Robert A. Spangler

Transfer function analysis of an oscillatory model chemical system

Abstract Oscillation occurring in the time course of a particular model reaction system is examined, utilizing the transfer function method of analysis developed in a previous paper. System properties predicted by the analytic technique correspond with those observed in analog computer solutions of the kinetic equations describing the system. The transfer function approach provides kinetic criteria for the existence of oscillation in terms of loop gain and phase shift, and elucidates the relation between oscillation and bistability, or flip-flop behavior. Although formulated to be biologically feasible, the model oscillating system is purely hypothetical, and is presented primarily as a basis for the development of general principles concerning periodicity and instability in complex reaction systems.

Repetitive response of the Hodgkin-Huxley model for the squid giant axon

Abstract The complex frequency current-voltage relation for the membrane, derived by linearizing the Hodgkin-Huxley equations about an assumed steady state, is interpreted in terms of a signal flow diagram of a feedback system. From the Nyquist plots thus obtained, the variation of the angular frequency of the oscillating linearized system with the magnitude of the constant current stimulus is determined and compared with the corresponding relation for the Hodgkin-Huxley model over the range of repetitive activity. The variation of the amplitude of the repetitive response with the magnitude of the constant current stimulus is compared with the corresponding relation derived from a first harmonic approximation. Good agreement is found for both the frequency and amplitude characteristics, except for low values of the constant current stimulus. The frequency of the repetitive response of the Hodgkin-Huxley model is found to be almost linearly related to the d.c. level of membrane potential.

Statistical‐Mechanical Derivation of the Partial Molecular Stress Tensors in Isothermal Multicomponent Systems

Commencing with the general equations of molecular dynamics as used by Bearman and Kirkwood, the hydrodynamic equations of motion are derived for each component in an isothermal multicomponent system consisting of sensibly spherical nonreacting molecules. It was the primary purpose of the investigation of which this is a report to attempt to obtain a microscopic statistical basis for the macroscopic phenomenologic development of Snell and Spangler, especially in regard to their new formulation for the partial molecular stress tensors. An expansion of the number densities in pair space of perturbed nonequilibrium states alternate to that used by Bearman and Kirkwood is employed. Our expansion esplicitly recognizes the position vector arguments of both the number densities in singlet space and the local mean velocities of the individual components, as well as for the equilibrium pair correlation function. The quantities are then expanded about the central position vector in a Taylors series. The results ar...

Voltage Clamp for Biological Investigations

A unique voltage clamp circuit for certain biological investigations, which features the provision of maintaining the clamped region at ground potential with the residual error balanced about ground, is discussed. Theoretical consideration of the circuit function indicates that the possibility of error arising from stray current pathways and loading of the electrodes is reduced by holding the clamped region close to ground. An additional secondary feedback loop, in conjunction with this circuit, reduces switching transients and other high frequency noise and allows dynamic balance of the clamped region about ground potential despite assymmetries in the experimental circuit. This circuit has been employed, using commercially available operational amplifier units, to clamp the isolated frog skin for measurement of sodium transport flux. In this application, the assembly clamped the skin to well within 1 mv, with excellent dc stability and a theoretical error of 0.1% in response to 1-msec transients.

Adenosine and adenosine triphosphate modulate the substrate binding affinity of glucose transporter GLUT1 in vitro.

Evidence indicates that a large portion of the facilitative glucose transporter isoform GLUT1 in certain animal cells is kept inactive and activated in response to acute metabolic stresses. A reversible interaction of a certain inhibitor molecule with GLUT1 protein has been implicated in this process. In an effort to identify this putative GLUT1 inhibitor molecule, we studied here the effects of adenosine and adenosine triphosphate (ATP) on the binding of D-glucose to GLUT1 by assessing their abilities to displace cytochalasin B (CB), using purified GLUT1 in vesicles. At pH 7.4, adenosine competitively inhibited CB binding to GLUT1 and also reduced the substrate binding affinity by more than an order of magnitude, both with an apparent dissociation constant (K(D)) of 3.0 mM. ATP had no effect on CB and D-glucose binding to GLUT1, but reduced adenosine binding affinity to GLUT1 by 2-fold with a K(D) of 30 mM. At pH 3.6, however, ATP inhibited the CB binding nearly competitively, and increased the substrate binding affinity by 4--5-fold, both with an apparent K(D) of 1.22 mM. These findings clearly demonstrate that adenosine and ATP interact with GLUT1 in vitro and modulate its substrate binding affinity. They also suggest that adenosine and ATP may regulate GLUT1 intrinsic activity in certain cells where adenosine reduces the substrate-binding affinity while ATP increases the substrate-binding affinity by interfering with the adenosine effect and/or by enhancing the substrate-binding affinity at an acidic compartment.

