A Collision Coupling Model Governs the Activation of Neuronal GIRK1/2 Channels by Muscarinic-2 Receptors.

The G protein-activated Inwardly Rectifying K+-channel (GIRK) modulates heart rate and neuronal excitability. Following G-Protein Coupled Receptor (GPCR)-mediated activation of heterotrimeric G proteins (Gαßγ), opening of the channel is obtained by direct binding of Gßγ subunits. Interestingly, GIRKs are solely activated by Gßγ subunits released from Gαi/o-coupled GPCRs, despite the fact that all receptor types, for instance Gαq-coupled, are also able to provide Gßγ subunits. It is proposed that this specificity and fast kinetics of activation stem from pre-coupling (or pre-assembly) of proteins within this signaling cascade. However, many studies, including our own, point towards a diffusion-limited mechanism, namely collision coupling. Here, we set out to address this long-standing question by combining electrophysiology, imaging, and mathematical modeling. Muscarinic-2 receptors (M2R) and neuronal GIRK1/2 channels were coexpressed in Xenopus laevis oocytes, where we monitored protein surface expression, current amplitude, and activation kinetics. Densities of expressed M2R were assessed using a fluorescently labeled GIRK channel as a molecular ruler. We then incorporated our results, along with available kinetic data reported for the G-protein cycle and for GIRK1/2 activation, to generate a comprehensive mathematical model for the M2R-G-protein-GIRK1/2 signaling cascade. We find that, without assuming any irreversible interactions, our collision coupling kinetic model faithfully reproduces the rate of channel activation, the changes in agonist-evoked currents and the acceleration of channel activation by increased receptor densities.

The coupling of the M2 muscarinic receptor to its G protein is voltage dependent.

G protein coupled receptors (GPCRs) participate in the majority of signal transduction processes in the body. Specifically, the binding of an external agonist promotes coupling of the GPCR to its G protein and this, in turn, induces downstream signaling. Recently, it was shown that agonist binding to the M2 muscarinic receptor (M2R) and to other GPCRs is voltage dependent. Here we examine, whether the coupling of the M2R to its G protein is also voltage-dependent. We first show, in Xenopus oocytes, that the activity of the M2R in the absence of agonist (constitutive activity) can be used to report the coupling. We then show that the coupling is, by itself, voltage dependent. This novel finding is of physiological importance, as it shows that the actual signal transduction, whose first step is the coupling of the GPCR to its cognate G protein, is voltage dependent.

A Novel Voltage Sensor in the Orthosteric Binding Site of the M2 Muscarinic Receptor.

G protein-coupled receptors (GPCRs) mediate many signal transduction processes in the body. The discovery that these receptors are voltage-sensitive has changed our understanding of their behavior. The M2 muscarinic acetylcholine receptor (M2R) was found to exhibit depolarization-induced charge movement-associated currents, implying that this prototypical GPCR possesses a voltage sensor. However, the typical domain that serves as a voltage sensor in voltage-gated channels is not present in GPCRs, making the search for the voltage sensor in the latter challenging. Here, we examine the M2R and describe a voltage sensor that is comprised of tyrosine residues. This voltage sensor is crucial for the voltage dependence of agonist binding to the receptor. The tyrosine-based voltage sensor discovered here constitutes a noncanonical by which membrane proteins may sense voltage.

Voltage affects the dissociation rate constant of the m2 muscarinic receptor.

G-protein coupled receptors (GPCRs) comprise the largest protein family and mediate the vast majority of signal transduction processes in the body. Until recently GPCRs were not considered to be voltage dependent. Newly it was shown for several GPCRs that the first step in GPCR activation, the binding of agonist to the receptor, is voltage sensitive: Voltage shifts the receptor between two states that differ in their binding affinity. Here we show that this shift involves the rate constant of dissociation. We used the m2 muscarinic receptor (m2R) a prototypical GPCR and measured directly the dissociation of [(3)H]ACh from m2R expressed Xenopus oocytes. We show, for the first time, that the voltage dependent change in affinity is implemented by voltage shifting the receptor between two states that differ in their rate constant of dissociation. Furthermore, we provide evidence that suggest that the above shift is achieved by voltage regulating the coupling of the GPCR to its G protein.

Selecting the particle size distribution for drugs with low water solubility - mathematical model.

