Competitive Tuning Among Ca2+/Calmodulin-Dependent Proteins: Analysis of in silico Model Robustness and Parameter Variability

Fitting and comparison of calcium-calmodulin kinetic schemes to a common data set using non-linear mixed effects modelling

Calmodulin is a calcium binding protein that is essential in calcium signalling in the brain. There are many computational models of calcium-calmodulin binding that capture various calmodulin features. However, existing models have generally been fit to different data sets, with some publications not reporting their training and validation performance. Moreover, there is no model comparison using a common benchmark data set as is common practice in other modeling domains. Finally, some calmodulin models have been fit as a part of a larger kinetic scheme, which may have resulted in parameters being underdetermined. We address these three limitations of previous models by fitting the published calcium-calmodulin schemes to a common calcium-calmodulin data set comprising equilibrium data from Shifman et al. and dynamical data from Faas et al. Due to technical limitations, the amount of uncaged calcium in Faas et al. data could not be predicted with certainty. To find good parameter fits, despite this uncertainty, we used non-linear mixed effects modelling as implemented in the Pumas.jl package. The Akaike information criterion values for our reaction rate constants were significantly lower than for the published parameters, indicating that the published parameters are suboptimal. Moreover, there were significant differences in calmodulin activation, both between the schemes and between our reaction rate and those previously published. A kinetic scheme with independent lobes and unique, rather than identical, binding sites fit the data best. Our results support two hypotheses: (1) partially bound calmodulin is important in cellular signalling; and (2) calcium binding sites within a calmodulin lobe are kinetically distinct rather than identical. We conclude that more attention should be given to validation and comparison of models of individual molecules.

Making time and space for calcium control of neuron activity

Calcium directly controls or indirectly regulates numerous functions that are critical for neuronal network activity. Intracellular calcium concentration is tightly regulated by numerous molecular mechanisms because spatial domains and temporal dynamics (not just peak amplitude) are critical for calcium control of synaptic plasticity and ion channel activation, which in turn determine neuron spiking activity. The computational models investigating calcium control are valuable because experiments achieving high spatial and temporal resolution simultaneously are technically unfeasible. Simulations of calcium nanodomains reveal that specific calcium sources can couple to specific calcium targets, providing a mechanism to determine the direction of synaptic plasticity. Cooperativity of calcium domains opposes specificity, suggesting that the dendritic branch might be the preferred computational unit of the neuron.

A Modeling and Analysis Study Reveals That CaMKII in Synaptic Plasticity Is a Dominant Affecter in CaM Systems in a T286 Phosphorylation-Dependent Manner

NMDAR-dependent synaptic plasticity in the hippocampus consists of two opposing forces: long-term potentiation (LTP), which strengthens synapses and long-term depression (LTD), which weakens synapses. LTP and LTD are associated with memory formation and loss, respectively. Synaptic plasticity is controlled at a molecular level by Ca2+-mediated protein signaling. Here, Ca2+ binds the protein, calmodulin (CaM), which modulates synaptic plasticity in both directions. This is because Ca2+-bound CaM activates both LTD-and LTP-inducing proteins. Understanding how CaM responds to Ca2+ signaling and how this translates into synaptic plasticity is therefore important to understanding synaptic plasticity induction. In this paper, CaM activation by Ca2+ and calmodulin binding to downstream proteins was mathematically modeled using differential equations. Simulations were monitored with and without theoretical knockouts and, global sensitivity analyses were performed to determine how Ca2+/CaM signaling occurred at various Ca2+ signals when CaM levels were limiting. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM becoming redistributed from low-affinity to high-affinity binding targets. Specifically, CaM was redistributed away from LTD-inducing proteins to bind the high-affinity LTP-inducing protein, calmodulin-dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM-binding protein targets. The model thereby showed a novel form of CaM signaling by which the two opposing pathways crosstalk indirectly. The model also found that CaMKII can repress cAMP production by repressing CaM-regulated proteins, which catalyze cAMP production. The model also found that at low Ca2+ stimulation levels, typical of LTD induction, CaM signaling was unstable and is therefore unlikely to alone be enough to induce synaptic depression. Overall, this paper demonstrates how limiting levels of CaM may be a fundamental aspect of Ca2+ regulated signaling which allows crosstalk among proteins without requiring directly interaction.

Overcoming Compensatory Mechanisms toward Chronic Drug Administration to Ensure Long-Term, Sustainable Beneficial Effects

Chronic administration of drugs leads to the activation of compensatory mechanisms that may inhibit some of their activity and induce unwanted toxicity. These mechanisms are an obstacle for maintaining a sustainable effect for many chronic medications. Pathways that adapt to the burden induced by chronic drugs, whether or not related to the underlying disease, can lead to a partial or complete loss of effect. Variability characterizes many biological systems and manifests itself as large intra- and inter-individual differences in the response to drugs. Circadian rhythm-based chronotherapy is further associated with variability in responses noted among patients. This paper reviews current knowledge regarding the loss of effect of chronic medications and the range of variabilities that have been described in responses and loss of responses. Establishment of a personalized platform for overcoming these prohibitive mechanisms is presented as a model for ensuring long-term sustained medication effects. This novel platform implements personalized variability signatures and individualized circadian rhythms for preventing and opposing the prohibitive effect of the compensatory mechanisms induced by chronic drug administration.