George Oster

Size and shape in ontogeny and phylogeny

We present a quantitative method for describing how heterochronic changes in ontogeny relate to phyletic trends. This is a step towards creating a unified view of developmental biology and evolu- tionary ecology in the study of morphological evolution. Using this representation, we obtain a greatly simplified and logical scheme of classification. We believe that this scheme will be particularly useful in studying the data of paleontology and comparative morphology and in the analysis of processes leading to adaptive radiation. We illustrate this scheme by examples drawn from the literature and our own work.

Cellular motions and thermal fluctuations: the Brownian ratchet

We present here a model for how chemical reactions generate protrusive forces by rectifying Brownian motion. This sort of energy transduction drives a number of intracellular processes, including filopodial protrusion, propulsion of the bacterium Listeria, and protein translocation.

The mechanical basis of morphogenesis: I. Epithelial folding and invagination☆

We present a mechanical model for the morphogenetic folding of embryonic epithelia based on hypothesized mechanical properties of the cellular cytoskeleton. In our model we consider a simple cuboidal epithelium whose cells are joined at their apices by circumferential junctions; to these junctions are attached circumferential arrays of microfilament bundles assembled into a “purse string” around the cell apex. We assume that this purse string has the following property: if its circumference is increased beyond a certain threshold, an active contraction is initiated which “draws the purse-string” and reduces the apical circumference of the cell to a new, shorter, resting length. The remainder of the cell is modeled as a visoelastic body of constant volume. Clearly contraction in one cell could stretch the apical circumferences of neighboring cells and, if the threshold is exceeded, cause them “to fire” and contract. The objective of this paper is to demonstrate that our model, based on the local behavior of individual cells, generates a propagating contraction wave which is sufficient to explain the globally coherent morphogenetic infolding of a wide variety of embryonic epithelia. Representative computer simulations, based on the model, are presented for the initial gastrulation movements of echinoderms, neural tube formation in urodele amphibians, and ventral furrow formation in Drosophila.

Theoretical studies of clonal selection: Minimal antibody repertoire size and reliability of self-non-self discrimination☆

Abstract Viewing the immune system as a molecular recognition device designed to identify “foreign shapes”, we estimate the probability that an immune system with N Ab monospecific antibodies in its repertoire can recognize a random foreign antigen. Furthermore, we estimate the improvement in recognition if antibodies are multispecific rather than monospecific. From our probabilistic model we conclude: (1) clonal selection is feasible, i.e. with a finite number of antibodies an animal can recognize an effectively infinite number of antigens; (2) there should not be great differences in the specificities of antibody molecules among different species; (3) the region of a foreign molecule recognized by an antibody must be severely limited in extent; (4) the probability of recognizing a foreign molecule, P , increases with the antibody repertoire size N Ab ; however, below a certain value of N Ab the immune system would be very ineffectual, while beyond some high value of N Ab further increases in N Ab yield diminishing small increases in P ; (5) multispecificity is equivalent to a modest increase (probably less than 10) in the antibody repertoire size N Ab , but this increase can substantially improve the probability of an immune system recognizing a foreign molecule. Besides recognizing foreign molecules, the immune system must distinguish them from self molecules. Using the mathematical theory of reliability we argue that multisite recognition is a more reliable method of distinguishing between molecules than single site recognition. This may have been an important evolutionary consideration in the selection of weak non-covalent interactions as the basis of antigen-antibody bonds.

Energy transduction in ATP synthase

Mitochondria, bacteria and chloroplasts use the free energy stored in transmembrane ion gradients to manufacture ATP by the action of ATP synthase. This enzyme consists of two principal domains. The asymmetric membrane-spanning Fo portion contains the proton channel, and the soluble F1 portion contains three catalytic sites which cooperate in the synthetic reactions. The flow of protons through Fo is thought to generate a torque which is transmitted to F1 by an asymmetric shaft, the coiled-coil γ-subunit. This acts as a rotating ‘cam’ within F1, sequentially releasing ATPs from the three active sites. The free-energy difference across the inner membrane of mitochondria and bacteria is sufficient to produce three ATPs per twelve protons passing through the motor. It has been suggested that this protonmotive force biases the rotors diffusion so that Fo constitutes a rotary motor turning the γ shaft. Here we show that biased diffusion, augmented by electrostatic forces, does indeed generate sufficient torque to account for ATP production. Moreover, the motors reversibility — supplying torque from ATP hydrolysis in F1 converts the motor into an efficient proton pump — can also be explained by our model.

