Cerebellar stellate cells (CSCs) are spontaneously active, tonically firing (5-30 Hz), inhibitory interneurons that synapse onto Purkinje cells. We previously analyzed the excitability properties of CSCs, focusing on four key features: type I excitability, non-monotonic first-spike latency, switching in responsiveness and runup (i.e., temporal increase in excitability during whole-cell configuration). In this study, we extend this analysis by using whole-cell configuration to show that these neurons can also burst when treated with certain pharmacological agents separately or jointly. Indeed, treatment with 4-Aminopyridine (4-AP), a partial blocker of delayed rectifier and A-type K+ channels, at low doses induces a bursting profile in CSCs significantly different than that produced at high doses or when it is applied at low doses but with cadmium (Cd2+), a blocker of high voltage-activated (HVA) Ca2+ channels. By expanding a previously revised Hodgkin-Huxley type model, through the inclusion of Ca2+-activated K+ (K(Ca)) and HVA currents, we explain how these bursts are generated and what their underlying dynamics are. Specifically, we demonstrate that the expanded model preserves the four excitability features of CSCs, as well as captures their bursting patterns induced by 4-AP and Cd2+. Model investigation reveals that 4-AP is potentiating HVA, inducing square-wave bursting at low doses and pseudo-plateau bursting at high doses, whereas Cd2+ is potentiating K(Ca), inducing pseudo-plateau bursting when applied in combination with low doses of 4-AP. Using bifurcation analysis, we show that spike adding in square-wave bursts is non-sequential when gradually changing HVA and K(Ca) maximum conductances, delayed Hopf is responsible for generating the plateau segment within the active phase of pseudo-plateau bursts, and bursting can become "chaotic" when HVA and K(Ca) maximum conductances are made low and high, respectively. These results highlight the secondary effects of the drugs applied and suggest that CSCs have all the ingredients needed for bursting.

Cell migration is a tightly-regulated process that involves protein gradients formed by the Rho family of GTPases, including Rho and Rac. The front (rear) of cells is generally characterized by higher active Rac (Rho) and lower active Rho (Rac) concentrations. Protein clusters, called adhesions, that anchor cells to their external environment have been shown to be dynamic and small (stable and large) at the cell front (rear), forming the force-transmission points necessary for persistent movement. Differences in adhesion sizes and dynamics have been linked to gradients in Rac and Rho activity. Here, we study the effects of Rac activation and gradients in Rac and Rho concentrations and activities on cellular polarity and adhesion size using mathematical and experimental approaches. The former is accomplished by expanding an existing reaction-diffusion model to a 2D domain utilizing stochastic dynamics. The model revealed that a hysteresis between the induced/uninduced states (corresponding to higher/lower Rac concentrations, respectively) along with Rac and Rho activation gradients, generated by chemical cues, were vital for forming polarity. Experimentally, the induced state was generated by increasing the cellular βPIX (a Rac-GEF) level and/or decreasing ROCK (a Rac-GAP effector protein) activity with Y-27632 (a ROCK-inhibitor). In agreement with the simulations, our results showed that cells with elevated RacGTP migrated faster, indicating more robust cellular polarization. However, the directionality of cells was not changed significantly, suggesting that external and/or internal physical or chemical cues were needed. Complementing the faster migration observed, adhesions were smaller, generating the phenotype expected with the induced state.

Neuronal excitability in the vertebrate brain is governed by the coordinated activity of both ligand- and voltage-gated ion channels. In the cerebellum, spontaneous action potential (AP) firing of inhibitory stellate cells (SCs) is variable, typically operating within the 5- to 30-Hz frequency range. AP frequency is shaped by the activity of somatodendritic A-type K+ channels and the inhibitory effect of GABAergic transmission. An added complication, however, is that whole-cell recording from SCs induces a time-dependent and sustained increase in membrane excitability making it difficult to define the full range of firing rates. Here, we show that whole-cell recording in cerebellar SCs of both male and female mice augments firing rates by reducing the membrane potential at which APs are initiated. AP threshold is lowered due to a hyperpolarizing shift in the gating behavior of voltage-gated Na+ channels. Whole-cell recording also elicits a hyperpolarizing shift in the gating behavior of A-type K+ channels which contributes to increased firing rates. Hodgkin-Huxley modeling and pharmacological experiments reveal that gating shifts in A-type K+ channel activity do not impact AP threshold, but rather promote channel inactivation which removes restraint on the upper limit of firing rates. Taken together, our work reveals an unappreciated impact of voltage-gated Na+ channels that work in coordination with A-type K+ channels to regulate the firing frequency of cerebellar SCs.

