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.

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abstract: 1. The normal developmental pattern of voltage‐gated ion channel expression in embryonic skeletal muscle cells of the frog Xenopus laevis was disrupted by introduction of cloned rat brain Na+ channels. 2. Following injection of channel mRNA into fertilized eggs, large Na+ currents were observed in muscle cells at the earliest developmental stage at which they could be uniquely identified. Muscle cells normally have no voltage‐gated currents at this stage. 3. Muscle cells expressing exogenous Na+ channels showed increased expression of at least two classes of endogenous K+ currents. 4. This increase in K+ current expression was inhibited by the Na+ channel blocker tetrodotoxin, suggesting that increased electrical activity caused by Na+ channel mis‐expression triggers a compensatory increase in K+ channel expression. 5. Block of endogenous Na+ channels in later control myocytes retards K+ current development, indicating that a similar compensatory mechanism to that triggered by Na+ channel mis‐expression operates to balance Na+ and K+ current densities during normal muscle development.

title: Protein Ion Channels as Molecular Ratchets. Switchable Current Modulation in Outer Membrane Protein F Porin Induced by Millimolar La3+ Ions
abstract: The quest for innovative tunable nanodevices has mainly focused on switches that modulate their properties through engineered conformational changes. We propose here an alternative route that takes advantage of the crucial role that trace elements play in biological nanosystems. To this end, the effect of lanthanum, a high-valence rare-earth metal, known as blocker and modulator of many ion channels, has been studied in a wide, weakly selective biological pore, the bacterial porin outer membrane protein F (OmpF). We show that millimolar concentrations of lanthanum chloride have a dramatic impact on OmpF, reducing the conductance for positive but not for negative applied voltages, thus inducing switchable, reversible ion current rectification. By applying an external wave to this lanthanum-induced diode, we show that the system can consistently perform like a wave rectifier at considerably higher frequencies than previous nanofluidic diodes. This finding may be the starting point to develop molecular ratch...

title: Oscillations and temporal signalling in cells.
abstract: The development of new techniques to quantitatively measure gene expression in cells has shed light on a number of systems that display oscillations in protein concentration. Here we review the different mechanisms which can produce oscillations in gene expression or protein concentration using a framework of simple mathematical models. We focus on three eukaryotic genetic regulatory networks which show 'ultradian' oscillations, with a time period of the order of hours, and involve, respectively, proteins important for development (Hes1), apoptosis (p53) and immune response (NF-kappaB). We argue that underlying all three is a common design consisting of a negative feedback loop with time delay which is responsible for the oscillatory behaviour.

title: Kinetic models of gene expression including non-coding RNAs
abstract: In cells, genes are transcribed into mRNAs, and the latter are translated into proteins. Due to the feedbacks between these processes, the kinetics of gene expression may be complex even in the simplest genetic networks. The corresponding models have already been reviewed in the literature. A new avenue in this field is related to the recognition that the conventional scenario of gene expression is fully applicable only to prokaryotes whose genomes consist of tightly packed protein-coding sequences. In eukaryotic cells, in contrast, such sequences are relatively rare, and the rest of the genome includes numerous transcript units representing non-coding RNAs (ncRNAs). During the past decade, it has become clear that such RNAs play a crucial role in gene expression and accordingly influence a multitude of cellular processes both in the normal state and during diseases. The numerous biological functions of ncRNAs are based primarily on their abilities to silence genes via pairing with a target mRNA and subsequently preventing its translation or facilitating degradation of the mRNA-ncRNA complex. Many other abilities of ncRNAs have been discovered as well. Our review is focused on the available kinetic models describing the mRNA, ncRNA and protein interplay. In particular, we systematically present the simplest models without kinetic feedbacks, models containing feedbacks and predicting bistability and oscillations in simple genetic networks, and models describing the effect of ncRNAs on complex genetic networks. Mathematically, the presentation is based primarily on temporal mean-field kinetic equations. The stochastic and spatio-temporal effects are also briefly discussed.