The dynamics of density dependent population models

SummaryThe dynamics of density-dependent population models can be extraordinarily complex as numerous authors have displayed in numerical simulations. Here we commence a theoretical analysis of the mathematical mechanisms underlying this complexity from the viewpoint of modern dynamical systems theory. After discussing the chaotic behavior of one-dimensional difference equations we proceed to illustrate the general theory on a density-dependent Leslie model with two age classes. The pattern of bifurcations away from the equilibrium point is investigated and the existence of a “strange attractor” is demonstrated — i.e. an attracting limit set which is neither an equilibrium nor a limit cycle. Near the strange attractor the system exhibits essentially random behavior. An approach to the statistical analysis of the dynamics in the chaotic regime is suggested. We then generalize our conclusions to higher dimensions and continuous models (e.g. the nonlinear von Foerster equation).

Energy transduction in the F1 motor of ATP synthase

ATP synthase is the universal enzyme that manufactures ATP from ADP and phosphate by using the energy derived from a transmembrane protonmotive gradient. It can also reverse itself and hydrolyse ATP to pump protons against an electrochemical gradient. ATP synthase carries out both its synthetic and hydrolytic cycles by a rotary mechanism. This has been confirmed in the direction of hydrolysis, after isolation of the soluble F1 portion of the protein and visualization of the actual rotation of the central ‘shaft’ of the enzyme with respect to the rest of the molecule, making ATP synthase the worlds smallest rotary engine. Here we present a model for this engine that accounts for its mechanochemical behaviour in both the hydrolysing and synthesizing directions. We conclude that the F1 motor achieves its high mechanical torque and almost 100% efficiency because it converts the free energy of ATP binding into elastic strain, which is then released by a coordinated kinetic and tightly coupled conformational mechanism to create a rotary torque.

Network thermodynamics: dynamic modelling of biophysical systems

The success of equilibrium thermodynamics in describing static phenomena has inspired many attempts to develop a rigorous thermodynamics of rate processes.

How Myxobacteria Glide

BACKGROUND Many microorganisms, including myxobacteria, cyanobacteria, and flexibacteria, move by gliding. Although gliding always describes a slow surface-associated translocation in the direction of the cells long axis, it can result from two very different propulsion mechanisms: social (S) motility and adventurous (A) motility. The force for S motility is generated by retraction of type 4 pili. A motility may be associated with the extrusion of slime, but evidence has been lacking, and how force might be generated has remained an enigma. Recently, nozzle-like structures were discovered in cyanobacteria from which slime emanated at the same rate at which the bacteria moved. This strongly implicates slime extrusion as a propulsion mechanism for gliding. RESULTS Here we show that similar but smaller nozzle-like structures are found in Myxococcus xanthus and that they are clustered at both cell poles, where one might expect propulsive organelles. Furthermore, light and electron microscopical observations show that slime is secreted in ribbons from the ends of cells. To test whether the slime propulsion hypothesis is physically reasonable, we construct a mathematical model of the slime nozzle to see if it can generate a force sufficient to propel M. xanthus at the observed velocities. The model assumes that the hydration of slime, a cationic polyelectrolyte, is the force-generating mechanism. CONCLUSIONS The discovery of nozzle-like organelles in various gliding bacteria suggests their role in prokaryotic gliding. Our calculations and our observations of slime trails demonstrate that slime extrusion from such nozzles can account for most of the observed properties of A motile gliding.

EVOLUTION AND MORPHOGENETIC RULES: THE SHAPE OF THE VERTEBRATE LIMB IN ONTOGENY AND PHYLOGENY

The notion of a “developmental constraint” has become a catchphrase for a collection of poorly defined notions about how ontogeny affects phylogeny. In this paper, we shall attempt to define this idea more precisely by examining the vertebrate limb from three viewpoints. First, theoretical models of morphogenesis suggest several generalizations about how limb geometry is laid down during development. Comparative studies and experimental manipulations of developing limbs independently confirm these generalizations, which amount to a set of “construction rules” for determining how the major features of limb architecture are established in ontogeny. Armed with these rules, we can inquire how limb morphology can be varied during evolution and suggest a more precise operational definition of “developmental constraints” on morphological evolution.