Cellular Automata Modeling of Stem‐Cell‐Driven Development of Tissue in the Nervous System

Mathematical and computational modeling enables biologists to integrate data from observations and experiments into a theoretical framework. In this review, we describe how developmental processes associated with stem‐cell‐driven growth of tissue in both the embryonic and adult nervous system can be modeled using cellular automata (CA). A cellular automaton is defined by its discrete nature in time, space, and state. The discrete space is represented by a uniform grid or lattice containing agents that interact with other agents within their local neighborhood. This possibility of local interactions of agents makes the cellular automata approach particularly well suited for studying through modeling how complex patterns at the tissue level emerge from fundamental developmental processes (such as proliferation, migration, differentiation, and death) at the single‐cell level. As part of this review, we provide a primer for how to define biologically inspired rules governing these processes so that they can be implemented into a CA model. We then demonstrate the power of the CA approach by presenting simulations (in the form of figures and movies) based on building models of three developmental systems: the formation of the enteric nervous system through invasion by neural crest cells; the growth of normal and tumorous neurospheres induced by proliferation of adult neural stem/progenitor cells; and the neural fate specification through lateral inhibition of embryonic stem cells in the neurogenic region of Drosophila.     

Structural and functional regeneration after spinal cord injury in the weakly electric teleost fish, <Emphasis Type="Italic">Apteronotus</Emphasis><Emphasis Type="Italic">leptorhynchus</Emphasis>

In contrast to mammals, teleost fish exhibit an enormous potential to regenerate adult spinal cord tissue after injury. However, the mechanisms mediating this ability are largely unknown. Here, we analyzed the major processes underlying structural and functional regeneration after amputation of the caudal portion of the spinal cord in Apteronotus leptorhynchus, a weakly electric teleost. After a transient wave of apoptotic cell death, cell proliferation started to increase 5 days after the lesion and persisted at high levels for at least 50 days. New cells differentiated into neurons, glia, and ependymal cells. Retrograde tract tracing revealed axonal re-growth and innervation of the regenerate. Functional regeneration was demonstrated by recovery of the amplitude of the electric organ discharge, a behavior generated by spinal motoneurons. Computer simulations indicated that the observed rates of apoptotic cell death and cell proliferation can adequately explain the re-growth of the spinal cord. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Neurogenesis and neuronal regeneration in the adult fish brain

Fish are distinctive in their enormous potential to continuously produce new neurons in the adult brain, whereas in mammals adult neurogenesis is restricted to the olfactory bulb and the hippocampus. In fish new neurons are not only generated in structures homologous to those two regions, but also in dozens of other brain areas. In some regions of the fish brain, such as the optic tectum, the new cells remain near the proliferation zones in the course of their further development. In others, as in most subdivisions of the cerebellum, they migrate, often guided by radial glial fibers, to specific target areas. Approximately 50% of the young cells undergo apoptotic cell death, whereas the others survive for the rest of the fish’s life. A large number of the surviving cells differentiate into neurons. Two key factors enabling highly efficient brain repair in fish after injuries involve the elimination of damaged cells by apoptosis (instead of necrosis, the dominant type of cell death in mammals) and the replacement of cells lost to injury by newly generated ones. Proteome analysis has suggested well over 100 proteins, including two dozen identified ones, to be involved in the individual steps of this phenomenon of neuronal regeneration.     

Numerical chromosome variation and mitotic segregation defects in the adult brain of teleost fish

Teleost fish are distinguished by their enormous potential for the generation of new cells in both the intact and the injured adult brain. Here, we present evidence that these cells are a genetic mosaic caused by somatic genomic alteration. Metaphase chromosome spreads from whole brains of the teleost Apteronotus leptorhynchus revealed an euploid complement of 22 chromosomes in only 22% of the cells examined. The rate of aneuploidy is substantially higher in brain cells than in liver cells, as shown by both metaphase chromosome spreads and flow cytometric analysis. Among the aneuploid cells in the brain, approximately 84% had fewer, and the remaining 16% more, than 22 chromosomes. Typically, multiple chromosomes were lost or gained. The aneuploidy is putatively caused by segregation defects during mitotic division. Labeling of condensed chromosomes of M-phase cells by phosphorylated histone-H3 revealed laggards, anaphase bridges, and micronuclei, all three of which indicate displaced mitotic chromosomes. Quantitative analysis has shown that in the entire brain on average 14% of all phosphorylated histone-H3-labeled cells exhibit such signs of segregation defects. Together with the recent discovery of aneuploidy in the adult mammalian brain, the results of the present investigation suggest that the loss or gain of chromosomes might provide a mechanism to regulate gene expression during development of new cells in the adult vertebrate brain.     