Among purinergic P2X receptor (P2XR) channels, the P2X7R exhibits the most complex gating kinetics; the binding of orthosteric agonists at the ectodomain induces a conformational change in the receptor complex that favors a gating transition from closed to open and dilated states. Bath Ca(2+) affects P2X7R gating through a still uncharacterized mechanism: it could act by reducing the adenosine triphosphate(4-) (ATP(4-)) concentration (a form proposed to be the P2X7R orthosteric agonist), as an allosteric modulator, and/or by directly altering the selectivity of pore to cations. In this study, we combined biophysical and mathematical approaches to clarify the role of calcium in P2X7R gating. In naive receptors, bath calcium affected the activation permeability dynamics indirectly by decreasing the potency of orthosteric agonists in a concentration-dependent manner and independently of the concentrations of the free acid form of agonists and status of pannexin-1 (Panx1) channels. Bath calcium also facilitated the rates of receptor deactivation in a concentration-dependent manner but did not affect a progressive delay in receptor deactivation caused by repetitive agonist application. The effects of calcium on the kinetics of receptor deactivation were rapid and reversible. A438079, a potent orthosteric competitive antagonist, protected the rebinding effect of 2'(3')-O-4-benzoylbenzoyl)ATP on the kinetics of current decay during the washout period, but in the presence of A438079, calcium also increased the rate of receptor deactivation. The corresponding kinetic (Markov state) model indicated that the decrease in binding affinity leads to a decrease in current amplitudes and facilitation of receptor deactivation, both in an extracellular calcium concentration-dependent manner expressed as a Hill function. The results indicate that calcium in physiological concentrations acts as a negative allosteric modulator of P2X7R by decreasing the affinity of receptors for orthosteric ligand agonists, but not antagonists, and not by affecting the permeability dynamics directly or indirectly through Panx1 channels. We expect these results to generalize to other P2XRs.

Adenosine triphosphate (ATP)-gated P2X2 receptors exhibit two opposite activation-dependent changes, pore dilation and pore closing (desensitization), through a process that is incompletely understood. To address this issue and to clarify the roles of calcium and the C-terminal domain in gating, we combined biophysical and mathematical approaches using two splice forms of receptors: the full-size form (P2X2aR) and the shorter form missing 69 residues in the C-terminal domain (P2X2bR). Both receptors developed conductivity for N-methyl-D-glucamine within 2-6 s of ATP application. However, pore dilation was accompanied with a decrease rather than an increase in the total conductance, which temporally coincided with rapid and partial desensitization. During sustained agonist application, receptors continued to desensitize in calcium-independent and calcium-dependent modes. Calcium-independent desensitization was more pronounced in P2X2bR, and calcium-dependent desensitization was more pronounced in P2X2aR. In whole cell recording, we also observed use-dependent facilitation of desensitization of both receptors. Such behavior was accounted for by a 16-state Markov kinetic model describing ATP binding/unbinding and activation/desensitization. The model assumes that naive receptors open when two to three ATP molecules bind and undergo calcium-independent desensitization, causing a decrease in the total conductance, or pore dilation, causing a shift in the reversal potential. In calcium-containing media, receptor desensitization is facilitated and the use-dependent desensitization can be modeled by a calcium-dependent toggle switch. The experiments and the model together provide a rationale for the lack of sustained current growth in dilating P2X2Rs and show that receptors in the dilated state can also desensitize in the presence of calcium.

