The spatiotemporal expression of genes in an organism is determined by regulatory systems that involve a large number of genes connected through a complex network of interactions. As an intuitive understanding of the behavior of these systems is hard to obtain, computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This report reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, ordinary and partial differential equations, stochastic equations, Boolean networks and their generalizations, qualitative differential equations, and rule-based formalisms. In addition, the report discusses how these formalisms have been used in the modeling and simulation of regulatory systems.

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Modeling and simulation of genetic regulatory systems: a literature review.

Limb muscles develop from cells that migrate from the somites. The signal that induces migration of myogenic precursor cells to the limb emanates from the mesenchyme of the limb bud. Here we report that the c-met-encoded receptor tyrosine kinase is essential for migration of myogenic precursor cells into the limb anlage and for migration into diaphragm and tip of tongue. In c-met homozygous mutant (-/-) mouse embryos, the limb bud and diaphragm are not colonized by myogenic precursor cells and, as a consequence, skeletal muscles of the limb and diaphragm do not form. In contrast, development of the axial skeletal muscles proceeds in the absence of c-met signalling. The specific ligand of the c-met protein, the motility and growth factor scatter factor/hepatocyte growth factor, is expressed in limb mesenchyme and can thus provide the signal for migration which is received by c-met. We have therefore identified a paracrine signalling system that regulates migration of myogenic precursor cells.

Essential role for the c-met receptor in the migration of myogenic precursor cells into the limb bud.

The role of fossils in dating the tree of life has been misunderstood. Fossils can provide good "minimum" age estimates for branches in the tree, but "maximum" constraints on those ages are poorer. Current debates about which are the "best" fossil dates for calibration move to consideration of the most appropriate constraints on the ages of tree nodes. Because fossil-based dates are constraints, and because molecular evolution is not perfectly clock-like, analysts should use more rather than fewer dates, but there has to be a balance between many genes and few dates versus many dates and few genes. We provide "hard" minimum and "soft" maximum age constraints for 30 divergences among key genome model organisms; these should contribute to better understanding of the dating of the animal tree of life.

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Paleontological Evidence to Date the Tree of Life

IN 1952, Turing proposed a hypothetical molecular mechanism, called the reaction–diffusion system1, which can develop periodic patterns from an initially homogeneous state. Many theoretical models based on reaction–diffusion have been proposed to account for patterning phenomena in morphogenesis2–4, but, as yet, there is no conclusive experimental evidence for the existence of such a system in the field of biology5–8. The marine angelfish, Pomacanthus has stripe patterns which are not fixed in their skin. Unlike mammal skin patterns, which simply enlarge proportionally during their body growth, the stripes of Pomacanthus maintain the spaces between the lines by the continuous rearrangement of the patterns. Although the pattern alteration varies depending on the conformation of the stripes, a simulation program based on a Turing system can correctly predict future patterns. The striking similarity between the actual and simulated pattern rearrangement strongly suggests that a reaction–diffusion wave is a viable mechanism for the stripe pattern of Pomacanthus.

A reaction-diffusion wave on the skin of the marine angelfish Pomacanthus

Functional studies seem now to confirm, as first suggested by E. Geoffrey Saint-Hilaire in 1822, that there was an inversion of the dorsoventral axis during animal evolution. A conserved system of extracellular signals provides positional information for the allocation of embryonic cells to specific tissue types both in Drosophila and vertebrates; the ventral region of Drosophila is homologous to the dorsal side of the vertebrate. Developmental studies are now revealing some of the characteristics of the ancestral animal that gave rise to the arthropod and mammalian lineages, for which we propose the name Urbilateria.

A common plan for dorsoventral patterning in Bilateria

The anterior end of the dorsal nerve cord of amphioxus is described at the 3-4 gill slit stage based on serial transmission electron microscopy and three-dimensional reconstruction, with special attention to structures that are potential landmarks for comparing amphioxus with other chordates. The larval nerve cord is divisible, at approximately the level of the first somite, into a short anterior region, the cerebral vesicle (c.v.), and an extended posterior region that is thought to include homologues of the vertebrate hindbrain and spinal cord. The c.v., in turn, has an anterior part with a tubular neural canal and a posterior part with a keyhole-shaped neural canal similar to that found in the rest of the cord. The junction between these two parts of the c.v. is marked by a cluster of infundibular cells. The anterior c.v., whose cells have cilia that point anteriorly, includes (i) a structure we call the frontal eye, consisting of a pigment spot and transverse rows of putative receptor and nerve cells, and (ii) several small ventral commissures bridging the major nerve tracts that run ventrolaterally along either side of the nerve cord. The posterior c.v., in contrast, contains cells whose cilia point posteriorly, and includes (i) the beginnings of the floorplate, which continues posteriorly through the rest of the nerve cord, (ii) the dorsal lamellar body, made up of cells with cilia that expand into flattened lamellae, and (iii) a large ventral commissure that incorporates fibres arising from cells of the lamellar body. Where probable homologues of c.v. structures can be identified in vertebrate brain, they are found in the diencephalon, which suggests the c.v. and the vertebrate diencephalon are, to a degree, homologous. On structural evidence, the frontal eye and the lamellar body are both ciliary photoreceptors, contrasting with the microvillar ocelli (organs of Hesse) distributed along most of the rest of the nerve cord. In young larvae the lamellar body is large and conspicuous. We suggest it functions as a high sensitivity, non-directional photoreceptor. The frontal eye is smaller, but organizationally more complex. We suggest it functions as a low sensitivity directional photoreceptor. The frontal eye is potentially of considerable interest from an evolutionary standpoint. Two issues are discussed: (i) that it is sufficiently similar in structure and organization to the paired eyes of vertebrates to indicate homology; and (ii) that its position at the extreme anterior end of the cord, together with structural and histochemical evidence, suggests it may derive from the apical organ, an evolutionarily ancient structure marking the embryonic anterior pole in diverse invertebrate phyla, whose homologue in chordates has hitherto not been identified.