PURPOSE: To introduce guidelines in selecting the particle size distribution (n(0), cm(-1)) that will guarantee optimal oral absorption for drugs with low solubility. METHODS: Unlike other multi-compartmental models the gastrointestinal tract is modeled as a continuous tube with spatially varying properties. The transport through the intestinal lumen is described using the dispersion model. The model accounts for the dissolution of poly-dispersed powders. RESULTS: The model was used to examine the sensitivity of the absorption on permeability (P) and water solubility (C(s)) following administration in different log-normal powders. The absorption exhibits inverse sigmoidal dependence on the mean particle size (r(m), µm) regardless of the administrated dose or drug properties. Thus, there is an optimal r(m) that maximizes the benefit-cost ratio of the formulation; finer particles do not improve the absorption while coarser particles decrease it. Using the model we find that the optimal r(m) depends mainly on the drug C(s) and on the geometrical standard deviation (gSTD). CONCLUSIONS: The results of this work provide the formulator with guidelines to select both r(m) and gSTD that guarantee optimal absorption.

Depolarization induces a conformational change in the binding site region of the M2 muscarinic receptor.

G protein-coupled receptors play a central role in signal transduction and were only known to be activated by agonists. Recently it has been shown that membrane potential also affects the activity of G protein-coupled receptors. For the M(2) muscarinic receptor, it was further shown that depolarization induces charge movement. A tight correlation was found between the voltage-dependence of the charge movement and the voltage-dependence of the agonist binding. Here we examine whether depolarization-induced charge movement causes a conformational change in the M(2) receptor that may be responsible for the voltage-dependence of agonist binding. Using site-directed fluorescence labeling we show a voltage-dependent fluorescence signal, reflecting a conformational change, which correlates with the voltage-dependent charge movement. We further show that selected mutations in the orthosteric site abolish the fluorescence signal and concomitantly, the voltage-dependence of the agonist binding. Surprisingly, mutations in the allosteric site also abolished the voltage-dependence of agonist binding but did not reduce the fluorescence signal. Finally, we show that treatments, which reduced the charge movement or hindered the coupling between the charge movement and the voltage-dependent binding, also reduced the fluorescence signal. Our results demonstrate that depolarization-induced conformational changes in the orthosteric binding site underlie the voltage-dependence of agonist binding. Our results are also unique in suggesting that the allosteric site is also involved in controlling the voltage-dependent agonist binding.

A novel fast mechanism for GPCR-mediated signal transduction--control of neurotransmitter release.

Reliable neuronal communication depends on accurate temporal correlation between the action potential and neurotransmitter release. Although a requirement for Ca(2+) in neurotransmitter release is amply documented, recent studies have shown that voltage-sensitive G protein-coupled receptors (GPCRs) are also involved in this process. However, how slow-acting GPCRs control fast neurotransmitter release is an unsolved question. Here we examine whether the recently discovered fast depolarization-induced charge movement in the M(2)-muscarinic receptor (M(2)R) is responsible for M(2)R-mediated control of acetylcholine release. We show that inhibition of the M(2)R charge movement in Xenopus oocytes correlated well with inhibition of acetylcholine release at the mouse neuromuscular junction. Our results suggest that, in addition to Ca(2+) influx, charge movement in GPCRs is also necessary for release control.

Control of neurotransmitter release: From Ca2+ to voltage dependent G-protein coupled receptors.

This review discusses two theories that try to explain mechanisms of control of neurotransmitter release in fast synapses: the Ca(2+) hypothesis and the Ca(2+) voltage hypothesis. The review summarizes experimental results that are incompatible with predictions from the Ca(2+) hypothesis and concludes that Ca(2+) is involved in the control of the amount of release but not in the control of the time course of evoked release, i.e., initiation and termination of evoked release. Results summarizing direct effects of changes in membrane potential on the release machinery are then presented. These changes in membrane potential affect the affinity (for the transmitter) of presynaptic autoinhibitory G-protein coupled receptors (GPCRs). The voltage dependence of these GPCRs and their pivotal role in determining the time course of evoked release is discussed.

New mechanism for voltage induced charge movement revealed in GPCRs--theory and experiments.

Depolarization induced charge movement associated currents, analogous to gating currents in channels, were recently demonstrated in G-protein coupled receptors (GPCRs), and were found to affect the receptor's Agonist binding Affinity, hence denoted AA-currents. Here we study, employing a combined theoretical-experimental approach, the properties of the AA-currents using the m2-muscarinic receptor (m2R) as a case study. We found that the AA-currents are characterized by a "bump", a distinct rise followed by a slow decline, which appears both in the On and the Off responses. The cumulative features implied a directional behavior of the AA-currents. This forced us to abandon the classical chemical reaction type of models and develop instead a model that includes anisotropic processes, thus producing directionality. This model fitted well the experimental data. Our main findings are that the AA-currents include two components. One is extremely fast, approximately 0.2 ms, at all voltages. The other is slow, 2-3 ms at all voltages. Surprisingly, the slow component includes a process which strongly depends on voltage and can be as fast as 0.3 ms at + 40 mV. The reason that it does not affect the overall time constant of the slow component is that it carries very little charge. The two fast processes are suitable candidates to link between charge movement and agonist binding affinity under physiological conditions.

