Calcium currents in the A7r5 smooth muscle-derived cell line. An allosteric model for calcium channel activation and dihydropyridine agonist action

We have investigated the gating kinetics of calcium channels in the A7r5 cell line at the level of single channels and whole cell currents, in the absence and presence of dihydropyridine (DHP) calcium channel agonists. Although latencies to first opening and macroscopic currents are strongly voltage dependent, analysis of amplitude histograms indicates that the primary open-closed transition is voltage independent. This suggests that the molecular mechanisms for voltage sensing and channel opening are distinct, but coupled. We propose a modified Monod-Wyman-Changeux (MWC) model for channel activation, where movement of a voltage sensor is analogous to ligand binding, and the closed and open channels correspond to inactive (T) and active (R) states. This model can account for the activation kinetics of the calcium channel, and is consistent with the existence of four homologous domains in the main subunit of the calcium channel protein. DHP agonists slow deactivation kinetics, shift the activation curve to more negative potentials with an increase in slope, induce intermingled fast and slow channel openings, and reduce the latency to first opening. These effects are predicted by the MWC model if we make the simple assumption that DHP agonists act as allosteric effectors to stabilize the open states of the channel.     

Quantification of dopaminergic supersensitization using apomorphine-induced behavior in the mouse

Dose-response curves for apomorphine-induced behavior were determined in C57BL/6J mice with and without a 30 day treatment with 2.5 mg/kg/day haloperidol. The effect of the chronic neuroleptic, whether assessed by the dose-response curve for total ratings or by a multiple logistic method determining ED50's for transitions between individual stereotype ratings, was to shift the curve to the left by a factor of slightly less than 2. This estimate is considerably different from those using the rotational model and denervation as the supersensitizing stimulus. There was no indication of selective effects of the neuroleptic treatment on individual components of the behavioral response.     

A new measure of cooperativity in protein-ligand binding

An allosteric binding system consisting of a single ligand and a nondissociating macromolecule having multiple binding sites can be represented by a binding polynomial. Various properties of the binding process can be obtained by analyzing the coefficients of the binding polynomial and such functions as the binding curve and the Hill plot. The Hill plot has an asymptote of unit slope at each end and the departure of the slope from unity at any point can be used to measure the effective interaction free energy at that point. Of particular interest in detecting and measuring cooperativity are extrema of the Hill slope and its value at the half-saturation point. If the binding polynomial is symmetric, then there is an extremum of the Hill slope at the half-saturation point. This value, the Hill coefficient, is a convenient measure of cooperativity. The purpose of this paper is to express the Hill coefficient for symmetric binding polynomials in terms of the roots of the polynomial and to give an interpretation of cooperativity in terms of the geometric pattern of the roots in the complex plane. This interpretation is then applied to the binding polynomials for the MWC (Monod-Wyman-Changeux) and KNF (Koshland-Nemethy-Filmer) models.     

Additive and independent responses in a single receptor: aspartate and maltose stimuli on the tar protein

The aspartate and maltose responses of E. coli are mediated through a single membrane receptor, yet the responses are independent and additive. Both stimuli cause methylation of the same 4 glutamic acid residues. More extensive methylation occurs when a cell that has adapted to one stimulus is exposed to the second, or when both stimuli are added simultaneously. The degree of methylation, as well as receptor migration on two-dimensional gels, demonstrates that only one type of protein is involved, rather than two different receptors arising from differential processing of a single gene. A conformational "push-pull" mechanism in which binding of stimulus and covalent modification, producing opposing stresses, can explain these diverse results.     

Integrated allosteric model of voltage gating of HCN channels

Hyperpolarization-activated (pacemaker) channels are dually gated by negative voltage and intracellular cAMP. Kinetics of native cardiac f-channels are not compatible with HH gating, and require closed/open multistate models. We verified that members of the HCN channel family (mHCN1, hHCN2, hHCN4) also have properties not complying with HH gating, such as sigmoidal activation and deactivation, activation deviating from fixed power of an exponential, removal of activation "delay" by preconditioning hyperpolarization. Previous work on native channels has indicated that the shifting action of cAMP on the open probability (Po) curve can be accounted for by an allosteric model, whereby cAMP binds more favorably to open than closed channels. We therefore asked whether not only cAMP-dependent, but also voltage-dependent gating of hyperpolarization-activated channels could be explained by an allosteric model. We hypothesized that HCN channels are tetramers and that each subunit comprises a voltage sensor moving between "reluctant" and "willing" states, whereas voltage sensors are independently gated by voltage, channel closed/open transitions occur allosterically. These hypotheses led to a multistate scheme comprising five open and five closed channel states. We estimated model rate constants by fitting first activation delay curves and single exponential time constant curves, and then individual activation/deactivation traces. By simply using different sets of rate constants, the model accounts for qualitative and quantitative aspects of voltage gating of all three HCN isoforms investigated, and allows an interpretation of the different kinetic properties of different isoforms. For example, faster kinetics of HCN1 relative to HCN2/HCN4 are attributable to higher HCN1 voltage sensors' rates and looser voltage-independent interactions between subunits in closed/open transitions. It also accounts for experimental evidence that reduction of sensors' positive charge leads to negative voltage shifts of Po curve, with little change of curve slope. HCN voltage gating thus involves two processes: voltage sensor gating and allosteric opening/closing.     