The P2 purinergic receptor family implicated in many physiological processes, including neurotransmission, mechanical adaptation and inflammation, consists of ATP-gated non-specific cation channels P2XRs and G-protein coupled receptors P2YRs. Different cells, including bone forming osteoblasts, express multiple P2 receptors; however, how P2X and P2Y receptors interact in generating cellular responses to various doses of [ATP] remains poorly understood. Using primary bone marrow and compact bone derived osteoblasts and BMP2-expressing C2C12 osteoblastic cells, we demonstrated conserved features in the P2-mediated Ca2+ responses to ATP, including a transition of Ca2+ response signatures from transient at low [ATP] to oscillatory at moderate [ATP], and back to transient at high [ATP], and a non-monotonic changes in the response magnitudes which exhibited two troughs at 10-4 and 10-2 M [ATP]. We identified P2Y2 and P2X7 receptors as predominantly contributing to these responses and constructed a mathematical model of P2Y2R-induced inositol trisphosphate (IP3) mediated Ca2+ release coupled to a Markov model of P2X7R dynamics to study this system. Model predictions were validated using parental and CRISPR/Cas9-generated P2Y2 and P2Y7 knockouts in osteoblastic C2C12-BMP cells. Activation of P2Y2 by progressively increasing [ATP] induced a transition from transient to oscillatory to transient Ca2+ responses due to the biphasic nature of IP3Rs and the interaction of SERCA pumps with IP3Rs. At high [ATP], activation of P2X7R modulated the response magnitudes through an interplay between the biphasic nature of IP3Rs and the desensitization kinetics of P2X7Rs. Moreover, we found that P2Y2 activity may alter the kinetics of P2X7 towards favouring naïve state activation. Finally, we demonstrated the functional consequences of lacking P2Y2 or P2X7 in osteoblast mechanotransduction. This study thus provides important insights into the biophysical mechanisms underlying ATP-dependent Ca2+ response signatures, which are important in mediating bone mechanoadaptation.

In developing embryos, specific cell populations are often removed to remodel tissue architecture for organogenesis. During urinary tract development, an epithelial duct called the common nephric duct (CND) gets shortened and eventually eliminated to remodel the entry point of the ureter into the bladder. Here we show that non-professional efferocytosis (the process in which epithelial cells engulf apoptotic bodies) is the main mechanism that contributes to CND shortening. Combining biological metrics and computational modeling, we show that efferocytosis with actomyosin contractility are essential factors that drive the CND shortening without compromising the ureter-bladder structural connection. The disruption of either apoptosis, non-professional efferocytosis, or actomyosin results in contractile tension reduction and deficient CND shortening. Actomyosin activity helps to maintain tissue architecture while non-professional efferocytosis removes cellular volume. Together our results demonstrate that non-professional efferocytosis with actomyosin contractility are important morphogenetic factors controlling CND morphogenesis.

In mesenchymal cell motility, several migration patterns have been observed, including directional, exploratory and stationary. Two key members of the Rho-family of GTPases, Rac and Rho, along with an adaptor protein called paxillin, have been particularly implicated in the formation of such migration patterns and in regulating adhesion dynamics. Together, they form a key regulatory network that involves the mutual inhibition exerted by Rac and Rho on each other and the promotion of Rac activation by phosphorylated paxillin. Although this interaction is sufficient in generating wave-pinning that underscores cellular polarization comprised of cellular front (high active Rac) and back (high active Rho), it remains unclear how they interact collectively to induce other modes of migration detected in Chinese hamster Ovary (CHO-K1) cells. We previously developed a six-variable (6V) reaction-diffusion model describing the interactions of these three proteins (in their active/phosphorylated and inactive/unphosphorylated forms) along with other auxiliary proteins, to decipher their role in generating wave-pinning. In this study, we explored, through computational modeling and image analysis, how differences in timescales within this molecular network can potentially produce the migration patterns in CHO-K1 cells and how switching between migration modes could occur. To do so, the 6V model was reduced to an excitable 4V spatiotemporal model possessing three different timescales. The model produced not only wave-pinning in the presence of diffusion, but also mixed-mode oscillations (MMOs) and relaxation oscillations (ROs). Implementing the model using the Cellular Potts Model (CPM) produced outcomes in which protrusions in the cell membrane changed Rac-Rho localization, resulting in membrane oscillations and fast directionality variations similar to those observed experimentally in CHO-K1 cells. The latter was assessed by comparing the migration patterns of experimental with CPM cells using four metrics: instantaneous cell speed, exponent of mean-square displacement ([Formula: see text]-value), directionality ratio and protrusion rate. Variations in migration patterns induced by mutating paxillin's serine 273 residue were also captured by the model and detected by a machine classifier, revealing that this mutation alters the dynamics of the system from MMOs to ROs or nonoscillatory behaviour through variation in the scaled concentration of an active form of an adhesion protein called p21-Activated Kinase 1 (PAK). These results thus suggest that MMOs and adhesion dynamics are the key mechanisms regulating CHO-K1 cell motility.