title: Modelling the Effect of Gap Junction Nonlinearities in Systems of Coupled Cells
abstract: A general model for the transfer of ions and molecules between two cells via a gap junction is presented. This constitutes a dynamical system consisting of two connected parts: the dynamics of intracellular concentrations and electrical potentials, and the dynamics of the gating in the gap junction. The analysis focuses on a particular approximation in which the concentration changes are assumed negligible, so that the dynamics then describes the evolution of the potential differences across the cell membranes. This matches the conditions of voltage clamp experiments on Xenopus cell pairs. It is argued that the cell pair is unlikely to possess oscillatory behaviour; rather every initial state of the system evolves towards a stable steady state. It is shown that, in theory, coupled Xenopus cell pairs can demonstrate hysteretic behaviour for certain cell and junctional parameter ranges. The model fits data from recent electrophysiological experiments on Xenopus cell pairs. It is argued that cell pairs could operate under conditions in which hysteretic changes take place and we show that the hysteretic behaviour is more likely when the gap junction displays a residual conductance.

title: Defective gap junctional intercellular communication in the carcinogenic process.
abstract: Gap junctions are membrane structures made of intercellular channels which permit the diffusion from cytoplasm to cytoplasm of small hydrophilic molecules. Nearly 40 years ago, the loss of functional gap junctions has been described in cancer cells and led to the hypothesis that such type of intercellular communication is involved in the carcinogenesis process. From this time, a lot of data has been accumulated confirming that gap junctions are frequently decreased or absent in cancer cells whatever their tissue and species origins. Here, we review such data by insisting on the possible links existing between altered gap-junctional intercellular communication capacity (or the altered expression of their constitutive proteins, the connexins) and the stages of cancer progression in various cancer models. Then, we analyse particular aspects of the disturbance of connexin-mediated communication in cancer such as the cytoplasmic localization of connexins, the lack of heterologous communication between cancer cells and normal cells, the role of connexin gene mutations in cancer. In a separate part of the review, we also analyse the disturbance of gap-junctional intercellular communication during the late stages of cancer (invasion and metastasis processes).

title: MicroRNA Intercellular Transfer and Bioelectrical Regulation of Model Multicellular Ensembles by the Gap Junction Connectivity.
abstract: We have studied theoretically the microRNA (miRNA) intercellular transfer through voltage-gated gap junctions in terms of a biophysically grounded system of coupled differential equations. Instead of modeling a specific system, we use a general approach describing the interplay between the genetic mechanisms and the single-cell electric potentials. The dynamics of the multicellular ensemble are simulated under different conditions including spatially inhomogeneous transcription rates and local intercellular transfer of miRNAs. These processes result in spatiotemporal changes of miRNA, mRNA, and ion channel protein concentrations that eventually modify the bioelectrical states of small multicellular domains because of the ensemble average nature of the electrical potential. The simulations allow a qualitative understanding of the context-dependent nature of the effects observed when specific signaling molecules are transferred through gap junctions. The results suggest that an efficient miRNA intercellular transfer could permit the spatiotemporal control of small cellular domains by the conversion of single-cell genetic and bioelectric states into multicellular states regulated by the gap junction interconnectivity.

title: Membrane potential bistability in nonexcitable cells as described by inward and outward voltage-gated ion channels.
abstract: The membrane potential of nonexcitable cells, defined as the electrical potential difference between the cell cytoplasm and the extracellular environment when the current is zero, is controlled by the individual electrical conductance of different ion channels. In particular, inward- and outward-rectifying voltage-gated channels are crucial for cell hyperpolarization/depolarization processes, being amenable to direct physical study. High (in absolute value) negative membrane potentials are characteristic of terminally differentiated cells, while low membrane potentials are found in relatively depolarized, more plastic cells (e.g., stem, embryonic, and cancer cells). We study theoretically the hyperpolarized and depolarized values of the membrane potential, as well as the possibility to obtain a bistability behavior, using simplified models for the ion channels that regulate this potential. The bistability regions, which are defined in the multidimensional state space determining the cell state, can be relevant for the understanding of the different model cell states and the transitions between them, which are triggered by changes in the external environment.

title: Engineering biosynthetic excitable tissues from unexcitable cells for electrophysiological and cell therapy studies.
abstract: Patch-clamp recordings in single-cell expression systems have been traditionally used to study the function of ion channels. However, this experimental setting does not enable assessment of tissue-level function such as action potential (AP) conduction. Here we introduce a biosynthetic system that permits studies of both channel activity in single cells and electrical conduction in multicellular networks. We convert unexcitable somatic cells into an autonomous source of electrically excitable and conducting cells by stably expressing only three membrane channels. The specific roles that these expressed channels have on AP shape and conduction are revealed by different pharmacological and pacing protocols. Furthermore, we demonstrate that biosynthetic excitable cells and tissues can repair large conduction defects within primary 2- and 3-dimensional cardiac cell cultures. This approach enables novel studies of ion channel function in a reproducible tissue-level setting and may stimulate the development of new cell-based therapies for excitable tissue repair.

