Chronic infection control relies on T cells with lower foreign antigen binding strength generated by N-nucleotide diversity.

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.

Modulation of SK Channels via Calcium Buffering Tunes Intrinsic Excitability of Parvalbumin Interneurons in Neuropathic Pain: A Computational and Experimental Investigation.

Parvalbumin-expressing interneurons (PVINs) play a crucial role within the dorsal horn of the spinal cord by preventing touch inputs from activating pain circuits. In both male and female mice, nerve injury decreases PVINs' output via mechanisms that are not fully understood. In this study, we show that PVINs from nerve-injured male mice change their firing pattern from tonic to adaptive. To examine the ionic mechanisms responsible for this decreased output, we used a reparametrized Hodgkin-Huxley type model of PVINs, which predicted (1) the firing pattern transition is because of an increased contribution of small conductance calcium-activated potassium (SK) channels, enabled by (2) impairment in intracellular calcium buffering systems. Analyzing the dynamics of the Hodgkin-Huxley type model further demonstrated that a generalized Hopf bifurcation differentiates the two types of state transitions observed in the transient firing of PVINs. Importantly, this predicted mechanism holds true when we embed the PVIN model within the neuronal circuit model of the spinal dorsal horn. To experimentally validate this hypothesized mechanism, we used pharmacological modulators of SK channels and demonstrated that (1) tonic firing PVINs from naive male mice become adaptive when exposed to an SK channel activator, and (2) adapting PVINs from nerve-injured male mice return to tonic firing on SK channel blockade. Our work provides important insights into the cellular mechanism underlying the decreased output of PVINs in the spinal dorsal horn after nerve injury and highlights potential pharmacological targets for new and effective treatment approaches to neuropathic pain.SIGNIFICANCE STATEMENT Parvalbumin-expressing interneurons (PVINs) exert crucial inhibitory control over Aß fiber-mediated nociceptive pathways at the spinal dorsal horn. The loss of their inhibitory tone leads to neuropathic symptoms, such as mechanical allodynia, via mechanisms that are not fully understood. This study identifies the reduced intrinsic excitability of PVINs as a potential cause for their decreased inhibitory output in nerve-injured condition. Combining computational and experimental approaches, we predict a calcium-dependent mechanism that modulates PVINs' electrical activity following nerve injury: a depletion of cytosolic calcium buffer allows for the rapid accumulation of intracellular calcium through the active membranes, which in turn potentiates SK channels and impedes spike generation. Our results therefore pinpoint SK channels as potential therapeutic targets for treating neuropathic symptoms.

Myelin basic protein mRNA levels affect myelin sheath dimensions, architecture, plasticity, and density of resident glial cells.

Myelin Basic Protein (MBP) is essential for both elaboration and maintenance of CNS myelin, and its reduced accumulation results in hypomyelination. How different Mbp mRNA levels affect myelin dimensions across the lifespan and how resident glial cells may respond to such changes are unknown. Here, to investigate these questions, we used enhancer-edited mouse lines that accumulate Mbp mRNA levels ranging from 8% to 160% of wild type. In young mice, reduced Mbp mRNA levels resulted in corresponding decreases in Mbp protein accumulation and myelin sheath thickness, confirming the previously demonstrated rate-limiting role of Mbp transcription in the control of initial myelin synthesis. However, despite maintaining lower line specific Mbp mRNA levels into old age, both MBP protein levels and myelin thickness improved or fully normalized at rates defined by the relative Mbp mRNA level. Sheath length, in contrast, was affected only when mRNA levels were very low, demonstrating that sheath thickness and length are not equally coupled to Mbp mRNA level. Striking abnormalities in sheath structure also emerged with reduced mRNA levels. Unexpectedly, an increase in the density of all glial cell types arose in response to reduced Mbp mRNA levels. This investigation extends understanding of the role MBP plays in myelin sheath elaboration, architecture, and plasticity across the mouse lifespan and illuminates a novel axis of glial cell crosstalk.