Focal adhesions are protein complexes that anchor cells to the extracellular matrix. During migration, the growth and disassembly of these structures are spatiotemporally regulated, with new adhesions forming at the leading edge of the cell and mature adhesions disassembling at the rear. Signalling proteins and structural cytoskeletal components tightly regulate adhesion dynamics. Paxillin, an adaptor protein within adhesions, is one of these proteins. Its phosphorylation at serine 273 (S273) is crucial for maintaining fast adhesion assembly and disassembly. Paxillin is known to bind to a GIT1-βPIX-PAK1 complex, which increases the local activation of the small GTPase Rac. To understand quantitatively the behaviour of this system and how it relates to adhesion assembly/disassembly, we developed a mathematical model describing the dynamics of the small GTPases Rac and Rho as determined by paxillin S273 phosphorylation. Our model revealed that the system possesses bistability, where switching between uninduced (active Rho) and induced (active Rac) states can occur through a change in rate of paxillin phosphorylation or PAK1 activation. The bistable switch is characterized by the presence of memory, minimal change in the levels of active Rac and Rho within the induced and uninduced states, respectively, and the limited regime of monostability associated with the uninduced state. These results were validated experimentally by showing the presence of bimodality in adhesion assembly and disassembly rates, and demonstrating that Rac activity increases after treating Chinese Hamster Ovary cells with okadaic acid (a paxillin phosphatase inhibitor), followed by a modest recovery after 20 min washout. Spatial gradients of phosphorylated paxillin in a reaction-diffusion model gave rise to distinct regions of Rac and Rho activities, resembling polarization of a cell into front and rear. Perturbing several parameters of the model also revealed important insights into how signalling components upstream and downstream of paxillin phosphorylation affect dynamics.

The P2X4 receptor (P2X4R) is a member of a family of purinergic channels activated by extracellular ATP through three orthosteric binding sites and allosterically regulated by ivermectin (IVM), a broad-spectrum antiparasitic agent. Treatment with IVM increases the efficacy of ATP to activate P2X4R, slows both receptor desensitization during sustained ATP application and receptor deactivation after ATP washout, and makes the receptor pore permeable to NMDG+, a large organic cation. Previously, we developed a Markov model based on the presence of one IVM binding site, which described some effects of IVM on rat P2X4R. Here we present two novel models, both with three IVM binding sites. The simpler one-layer model can reproduce many of the observed time series of evoked currents, but does not capture well the short time scales of activation, desensitization, and deactivation. A more complex two-layer model can reproduce the transient changes in desensitization observed upon IVM application, the significant increase in ATP-induced current amplitudes at low IVM concentrations, and the modest increase in the unitary conductance. In addition, the two-layer model suggests that this receptor can exist in a deeply inactivated state, not responsive to ATP, and that its desensitization rate can be altered by each of the three IVM binding sites. In summary, this study provides a detailed analysis of P2X4R kinetics and elucidates the orthosteric and allosteric mechanisms regulating its channel gating.

The forces actively generated by motile cells must be transmitted to their environment in a spatiotemporally regulated manner, in order to produce directional cellular motion. This task is accomplished through integrin-based adhesions, large macromolecular complexes that link the actin-cytoskelton inside the cell to its external environment. Despite their relatively large size, adhesions exhibit rapid dynamics, switching between assembly and disassembly in response to chemical and mechanical cues exerted by cytoplasmic biochemical signals, and intracellular/extracellular forces, respectively. While in material science, force typically disrupts adhesive contact, in this biological system, force has a more nuanced effect, capable of causing assembly or disassembly. This initially puzzled experimentalists and theorists alike, but investigation into the mechanisms regulating adhesion dynamics have progressively elucidated the origin of these phenomena. This review provides an overview of recent studies focused on the theoretical understanding of adhesion assembly and disassembly as well as the experimental studies that motivated them. We first concentrate on the kinetics of integrin receptors, which exhibit a complex response to force, and then investigate how this response manifests itself in macromolecular adhesion complexes. We then turn our attention to studies of adhesion plaque dynamics that link integrins to the actin-cytoskeleton, and explain how force can influence the assembly/disassembly of these macromolecular structure. Subsequently, we analyze the effect of force on integrins populations across lengthscales larger than single adhesions. Finally, we cover some theoretical studies that have considered both integrins and the adhesion plaque and discuss some potential future avenues of research.

