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Biomedical subjects

R S Eisenberg

Publications and source records attributed to R S Eisenberg.

At least 19 recordsLinked to original sources
PubMed2005

Computing numerically the access resistance of a pore.

The access resistance (AR) of a channel is an important component of the conductance of ion channels, particularly in wide and short channels, where it accounts for a substantial fraction of the total resistance to the movement of ions. The AR is usually calculated by using a classical and simple expression derived by Hall from electrostatics (J.E. Hall 1975 J. Gen. Phys. 66:531-532), though other expressions, both analytical and numerical, have been proposed. Here we report some numerical results for the AR of a channel obtained by solving the Poisson-Nernst-Planck equations at the entrance of a circular pore. Agreement is found between numerical calculations and analytical results from Hall's equation for uncharged pores in neutral membranes. However, for channels embedded in charged membranes, Hall's expression overestimates the AR, which is much lower and can even be neglected in some cases. The weak dependence of AR on the pore radius for charged membranes at low salt concentration can be exploited to separate the channel and the access contributions to the measured conductance.

Biological Transport↗
PubMed2004

Memoryless control of boundary concentrations of diffusing particles.

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of noninteracting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. To maintain average concentrations at the boundaries of the region at their values in the baths, a control mechanism is needed to set the boundary dynamics of the trajectories. Different control mechanisms are used in Langevin and Brownian simulations of such systems. We analyze models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a nonrenewal controller that maintains concentrations of noninteracting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).

Biological Transport↗
PubMed2004

Saturation of conductance in single ion channels: the blocking effect of the near reaction field.

The ionic current flowing through a protein channel in the membrane of a biological cell depends on the concentration of the permeant ion, as well as on many other variables. As the concentration increases, the rate of arrival of bath ions to the channel's entrance increases, and typically so does the net current. This concentration dependence is part of traditional diffusion and rate models that predict Michaelis-Menten current-concentration relations for a single ion channel. Such models, however, neglect other effects of bath concentrations on the net current. The net current depends not only on the entrance rate of ions into the channel, but also on forces acting on ions inside the channel. These forces, in turn, depend not only on the applied potential and charge distribution of the channel, but also on the long-range Coulombic interactions with the surrounding bath ions. In this paper, we study the effects of bath concentrations on the average force on an ion in a single ion channel. We show that the force of the reaction field on a discrete ion inside a channel embedded in an uncharged lipid membrane contains a blocking (shielding) term that is proportional to the square root of the ionic bath concentration. We then show that different blocking strengths yield different behavior of the current-concentration and conductance-concentration curves. Our theory shows that at low concentrations, when the blocking force is weak, conductance grows linearly with concentration, as in traditional models, e.g., Michaelis-Menten formulations. As the concentration increases to a range of moderate shielding, conductance grows as the square root of concentration, whereas at high concentrations, with high shielding, conductance may actually decrease with increasing concentrations: the conductance-concentration curve can invert. Therefore, electrostatic interactions between bath ions and the single ion inside the channel can explain the different regimes of conductance-concentration relations observed in experiments.

Animals↗
PubMed2003

Dielectric boundary force and its crucial role in gramicidin.

In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielectric boundary charges (DBC)] at boundaries between different dielectrics. These induced surface charges, in return, exert a force [called dielectric boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in standard continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielectric interfaces, for example, when ions permeate through protein channels embedded in biological membranes. In this paper, we define the DBF and calculate it explicitly for a planar dielectric wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a solution of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A positive ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the positive ion is reduced. A negative ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the negative ion is increased. Thus, a positive ion can permeate the channel, while a negative ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged positive ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion's radius.

Biophysical Phenomena↗
PubMed2001

Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.

Electrophysiology↗
PubMed2001

Modified Donnan potentials for ion transport through biological ion channels.

In the classical study of ion transport through charged membranes, Donnan potentials are used to approximate the difference between the applied electrostatic potential and the potential at the liquid/membrane interface. For very thin membranes (e.g., biological lipid bilayers), this discontinuous approximation of the potential is not sufficient. Here we derive a modification to the classic Donnan potential for ion transport through a biological ion channel embedded in a lipid bilayer. We also show how to derive the classic Donnan potential without the usual assumptions and estimate the amount of space charge at the liquid/membrane interface.

Biophysics↗
PubMed2000

Genomics in the public domain: strategy and policy.

The public domain has been conspicuous in media accounts of public and private sector initiatives to complete the sequence of the human genome. The issue of whether the human genome will be freely available to the public or privately held as a proprietary resource has captured the attention of the scientific, trade and popular press, the financial markets, and even heads of state. Although some media commentary has framed the issue as a conflict between ethics and greed, strategic considerations go a long way towards explaining the timing and quality of information disclosures on both sides of the public-private divide.

DNA↗
PubMed1998

Can patents deter innovation? The anticommons in biomedical research.