The influence of circadian rhythms on CD8+ T cell activation upon vaccination: A mathematical modeling perspective.

Circadian rhythms have been implicated in the modulation of many physiological processes, including those associated with the immune system. For example, these rhythms influence CD8+ T cell responses within the adaptive immune system. The mechanism underlying this immune-circadian interaction, however, remains unclear, particularly in the context of vaccination. Here, we devise a molecularly-explicit gene regulatory network model of early signaling in the naïve CD8+ T cell activation pathway, comprised of three axes (or subsystems) labeled ZAP70, LAT and CD28, to elucidate the molecular details of this immune-circadian mechanism and its relation to vaccination. This is done by coupling the model to a periodic forcing function to identify the molecular players targeted by circadian rhythms, and analyzing how these rhythms subsequently affect CD8+ T cell activation under differing levels of T cell receptor (TCR) phosphorylation, which we designate as vaccine load. By performing both bifurcation and parameter sensitivity analyses on the model at the single cell and ensemble levels, we find that applying periodic forcing on molecular targets within the ZAP70 axis is sufficient to create a day-night discrepancy in CD8+ T cell activation in a manner that is dependent on the bistable switch inherent in CD8+ T cell early signaling. We also demonstrate that the resulting CD8+ T cell activation is dependent on the strength of the periodic coupling as well as on the level of TCR phosphorylation. Our results show that this day-night discrepancy is not transmitted to certain downstream molecules within the LAT subsystem, such as mTORC1, suggesting a secondary, independent circadian regulation on that protein complex. We also corroborate experimental results by showing that the circadian regulation of CD8+ T cell primarily acts at a baseline, pre-vaccination state, playing a facilitating role in priming CD8+ T cells to vaccine inputs according to the time of day. By applying an ensemble level analysis using bifurcation theory and by including several hypothesized molecular targets of this circadian rhythm, we further demonstrate an increased variability between CD8+ T cells (due to heterogeneity) induced by its circadian regulation, which may allow an ensemble of CD8+ T cells to activate at a lower vaccine load, improving its sensitivity. This modeling study thus provides insights into the immune targets of the circadian clock, and proposes an interaction between vaccine load and the influence of circadian rhythms on CD8+ T cell activation.

Excitable dynamics in a molecularly-explicit model of cell motility: Mixed-mode oscillations and beyond.

Mesenchymal cell motility is mainly regulated by two members of the Rho-family of GTPases, called Rac and Rho. The mutual inhibition exerted by these two proteins on each other's activation and the promotion of Rac activation by an adaptor protein called paxillin have been implicated in driving cellular polarization comprised of front (high active Rac) and back (high active Rho) during cell migration. Mathematical modeling of this regulatory network has previously shown that bistability is responsible for generating a spatiotemporal pattern underscoring cellular polarity called wave-pinning when diffusion is included. We previously developed a 6V reaction-diffusion model of this network to decipher the role of Rac, Rho and paxillin (along with other auxiliary proteins) in generating wave-pinning. In this study, we simplify this model through a series of steps into an excitable 3V ODE model comprised of one fast variable (the scaled concentration of active Rac), one slow variable (the maximum paxillin phosphorylation rate - turned into a variable) and a very slow variable (a recovery rate - also turned into a variable). We then explore, through slow-fast analysis, how excitability is manifested by showing that the model can exhibit relaxation oscillations (ROs) as well as mixed-mode oscillations (MMOs) whose underlying dynamics are consistent with a delayed Hopf bifurcation with a canard explosion. By reintroducing diffusion and the scaled concentration of inactive Rac into the model, we obtain a 4V PDE model that generates several unique spatiotemporal patterns that are relevant to cell motility. These patterns are then characterized and their impact on cell motility are explored by employing the cellular potts model (CPM). Our results reveal that wave pinning produces purely very directed motion in CPM, while MMOs allow for meandering and non-motile behaviors to occur. This highlights the role of MMOs as a potential mechanism for mesenchymal cell motility.