Voltage-gated sodium (Nav) channels produce the upstroke of action potentials in excitable tissues throughout the body. The gating of these channels is determined by the asynchronous movements of four voltage-sensing domains (VSDs). Past studies on the skeletal muscle Nav1.4 channel have indicated that VSD-I, -II, and -III are sufficient for pore opening, whereas VSD-IV movement is sufficient for channel inactivation. Here, we studied the cardiac sodium channel, Nav1.5, using charge-neutralizing mutations and voltage-clamp fluorometry. Our results reveal that both VSD-III and -IV are necessary for Nav1.5 inactivation, and that steady-state inactivation can be modulated by all VSDs. We also demonstrate that channel activation is partially determined by VSD-IV movement. Kinetic modeling suggests that these observations can be explained from the cardiac channel's propensity to enter closed-state inactivation (CSI), which is significantly higher than that of other Nav channels. We show that skeletal muscle Nav1.4, cardiac Nav1.5, and neuronal Nav1.6 all have different propensities for CSI and postulate that these differences produce isoform-dependent roles for the four VSDs.

The breadth of pathogens to which T cells can respond is determined by the T cell receptors (TCRs) present in an individual's repertoire. Although more than 90% of the sequence diversity among TCRs is generated by terminal deoxynucleotidyl transferase (TdT)-mediated N-nucleotide addition during V(D)J recombination, the benefit of TdT-altered TCRs remains unclear. Here, we computationally and experimentally investigated whether TCRs with higher N-nucleotide diversity via TdT make distinct contributions to acute or chronic pathogen control specifically through the inclusion of TCRs with lower antigen binding strengths (i.e., lower reactivity to peptide-major histocompatibility complex (pMHC)). When T cells with high pMHC reactivity have a greater propensity to become functionally exhausted than those of low pMHC reactivity, our computational model predicts a shift toward T cells with low pMHC reactivity over time during chronic, but not acute, infections. This TCR-affinity shift is critical, as the elimination of T cells with lower pMHC reactivity in silico substantially increased the time to clear a chronic infection, while acute infection control remained largely unchanged. Corroborating an affinity-centric benefit for TCR diversification via TdT, we found evidence that TdT-deficient TCR repertoires possess fewer T cells with weaker pMHC binding strengths in vivo and showed that TdT-deficient mice infected with a chronic, but not an acute, viral pathogen led to protracted viral clearance. In contrast, in the case of a chronic fungal pathogen where T cells fail to clear the infection, both our computational model and experimental data showed that TdT-diversified TCR repertoires conferred no additional protection to the hosts. Taken together, our in silico and in vivo data suggest that TdT-mediated TCR diversity is of particular benefit for the eventual resolution of prolonged pathogen replication through the inclusion of TCRs with lower foreign antigen binding strengths.

Electroencephalograms (EEGs) display a mixture of rhythmic and broadband fluctuations, the latter manifesting as an apparent 1/f spectral trend. While network oscillations are known to generate rhythmic EEG, the neural basis of broadband EEG remains unexplained. Here, we use biophysical modelling to show that aperiodic neural activity can generate detectable scalp potentials and shape broadband EEG features, but that these aperiodic signals do not significantly perturb brain rhythm quantification. Further model analysis demonstrated that rhythmic EEG signals are profoundly corrupted by shifts in synapse properties. To examine this scenario, we recorded EEGs of human subjects being administered propofol, a general anesthetic and GABA receptor agonist. Drug administration caused broadband EEG changes that quantitatively matched propofol's known effects on GABA receptors. We used our model to correct for these confounding broadband changes, which revealed that delta power, uniquely, increased within seconds of individuals losing consciousness. Altogether, this work details how EEG signals are shaped by neurophysiological factors other than brain rhythms and elucidates how these signals can undermine traditional EEG interpretation.