The effect of negative feedback loops on the dynamics of boolean networks

Feedback loops play an important role in determining the dynamics of biological networks. To study the role of negative feedback loops, this article introduces the notion of distance-to-positive-feedback which, in essence, captures the number of independent negative feedback loops in the network, a property inherent in the network topology. Through a computational study using Boolean networks, it is shown that distance-to-positive-feedback has a strong influence on network dynamics and correlates very well with the number and length of limit cycles in the phase space of the network. To be precise, it is shown that, as the number of independent negative feedback loops increases, the number (length) of limit cycles tends to decrease (increase). These conclusions are consistent with the fact that certain natural biological networks exhibit generally regular behavior and have fewer negative feedback loops than randomized networks with the same number of nodes and same connectivity.     

Boolean dynamics of biological networks with multiple coupled feedback loops

Boolean networks have been frequently used to study the dynamics of biological networks. In particular, there have been various studies showing that the network connectivity and the update rule of logical functions affect the dynamics of Boolean networks. There has been, however, relatively little attention paid to the dynamical role of a feedback loop, which is a circular chain of interactions between Boolean variables. We note that such feedback loops are ubiquitously found in various biological systems as multiple coupled structures and they are often the primary cause of complex dynamics. In this article, we investigate the relationship between the multiple coupled feedback loops and the dynamics of Boolean networks. We show that networks have a larger proportion of basins corresponding to fixed-point attractors as they have more coupled positive feedback loops, and a larger proportion of basins for limit-cycle attractors as they have more coupled negative feedback loops.     

Structural discrimination of robustness in transcriptional feedforward loops for pattern formation

Signaling pathways are interconnected to regulatory circuits for sensing the environment and expressing the appropriate genetic profile. In particular, gradients of diffusing molecules (morphogens) determine cell fate at a given position, dictating development and spatial organization. The feedforward loop (FFL) circuit is among the simplest genetic architectures able to generate one-stripe patterns by operating as an amplitude detection device, where high output levels are achieved at intermediate input ones. Here, using a heuristic optimization-based approach, we dissected the design space containing all possible topologies and parameter values of the FFL circuits. We explored the ability of being sensitive or adaptive to variations in the critical morphogen level where cell fate is switched. We found four different solutions for precision, corresponding to the four incoherent architectures, but remarkably only one mode for adaptiveness, the incoherent type 4 (I4-FFL). We further carried out a theoretical study to unveil the design principle for such structural discrimination, finding that the synergistic action and cooperative binding on the downstream promoter are instrumental to achieve absolute adaptive responses. Subsequently, we analyzed the robustness of these optimal circuits against perturbations in the kinetic parameters and molecular noise, which has allowed us to depict a scenario where adaptiveness, parameter sensitivity and noise tolerance are different, correlated facets of the robustness of the I4-FFL circuit. Strikingly, we showed a strong correlation between the input (environment-related) and the intrinsic (mutation-related) susceptibilities. Finally, we discussed the evolution of incoherent regulations in terms of multifunctionality and robustness.     

Connectomic constraints on computation in feedforward networks of spiking neurons

Several efforts are currently underway to decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function of the said circuit is unknown. We consider, here, the question of how the wiring diagram of neurons imposes constraints on what neural circuits can compute, when we cannot assume detailed information on the physiological response properties of the neurons. We call such constraints—that arise by virtue of the connectome—connectomic constraints on computation. For feedforward networks equipped with neurons that obey a deterministic spiking neuron model which satisfies a small number of properties, we ask if just by knowing the architecture of a network, we can rule out computations that it could be doing, no matter what response properties each of its neurons may have. We show results of this form, for certain classes of network architectures. On the other hand, we also prove that with the limited set of properties assumed for our model neurons, there are fundamental limits to the constraints imposed by network structure. Thus, our theory suggests that while connectomic constraints might restrict the computational ability of certain classes of network architectures, we may require more elaborate information on the properties of neurons in the network, before we can discern such results for other classes of networks.