Developmental canalization can enhance species survival.

We investigate the behavior of haploid, asexual populations undergoing an evolutionary process. Each individual is endowed with a genotype, and one of several possible developmental mechanisms mapping this genotype onto a phenotype. We show that various properties of the mapping itself have important consequences for the survival of the groups. The populations which are most successful, both alone (but in a changing environment) as well as in competition against other groups (for which the mapping is different) consist of organisms where gene expression is characterized by pleiotropism, polygenic inheritance, and some amount of canalization (i.e. error damping). These same features lead to the appearance of patterns of punctuated equilibrium during evolution. Punctuated evolution was sometimes observed even in the absence of stabilizing selection; it then arose solely from the internal developmental constraints.

Accurate reading of morphogen concentrations by nuclear receptors: a formal model of complex transduction pathways.

Signal transduction in development follows multiple, interactive, and overlapping pathways. How does this contribute to accuracy and stability? I show that a formal model of retinoic acid receptors, based on the details of their molecular biology, demonstrates striking precision and robustness while converting a graded morphogen distribution into gene transcription patterns. Thus, transcription can be reliably established in a single row of cells, despite the absence, in the model, of intercellular signalling mechanisms. The subtle interplay of two nuclear receptor types is fundamental for this achievement: one of them ubiquitous, the other controlled itself by morphogen, they act as homodimers or heterodimers, ensuring that many errors cancel out by affecting both activation and repression pathways; regulatory molecular "reservoirs" are also formed. In spite of this robustness, some shifts in gene regulation may well have interesting evolutionary consequences. These conclusions regarding precision in transduction will remain of interest whether retinoic acid turns out to be a morphogen or not, and generalize easily to other experimental situations.

Genetics and epigenetics of neural function: a model.

A neural model for one- or few-trial irreversible behavior learning such as occurs in imprinting is introduced. It is assumed that synaptic connections in the relevant parts of the central nervous system are initially set up in a largely, but not totally random fashion, as a result, for instance, of differential cell-cell adhesion. The behavior to be learned is then sometimes exhibited, but not in a reproducible, mature way. During early neural activity, active postsynaptic neurons may, however, deliver a putative retrograde trophic factor to some of their afferent synaptic boutons. This is taken to occur according to a Hebb-type rule. At a later stage, only those synapses that have accumulated enough trophic factor are stabilized selectively. We show explicitly how this process may lead to a perfectly wired circuit. The calculations indicate that if the connections were relatively well defined from the beginning, then random pulses at the inputs suffice for this refinement process to take place. This is analogous to the maturation of neural circuits under spontaneous electrical activity (unsupervised learning). If the initial connections are "fuzzy," however, well-defined patterns of activation are needed at the inputs so that selective stabilization leads to a correct functional system (the model now behaves in an instructionist mode). Experiments suggested by the model are discussed, and involve the manipulation of afferent inputs, of the initial synapse distribution, or of the stabilization phase.

Morphogen propagation and action: towards molecular models.

Theoretical views on morphogen gradients have altered dramatically with the massive arrival of molecular data regarding the establishment of graded concentrations in the embryo, and the finely tuned reading by cells of these concentration levels. I review these new perspectives, and analyze in detail two models, one pertaining to the propagation of activin in Xenopus embryos, the other to the interpretation of retinoic acid levels into transcription patterns by nuclear receptors. The unifying threads that seem to emerge are the combinatorial uses of receptor subtypes, cooperativity and autocatalysis (positive feedback) to achieve specificity and reliability.

The survival of slow reproducers.