Characterizing spontaneous Ca2+ local transients in OPCs using computational modeling.

Spontaneous Ca2+ local transients (SCaLTs) in isolated oligodendrocyte precursor cells are largely regulated by the following fluxes: store-operated Ca2+ entry (SOCE), Na+/Ca2+ exchange, Ca2+ pumping through Ca2+-ATPases, and Ca2+-induced Ca2+-release through ryanodine receptors and inositol-trisphosphate receptors. However, the relative contributions of these fluxes in mediating fast spiking and the slow baseline oscillations seen in SCaLTs remain incompletely understood. Here, we developed a stochastic spatiotemporal computational model to simulate SCaLTs in a homogeneous medium with ionic flow between the extracellular, cytoplasmic, and endoplasmic-reticulum compartments. By simulating the model and plotting both the histograms of SCaLTs obtained experimentally and from the model as well as the standard deviation of inter-SCaLT intervals against inter-SCaLT interval averages of multiple model and experimental realizations, we revealed the following: (1) SCaLTs exhibit very similar characteristics between the two data sets, (2) they are mostly random, (3) they encode information in their frequency, and (4) their slow baseline oscillations could be due to the stochastic slow clustering of inositol-trisphosphate receptors (modeled as an Ornstein-Uhlenbeck noise process). Bifurcation analysis of a deterministic temporal version of the model showed that the contribution of fluxes to SCaLTs depends on the parameter regime and that the combination of excitability, stochasticity, and mixed-mode oscillations are responsible for irregular spiking and doublets in SCaLTs. Additionally, our results demonstrated that blocking each flux reduces SCaLTs' frequency and that the reverse (forward) mode of Na+/Ca2+ exchange decreases (increases) SCaLTs. Taken together, these results provide a quantitative framework for SCaLT formation in oligodendrocyte precursor cells.

High-affinity P2Y2 and low-affinity P2X7 receptor interaction modulates ATP-mediated calcium signaling in murine osteoblasts.

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.

Deciphering the dynamics of lamellipodium in a fish keratocytes model.

Motile cells depend on an intricate network of feedback loops that are essential in driving cell movement. Integrin-based focal adhesions (FAs) along with actin are the two key factors that mediate such motile behaviour. Together, they generate excitable dynamics that are essential for forming protrusions at the leading edge of the cell and, in certain cases, traveling waves along the membrane. A partial differential equation (PDE) model of a self-organizing lamellipodium in crawling keratocytes has been previously developed to understand how the three spatiotemporal patterns of activity observed in such cells, namely, stalling, waving and smooth motility, are produced. The model consisted of three key variables: the density of barbed actin filaments, newly formed FAs called nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping techniques, the distinct regimes of behaviour associated with the three activity patterns were identified. In this study, we convert the PDE model into an ordinary differential equation (ODE) model to examine its excitability properties and determine all the patterns of activity exhibited by this system. Our results reveal that there are two additional regimes not previously identified, including bistability and oscillatory-like type IV excitability (generated by three steady states and their manifolds, rather than limit cycles). These regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model shows that it exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes is likely due to noise-dependent motility governed by dynamics near the interface of bistability and type IV excitability. The two parameter bifurcation suggests that the increase in the proportion of rough motion is due to a shift in activity towards the bistable and type IV excitable regimes induced by a decrease in NA maturation rate. Our results thus provide important insight into how microscopic mechanical effects are integrated to produce the observed modes of motility.

Bursting in cerebellar stellate cells induced by pharmacological agents: Non-sequential spike adding.

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.

Quantifying immunoregulation by autoantigen-specific T-regulatory type 1 cells in mice with simultaneous hepatic and extra-hepatic autoimmune disorders.