The "tragedy of the commons" metaphor helps explain why people overuse shared resources. However, the recent proliferation of intellectual property rights in biomedical research suggests a different tragedy, an "anticommons" in which people underuse scarce resources because too many owners can block each other. Privatization of biomedical research must be more carefully deployed to sustain both upstream research and downstream product development. Otherwise, more intellectual property rights may lead paradoxically to fewer useful products for improving human health.

Animals↗
PubMed1997

Structure and function in gene patenting.

The United States patent system treats DNA sequences as large chemical compounds in determining their patentability. This approach has been helpful to those who seek to patent previously unidentified DNA sequences, but it may prove less advantageous from the perspective of those who elucidate biological functions and disease relevance of previously identified genes. A current controversy over patent rights for DNA sequences encoding leptin receptors provides a useful case study for illustrating some of the issues that are likely to arise in applying doctrine derived from chemical patent cases in the context of gene discovery.

Animals↗
PubMed1996

Intellectual property issues in genomics.

Controversy over intellectual property rights in the results of large-scale cDNA sequencing raises intriguing questions about the roles of the public and private sectors in genomics research, and about who stands to benefit (and who stands to lose) from the private appropriation of genomic information. While the US Patent and Trademark Office has rejected patent applications on cDNA fragments of unknown function from the National Institutes of Health, private firms have pursued three distinct strategies for exploiting unpatented cDNA sequence information: exclusive licensing, non-exclusive licensing and dedication to the public domain.

Biotechnology↗
PubMed1995

Hydrodynamic model of temperature change in open ionic channels.

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel.

Electrochemistry↗
PubMed1994

Origins of open-channel noise in the large potassium channel of sarcoplasmic reticulum.

Open-channel noise was studied in the large potassium channel of the sarcoplasmic reticulum (SR). Inside-out patches were excised directly from the SR of split skeletal muscle fibers of lobster, with lobster relaxing ringer (LRR) in bath and pipette. The power spectrum of open-channel noise is very low and approximately flat in the 100 Hz-10 kHz frequency range. At 20 degrees C, with an applied voltage of 50 mV, the mean single-channel current (i) is 9 pA (mean single-channel conductance = 180 pS) and the mean power spectral density 1.1 x 10(-29) A2/Hz. The latter increases nonlinearly with (i), showing a progressively steeper dependence as (i) increases. At 20 mV, the mean power spectral density is almost independent of (i) and approximately 1.4 times that of the Johnson noise calculated for the equivalent ideal resistor with zero net current; at 70 mV it increases approximately in proportion to (i)2. The mean power spectral density has a weak temperature dependence, very similar to that of (i), and both are well described by a Q10 of 1.3 throughout the range 3-40 degrees C. Discrete ion transport events are thought to account for a significant fraction of the measured open-channel noise, probably approximately 30-50% at 50 mV. Brief interruptions of the single-channel current, due either to blockage of the open channel by an extrinsic aqueous species, or to intrinsic conformational changes in the channel molecule itself, were a possible additional source of open-channel noise. Experiments in modified bathing solutions indicate, however, that open-channel noise is not affected by any of the identified aqueous species present in LRR. In particular, magnesium ions, the species thought most likely to cause brief blockages, and calcium and hydrogen ions, have no detectable effect. This channel's openings exhibit many brief closings and substrates, due to intrinsic gating of the channel. Unresolved brief full closings are calculated to make a negligible contribution (< 1%) to the measured power spectral density. The only significant source of noise due to band width-limited missed events is brief, frequent 80% substrates (mean duration 20 microseconds, mean frequency 1,000 s-1) which account for a small part of the measured power spectral density (approximately 14%, at 50 mV, 20 degrees C). We conclude that a large fraction of the measured open-channel noise results from intrinsic conductance fluctuations, with a corner frequency higher than the resolution of our recordings, in the range 10(4)-10(7) Hz.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1993

Flux, coupling, and selectivity in ionic channels of one conformation.

Ions crossing biological membranes are described as a concentration of charge flowing through a selective open channel of one conformation and analyzed by a combination of Poisson and Nernst-Planck equations and boundary conditions, called the PNP theory for short. The ion fluxes in this theory interact much as ion fluxes interact in biological channels and mediated transporters, provided the theoretical channel contains permanent charge and has selectivity created by (electro-chemical) resistance at its ends. Interaction occurs because the flux of different ionic species depends on the same electric field. That electric field is a variable, changing with experimental conditions because the screening (i.e., shielding) of the permanent charge within the channel changes with experimental conditions. For example, the screening of charge and the shape of the electric field depend on the concentration of all ionic species on both sides of the channel. As experimental interventions vary the screening, the electric field varies, and thus the flux of each ionic species varies conjointly, and is, in that sense, coupled. Interdependence and interaction are the rule, independence is the exception, in this channel.

Biological Transport, Active↗