Landmarks in the Anterior Central Nervous System of Amphioxus Larvae

The cells comprising the frontal eye of a 12.5 day amphioxus larva are described based on 3D reconstructions from serial electron micrographs, along with the fibre tracts and more caudal groupings of cells in the nerve cord to which the frontal eye appears to be linked. The frontal eye consists of a pigment cup, two transverse rows of receptor cells, and clusters of neurons whose close association with the medial receptor cells suggests they may function as an integral part of the eye complex. Neurites from both the receptor cells and neurons supply the ventrolateral nerve tracts, which consist mainly of axons arising from sensory cells located at the rostral tip of the larva. A core group of 3—4 rostral fibres on each side innervate two ventral giant cells located just behind the cerebral vesicle in the primary motor centre (PMC). The circuitry suggests these cells may be responsible for triggering the larval startle response. The ventrolateral tracts also include two types of axial dendrite-like fibres: (i) a single unpaired fibre, a forward continuation of the principal dendrite of the left giant cell, which is the main target for synapses from neurons in the frontal eye; and (ii) sets of paired fibres from cells in the tectum, a dorsal cortex-like structure located at the back of the cerebral vesicle through which the dorsal sensory nerves pass in transit to the PMC. Recent behavioural studies show that larvae feed in a hovering posture that maximally shades the frontal eye. They also orient to light in this position. The shape and orientation of the frontal eye suggests it could be responsible for this response. The existence of separate pathways from lateral and medial receptor cells, both directly and indirectly to the PMC, suggests the frontal eye may also be involved in modulating locomotory behaviour during hovering. The visual ‘system’ described here for amphioxus larvae is more like that of vertebrates than has previously been recognized. Specifically: ( i )the medial nerve cells of the frontal eye appear to form local circuits with relay and integrative functions similar to those of the retina, involving cell types that resemble specific retinal interneurons; and (ii) output is directed to a region at the back of the posterior c.v. that resembles the vertebrate midbrain, and which may be its homologue. This region has a dorsal tectum and, like the midbrain, includes the anterior part of a ventral zone of motoneurons and reticulospinal interneurons. The morphological evidence supports the idea that the ‘brain’ of amphioxus is sufficiently like that of vertebrates to provide important clues concerning the basic organization and subdivision of the vertebrate brain.

Frontal eye circuitry, rostral sensory pathways and brain organization in amphioxus larvae: evidence from 3D reconstructions

Amphioxus has an assortment of cells and organs for sensing light and mechanical stimuli. Vertebrate counterparts of these structures are not always apparent, and a strong case can be made for homology in only a few instances. For example, amphioxus has anatomically simple but plausible homologs of both the pineal and paired eyes of vertebrates. Placodal and neural crest derivatives are, however, more problematic: the evidence for an olfactory system in amphioxus is only circumstantial and, despite the variety of secondary sensory cell types that occur on the body surface in amphioxus, none are obvious homologs of vertebrate taste buds, neuromasts or acoustic hair cells. A useful perspective can nevertheless be gained by examining differences in amphioxus and vertebrate development, specifically how each specifies and positions sensory precursors, controls their proliferation, and deploys them through the body. The much larger size of vertebrate embryos and the need to cope developmentally with increased scale and cell numbers may account for some key vertebrate innovations, including placodes and neural crest. The presence or absence of specific structural adaptations, like the latter, is therefore less useful for judging homology between amphioxus and vertebrates than shared features of specific cell types. It is also clear that the duration of embryogenesis in vertebrates has been significantly extended in comparison with ancestral chordates so as to incorporate events that would originally have occurred during the post-embryonic growth period, including events of neurogenesis. Consequently, no scenario for the origin of vertebrates can be considered complete unless it deals explicitly with the whole of the life history and changes to it.

Sensory Systems in Amphioxus: A Window on the Ancestral Chordate Condition

Amphioxus neuroanatomy is important not just in its own right but also for the insights it provides regarding the evolutionary origin and basic organization of the vertebrate nervous system. This r...

The nervous system of amphioxus : structure, development, and evolutionary significance

Synopsis. The apical organ is a key structural landmark in a wide range of invertebrate larvae, but its homolog in chordates has not been iden? tified. A widely accepted explanation of chordate origins, Garstang's auri? cularia hypothesis, suggests several possibilities. Structural and biochem? ical evidence both support the idea that the apical organ, in amphioxus, has been incorporated into the frontal eye complex. Structural and posi? tional similarities between this eye-like structure and paired eyes in ver? tebrates suggest the two may be homologous. The implication is that the cells ofthe neural retina in vertebrates may be derivatives ofthe primitive apical organ. Other implications of Garstang's hypothesis are discussed: that it provides (1) an evolutionary rationale for the restriction of Hox expression in ectoderm to neural tissue, (2) grounds for doubting that the CNS in chordates and that of protostome invertebrates can in any way be homologous, and a starting point for exploring (3) whether the eyes of ancestral chordates were single or paired, and (4) the origin of the ver? tebrate telencephalon.

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Thurston C. Lacalli

Papers

Landmarks in the Anterior Central Nervous System of Amphioxus Larvae

Frontal eye circuitry, rostral sensory pathways and brain organization in amphioxus larvae: evidence from 3D reconstructions

Sensory Systems in Amphioxus: A Window on the Ancestral Chordate Condition

The nervous system of amphioxus : structure, development, and evolutionary significance

Apical Organs, Epithelial Domains, and the Origin of the Chordate Central Nervous System