Nanoparticles (NPs) displaying autoimmune disease-relevant peptide-major histocompatibility complex class II molecules (pMHCII-NPs) trigger cognate T-regulatory type 1 (Tr1)-cell formation and expansion, capable of reversing organ-specific autoimmune responses. These pMHCII-NPs that display epitopes from mitochondrial protein can blunt the progression of both autoimmune hepatitis (AIH) and experimental autoimmune encephalomyelitis (EAE) in mice carrying either disease. However, with co-morbid mice having both diseases, these pMHCII-NPs selectively treat AIH. In contrast, pMHCII-NPs displaying central nervous system (CNS)-specific epitopes can efficiently treat CNS autoimmunity, both in the absence and presence of AIH, without having any effects on the progression of the latter. Here, we develop a compartmentalized population model of T-cells in co-morbid mice to identify the mechanisms by which Tr1 cells mediate organ-specific immunoregulation. We perform time-series simulations and bifurcation analyses to study how varying physiological parameters, including local cognate antigenic load and rates of Tr1-cell recruitment and retention, affect T-cell allocation and Tr1-mediated immunoregulation. Various regimes of behaviour, including 'competitive autoimmunity' where pMHCII-NP-treatment fails against both diseases, are identified and compared with experimental observations. Our results reveal that a transient delay in Tr1-cell recruitment to the CNS, resulting from inflammation-dependent Tr1-cell allocation, accounts for the liver-centric effects of AIH-specific pMHCII-NPs in co-morbid mice as compared with mice exclusively having EAE. They also suggest that cognate autoantigen expression and local Tr1-cell retention are key determinants of effective regulatory-cell function. These results thus provide new insights into the rules that govern Tr1-cell recruitment and their autoregulatory function.

Switching in Cerebellar Stellate Cell Excitability in Response to a Pair of Inhibitory/Excitatory Presynaptic Inputs: A Dynamical System Perspective.

Cerebellar stellate cells form inhibitory synapses with Purkinje cells, the sole output of the cerebellum. Upon stimulation by a pair of varying inhibitory and fixed excitatory presynaptic inputs, these cells do not respond to excitation (i.e., do not generate an action potential) when the magnitude of the inhibition is within a given range, but they do respond outside this range. We previously used a revised Hodgkin-Huxley type of model to study the nonmonotonic first-spike latency of these cells and their temporal increase in excitability in whole cell configuration (termed run-up). Here, we recompute these latency profiles using the same model by adapting an efficient computational technique, the two-point boundary value problem, that is combined with the continuation method. We then extend the study to investigate how switching in responsiveness, upon stimulation with presynaptic inputs, manifests itself in the context of run-up. A three-dimensional reduced model is initially derived from the original six-dimensional model and then analyzed to demonstrate that both models exhibit type 1 excitability possessing a saddle-node on an invariant cycle (SNIC) bifurcation when varying the amplitude of Iapp. Using slow-fast analysis, we show that the original model possesses three equilibria lying at the intersection of the critical manifold of the fast subsystem and the nullcline of the slow variable hA (the inactivation of the A-type K+ channel), the middle equilibrium is of saddle type with two-dimensional stable manifold (computed from the reduced model) acting as a boundary between the responsive and non-responsive regimes, and the (ghost of) SNIC is formed when the hA-nullcline is (nearly) tangential to the critical manifold. We also show that the slow dynamics associated with (the ghost of) the SNIC and the lower stable branch of the critical manifold are responsible for generating the nonmonotonic first-spike latency. These results thus provide important insight into the complex dynamics of stellate cells.

Dynamics of Mechanosensitive Nascent Adhesion Formation.

