Channeling the Central Dogma

Synchronization of Bioelectric Oscillations in Networks of Nonexcitable Cells: From Single-Cell to Multicellular States

Biological networks use collective oscillations for information processing tasks. In particular, oscillatory membrane potentials have been observed in nonexcitable cells and bacterial communities where specific ion channel proteins contribute to the bioelectric coordination of large populations. We aim at describing theoretically the oscillatory spatiotemporal patterns that emerge at the multicellular level from the single-cell bioelectric dynamics. To this end, we focus on two key questions: (i) What single-cell properties are relevant to multicellular behavior? (ii) What properties defined at the multicellular level can allow an external control of the bioelectric dynamics? In particular, we explore the interplay between transcriptional and translational dynamics and membrane potential dynamics in a model multicellular ensemble, describe the spatiotemporal patterns that arise when the average electric potential allows groups of cells to act as a coordinated multicellular patch, and characterize the resulting synchronization phenomena. The simulations concern bioelectric networks and collective communication across different scales based on oscillatory and synchronization phenomena, thus shedding light on the physiological dynamics of a wide range of endogenous contexts across embryogenesis and regeneration.

Cell-cell bioelectrical interactions and local heterogeneities in genetic networks: a model for the stabilization of single-cell states and multicellular oscillations

Genetic networks operate in the presence of local heterogeneities in single-cell transcription and translation rates. Bioelectrical networks and spatio-temporal maps of cell electric potentials can influence multicellular ensembles. Could cell-cell bioelectrical interactions mediated by intercellular gap junctions contribute to the stabilization of multicellular states against local genetic heterogeneities? We theoretically analyze this question on the basis of two well-established experimental facts: (i) the membrane potential is a reliable read-out of the single-cell electrical state and (ii) when the cells are coupled together, their individual cell potentials can be influenced by ensemble-averaged electrical potentials. We propose a minimal biophysical model for the coupling between genetic and bioelectrical networks that associates the local changes occurring in the transcription and translation rates of an ion channel protein with abnormally low (depolarized) cell potentials. We then analyze the conditions under which the depolarization of a small region (patch) in a multicellular ensemble can be reverted by its bioelectrical coupling with the (normally polarized) neighboring cells. We show also that the coupling between genetic and bioelectric networks of non-excitable cells, modulated by average electric potentials at the multicellular ensemble level, can produce oscillatory phenomena. The simulations show the importance of single-cell potentials characteristic of polarized and depolarized states, the relative sizes of the abnormally polarized patch and the rest of the normally polarized ensemble, and intercellular coupling.

Intercellular Connectivity and Multicellular Bioelectric Oscillations in Nonexcitable Cells: A Biophysical Model

Bioelectricity is emerging as a crucial mechanism for signal transmission and processing from the single-cell level to multicellular domains. We explore theoretically the oscillatory dynamics that result from the coupling between the genetic and bioelectric descriptions of nonexcitable cells in multicellular ensembles, connecting the genetic prepatterns defined over the ensemble with the resulting spatio-temporal map of cell potentials. These prepatterns assume the existence of a small patch in the ensemble with locally low values of the genetic rate constants that produce a specific ion channel protein whose conductance promotes the cell-polarized state (inward-rectifying channel). In this way, the short-range interactions of the cells within the patch favor the depolarized membrane potential state, whereas the long-range interaction of the patch with the rest of the ensemble promotes the polarized state. The coupling between the local and long-range bioelectric signals allows a binary control of the patch membrane potentials, and alternating cell polarization and depolarization states can be maintained for optimal windows of the number of cells and the intercellular connectivity in the patch. The oscillatory phenomena emerge when the feedback between the single-cell bioelectric and genetic dynamics is coupled at the multicellular level. In this way, the intercellular connectivity acts as a regulatory mechanism for the bioelectrical oscillations. The simulation results are qualitatively discussed in the context of recent experimental studies.

