Robustness, flexibility, and sensitivity in a multifunctional motor control model.

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.

The significance of dynamical architecture for adaptive responses to mechanical loads during rhythmic behavior.

Many behaviors require reliably generating sequences of motor activity while adapting the activity to incoming sensory information. This process has often been conceptually explained as either fully dependent on sensory input (a chain reflex) or fully independent of sensory input (an idealized central pattern generator, or CPG), although the consensus of the field is that most neural pattern generators lie somewhere between these two extremes. Many mathematical models of neural pattern generators use limit cycles to generate the sequence of behaviors, but other models, such as a heteroclinic channel (an attracting chain of saddle points), have been suggested. To explore the range of intermediate behaviors between CPGs and chain reflexes, in this paper we describe a nominal model of swallowing in Aplysia californica. Depending upon the value of a single parameter, the model can transition from a generic limit cycle regime to a heteroclinic regime (where the trajectory slows as it passes near saddle points). We then study the behavior of the system in these two regimes and compare the behavior of the models with behavior recorded in the animal in vivo and in vitro. We show that while both pattern generators can generate similar behavior, the stable heteroclinic channel can better respond to changes in sensory input induced by load, and that the response matches the changes seen when a load is added in vivo. We then show that the underlying stable heteroclinic channel architecture exhibits dramatic slowing of activity when sensory and endogenous input is reduced, and show that similar slowing with removal of proprioception is seen in vitro. Finally, we show that the distributions of burst lengths seen in vivo are better matched by the distribution expected from a system operating in the heteroclinic regime than that expected from a generic limit cycle. These observations suggest that generic limit cycle models may fail to capture key aspects of Aplysia feeding behavior, and that alternative architectures such as heteroclinic channels may provide better descriptions.

The consequences of rare sexual reproduction by means of selfing in an otherwise clonally reproducing species.

Clonal reproduction of diploids leads to an increase in heterozygosity over time. A single round of selfing will then create new homozygotic genotypes. Given the same allele frequencies, heritable genetic variation is larger when there are more extreme, i.e. homozygotic genotypes. So after a long clonal expansion, one round of selfing increases heritable genetic variation, but any fully or partially recessive deleterious alleles simultaneously impose a fitness cost. Here we calculate that the cost of selfing in the yeast Saccharomyces is experienced only by a minority of zygotes. This allows a round of selfing to act as an evolutionary capacitor to unlock genetic variation previously found in a cryptic heterozygous form. We calculate the evolutionary consequences rather than the evolutionary causes of sex. We explore a range of parameter values describing sexual frequencies, focusing especially on the parameter values known for wild Saccharomyces. Our results are largely robust to many other parameter value choices, so long as meiosis is rare relative to the strength of selection on heterozygotes. Results may also be limited to organisms with a small number of genes. We therefore expect the same phenomenon in some other species with similar reproductive strategies.