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P K Maini

Publications and source records attributed to P K Maini.

12 recordsLinked to original sources
PubMed1992

Sequential pattern formation in a model for skin morphogenesis.

During morphogenesis regular patterns often develop behind a frontier of pattern formation which travels across the prospective tissue. Here the authors consider the propagating patterns exhibited in a two-dimensional domain by a tissue interaction mechanochemical model for skin pattern formation. It is shown that the model can exhibit travelling waves of complex spatial pattern formation. Two alternative mechanisms that can produce such sequential patterning are presented. In particular, it is demonstrated that the specification of a simple quasi-one-dimensional pattern is all that is required to determine a complex two-dimensional pattern. Finally, the model solutions are related to actual pattern propagation during chick feather primordia initiation.

Animals↗
PubMed1991

Bifurcating spatially heterogeneous solutions in a chemotaxis model for biological pattern generation.

We consider a simple cell-chemotaxis model for spatial pattern formation on two-dimensional domains proposed by Oster and Murray (1989, J. exp. Zool. 251, 186-202). We determine finite-amplitude, steady-state, spatially heterogeneous solutions and study the effect of domain growth on the resulting patterns. We also investigate in-depth bifurcating solutions as the chemotactic parameter varies. This numerical study shows that this deceptively simple-chemotaxis model can produce a surprisingly rich spectrum of complex spatial patterns.

Animals↗
PubMed1991

Analysis of a risk-based model for the growth of AIDS infection.

Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the features of these more complex models. Analytical expressions are derived for the time to the state of maximum infection (SMI) in a particular risk group, the proportion infected at SMI, and the number of infected individuals as the group approaches SMI. These results agree qualitatively with numerical simulations of the model.

Acquired Immunodeficiency Syndrome↗
PubMed1990

On the kinetics of suicide substrates.

We consider a realistic suicide substrate reaction which can be represented by four rate equations for the concentrations of the various molecules as functions of time. We present a general procedure to obtain accurate, approximate solutions analytically in terms of the rate equation parameters. This systematic technique provides more accurate approximations to the exact (numerical) solutions than other approximate methods which have been proposed based on a pseudo-steady state hypothesis.

Enzyme Inhibitors↗
PubMed1990

Superposition of modes in a caricature of a model for morphogenesis.

In a model proposed for cell pattern formation by Nagorcka et al. (J. Theor. Biol. 1987) linear analysis revealed the possibility of an initially spatially uniform cell density going unstable to perturbations of two distinct spatial modes. Here we examine a simple one-dimensional caricature of their model which exhibits similar linear behaviour and present a nonlinear analysis which shows the possibility of superposition of modes subject to appropriate parameter values and initial conditions.

Animals↗
PubMed1989

On the spatial spread of the grey squirrel in Britain.

We present a diffusion-competition model to describe the interaction between the externally introduced grey squirrel and the indigenous red squirrel in Britain. We estimate the model parameters from field data. Solution of the model predicts waves of grey squirrel invasion with speed of invasion typical of that observed in the field. Numerical solution of the model on a two-dimensional domain gives population distributions qualitatively similar to those observed. We suggest that competition alone could account for the observed displacement of the red squirrel by the grey in large regions of Britain. The solutions are qualitatively similar to those for a single species spreading in the absence of competition. The quantitative difference is because competition slows down the speed of advance of the invading species.

Animals↗
PubMed1989

Spatial and spatio-temporal patterns in a cell-haptotaxis model.

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.

Animals↗
PubMed1988

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios.

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.

Enzymes↗
PubMed1986

Nonlinear pattern selection in a mechanical model for morphogenesis.

We present a numerical study of the nonlinear mechanical model for morphogenesis proposed by Oster et al. (1983) with the aim of establishing the pattern forming capability of the model. We present a technique for mode selection based on linear analysis and show that, in many cases, it is a reliable predictor for nonlinear mode selection. In order to determine the set of model parameters that can generate a particular pattern we develop a technique based on nonlinear least square fitting to a dispersion relation. As an application we present a scenario for sequential pattern formation of dermal aggregations in chick embryos which leads to the hexagonal array of cell aggregations observed in feather germ formation in vivo.

Animals↗
PubMed1985

A model for chondrogenic condensations in the developing limb: the role of extracellular matrix and cell tractions.

The hyaluronate component of the extracellular matrix is a powerfully hydrophilic polymer, capable of osmotically swelling and deswelling by a volume factor of 5 or more. At the time of cartilage condensation in the limb bud the chondrocytes start to produce hyaluronidase, an enzyme which degrades hyaluronate. The consequent deswelling brings the chondrocytes closer together - close enough for intercellular cell tractions to become effective and intercellular junctions to form. By analysing the physicochemical situation we show how these processes, principally the coupling of the osmotic deswelling with cellular traction forces, can produce cartilage condensation patterns resembling those in the early limb bud. In distinction from our earlier model for chondrogenic condensations this mechanism does not depend on cell motions other than convective transport by contraction.

Animals↗