title: Local and long-range endogenous resting potential gradients antagonistically regulate apoptosis and proliferation in the embryonic CNS.
abstract: Bioelectric signals, particularly transmembrane voltage potentials (Vmem), play an important role in large-scale patterning during embryonic development. Endogenous bioelectric gradients across tissues function as instructive factors during eye, brain, and other morphogenetic processes. An important and still poorly-understood aspect is the control of cell behaviors by the voltage states of distant cell groups. Here, experimental alteration of endogenous Vmem was induced in Xenopus laevis embryos by misexpression of well-characterized ion channel mRNAs, a strategy often used to identify functional roles of Vmem gradients during embryonic development and regeneration. Immunofluorescence analysis (for activated caspase 3 and phosphor-histone H3P) on embryonic sections was used to characterize apoptosis and proliferation. Disrupting local bioelectric signals (within the developing neural tube region) increased caspase 3 and decreased H3P in the brain, resulting in brain mispatterning. Disrupting remote (ventral, non-neural region) bioelectric signals decreased caspase 3 and highly increased H3P within the brain, with normal brain patterning. Disrupting both the local and distant bioelectric signals produced antagonistic effects on caspase 3 and H3P. Thus, two components of bioelectric signals regulate apoptosis-proliferation balance within the developing brain and spinal cord: local (developing neural tube region) and distant (ventral non-neural region). Together, the local and long-range bioelectric signals create a binary control system capable of fine-tuning apoptosis and proliferation with the brain and spinal cord to achieve correct pattern and size control. Our data suggest a roadmap for utilizing bioelectric state as a diagnostic modality and convenient intervention parameter for birth defects and degenerative disease states of the CNS.

title: Transmembrane voltage potential of somatic cells controls oncogene-mediated tumorigenesis at long-range
abstract: The microenvironment is increasingly recognized as a crucial aspect of cancer. In contrast and complement to the field's focus on biochemical factors and extracellular matrix, we characterize a novel aspect of host:tumor interaction – endogenous bioelectric signals among non-excitable somatic cells. Extending prior work focused on the bioelectric state of cancer cells themselves, we show for the first time that the resting potentials of distant cells are critical for oncogene-dependent tumorigenesis. In the Xenopus laevis tadpole model, we used human oncogenes such as mutant KRAS to drive formation of tumor-like structures that exhibited overproliferation, increased nuclear size, hypoxia, acidity, and leukocyte attraction. Remarkably, misexpression of hyperpolarizing ion channels at distant sites within the tadpole significantly reduced the incidence of these tumors. The suppression of tumorigenesis could also be achieved by hyperpolarization using native CLIC1 chloride channels, suggesting a treatment modality not requiring gene therapy. Using a dominant negative approach, we implicate HDAC1 as the mechanism by which resting potential changes affect downstream cell behaviors. Based on published data on the voltage-mediated changes of butyrate flux through the SLC5A8 transporter, we present a model linking resting potentials of host cells to the ability of oncogenes to initiate tumorigenesis. Antibiotic data suggest that the relevant butyrate is generated by a native bacterial species, identifying a novel link between the microbiome and cancer that is mediated by alterations in bioelectric signaling.

title: Ultradian oscillations and pulses: coordinating cellular responses and cell fate decisions
abstract: Biological clocks play key roles in organismal development, homeostasis and function. In recent years, much work has focused on circadian clocks, but emerging studies have highlighted the existence of ultradian oscillators – those with a much shorter periodicity than 24 h. Accumulating evidence, together with recently developed optogenetic approaches, suggests that such ultradian oscillators play important roles during cell fate decisions, and analyzing the functional links between ultradian oscillation and cell fate determination will contribute to a deeper understanding of the design principle of developing embryos. In this Review, we discuss the mechanisms of ultradian oscillatory dynamics and introduce examples of ultradian oscillators in various biological contexts. We also discuss how optogenetic technology has been used to elucidate the biological significance of ultradian oscillations.

title: Chemical waves in cell and developmental biology
abstract: Deneke and Di Talia review how the spatiotemporal coordination of cellular functions across large distances is controlled by chemical waves.

title: Bioelectrical signals improve cardiac function and modify gene expression of extracellular matrix components
abstract: Beyond the influence of stimulating devices on cardiac excitation, their use in treating patients with heart failure has positive effects on the myocardium at the molecular level. Electrical signals can induce a wide spectrum of effects in living tissue. Therefore, we sought to determine whether applying electrical microcurrent directly to failing hearts leads to functional improvement.