A model for nonlinear stochastic behavior of the pupil

In binocular fusion, pairs of left and right stimuli yielding the same brightness perception constitute an equibrightness curve in a coordinate system whose ordinate and abscissa correspond to the left and right stimulus strengths. A neural network model is presented to elucidate the characteristics of the curve. According to the model, Fechner's paradox is due to the threshold characteristics of the neuron. If the shapes or movements are radically different between the left and right stimuli, the retinal rivalry is caused. That is, only the left stimulus is perceived at one moment and the right stimulus at another moment. The period of left or right eye dominance alternates randomly from time to time. The distribution of the period is approximate to the gamma distribution. In order to account for this fact, a neural network model is proposed, which consists of a pair of neurons receiving inputs with stochastic fluctuations. The computer simulation was carried out with satisfactory results. The model of retinal rivalry is integrated with that of brightness perception.     

On the relationship between the Hill coefficients for steady-state and transient kinetic data: A criterion for concerted transitions in allosteric proteins

A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.     

Dose-response function for Painter's SCE-model

Summary The replication model for sister chromatid exchange (SCE), when introduced in 1980 by Painter, was claimed to be consistent with the one hit property of SCE. However, the argument offered in favour of the one hit property was based on a defective dose-response function, as shown in this paper, since dose as the independent parameter of any dose-response function was not included in the considerations. This missing part of the model's dose-response function is added and, by using Bessel functions, a formula for the complete dose-response function is presented. A re-examination of the newly derived function shows that, in the model, linearity holds only under certain restricted circumstances.     

Self-association of the cardiac fatty acid binding protein. Influence on membrane-bound, fatty acid dependent enzymes

The present study on the fatty acid binding protein, purified from pig heart and studied by three independent techniques (electron spin resonance, circular dichroism, and polyacrylamide gel electrophoresis), suggests that the protein self-aggregates and exists in at least four distinct molecular species. This plurality is demonstrated by the presence of four bands after electrophoretic migration at pH 7.2 and by three transitions of molar ellipticity theta 225 that depend on protein concentration. A mathematical model is formulated to simulate the three transitions and to calculate the concentrations of the four species. The multistates manifest themselves in a complex binding capacity for fatty acid, with two sigmoidal components in the binding curve. A general equation for the curve is formulated, and the characteristic constants are evaluated by a nonlinear least-squares fit. The experimental results and their interpretation in quantitative terms lead to a theoretical evaluation of the importance of this new property of self-aggregation of the protein on the activity of membrane-bound model enzymes which are fatty acid or acyl coenzyme A dependent.     

Stimulus motion propels traveling waves in binocular rivalry

State transitions in the nervous system often take shape as traveling waves, whereby one neural state is replaced by another across space in a wave-like manner. In visual perception, transitions between the two mutually exclusive percepts that alternate when the two eyes view conflicting stimuli (binocular rivalry) may also take shape as traveling waves. The properties of these waves point to a neural substrate of binocular rivalry alternations that have the hallmark signs of lower cortical areas. In a series of experiments, we show a potent interaction between traveling waves in binocular rivalry and stimulus motion. The course of the traveling wave is biased in the motion direction of the suppressed stimulus that gains dominance by means of the wave-like transition. Thus, stimulus motion may propel the traveling wave across the stimulus to the extent that the stimulus motion dictates the traveling wave's direction completely. Using a computational model, we show that a speed-dependent asymmetry in lateral inhibitory connections between retinotopically organized and motion-sensitive neurons can explain our results. We argue that such a change in suppressive connections may play a vital role in the resolution of dynamic occlusion situations.     

