Identifying Crucial Parameter Correlations Maintaining Bursting Activity

Abstract

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, Leak; a persistent K current, K2; and of a persistent Na+ current, P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of Leak, K2, and P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.

Closed-loop control of a minimal central pattern generator network

“…see [27,11,28,29,30,31,32,33]). Although some studies have included the role of sensory feedback [34] in a half-center oscillator, the closed-loop control of the irregular activity in this minimal CPG circuit is largely understudied.…”

Analysis of Family Structures Reveals Robustness or Sensitivity of Bursting Activity to Parameter Variations in a Half-Center Oscillator (HCO) Model

“…The values for the maximal conductances and the leak reversal potential are the free parameters in the model. For our canonical model, these values are ḡ CaS = 3.2 nS, ḡ h = 4 nS, ḡ P = 7 nS, ḡ K2 = 80 nS, ḡ Leak = 8 nS, ḡ SynS = 60 nS, ḡ SynG = 30 nS, ḡ Na = 200 nS, ḡ CaF = 5 nS, ḡ K1 = 100 nS, ḡ KA = 80 nS, and E leak = −60 mV (Doloc-Mihu and Calabrese, 2011). The kinetics, voltage dependencies, reversal potentials of the intrinsic currents, and the synaptic connections of the HCO model interneurons have all been verified and previously adjusted to fit the biological data of leech interneurons (Hill et al, 2001).…”

“…To explore the HCO parameter space [maximal conductances (ḡ values) of intrinsic and synaptic currents], we simulated ∼10.5 million model instances, whose characteristics we recorded into a database named HCO-db (Doloc-Mihu and Calabrese, 2011). Here, we systematically explored the parameter space of two identified groups from the database: realistic HCOs or ( r HCOs), which show normal physiological activity with 99,066 instances; and functional HCOs ( f HCOs), which show nonphysiological but functional alternating bursting activity with 1.1 million instances.…”

Computational models in the age of large datasets

“…For example, even if one specifies quite rigidly the desired output of a neuronal network, the underlying parameters that can give rise to these properties is weakly constrained as multiple solutions to neuronal and network dynamics are found [19,20]. Subsequent work, informed by this general finding, explored families of models with parameters scattered over plausible ranges [21,22,23,24*]. Although these studies abandoned the idea of finding unique fits to data, they nonetheless revealed important principles about how specific combinations of conductances contribute to neuronal and network behavior [22,23], and how temperature-robust neuronal function might emerge in cold-blooded animals that experience significant changes in temperature [21,24*].…”

“…Second, biological systems have degenerate pathways and components, meaning that properties and functions of structurally distinct components overlap. While this confers robustness to the systems themselves, it means that models can be remarkably insensitive to many combinations of parameters [5**,21,22,23,27,29,30,31]. This ‘sloppy’ property of biological systems is well-documented in systems biology [8**] and neuroscientists may benefit from a wider appreciation of the tribulations and successes of model building in this sister field [32].…”