Narrow Results

We study the computational capabilities of a biologically inspired neural model where the synaptic weights, the connectivity pattern, and the number of neurons can evolve over time rather than stay static. Our study focuses on the mere concept of plasticity of the model so that the nature of the updates is assumed to be not constrained. In this context, we show that the so-called plastic recurrent neural networks (RNNs) are capable of the precise super-Turing computational power — as the static analog neural networks — irrespective of whether their synaptic weights are modeled by rational or real numbers, and moreover, irrespective of whether their patterns of plasticity are restricted to bi-valued updates or expressed by any other more general form of updating. Consequently, the incorporation of only bi-valued plastic capabilities in a basic model of RNNs suffices to break the Turing barrier and achieve the super-Turing level of computation. The consideration of more general mechanisms of architectural plasticity or of real synaptic weights does not further increase the capabilities of the networks. These results support the claim that the general mechanism of plasticity is crucially involved in the computational and dynamical capabilities of biological neural networks. They further show that the super-Turing level of computation reflects in a suitable way the capabilities of brain-like models of computation.

The question of what properties of biological systems allow for efficient evolutionary search in complex fitness landscapes (evolvability) is one of the central interests both for the research in the field of evolutionary biology and artificial life. Here, we attempt to address this issue by using a model of 3D multicellular development in which cell fate is determined by differential gene expression in each cell. In our model, cells can vary in size and can move freely in 3D space, affected by forces of adhesion and repulsion. The development relies on an indirect mapping between the genotype and the morphology (the phenotype). Cell differentiation is allowed by positional information provided by diffusible factors. The state of the gene regulatory network (GRN) coded by the genome determines the cell fate (such as division, death, growth). The genetic elements in our systems define points in N-dimensional space. The connectivity in the GRN is determined by the proximity of these points; one can imagine the evolutionary process as their movement in space. Changing the number of dimensions of this space allows to ask directly the questions about the effect of the complexity of the search space on the efficiency of the evolutionary search. Higher dimensionality results in a larger search space, but in our model this search space can still be explored thanks to the action of genetic operators that allow for duplications of genetic elements, a mutational mechanism that allows for regulatory innovations in the network.

From the definition, it appears that phenotypic robustness and evolvability of an organism are inversely related to each other. However, a number of studies exploring this question have found conflicting evidences in this regard. This question motivated the current work where we explore the relationship between robustness and evolvability. As a model system, we pick the Feed Forward Loops (FFLs), and develop a framework to characterize their performance in terms of their ability to resist changes to steady state expression (robustness), and their ability to evolve towards novel phenotypes (evolvability). We demonstrate that robustness and evolvability are positively correlated in some FFL topologies. We compare this against other small regulatory topologies, and show that the same trend does not hold among them. We postulate that the ability to positively link robustness and evolvability could be an additional reason for over-representation of FFLs in living organisms, as compared to other regulatory topologies.

Recent computational modeling of early fruit fly (Drosophila) development has characterized the degree to which gene regulation networks can be robust to natural variability. In the first few hours of development, broad spatial gradients of maternally derived transcription factors activate embryonic gap genes. These gap patterns determine the subsequent segmented insect body plan through pair-rule gene expression. Gap genes are expressed with greater spatial precision than the maternal patterns. Computational modeling of the gap–gap regulatory interactions provides a mechanistic understanding for this robustness to maternal variability in wild-type (WT) patterning. A long-standing question in evolutionary biology has been how a system which is robust, such as the developmental program creating any particular species’ body plan, is also evolvable, i.e. how can a system evolve or speciate, if the WT form is strongly buffered and protected? In the present work, we use the WT model to explore the breakdown of such Waddington-type ‘canalization’. What levels of variability will push the system out of the WT form; are there particular pathways in the gene regulatory mechanism which are more susceptible to losing the WT form; and when robustness is lost, what types of forms are most likely to occur (i.e. what forms lie near the WT)? Manipulating maternal effects in several different pathways, we find a common gap ‘peak-to-step’ pattern transition in the loss of WT. We discuss these results in terms of the evolvability of insect segmentation, and in terms of experimental perturbations and mutations which could test the model predictions. We conclude by discussing the prospects for using continuum models of pattern dynamics to investigate a wider range of evo-devo problems.