Sodium-dependent glucose transport by cultured proximal tubule cells

The cotransport of sodium ion and alpha-methyl glucose, a non-metabolized hexose, was studied in rabbit proximal tubule cells cultured in defined medium. The rate of uptake of alpha-methyl glucose shows saturation kinetics, in which Km, but not Vmax, is dependent upon the Na+ concentration in the medium. The transport system was found to be of the high-affinity type, characteristic of the straight portion of the proximal tubule. Analysis of the rates of initial uptake within the context of a generalized cotransport model, suggests that two Na+ ions are bound in the activation of the hexose transport. The steady-state level of accumulation of alpha-methyl glucose also depends upon sodium concentration, consistent with the initial rate findings. The uptake of alpha-methyl glucose is inhibited by other sugars with the relative potencies of D-glucose greater than alpha-methyl glucose greater than D-galactose = 3-O methylglucose. L-Glucose, D-fructose, and D-mannose show no inhibition. Phlorizin inhibits the alpha-methyl glucose uptake with a Ki of 9 X 10(-6) M. Ouabain (10(-3) M) decreases the steady-state alpha-methyl glucose accumulation by 60%. In the absence of sodium, the accumulation of alpha-methyl glucose is 7-fold less than at 142 mM Na+, reaching a level comparable to the sodium-independent accumulation of 3-O-methyl-D-glucose. These findings are similar to those observed in the proximal tubule of the intact kidney.

Scope and limitations of thermal imaging using multiwavelength infrared detection

In determining temperature of surfaces by their blackbody emission, simultaneous acquisition of infrared emission at different wavelengths can provide a set of parameters needed to compute the absolute temperature of the object. A graybody model can be used to derive a set of equations that correlates the effects of emissivity variation and reflection of ambient radiation on the apparent and true temperatures of the object. Such a model is presented and its sensitivities to noise are evaluated. A four-wavelength digital thermal imager has been constructed to evaluate the practical implementation of the model. Finally, utilizing a phantom that simulates a graybody, and human skin data, the validity of the model has been demonstrated. It is shown that the system noise and the computational errors of series expansion are the factors that limit the precision of the computed temperature.

Dynamic properties of polyelectrolyte calcium membranes

SummaryShashoua observed spontaneous oscillations in a polyelectrolyte membrane formed by interfacial precipitates of polyacid and polybase. We have here undertaken experimental and theoretical studies of polyglutamic acid-Ca++ membrane in order to clarify the processes involved in this dynamic behavior. We find a region of distinct hysteresis in the voltage current curve for this system. A sharp transition from a state of low membrane resistance to one of high resistance occurs at a current density different from that of inverse transition.This membrane system is modeled as a two layer structure: a negatively charged layer α made of ionized polyelectrolyte in series with a neutral region β in which the polymeric ionic sites are masked by calcium ion. This structure results in a difference in the transference number for the mobile ions, causing salt accumulation at the interfacial region during a current flow in the α to β direction. This altered salt concentration induces a change of polymeric conformation, which in turn affects the membrane permeability and the rate of accumulation. Based upon nonequilibrium thermodynamic flow equations, and a two-state representation of membrane macromolecular conformation, this model displays a region of hysteresis in the current range of experimental observations.

Transfer function analysis of chemical kinetic systems

Abstract A technique is developed for the analysis of complex coupled chemical reaction systems utilizing transfer functions to characterize the kinetic properties of each reaction process. The method of analysis involves linearization in the vicinity of some steady state of the system. A closed loop configuration of the reaction system imposes constraints upon the time course exhibited by the system, since the product of transfer functions around the loop must be unity. Instability of a particular steady state, and oscillatory behavior may be examined through this analytic approach.

Negative Feedback Electrometer Circuit

An electrometer circuit, utilizing a commercially available differential operational amplifier, is described and its basis of operation briefly analyzed. By virtue of the negative feedback configuration employed, interelectrode potential relationships in the electrometer tube are maintained virtually constant, thus providing highly stable performance, linear gain characteristics, and a high effective input impedance. Provision for compensation of nonideal amplifier characteristics and input capacitance neutralization is included.