title: Small molecule fluorescent voltage indicators for studying membrane potential.
abstract: Voltage imaging has the potential to unravel the contributions that rapid changes in membrane voltage make to cellular physiology, especially in the context of neuroscience. In particular, small molecule fluorophores are especially attractive because they can, in theory, provide fast and sensitive measurements of membrane potential dynamics. A number of classes of small molecule voltage indicators will be discussed, including dyes with improved two-photon voltage sensing, near infrared optical profiles for use in in vivo applications, and newly developed electron-transfer based indicators, or VoltageFluors, that can be tuned across a range of wavelengths to enable all-optical voltage manipulation and measurement. Limitations and a 'wish-list' for voltage indicators will also be discussed.

title: Bioelectric patterning during oogenesis: stage-specific distribution of membrane potentials, intracellular pH and ion-transport mechanisms in Drosophila ovarian follicles
abstract: BackgroundBioelectric phenomena have been found to exert influence on various developmental and regenerative processes. Little is known about their possible functions and the cellular mechanisms by which they might act during Drosophila oogenesis. In developing follicles, characteristic extracellular current patterns and membrane-potential changes in oocyte and nurse cells have been observed that partly depend on the exchange of protons, potassium ions and sodium ions. These bioelectric properties have been supposed to be related to various processes during oogenesis, e. g. pH-regulation, osmoregulation, cell communication, cell migration, cell proliferation, cell death, vitellogenesis and follicle growth. Analysing in detail the spatial distribution and activity of the relevant ion-transport mechanisms is expected to elucidate the roles that bioelectric phenomena play during oogenesis.ResultsTo obtain an overview of bioelectric patterning along the longitudinal and transversal axes of the developing follicle, the spatial distributions of membrane potentials (Vmem), intracellular pH (pHi) and various membrane-channel proteins were studied systematically using fluorescent indicators, fluorescent inhibitors and antisera. During mid-vitellogenic stages 9 to 10B, characteristic, stage-specific Vmem-patterns in the follicle-cell epithelium as well as anteroposterior pHi-gradients in follicle cells and nurse cells were observed. Corresponding distribution patterns of proton pumps (V-ATPases), voltage-dependent L-type Ca2+-channels, amiloride-sensitive Na+-channels and Na+,H+-exchangers (NHE) and gap-junction proteins (innexin 3) were detected. In particular, six morphologically distinguishable follicle-cell types are characterized on the bioelectric level by differences concerning Vmem and pHi as well as specific compositions of ion channels and carriers. Striking similarities between Vmem-patterns and activity patterns of voltage-dependent Ca2+-channels were found, suggesting a mechanism for transducing bioelectric signals into cellular responses. Moreover, gradients of electrical potential and pH were observed within single cells.ConclusionsOur data suggest that spatial patterning of Vmem, pHi and specific membrane-channel proteins results in bioelectric signals that are supposed to play important roles during oogenesis, e. g. by influencing spatial coordinates, regulating migration processes or modifying the cytoskeletal organization. Characteristic stage-specific changes of bioelectric activity in specialized cell types are correlated with various developmental processes.

title: Use of genetically encoded, light-gated ion translocators to control tumorigenesis
abstract: It has long been known that the resting potential of tumor cells is depolarized relative to their normal counterparts. More recent work has provided evidence that resting potential is not just a readout of cell state: it regulates cell behavior as well. Thus, the ability to control resting potential in vivo would provide a powerful new tool for the study and treatment of tumors, a tool capable of revealing living-state physiological information impossible to obtain using molecular tools applied to isolated cell components. Here we describe the first use of optogenetics to manipulate ion-flux mediated regulation of membrane potential specifically to prevent and cause regression of oncogene-induced tumors. Injection of mutant-KRAS mRNA induces tumor-like structures with many documented similarities to tumors, in Xenopus tadpoles. We show that expression and activation of either ChR2D156A, a blue-light activated cation channel, or Arch, a green-light activated proton pump, both of which hyperpolarize cells, significantly lowers the incidence of KRAS tumor formation. Excitingly, we also demonstrate that activation of co-expressed light-activated ion translocators after tumor formation significantly increases the frequency with which the tumors regress in a process called normalization. These data demonstrate an optogenetic approach to dissect the biophysics of cancer. Moreover, they provide proof-of-principle for a novel class of interventions, directed at regulating cell state by targeting physiological regulators that can over-ride the presence of mutations.