some models of tissue growth. These typically consist of a model mechanism for the diffusion of a mitotic inhibitor (growth inhibitory factor, GIF) throughout the tissue. Central to the modeling is the inclusion of a source function that models the production of GIF throughout the tissue. We examine the effect this term has on the resulting distribution of GIF in the tissue and comment on the appropriateness of different source functions, in particular a uniform production rate or a nonuniform production rate of inhibitor. Given that it is more appropriate to infer from the patterns of mitosis that are observed experimentally in various tissues the GIF concentration profile rather than the source function profile, it may be more appropriate to use these types of models to determine the qualitative form of the source term rather than proposing this function a priori.

Animals↗

PubMed1993

On the concentration profile of a growth inhibitory factor in multicell spheroids.

A mathematical model is presented for the production of a growth inhibitory factor (GIF) within a multicell spheroid. The main assumption of the model is that the GIF is produced by cells within the spheroid in some prescribed nonlinear, spatially dependent manner. Given that the diffusion of the GIF is known to take place over a much shorter time scale than that of spheroid growth, the steady-state profile of the GIF in various spheroids of differing radii is examined and theoretical results are compared with actual experimental data.

Animals↗

PubMed1989

A mathematical model of the gate control theory of pain.

The first test which any theory of pain must pass is that it must be able to explain the phenomena observed in acute pain in humans. This criterion is used to test the major theory of pain at present, the gate control theory of Melzack & Wall (1965, 1982). The theory is explicit enough to be cast in mathematical terms, and the mathematical model is shown to explain the observations considered. It also points up a common misconception on the consequences of the theory, and thus demolishes an argument which has been used against it. A hypothesis of the origin of rhythmic pain is then made, and consequent testable predictions given. This is the first time that the gate control theory has been used to explain any quality of pain. It has important consequences for the treatment of such pain. Finally, the applicability of the gate control theory as an explanation for chronic pain is discussed.

Humans↗

PubMed1989

Aggregation and the competitive exclusion principle.

A mathematical model for aggregation in a single animal population is set up. It relies on two premises. First, there is an advantage to individuals in the population in grouping together, for example for social purposes or to reduce the risk of predation. Second, the intra-specific competition at a point depends not simply on the population density at that point but on the average population density near the point, since the animals may move to find resources. The model is then extended to competing populations, and inter-specific competition is also assumed to depend on an average population density. It is shown that the resulting aggregation may lead to the co-existence of populations one of which would otherwise be excluded by the other. This finding is discussed with regard to the Competitive Exclusion Principle.

Animals↗

PubMed1988

A singular dispersion relation arising in a caricature of a model for morphogenesis.

In 1983 Oster et al. proposed a model for morphogenesis consisting of a system of partial differential equations in which the dispersion relation for the problem linearised about the zero solution has a singularity. That is, the initial growth rate sigma of a small perturbation of wave number k from the zero solution tends to positive or negative infinity as k tends to some critical value kc from above or below respectively. We consider here as a caricature of the model a single partial differential equation with a similar dispersion relation in a bounded one-dimensional domain. The wave number, or equivalently the domain size, may be thought of as a bifurcation parameter. For the Neumann problem a phenomenon arises in which, as the domain size l increases past a critical value ln, the linear stability of the n-th mode jumps from one solution to a remote solution. That is, for l less than ln the trivial solution is unstable and a certain non-trivial solution is stable to perturbations of mode n, whereas for l greater than ln the opposite is true. For the Dirichlet or the Robin problem a linear stability change in the trivial solution occurs, but no corresponding change in any other solution has been found. The corresponding initial boundary value problems are then considered. An asymptotic analysis is performed in the weakly nonlinear limit in the particular case in which only one mode is unstable and gives an asymptotic solution for two classes of nonlinearity, one symmetric and the other asymmetric about u = 0. A development of the method of harmonic balance is then used to obtain approximate solutions in the strongly nonlinear case and when more than one mode may be unstable.

Mathematics↗

PubMed1987

Mathematical models for a G0 phase in Saccharomyces cerevisiae.

Three models for the cell cycle of the budding yeast, Saccharomyces cerevisiae, which include a reversible G0 phase during proliferation, are presented. The analysis gives estimates for various quantities of biological interest, such as the probability of entry to and rate of exit from the G0 phase, the average duration of a cell in the G0 phase, the cycle time of cycling daughters and the population doubling time of cycling cells, none of which is easily measurable.

Cell Cycle↗

PubMed1987

Self-esteem and perception of attractiveness: an investigation of early rheumatoid arthritis.

During an investigation into the self-esteem of early rheumatoid patients and controls matched individually by age and sex, it was found that at their first visit to out-patients, patients had lower self-esteem. The items of low self-esteem showed a similarity with features of the rheumatoid personality. An observation that the word attractive in the Carlson Adjective Checklist was rarely used by both groups, and that items at the beginning and end of the checklist were less often ticked, led to a second study of 67 undergraduates where the position of the word attractive was experimentally varied in three forms of the scale. The results show that position only marginally affects response to this item. Probability analyses confirm that the word attractive is used very rarely by patients, rarely by healthy adults and less often than expected by healthy students, possibly demonstrating the respective effects of pain and illness, and age. Attractive tends to be included in the self-concept only after self-esteem reaches a relatively high level.

Adolescent↗

PubMed1984

A mathematical model for a thermal clearance probe.

We introduce a new mathematical model for a thermal clearance probe for the measurement of skin blood flow. It is concluded that the technique is more sensitive to differences in the thermal conductivity of the skin than to differences in blood flow. The depth of measurement is also considered.

Body Temperature Regulation↗