Bioelectric signaling in regeneration: Mechanisms of ionic controls of growth and form

The ability to control pattern formation is critical for the both the embryonic development of complex structures as well as for the regeneration/repair of damaged or missing tissues and organs. In addition to chemical gradients and gene regulatory networks, endogenous ion flows are key regulators of cell behavior. Not only do bioelectric cues provide information needed for the initial development of structures, they also enable the robust restoration of normal pattern after injury. In order to expand our basic understanding of morphogenetic processes responsible for the repair of complex anatomy, we need to identify the roles of endogenous voltage gradients, ion flows, and electric fields. In complement to the current focus on molecular genetics, decoding the information transduced by bioelectric cues enhances our knowledge of the dynamic control of growth and pattern formation. Recent advances in science and technology place us in an exciting time to elucidate the interplay between molecular-genetic inputs and important biophysical cues that direct the creation of tissues and organs. Moving forward, these new insights enable additional approaches to direct cell behavior and may result in profound advances in augmentation of regenerative capacity.

The interplay between genetic and bioelectrical signaling permits a spatial regionalisation of membrane potentials in model multicellular ensembles

The single cell-centred approach emphasises ion channels as specific proteins that determine individual properties, disregarding their contribution to multicellular outcomes. We simulate the interplay between genetic and bioelectrical signals in non-excitable cells from the local single-cell level to the long range multicellular ensemble. The single-cell genetic regulation is based on mean-field kinetic equations involving the mRNA and protein concentrations. The transcription rate factor is assumed to depend on the absolute value of the cell potential, which is dictated by the voltage-gated cell ion channels and the intercellular gap junctions. The interplay between genetic and electrical signals may allow translating single-cell states into multicellular states which provide spatio-temporal information. The model results have clear implications for biological processes: (i) bioelectric signals can override slightly different genetic pre-patterns; (ii) ensembles of cells initially at the same potential can undergo an electrical regionalisation because of persistent genetic differences between adjacent spatial regions; and (iii) shifts in the normal cell electrical balance could trigger significant changes in the genetic regulation.

Consequences of degeneracy in network function

Often distinct elements serve similar functions within a network. However, it is unclear whether this network degeneracy is beneficial, or merely a reflection of tighter regulation of overall network performance relative to individual neuronal properties. We review circumstances where data strongly suggest that degeneracy is beneficial in that it makes network function more robust. Importantly, network degeneracy is likely to have functional consequences that are not widely appreciated. This is likely to be true when network activity is configured by modulators with persistent actions, and the history of network activity potentially impacts subsequent functioning. Data suggest that degeneracy in this context may be important for the creation of latent memories, and for state-dependent task switching.

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

The underlying mechanisms that support robustness in neuronal networks are as yet unknown. However, recent studies provide evidence that neuronal networks are robust to natural variations, modulation, and environmental perturbations of parameters, such as maximal conductances of intrinsic membrane and synaptic currents. Here we sought a method for assessing robustness, which might easily be applied to large brute-force databases of model instances. Starting with groups of instances with appropriate activity (e.g., tonic spiking), our method classifies instances into much smaller subgroups, called families, in which all members vary only by the one parameter that defines the family. By analyzing the structures of families, we developed measures of robustness for activity type. Then, we applied these measures to our previously developed model database, HCO-db, of a two-neuron half-center oscillator (HCO), a neuronal microcircuit from the leech heartbeat central pattern generator where the appropriate activity type is alternating bursting. In HCO-db, the maximal conductances of five intrinsic and two synaptic currents were varied over eight values (leak reversal potential also varied, five values). We focused on how variations of particular conductance parameters maintain normal alternating bursting activity while still allowing for functional modulation of period and spike frequency. We explored the trade-off between robustness of activity type and desirable change in activity characteristics when intrinsic conductances are altered and identified the hyperpolarization-activated (h) current as an ideal target for modulation. We also identified ensembles of model instances that closely approximate physiological activity and can be used in future modeling studies.