Molecular mechanisms that control initiation and termination of physiological depolarization-evoked transmitter release.

Ca(2+) is essential for physiological depolarization-evoked synchronous neurotransmitter release. But, whether Ca(2+) influx or another factor controls release initiation is still under debate. The time course of ACh release is controlled by a presynaptic inhibitory G protein-coupled autoreceptor (GPCR), whose agonist-binding affinity is voltage-sensitive. However, the relevance of this property for release control is not known. To resolve this question, we used pertussis toxin (PTX), which uncouples GPCR from its G(i/o) and in turn reduces the affinity of GPCR toward its agonist. We show that PTX enhances ACh and glutamate release (in mice and crayfish, respectively) and, most importantly, alters the time course of release without affecting Ca(2+) currents. These effects are not mediated by G(beta)gamma because its microinjection into the presynaptic terminal did not alter the time course of release. Also, PTX reduces the association of the GPCR with the exocytotic machinery, and this association is restored by the addition of agonist. We offer the following mechanism for control of initiation and termination of physiological depolarization-evoked transmitter release. At rest, release is under tonic block achieved by the transmitter-bound high-affinity presynaptic GPCR interacting with the exocytotic machinery. Upon depolarization, the GPCR uncouples from its G protein and consequently shifts to a low-affinity state toward the transmitter. The transmitter dissociates, the unbound GPCR detaches from the exocytotic machinery, and the tonic block is alleviated. The free machinery, together with Ca(2+) that had already entered, initiates release. Release terminates when the reverse occurs upon repolarization.

The chemical synapse goes electric: Ca2+- and voltage-sensitive GPCRs control neurotransmitter release.

It is widely believed that the initiation of transmitter release in fast synapses is triggered by rapid Ca2+ entry and that the termination of release is governed by removal of Ca2+ from below the release sites. We argue that, although Ca2+ is essential for release, fast-entry kinetics render Ca2+ incapable of being the limiting factor for the initiation of release, and the relatively slow removal of Ca2+ cannot be the limiting factor for the termination of release. We suggest, and provide supporting evidence for, a novel general mechanism for control of fast transmitter release (in the range of milliseconds) from nerve terminals. According to this mechanism, two factors control release: Ca2+ and voltage-sensitive presynaptic inhibitory G-protein-coupled receptors (GPCRs). Inhibitory autoreceptors are known to mediate slow feedback inhibition of transmitter release. We discuss the evidence showing that these receptors also control the initiation and termination of transmitter release by directly interacting with core proteins in the exocytotic machinery. This novel mechanism has important implications for understanding the regulation of transmitter release, synaptic plasticity and neuronal circuit properties.

Movement of 'gating charge' is coupled to ligand binding in a G-protein-coupled receptor.

Activation by agonist binding of G-protein-coupled receptors (GPCRs) controls most signal transduction processes. Although these receptors span the cell membrane, they are not considered to be voltage sensitive. Recently it was shown that both the activity of GPCRs and their affinity towards agonists are regulated by membrane potential. However, it remains unclear whether GPCRs intrinsically respond to changes in membrane potential. Here we show that two prototypical GPCRs, the m2 and m1 muscarinic receptors (m2R and m1R), display charge-movement-associated currents analogous to 'gating currents' of voltage-gated channels. The gating charge-voltage relationship of m2R correlates well with the voltage dependence of the affinity of the receptor for acetylcholine. The loop that couples m2R and m1R to their G protein has a crucial function in coupling voltage sensing to agonist-binding affinity. Our data strongly indicate that GPCRs serve as sensors for both transmembrane potential and external chemical signals.

On the feedback between theory and experiment in elucidating the molecular mechanisms underlying neurotransmitter release.

This review describes the development of the molecular level Ca(2+)-voltage hypothesis. Theoretical considerations and feedback between theory and experiments played a key role in its development. The theory, backed by experiments, states that at fast synapses, membrane potential by means of presynaptic inhibitory autoreceptors controls initiation and termination of neurotransmitter release. A molecular kinetic scheme which depicts initiation and termination of evoked release is discussed. This scheme is able to account for both spontaneous release and evoked release. The physiological implications of this scheme are enumerated.