Multicellularity, and the attendant segregation of the germ line, entails the loss of reproductive capacity by the soma: in Volvox carteri, less than 1 cell in 100 contributes to the next generation. However, compensatory advantages are unlikely to be very large (Koufopanou & Bell, 1993. Proc. R. Soc. Lond. (B) 254,107-113). Somewhat similarly, sex implies the generation of males, hence a dramatic reproductive slowdown (Barton & Charlesworth, 1998. Science281, 1986-1990); yet, a compensating (two-fold) advantage of sex has not been found. Here, I try to evaluate the actual cost of maintaining slow reproductive cycles, namely cycles that necessitate the production of "dead end" units such as somatic cells or males. In a quantitative model for the competition of individuals with different, heritable reproductive rates, this cost turns out to be unexpectedly small, and may even sometimes become irrelevant. The bases for this are made fairly clear: thus, when all enjoy high fecundity (e.g. a long reproductive life) the handicap of a slower reproduction vanishes; alternatively, a slight separation of ecological niches may be sufficient for survival of slower but otherwise unchanged reproducers; and finally, inherent to slow reproduction is a low rate of destabilizing genetic change. These facts are largely independent of the formal model details, and are supported by direct computer simulations. They give a quantitative basis for analysing the evolution and prevalence of slow life cycles. The implications of these findings for the evolution of multicellularity are briefly discussed.

Mechanisms for positional signalling by morphogen transport: a theoretical study.

Gradients of cellular activities are ubiquitous in embryonic development. It is widely believed that the inhomogeneous spatial distribution of a morphogen would be able to set up such gradients. But how then does the morphogen propagate in the first place? Straightforward molecular diffusion is often proposed as a possible mechanism. We first show that, surprisingly, the mere binding of the diffusing morphogen to its membrane receptors suffices to prevent the establishment of a concentration-based positional signalling system. Instead, a flat, saturated distribution of receptor-bound morphogen builds up. Because the distribution spreads gradually from the morphogen source, however, cells may still know their position if they are able to integrate the morphogen signal in time. The irregularities of diffusion in the complex extracellular medium would in fact be partially compensated for by such time summation. Another, non-exclusive possibility is that morphogen transport does not occur by simple diffusion only. We put forth a novel model of receptor-aided, directed diffusion that achieves a spatial distribution of morphogen. Our model is based, as an illustration, on the properties of members of the TGFbeta family of molecules. We show that two simple hypotheses regarding the kinetics of TGBbeta binding to its receptors suffice to establish a remarkable transfer mechanism whereby a morphogen such as activin could be both propagated along cell membranes, and transferred between cells that are in contact. The model predicts that morphogen propagation properties depend strongly on the closeness of cell-cell appositions, does not necessitate protein synthesis, accumulation or slow degradation (in contrast to the diffusion/time integration model), and that the morphogen is localised mostly on or close to cell membranes.

Generation of synaptic noise: selective involvement of neuronal subsets.

All central neurons are subjected to continuous and random variations of their membrane potential because of "spontaneous" activity in their presynaptic afferents. This activity, which is called synaptic noise, is presumed to be responsible for the uncertainty of the input-output relation in these cells. In the Mauthner cell of teleosts, noise is mainly inhibitory, and is generated by the release of neurotransmitter in a probabilistic manner. This inhibitory activity has been studied in detail previously. Taking advantage of this understanding, we have constructed a model of the inhibitory networks and their target in order to determine the conditions required to reproduce the main stochastic aspects of synaptic noise. We have used a combination of computer simulations and simple semianalytical arguments. We conclude that, surprisingly, cells in the presynaptic networks do not contribute equally to these background fluctuations. Rather, noise is generated primarily by the operation of subsets of afferent cells: the spectrum is either dominated by signals originating from interneurons which make few terminals on the Mauthner cell, or by the output of "burster" cells firing spike trains rather than single spikes. Both possibilities lead to specific predictions, one of which has already been verified.

A clock and trail model for somite formation, specialization and polarization.

We present some theoretical considerations about the initial process of pre-patterning during embryonic segmentation, with particular reference to somite formation. We first suggest that the pre-pattern is a stable spatial sinusoidal (or, at least, periodic) wave. The periodic wave originates from an oscillator ("clock") in the proliferative region that gives rise to the cells. At the moment the cells leave the proliferative or "progress" zone, or somewhat later, a permanent record is made of the current state of the oscillation, which cells then keep during their pre-somitic phase, before explicit somite and somite boundary formation. Thus, a trail is left behind the progress zone in the form of a spatial sine wave. Second, we also observe that the factors involved in the progress-zone clock and its wave-like trail may form multimers, which will oscillate with higher space-time frequency and thus shorter wavelengths than the monomers. Whether or not our first suggestion is correct, this phenomenon may account for multiple wavelengths in somitogenesis, and may thus encompass somite formation, but also somite polarization (half-wavelength) into anterior and posterior halves, as well as the puzzling observation that expression of her1 in zebrafish is in primordia of alternating somites, i.e. it exhibits a 2-somite wavelength.

