Using Jensen's inequality to explain the role of regular calcium oscillations in protein activation

Differential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

Modeling the intracellular organization of calcium signaling

Calcium (Ca²⁺) is a key signaling ion that plays a fundamental role in many cellular processes in most types of tissues and organisms. The versatility of this signaling pathway is remarkable. Depending on the cell type and the stimulus, intracellular Ca²⁺ increases can last over different periods, as short spikes or more sustained signals. From a spatial point of view, they can be localized or invade the whole cell. Such a richness of behaviors is possible thanks to numerous exchange processes with the external medium or internal Ca²⁺ pools, mainly the endoplasmic or sarcoplasmic reticulum and mitochondria. These fluxes are also highly regulated. In order to get an accurate description of the spatiotemporal organization of Ca²⁺ signaling, it is useful to resort to modeling. Thus, each flux can be described by an appropriate kinetic expression. Ca²⁺ dynamics in a given cell type can then be simulated by a modular approach, consisting of the assembly of computational descriptions of the appropriate fluxes and regulations. Modeling can also be used to get insight into the mechanisms of decoding of the Ca²⁺ signals responsible for cellular responses. Cells can use frequency or amplitude coding, as well as take profit of Ca²⁺ oscillations to increase their sensitivity to small average Ca²⁺ increases.

Calmodulin and calmodulin kinase II mediate emergent bursting activity in the brainstem respiratory network (preBötzinger complex)

Emergence of persistent activity in networks can be controlled by intracellular signalling pathways but the mechanisms involved and their role are not yet fully explored. Using calcium imaging and patch-clamp we examined the rhythmic activity in the preBötzinger complex (preBötC) in the lower brainstem that generates the respiratory motor output. In functionally intact acute slices brief hypoxia, electrical stimulation and activation of AMPA receptors transiently depressed bursting activity which then recovered with augmentation. The effects were abrogated after chelation of intracellular calcium, blockade of L-type calcium channels and inhibition of calmodulin (CaM) and CaM kinase (CaMKII). Rhythmic calcium transients and synaptic drive currents in preBötC neurons in the organotypic slices showed similar CaM- and CaMKII-dependent responses. The stimuli increased the amplitude of spontaneous and miniature excitatory synaptic currents indicating postsynaptic changes at glutamatergic synapses. In the acute and organotypic slices, CaM stimulated and ADP inhibited calcium-dependent TRPM4 channels and CaMKII augmented synaptic drive currents. Experimental data and simulations show the role of ADP and CaMKII in the control of bursting activity and its relation to intracellular signalling. I propose that CaMKII-mediated facilitation of glutamatergic transmission strengthens emergent synchronous activity within preBötC that is then maintained by periodic surges of calcium during the bursts. This may find implications in restoration and consolidation of autonomous activity in the respiratory disorders.