The metabotropic glutamate G-protein-coupled receptors mGluR3 and mGluR1a are voltage-sensitive.

G-protein-coupled receptors play a key role in signal transduction processes. Despite G-protein-coupled receptors being transmembrane proteins, the notion that they exhibit voltage sensitivity is rather novel. Here we examine whether two metabotropic glutamate receptors, mGluR3 and mGluR1a, both involved in fundamental physiological processes, exhibit, by themselves, voltage sensitivity. Measuring mGluR3-induced K(+) currents and mGluR1a-induced Ca(2+)-activated Cl(-) currents in Xenopus oocytes, we show that the apparent affinity toward glutamate decreases (mGluR3) or increases (mGluR1a) upon depolarization. Measurements of binding of [(3)H]glutamate to oocytes expressing either mGluR3 or mGluR1a corroborated the electrophysiological results. Using the chimeric Galpha subunit, we further show that the voltage sensitivity does not reside in the G-protein. To locate sites within the receptors that are involved in the voltage sensitivity, we used chimeric mGluR1a, where the intracellular loops that couple to the G-protein were replaced by those of mGluR3. The voltage sensitivity of the chimeric mGluR1a resembled that of mGluR3 and not that of the parental mGluR1a. The cumulative results indicate that the voltage sensitivity does not reside downstream to the activation of the receptors but rather in the mGluR3 and mGluR1a themselves. Furthermore, the intracellular loops play a crucial role in relaying changes in membrane potential to changes in the affinity of the receptors toward glutamate.

Release of neurotransmitter induced by Ca2+-uncaging: reexamination of the ca-voltage hypothesis for release.

The primacy of Ca2+ in controlling the amount of released neurotransmitter is well established. However, it is not yet clear what controls the time-course (initiation and termination) of release. Various experiments indicated that the time-course is controlled by membrane potential per se. Consequently the phenomenological Ca-Voltage-Hypothesis (CVH) was formulated. The CVH was later embodied in a molecular level mathematical model, whose key predictions were affirmed experimentally. Nonetheless, the single most important basis for the CVH, namely that depolarization per se is needed to induce physiological phasic release, was challenged by two major experimental findings. (i) Release was induced by Ca2+ alone by means of Ca2+-uncaging. (ii) There was at most a small additional effect when depolarization was applied after release was induced by Ca2+-uncaging. Point (i) was dealt with previously, but additional conclusions are drawn here. Here we concentrate on (ii) and show that the experimental results can be fully accounted for by the molecular level CVH model, with essentially the same parameters.

Mathematical modeling and optimization of drug delivery from intratumorally injected microspheres.

PURPOSE: Paclitaxel is a highly promising phase-sensitive antitumor drug that could conceivably be improved by extended lower dosing as opposed to intermittent higher dosing. Although intratumoral delivery of paclitaxel to the whole tumor at different loads and rates has already been achieved, determining an optimal release mode of paclitaxel for tumor eradication remains difficult. This study set out to rationally design such an optimal microsphere release mode based on mathematical modeling. EXPERIMENTAL DESIGN: A computational reaction-diffusion framework was used to model drug release from intratumorally injected microspheres, drug transport and binding in tumor interstitum, and drug clearance by microvasculature and intracellular uptake and binding. RESULTS: Numerical simulations suggest that interstitial drug concentration is characterized by a fast spatially inhomogeneous rise phase, during which interstitial and intracellular binding sites are saturated, followed by a slow spatially homogeneous phase that is governed by the rate of drug release from microspheres. For zero-order drug release, the slow phase corresponds to a plateau drug concentration that is proportional to the ratio of the rate of blood clearance of drug to the rate of drug release from microspheres. Consequently, increasing the duration of intratumoral drug release extends the duration of cell exposure to the drug but lowers the plateau drug concentration. This tradeoff implies that intratumoral drug release can be designed to optimize tumor cell kill. Synthesizing our modeling predictions with published dose-response data, we propose an optimal protocol for the delivery of paclitaxel-loaded microspheres to small solid tumors.

The M2 muscarinic G-protein-coupled receptor is voltage-sensitive.