Auditory steady-state responses to multiple simultaneous stimuli

Steady-state responses can follow multiple simultaneous auditory stimuli. If the stimuli are modulated at different rates, responses specific to each stimulus can be assessed by measuring in the frequency domain response the spectral component corresponding to the rate of modulation. When each stimulus has a different carrier frequency or different ear of presentation, the responses when 8 stimuli are presented simultaneously are not significantly different than when each stimulus is presented alone. Since significant responses can be recognized down to intensities that average 14 dB above behavioral threshold, this technique may be useful in objective audiometry. It is also possible to record steady-state responses to multiple modulations of the same carrier frequency. In this case, the amplitude of the responses when the stimuli are combined is smaller than when the stimuli are presented alone. The decrease in amplitude depends upon the number of concomitant stimuli and their relative intensities. These effects are probably due to the compressive rectification occurring during cochlear transduction, and the data may be used to model cochlear processing of auditory stimuli.     

A computational model of stereoscopic prey capture in praying mantises

We present a simple model which can account for the stereoscopic sensitivity of praying mantis predatory strikes. The model consists of a single “disparity sensor”: a binocular neuron sensitive to stereoscopic disparity and thus to distance from the animal. The model is based closely on the known behavioural and neurophysiological properties of mantis stereopsis. The monocular inputs to the neuron reflect temporal change and are insensitive to contrast sign, making the sensor insensitive to interocular correlation. The monocular receptive fields have a excitatory centre and inhibitory surround, making them tuned to size. The disparity sensor combines inputs from the two eyes linearly, applies a threshold and then an exponent output nonlinearity. The activity of the sensor represents the model mantis’s instantaneous probability of striking. We integrate this over the stimulus duration to obtain the expected number of strikes in response to moving targets with different stereoscopic disparity, size and vertical disparity. We optimised the parameters of the model so as to bring its predictions into agreement with our empirical data on mean strike rate as a function of stimulus size and disparity. The model proves capable of reproducing the relatively broad tuning to size and narrow tuning to stereoscopic disparity seen in mantis striking behaviour. Although the model has only a single centre-surround receptive field in each eye, it displays qualitatively the same interaction between size and disparity as we observed in real mantids: the preferred size increases as simulated prey distance increases beyond the preferred distance. We show that this occurs because of a stereoscopic “false match” between the leading edge of the stimulus in one eye and its trailing edge in the other; further work will be required to find whether such false matches occur in real mantises. Importantly, the model also displays realistic responses to stimuli with vertical disparity and to pairs of identical stimuli offering a “ghost match”, despite not being fitted to these data. This is the first image-computable model of insect stereopsis, and reproduces key features of both neurophysiology and striking behaviour.     

Comparison of cytogenic response of human lymphocytes to in vivo and in vitro exposure to low doses of gamma-rays. Unstable chromosomal exchanges detected by FPG techniques

On peripheral lymphocytes of eight cancer patients undergone whole-body therapeutic irradiation (at daily dose of 10 cGy up to total dose of 50 cGy of 60Co gamma-rays) the dose-response of unstable chromosome exchanges (dicentrics and centric rings) was studied. This dose response fitted well linear function. The lower slope of dose-response curve was found for in vivo irradiated lymphocytes as compared to the dose response curve obtained for in vitro irradiated lymphocytes of the same patients. This finding seems to provide evidence that in case of protracted irradiation of individuals an absorbed dose could be underestimated if for biological dosimetry an in vitro dose response curve for unstable chromosome aberrations is used as referent one.     

Flux detectors versus concentration detectors: two types of chemoreceptors

Dose-response curves relating the external stimulus concentration to receptor occupancy differ in two types of chemoreceptor organs. In 'concentration detectors' the receptor molecules at the receptor cell membrane are directly exposed to the external stimulus concentration; these organs exhibit the well-known hyperbolic dose-response relationship reflecting the association-dissociation of stimulus and receptor molecules. In contrast, 'flux detectors' accumulate the stimulus molecules in a perireceptor compartment. In flux detectors, deactivation of stimulus molecules may be in balance with arrival, as a prerequisite for producing a constant effective stimulus concentration at constant adsorptive flux of stimulus molecules. In a simple model of a flux detector in which receptor molecules themselves catalyze the deactivation, the dose-response relationship is linear. It reflects the rate of stimulus deactivation. If the deactivation is catalyzed by a separate enzyme, the dose-response relationship can be close to hyperbolic, or linear. In all cases, the receptor molecules are maximally occupied if the adsorptive flux equals or exceeds the maximum rate of stimulus deactivation. The time course of the receptor potential recorded from moths' pheromone receptors depends on the odor compound, which suggests that a peripheral process, possibly the stimulus deactivation, is the slowest, rate-limiting process of the transduction cascade. Further evidence comes from experiments with stimuli oversaturating the mechanism responsible for the decline of the receptor potential.      