Use of spectral analysis to test hypotheses on the origin of pinnipeds

The evolutionary origin of the pinnipeds (seals, sea lions, and walruses) is still uncertain. Most authors support a hypothesis of a monophyletic origin of the pinnipeds from a caniform carnivore. A minority view suggests a diphyletic origin with true seals being related to the mustelids (otters and ferrets). The phylogenetic relationships of the walrus to other pinniped and carnivore families are also still particularly problematic. Here we examined the relative support for mono- and diphyletic hypotheses using DNA sequence data from the mitochondrial small subunit (12S) rRNA and cytochrome b genes. We first analyzed a small group of taxa representing the three pinniped families (Phocidae, Otariidae, and Odobenidae) and caniform carnivore families thought to be related to them. We inferred phylogenetic reconstructions from DNA sequence data using standard parsimony and neighbor-joining algorithms for phylogenetic inference as well as a new method called spectral analysis (Hendy and Penny) in which phylogenetic information is displayed independently of any selected tree. We identified and compensated for potential sources of error known to lead to selection of incorrect phylogenetic trees. These include sampling error, unequal evolutionary rates on lineages, unequal nucleotide composition among lineages, unequal rates of change at different sites, and inappropriate tree selection criteria. To correct for these errors, we performed additional transformations of the observed substitution patterns in the sequence data, applied more stringent structural constraints to the analyses, and included several additional taxa to help resolve long, unbranched lineages in the tree. We find that there is strong support for a monophyletic origin of the pinnipeds from within the caniform carnivores, close to the bear/raccoon/panda radiation. Evidence for a diphyletic origin was very weak and can be partially attributed to unequal nucleotide compositions among the taxa analyzed. Subsequently, there is slightly more evidence for grouping the walrus with the eared seals versus the true seals. A more conservative interpretation, however, is that the walrus is an early, but not the first, independent divergence from the common pinniped ancestor.      

Spontaneous modulations of the electric organ discharge in the weakly electric fish, Apteronotus leptorhynchus: a biophysical and behavioral analysis

Brown ghosts, Apteronotus leptorhynchus, are weakly electric gymnotiform fish whose wave-like electric organ discharges are distinguished by their enormous degree of regularity. Despite this constancy, two major types of transient electric organ discharge modulations occur: gradual frequency rises, which are characterized by a relatively fast increase in electric organ discharge frequency and a slow return to baseline frequency; and chirps, brief and complex frequency and amplitude modulations. Although in spontaneously generated gradual frequency rises both duration and amount of the frequency increase are highly variable, no distinct subtypes appear to exist. This contrasts with spontaneously generated chirps which could be divided into four "natural" subtypes based on duration, amount of frequency increase and amplitude reduction, and time-course of the frequency change. Under non-evoked conditions, gradual frequency rises and chirps occur rather rarely. External stimulation with an electrical sine wave mimicking the electric field of a neighboring fish leads to a dramatic increase in the rate of chirping not only during the 30 s of stimulation, but also in the period immediately following the stimulation. The rate of occurrence of gradual frequency rises is, however, unaffected by such a stimulation regime.     

Adult neurogenesis in the brain of the Mozambique tilapia, Oreochromis mossambicus

Although the generation of new neurons in the adult nervous system ('adult neurogenesis') has been studied intensively in recent years, little is known about this phenomenon in non-mammalian vertebrates. Here, we examined the generation, migration, and differentiation of new neurons and glial cells in the Mozambique tilapia (Oreochromis mossambicus), a representative of one of the largest vertebrate taxonomic orders, the perciform fish. The vast majority of new cells in the brain are born in specific proliferation zones of the olfactory bulb; the dorsal and ventral telencephalon; the periventricular nucleus of the posterior tuberculum, optic tectum, and nucleus recessi lateralis of the diencephalon; and the valvula cerebelli, corpus cerebelli, and lobus caudalis of the cerebellum. As shown in the olfactory bulb and the lateral part of the valvula cerebelli, some of the young cells migrate from their site of origin to specific target areas. Labeling of mitotic cells with the thymidine analog 5-bromo-2'-deoxyuridine, combined with immunostaining against the neuron-specific marker protein Hu or against the astroglial marker glial fibrillary acidic protein demonstrated differentiation of the adult-born cells into both neurons and glia. Taken together, the present investigation supports the hypothesis that adult neurogenesis is an evolutionarily conserved vertebrate trait.