A simple molecular model of neurulation.

A molecular model for the morphogenesis of the central nervous system is built and solved by computer. The formalism rests on molecular-biological data gathered from insects and vertebrates during neural differentiation and neuronal fate specification. Two genetic, hierarchically organized switches are introduced, one associated with f1p4al tissue formation, and the other with neuronal specification. The model switches evolve in time, setting up very similar "prepatterns" of genetic activity in both insects and vertebrates, as observed experimentally. We introduce the hypothesis that cell adhesion and motion are regulated by the switches. If cell motion is turned on by the neural switch, the whole neural tissue (neural plate) thickens, buckles, and folds, ultimately creating a closed neural tube (primary neurulation). When mitoses are more frequent in neural plate tissue, ingression of a neural cell mass takes place instead (secondary neurulation). If cell motions are controlled by the neuronal switch, rather than by the neural one, the differentiation of isolated neuroblasts is observed, which delaminate individually (as in insect neural cord formation). The model thus displays the three major known patterns of neurogenesis; the transition between the vertebrate and insect cases is predicted to result from changes in genetic regulation downstream of the switch genes, and affecting cell adhesion and motility properties. Little is known experimentally about the concerned pathways: their importance as a fruitful area for future investigation is emphasized by our theoretical results.

A model for reading morphogenetic gradients: autocatalysis and competition at the gene level.

How are morphogenetic gradients interpreted in terms of embryonic gene transcription patterns within a syncytium such as the Drosophila blastoderm? We propose a hypothetical model based on recent findings in the molecular biology of transcription factors. The model postulates a morphogen which is itself a spatially distributed transcription factor M or which generates a distribution of such a factor. We posit the existence of an additional, zygotically transcribed "vernier" factor V. M and V form all possible dimers: MM, MV, and VV. These are differentially translocated to the nuclei and bind with various affinities to responsive elements in the V promoter, thereby contributing to activation/inactivation of V transcription. We find four generic regimes. In order of complexity, they are as follows: (i) MM activates V; the M gradient gives rise to a sharp transcriptional boundary for V and to a secondary gradient in the concentration of protein V; (ii) MV activates V; a sharp boundary in transcription and distribution of V arises; (iii) MM and MV compete for binding; a stationary stripe of active V transcription is generated; (iv) MM and VV are in competition; a stripe of V transcription moves from one end of the embryo toward the other and may stop and/or dwindle at an intermediate position. Tentative interpretations in terms of Drosophila genes such as bicoid and hunchback are presented.

How neurons may compute: the case of insect sexual pheromone discrimination.

Recognition of pheromone scent by male insects probably depends on analyzing the blend's composition in terms of relative concentrations of major and minor molecular components. Based on anatomical, physiological and behavioral data concerning certain moth species and the cockroach, we propose a simple, biologically plausible neural circuit which is able to perform this task reliably. The model employs oscillations as a detecting device. This principle is easily generalized to other systems. As a computational device, ratio detection may find applications in a variety of biological situations, e.g. in the olfactory system of all animals.

A neuronal model of a global workspace in effortful cognitive tasks.

A minimal hypothesis is proposed concerning the brain processes underlying effortful tasks. It distinguishes two main computational spaces: a unique global workspace composed of distributed and heavily interconnected neurons with long-range axons, and a set of specialized and modular perceptual, motor, memory, evaluative, and attentional processors. Workspace neurons are mobilized in effortful tasks for which the specialized processors do not suffice. They selectively mobilize or suppress, through descending connections, the contribution of specific processor neurons. In the course of task performance, workspace neurons become spontaneously coactivated, forming discrete though variable spatio-temporal patterns subject to modulation by vigilance signals and to selection by reward signals. A computer simulation of the Stroop task shows workspace activation to increase during acquisition of a novel task, effortful execution, and after errors. We outline predictions for spatio-temporal activation patterns during brain imaging, particularly about the contribution of dorsolateral prefrontal cortex and anterior cingulate to the workspace.