Characterization of combinatorial patterns generated by multiple two-component sensors in E. coli that respond to many stimuli

Two-component systems enable bacteria to sense changes in their environment and adjust gene expression in response. Multiple two-component systems could function as a combinatorial sensor to discriminate environmental conditions. A combinatorial sensor is composed of a set of sensors that are non-specifically activated to different magnitudes by many stimuli, such that their collective activity pattern defines the signal. Using promoter reporters and flow cytometry, we measured the response of three two-component systems in Escherichia coli that have been previously reported to respond to many environmental stimuli (EnvZ/OmpR, CpxA/CpxR, and RcsC/RcsD/RcsB). A chemical library was screened for the ability to activate the sensors and 13 inducers were identified that produce different patterns of sensor activity. The activities of the three systems are uncorrelated with each other and the osmolarity of the inducing media. Five of the seven possible non-trivial patterns generated by three sensors are observed. This data demonstrate one mechanism by which bacteria are able to use a limited set of sensors to identify a diverse set of compounds and environmental conditions.     

The role of terminal-link stimuli in concurrent-chain schedules: revisited using a behavioral-history procedure

A behavioral-history procedure was used to study the function of terminal-link stimuli as conditioned reinforcers in multiple concurrent-chain schedules of reinforcement. First, three pigeons were exposed to multiple concurrent-chain schedules in which the two multiple-schedule components were correlated with a blue and a white stimulus, respectively. In each component the initial links were equal independent variable-interval (VI) 15 s schedules. A fixed-interval (FI) 10 s schedule operated on the red key in one terminal link while extinction operated on the green key in the alternative terminal link. When large preferences for the red stimulus had been established, two tests were conducted. In the terminal-link test, under new initial-link stimuli--purple and brown--an FI 10 s schedule operated for both the red and green terminal-link stimuli. In the subsequent initial-link test, the blue and white initial-link stimuli were reintroduced, and, as in the terminal-link test, FI 10s operated for both the red and the green terminal-link stimuli. In the terminal-link test, the three pigeons showed no preference for the terminal links with the red stimulus, but showed clear and consistent preferences for the red stimulus when blue and white stimuli were reintroduced as initial-link stimuli in the initial-link test. This suggests that there are multiple sources of control over initial-link response allocation in concurrent-chains, including control by both terminal- and initial-link stimuli.     

A neural network model of general olfactory coding in the insect antennal lobe.

A central problem in olfaction is understanding how the quality of olfactory stimuli is encoded in the insect antennal lobe (or in the analogously structured vertebrate olfactory bulb) for perceptual processing in the mushroom bodies of the insect protocerebrum (or in the vertebrate olfactory cortex). In the study reported here, a relatively simple neural network model, inspired by our current knowledge of the insect antennal lobes, is used to investigate how each of several features and elements of the network, such as synapse strengths, feedback circuits and the steepness of neural activation functions, influences the formation of an olfactory code in neurons that project from the antennal lobes to the mushroom bodies (or from mitral cells to olfactory cortex). An optimal code in these projection neurons (PNs) should minimize potential errors by the mushroom bodies in misidentifying the quality of an odor across a range of concentrations while maximizing the ability of the mushroom bodies to resolve odors of different quality. Simulation studies demonstrate that the network is able to produce codes independent or virtually independent of concentration over a given range. The extent of this range is moderately dependent on a parameter that characterizes how long it takes for the voltage in an activated neuron to decay back to its resting potential, strongly dependent on the strength of excitatory feedback by the PNs onto antennal lobe intrinsic neurons (INs), and overwhelmingly dependent on the slope of the activation function that transforms the voltage of depolarized neurons into the rate at which spikes are produced. Although the code in the PNs is degraded by large variations in the concentration of odor stimuli, good performance levels are maintained when the complexity of stimuli, as measured by the number of component odorants, is doubled. When excitatory feedback from the PNs to the INs is strong, the activity in the PNs undergoes transitions from initial states to stimulus-specific equilibrium states that are maintained once the stimulus is removed. When this PN-IN feedback is weak the PNs are more likely to relax back to a stimulus-independent equilibrium state, in which case the code is not maintained beyond the application of the stimulus. Thus, for the architecture simulated here, strong feedback from the PNs onto the INs, together with step-like neuronal activation functions, could well be important in producing easily discriminable odor quality codes that are invariant over several orders of magnitude in stimulus concentration.