G-protein coupled receptors are not considered to exhibit voltage sensitivity. Here, using Xenopus oocytes, we show that the M2 muscarinic receptor (m2R) is voltage-sensitive. The m2R-mediated potassium channel (GIRK) currents were used to assay the activity of m2R. We found that the apparent affinity of m2R toward acetylcholine (ACh) was reduced upon depolarization. Binding experiments of [3H]ACh to individual oocytes expressing m2R confirmed the electrophysiological findings. When the GIRK channels were activated either by overexpression of Gbetagamma subunits or by injection of GTPgammaS, the ratio between the currents measured at -60 mV and +40 mV was the same as for the basal activity of the GIRK channel. Thus, the steps downstream to agonist activation of m2R are not voltage-sensitive. We further found that, in contrast to m2R, the apparent affinity of m1R was increased upon depolarization. We also found that the voltage sensitivity of binding of [3H]ACh to oocytes expressing m2R was greatly diminished following pretreatment with pertussis toxin. The cumulative results suggest that m2R is, by itself, voltage-sensitive. Furthermore, the voltage sensitivity does not reside in the ACh binding site, rather, it most likely resides in the receptor region that couples to the G-protein.

Can the Ca2+ hypothesis and the Ca2+-voltage hypothesis for neurotransmitter release be reconciled?

It is well established that Ca2+ plays a key role in promoting the physiological depolarization-induced release (DIR) of neurotransmitters from nerve terminals (Ca2+ hypothesis). Yet, evidence has accumulated for the Ca2+-voltage hypothesis, which states that not only is Ca2+ required, but membrane potential as such also plays a pivotal role in promoting DIR. An essential aspect of the Ca2+-voltage hypothesis is that it is depolarization that is responsible for the initiation of release. This assertion seems to be contradicted by recent experiments wherein release was triggered by high concentrations of intracellular Ca2+ in the absence of depolarization [calcium-induced release (CIR)]. Here we show that there is no contradiction between CIR and the Ca2+-voltage hypothesis. Rather, CIR can be looked at as a manifestation of spontaneous release under conditions of high intracellular Ca2+ concentration. Spontaneous release in turn is governed by a subset of the molecular scheme for DIR, under conditions of no depolarization. Prevailing estimates for the intracellular calcium concentration, [Ca2+]i, in physiological DIR rely on experiments under conditions of CIR. Our theory suggests that these estimates are too high, because depolarization is absent in these experiments and [Ca2+]i is held at high levels for an extended period.

Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices.

Predicting the time course of in vivo biodegradation is a key issue in the design of an increasing number of biomedical applications such as sutures, tissue analogs and drug-delivery devices. The design of such biodegradable devices is hampered by the absence of quantitative models for the enzymatic erosion of solid protein matrices. In this work, we derive and simulate a reaction diffusion model for the enzymatic erosion of fibrillar gels that successfully reproduces the main qualitative features of this process. A key aspect of the proposed model is the incorporation of steric hindrance into the standard Michaelis-Menten scheme for enzyme kinetics. In the limit of instantaneous diffusion, the model equations are analogous to the standard equations for enzymatic degradation in solution. Invoking this analogy, the total quasi-steady-state approximation is used to derive approximate analytical solutions that are valid for a wide range of in vitro conditions. Using these analytical approximations, an experimental-theoretical method is derived to unambiguously estimate all the kinetic model parameters. Moreover, the analytical approximations correctly describe the characteristic hyperbolic dependence of the erosion rate on enzyme concentration and the zero-order erosion of thin fibers. For definiteness, the analysis of published experimental results of enzymatic degradation of fibrillar collagen is demonstrated, and the role of diffusion in these experiments is elucidated.

Ca2+-independent feedback inhibition of acetylcholine release in frog neuromuscular junction.

The effect of membrane potential on feedback inhibition of acetylcholine (ACh) release was studied using the frog neuromuscular junction. It was found that membrane potential affects the functional affinity (K(i)) of the presynaptic M2 muscarinic receptor. The K(i) for muscarine shifts from approximately 0.23 microm (at resting potential) to approximately 8 microm (at a high depolarization). Measurements of Ca2+ currents in axon terminals showed that the depolarization-mediated shift in K(i) does not stem from depolarization-dependent changes in Ca2+ influx. Pretreatments with pertussis toxin (PTX) abolished the depolarization-dependent shift in K(i); at all depolarizations K(i) was the same and higher (approximately 32 microm) than before PTX treatment. The inhibitory effect of muscarine on ACh release is produced by two independent mechanisms: a slow, PTX-sensitive process, which prevails at low to medium depolarizations and operates already at low muscarine concentrations, and a fast, PTX-insensitive and voltage-independent process, which requires higher muscarine concentrations. Neither of the two processes involves a reduction in Ca2+ influx.