L.E.H. Trainor

A field description of the cleavage process in embryogenesis.

Abstract The typical cleavage lines of holoblastic eggs are shown to bear a close correspondence to the nodal lines of selected harmonic functions on the sphere which result from a minimization principle for a generalized surface energy function and from the requirement of a binary cleavage process. The few degeneracies which occur are resolved by a weak polar field. The modifications which characterize radial, bilateral and spiral cleavage are analyzed in terms of secondary perturbing fields. The implications of this description in relation to laws of form and theories of organismic development are discussed.

A Parallel Distributed Model of the Behaviour of Ant Colonies

Members of an ant colony perform a variety of tasks outside the nest, such as foraging and nest maintenance work. The number of ants actively performing each task changes, because workers switch from one task to another and because workers are sometimes active, sometimes inactive. In field experiments with harvester ants ( Gordon, 1986 , Gordon, 1987 ), a perturbation that directly affects only the number of workers engaged in one task, causes changes in the numbers engaged in other activities. These dynamics must be the outcome of interactions among individuals; an ant cannot be expected to assess and respond to colony-level changes of behaviour. Here we present a parallel distributed model of the processes regulating changes in numbers of workers engaged in various tasks. The model is based on a Hopfield net, but differs from conventional Hopfield models in that when a unit or ant changes state, it changes its interaction patterns. Simulation results resemble experimental results; perturbations of one activity propagate to others. Depending on the pattern of interactions among worker groups, the distribution of active workers in different tasks either settles into a single, global attractor, or shows the dynamics associated with a landscape containing multiple attractors.

On the informational content of viral DNA

This paper is concerned primarily with how information is stored in viral DNA. The general problem of defining information content is discussed and a procedure for analysis extended from that of Gatlin (1972) is developed. Long range correlations in base sequences are analyzed for several viral genomes. The relationship of these correlations to the existence of strong codon biases is examined and the consequences discussed.

A thermodynamic theory of codon bias in viral genes

The relationship between degeneracy in the genetic code and the occurrence of a strong codon bias is examined, with particular reference to a group of viral genomes. The present paper shows how codon bias may have been imposed by thermodynamic considerations at the time the primitive DNA first formed in the primordial soup. Using a four-state Ising-like model with stacking interactions between successive base pairs, we show how primeval periodic DNA polymers could have arisen the remnants of which are still observed in codon biases today.

A non-linear field model of pattern formation: Intercalation in morphalactic regulation

Useful insights into pattern formation problems in regulating biological systems have been gained from the concept of positional information. In particular, the polar co-ordinate model of positional information ( French et al., 1976 , Science 193, 969–981) and its relatives (e.g. Bryant et al., 1981 , Science 212, 993–1002; Lewis, 1981 , J. theor. Biol. 88, 371–392; Mitthenthal, 1981 , Dev. Biol. 88, 15–26; Winfree, 1980 , The Geometry of Biological Time. New York: Springer) have helped to provide a qualitative framework for understanding epimorphic regulation, which involves localized growth and pattern formation at a discontinuity (e.g. at a cut surface). On the other hand, these models lack the formal structure to deal quantitatively with regulation; in particular, they are inadequate to treat morphallactic regulation, in which reorganization of the biological system occurs as a consequence of, e.g. changes in its size, rather than a distinct “discontinuity in the positional values”. To overcome this limitation, we propose a morphogenetic field model of pattern formation. We define a simple vector field (morphogenetic field) with generative dynamics arising from the minimization of a non-linear energy functional based on the positional information idea of an “optimal spacing of positional values” and an additional “smoothness” condition. As the system size is changed, transitions to solutions with pattern reversal regions take place, suggesting how reverse intercalation phenomena can arise in morphallactic regulation even without the presence of a discontinuity, as is observed in Tetrahymena doublets regulating to singlets ( Nelsen & Frankel, 1986 , Dev. Biol. 114, 53–71; Brandts & Trainor, 1990 ,J. theor. Biol. 146, 57–86). We view the success of our model as support for the unification of the formalism, phenomenology and concepts of physical theory with the foundations of theory in biology.

A non-linear vector field model of supernumerary limb production in salamanders†*

We critically analyze current data on supernumerary production in grafting experiments with salamanders and formulate a vector field model which captures the essence of these results in a unified and quantitative manner. The motivation for this work has been the difficulty other models have had in accounting for the data concerning ipsilateral grafts. The source of this difficulty is rooted in the boundary conditions imposed by continuity at the interfaces between the intercalary region and the stump and blastema tissues. In our approach supernumeraries arise in the intercalary region of the grafts as a result of symmetry-breaking bifurcations in the pattern specification field. This requires the pattern field to obey a non-linear dynamics which effects a coupling between the axial and proximo-distal components of the field. Steady state solutions of the model are presented which correspond to the production of normal supernumeraries. The number, positions and handedness of supernumeraries is, in general, well-predicted by the model for both contralateral and ipsilateral grafts. Twelve specific predictions are made which suggest future possible experiments.

Structure and function in biological hierarchies: An Ising model approach☆☆☆

Abstract In order to shed light upon the relationship between structure and function in biological systems, we investigate two simple hierarchically organized systems; namely, a two-level Ising-like system and a multi-level system introduced by Dyson in another context. Using equilibrium statistical mechanics we examine quantitatively the conditions for the functional decoupling of the levels in these model hierarchies.

Physical theory in biology : foundations and explorations

What is the physics of life and why does it matter? The essays in this book probe this question, celebrating modern biologys vibrant dialog with theoretical physics — a scientific adventure in which biological understanding is enriched by physical theory without losing its own inherent traditions and perspectives. The book explores organic complexity and self-organization through research applications to embryology, cell biology, behavioral neuroscience, and evolution. The essays will excite the interest of physics students in thinking about biologys “grand challenges”, in part by means of self-contained introductions to theoretical computer science, symmetry methods in bifurcation theory, and evolutionary games. Seasoned investigators in both the physical and life sciences will also find challenging ideas and applications presented in this volume.This is a Print On Demand title. We no longer stock the original but will recreate a copy for you. While all efforts are made to ensure that quality is the same as the original, there may be differences in some areas of the design and packaging.

On the statistical mechanics of constrained biophysical systems

A well-known class of biophysical models, first introduced by Kerner, is shown to admit a convenient Hamiltonian formulation in which motion through the phase space of system variables involves explicit constraints. To treat the macroscopic properties of such models, we develop an ensemble theory of systems subjected to phase space constraints. For such systems we obtain a generalized Hamiltonian statistical mechanics which preserves much of the structure and efficacy of the corresponding physical theory. In a first application of the method, we recover Kerners original “biological ensemble” as a special case involving information optimality and conservative biosystems.

A two vector field model of limb regeneration and transplant phenomena

We propose a new field description of limb regeneration in developmental biology. Central to our approach is the recognition of the importance of vector fields as descriptors in problems involving polarities or a sense of direction. In limb regeneration these vector fields represent the organisms sense of the distal direction, and its sense of the circumferential ordering of structures. Essentially all experimental results obtained to date are consistent with or explained by the model.