Cellular migration is a tightly regulated process that involves actin cytoskeleton, adaptor proteins, and integrin receptors. Forces are transmitted extracellularly through protein complexes of these molecules, called adhesions. Adhesions anchor the cell to its substrate, allowing it to migrate. In Chinese hamster ovary cells, three classes of adhesion can be identified: nascent adhesions (NAs), focal complexes, and focal adhesions, ranked here ascendingly based on size and stability. To understand the dynamics and mechanosensitive properties of NAs, a biophysical model of these NAs as colocalized clusters of integrins and adaptor proteins is developed. The model is then analyzed to characterize the dependence of NA area on biophysical parameters that regulate the number of integrins and adaptor proteins within NAs through a mechanosensitive coaggregation mechanism. Our results reveal that NA formation is triggered beyond a threshold of adaptor protein, integrin, or extracellular ligand densities, with these three factors listed in descending order of their relative influence on NA area. Further analysis of the model also reveals that an increase in coaggregation or reductions in integrin mobility inside the adhesion potentiate NA formation. By extending the model to consider the mechanosensitivity of the integrin bond, we identify mechanical stress, rather than mechanical load, as a permissive mechanical parameter that allows for noise-dependent and independent NA assembly, despite both parameters producing a bistable switch possessing a hysteresis. Stochastic simulations of the model confirm these results computationally. This study thus provides insight into the mechanical conditions defining NA dynamics.

Paxillin phosphorylation at serine 273 and its effects on Rac, Rho and adhesion dynamics.

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-ßPIX-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.

Deciphering the regulation of P2X4 receptor channel gating by ivermectin using Markov models.

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.

A unified model for two modes of bursting in GnRH neurons.

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca(2+) current I s, and the Ca(2+) -activated K(+) current I KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.

Mathematical model of galactose regulation and metabolic consumption in yeast.

The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ this approach to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine its two main components: the genetic branch, which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes that can be repressed by glucose. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates a bistable regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework with which they can determine how the galactose network functions under various conditions.

Allosteric regulation of the P2X4 receptor channel pore dilation.

Allosteric modulators of ligand-gated receptor channels induce conformational changes of the entire protein that alter potencies and efficacies for orthosteric ligands, expressed as the half maximal effective concentration (EC50) and maximum current amplitude, respectively. Here, we studied the influence of allostery on channel pore dilation, an issue not previously addressed. Experiments were done using the rat P2X4 receptor expressed in human embryonic kidney 293T cells and gated by adenosine 5'-triphosphate (ATP) in the presence and absence of ivermectin (IVM), an established positive allosteric regulator of this channel. In the absence of IVM, this channel activates and deactivates rapidly, does not show transition from open to dilated states, desensitizes completely with a moderate rate, and recovers only fractionally during washout. IVM treatment increases the efficacy of ATP to activate the channel and slows receptor desensitization during sustained ATP application and receptor deactivation after ATP washout. The rescue of the receptor from desensitization temporally coincides with pore dilation, and the dilated channel can be reactivated after washout of ATP. Experiments with vestibular and transmembrane domain receptor mutants further established that IVM has distinct effects on opening and dilation of the channel pore, the first accounting for increased peak current amplitude and the latter correlating with changes in the EC50 and kinetics of receptor deactivation. The corresponding kinetic (Markov state) model indicates that the IVM-dependent transition from open to dilated state is coupled to receptor sensitization, which rescues the receptor from desensitization and subsequent internalization. Allosterically induced sensitization of P2X4R thus provides sustained signaling during prolonged and repetitive ATP stimulation.

Unraveling the contribution of pancreatic beta-cell suicide in autoimmune type 1 diabetes.

In type 1 diabetes, an autoimmune disease mediated by autoreactive T-cells that attack insulin-secreting pancreatic beta-cells, it has been suggested that disease progression may additionally require protective mechanisms in the target tissue to impede such auto-destructive mechanisms. We hypothesize that the autoimmune attack against beta-cells causes endoplasmic reticulum stress by forcing the remaining beta-cells to synthesize and secrete defective insulin. To rescue beta-cell from the endoplasmic reticulum stress, beta-cells activate the unfolded protein response to restore protein homeostasis and normal insulin synthesis. Here we investigate the compensatory role of unfolded protein response by developing a multi-state model of type 1 diabetes that takes into account beta-cell destruction caused by pathogenic autoreactive T-cells and apoptosis triggered by endoplasmic reticulum stress. We discuss the mechanism of unfolded protein response activation and how it counters beta-cell extinction caused by an autoimmune attack and/or irreversible damage by endoplasmic reticulum stress. Our results reveal important insights about the balance between beta-cell destruction by autoimmune attack (beta-cell homicide) and beta-cell apoptosis by endoplasmic reticulum stress (beta-cell suicide). It also provides an explanation as to why the unfolded protein response may not be a successful therapeutic target to treat type 1 diabetes.

Continuum model of T-cell avidity: Understanding autoreactive and regulatory T-cell responses in type 1 diabetes.

Type 1 diabetes (T1D) is an autoimmune disease that results from the destruction of insulin-secreting pancreatic ß cells, leading to abolition of insulin secretion and onset of diabetes. Cytotoxic CD4(+) and CD8(+) T cells, activated by antigen presenting cells (APCs), are both implicated in disease onset and progression. Regulatory T cells (Tregs), on the other hand, play a leading role in regulating immunological tolerance and resistant homoeostasis in T1D by suppressing effector T cells (Teffs). Recent data indicates that after activation, conventional Teffs transiently produce interleukin IL-2, a cytokine that acts as a growth factor for both Teffs and Tregs. Tregs suppress Teffs through IL-2 deprivation, competition and Teff conversion into inducible Tregs (iTregs). To investigate the interactions of these components during T1D progression, a mathematical model of T-cell dynamics is developed as a predictor of ß-cell loss, with the underlying hypothesis that avidity of Teffs and Tregs, i.e., the binding affinity of T-cell receptors to peptide-major histocompatibility complexes on host cells, is continuum. The model is used to infer a set of criteria that determines susceptibility to T1D in high risk subjects. Our findings show that diabetes onset is guided by the absence of Treg-to-Teff dominance at specific high avidities, rather than over the whole range of avidity, and that the lack of overall dominance of Teffs-to-Tregs over time is the underlying cause of the "honeymoon period", the remission phase observed in some T1D patients. The model also suggests that competition between Teffs and Tregs is more effective than Teff-induction into iTregs in suppressing Teffs, and that a prolonged full width at half maximum of IL-2 release is a necessary condition for curbing disease onset. Finally, the model provides a rationale for observing rapid and slow progressors of T1D based on modest heterogeneity in the kinetic parameters.

Prediction and prevention of type 1 diabetes: update on success of prediction and struggles at prevention.

Type 1 diabetes mellitus (T1DM) is the archetypal example of a T cell-mediated autoimmune disease characterized by selective destruction of pancreatic ß cells. The pathogenic equation for T1DM presents a complex interrelation of genetic and environmental factors, most of which have yet to be identified. On the basis of observed familial aggregation of T1DM, it is certain that there is a decided heritable genetic susceptibility for developing T1DM. The well-known association of T1DM with certain human histocompatibility leukocyte antigen (HLA) alleles of the major histocompatibility complex (MHC) was a major step toward understanding the role of inheritance in T1DM. Type 1 diabetes is a polygenic disease with a small number of genes having large effects (e.g., HLA) and a large number of genes having small effects. Risk of T1DM progression is conferred by specific HLA DR/DQ alleles [e.g., DRB1*03-DQB1*0201 (DR3/DQ2) or DRB1*04-DQB1*0302 (DR4/DQ8)]. In addition, the HLA allele DQB1*0602 is associated with dominant protection from T1DM in multiple populations. A concordance rate lower than 100% between monozygotic twins indicates a potential involvement of environmental factors on disease development. The detection of at least two islet autoantibodies in the blood is virtually pre-diagnostic for T1DM. The majority of children who carry these biomarkers, regardless of whether they have an a priori family history of the disease, will develop insulin-requiring diabetes. Facilitating pre-diagnosis is the timing of seroconversion which is most pronounced in the first 2 yr of life. Unfortunately the significant progress in improving prediction of T1DM has not yet been paralleled by safe and efficacious intervention strategies aimed at preventing the disease. Herein we summarize the chequered history of prediction and prevention of T1DM, describing successes and failures alike, and thereafter examine future trends in the exciting, partially explored field of T1DM prevention.