Device Approach to Biology (and Engineering)
The goal of biological research is often more to control than to understand. Devices in biology (like ion channels) control individual functions just as they do in our technology. Study of control requires a multiscale approach because a handful of atoms, moving in 10-15 sec, control biological functions extending meters and taking seconds. Structural biology and molecular dynamics are essential (and beautiful!) parts of this hierarchy, but so are the functions themselves, and the electric field equations that link structure and function on all scales from atoms to nerve cells. Analyzing biological systems as devices is usually successful, and almost always productive.
Device approach to biology and engineeringBob Eisenberg
Device Approach to Biology (and Engineering)
The goal of biological research is often more to control than to understand. Devices in biology (like ion channels) control individual functions just as they do in our technology. Study of control requires a multiscale approach because a handful of atoms, moving in 10-15 sec, control biological functions extending meters and taking seconds. Structural biology and molecular dynamics are essential (and beautiful!) parts of this hierarchy, but so are the functions themselves, and the electric field equations that link structure and function on all scales from atoms to nerve cells. Analyzing biological systems as devices is usually successful, and almost always productive.
Ions in solutions liquid plasma of chemistry & biology february 27 2019Bob Eisenberg
Ions in water form a plasma of great importance in which much chemistry is done. All of life occurs in ionic solutions. We show how analysis based on a Poisson Fermi treatment of ionic solutions, based on the saturation which can occur when ions have finite volume, can account for the experimental properties of many solutions
This presentation has been moved. To view this presentation, please visit http://pubs.acs.org/iapps/liveslides/pages/index.htm?mscNo=jz300841u
Determination of Excited-State Energies and Dynamics in the B Band of the Bacterial Reaction Center with 2D Electronic Spectroscopy
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Tracking of Proton Transfer Reaction in Supercooled RNA Nucleoside
This presentation has been moved. To view this presentation, please visit http://pubs.acs.org/iapps/liveslides/pages/index.htm?mscNo=jz301064w
Quantum Dynamics of the HO + CO H + CO2 Reaction on an Accurate Potential Energy Surface
Device approach to biology and engineeringBob Eisenberg
Device Approach to Biology (and Engineering)
The goal of biological research is often more to control than to understand. Devices in biology (like ion channels) control individual functions just as they do in our technology. Study of control requires a multiscale approach because a handful of atoms, moving in 10-15 sec, control biological functions extending meters and taking seconds. Structural biology and molecular dynamics are essential (and beautiful!) parts of this hierarchy, but so are the functions themselves, and the electric field equations that link structure and function on all scales from atoms to nerve cells. Analyzing biological systems as devices is usually successful, and almost always productive.
Ions in solutions liquid plasma of chemistry & biology february 27 2019Bob Eisenberg
Ions in water form a plasma of great importance in which much chemistry is done. All of life occurs in ionic solutions. We show how analysis based on a Poisson Fermi treatment of ionic solutions, based on the saturation which can occur when ions have finite volume, can account for the experimental properties of many solutions
This presentation has been moved. To view this presentation, please visit http://pubs.acs.org/iapps/liveslides/pages/index.htm?mscNo=jz300841u
Determination of Excited-State Energies and Dynamics in the B Band of the Bacterial Reaction Center with 2D Electronic Spectroscopy
This presentation has been moved. To view this presentation, please visit http://pubs.acs.org/iapps/liveslides/pages/index.htm?mscNo=jz300541t
Tracking of Proton Transfer Reaction in Supercooled RNA Nucleoside
This presentation has been moved. To view this presentation, please visit http://pubs.acs.org/iapps/liveslides/pages/index.htm?mscNo=jz301064w
Quantum Dynamics of the HO + CO H + CO2 Reaction on an Accurate Potential Energy Surface
Bio-Molecular Engineering is the Future of Molecular BiologyBob Eisenberg
Bio-Molecular Engineering is the Future of Molecular Biology: Now that we have large numbers of excellent structures, we molecular biologists must turn to studying how they work. That is the task of BioMolecular Engineering that uses almost the same tools as classical membrane biophysics. Both treat systems as devices, with inputs, outputs and power supplies, that ONLY function with flow, away from equilibrium.
Talk multiscale analysis of ionic solutions is unavoidableBob Eisenberg
Ions in channels and solutions control most living functions. Analysis in atomic detail is needed, but so is prediction of functions on the macroscopic scale. Computational electronics has solved similar issues and we all benefit from the computational devices it provides us. These slides show how a similar approach can be used, and is necessary in my view, for ions solutions and biological systems, most notably in ion channels
Molecular Mean Field Theory of ions in Bulk and ChannelsBob Eisenberg
Life and most of chemistry occurs in ionic solutions, but ionic solutions have only recently been recognized as the complex fluids that they are. The molecular view shows ions interacting with surrounding water and nearby ions. Everything is correlated in a complex way because ions and water have diameters comparable to their interaction length. The molecular scale shows only a small part of the correlation enforced by electrodynamics. Current defined as Maxwell did to include the ethereal current is exactly conserved, and therefore correlated, over all scales reaching to macroscopic boundary conditions some 10^9× larger than atoms crucial in batteries and nerve cells.
Jinn Liang Liu and I have built a molecular field theory PNPB Poisson Nernst Planck Bikerman that deals with water as molecules and describes local interactions with a steric potential that depends on the volume fraction of molecules and voids between them. The correlations of electrodynamics are described by a fourth-order differential operator that gives (as outputs) ion-ion and ion-water correlations; the dielectric response (permittivity) of ionic solutions; and the polarization of water molecules, all using a single correlation length parameter. The theory fits experimental data on activity and differential capacitance in ionic solutions of varying composition and content, including mixtures. Potassium channels, Gramicidin, L-type calcium channels, and the Na/Ca transporter are computed in three dimensions from structures in the Protein Data Bank.
Numerical analysis faces challenges
Geometric singularities of molecular surfaces
strong electric fields (100 mV/nm) and resulting exponential nonlinearities, and the
enormous concentrations (> 10 M) often found where ions are important, for example, near electrodes in batteries, in ion channels, and in active sites of proteins.
Wide ranging concentrations of Ca^(2+) in (> 10M) and near (10^(-2) to 10^(-8)M) almost every protein in biological cells make matters worse.
Challenges have been overcome using methods developed over many decades by the large community that works on the computational electronics of semiconductors.
What is different about life? it is inherited oberwolfach march 7 1 2018Bob Eisenberg
What is different about life? Why do life sciences require different science and mathematics? I address these issues starting from the obvious: all of life is inherited from genes. Twenty thousand genes of say 30 atoms each control an animal of ~1e25 atoms. How is that possible? Answer: the structures of life form a hierarchy of devices that allow handfuls of atoms to control everything. A nerve signal involves meters of nerve but is controlled by a few atoms. Indeed, potassium and sodium differ only in the diameter of the atoms. Life depends on this difference in diameter. Sodium and potassium are otherwise identical. The task of the biological scientist is first to identify the hierarchy of devices and what they do. Then we want to know how the devices work. We want to understand life well enough to improve its devices, in disease and technology.
Ion Channel Simulations for Potassium, Sodium, Calcium, and Chloride Channels...Iowa State University
Computer simulations of realistic ion channel structures have always been challenging and a subject of rigorous study. Simulations based on continuum electrostatics have proven to be computationally cheap and reasonably accurate in predicting a channel's behavior. In this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for KcsA channel and study its steady-state response. SILVACO is a well-established program, typically used by electrical engineers to simulate the process flow and electrical characteristics of solid-state devices. By employing this simulation program, we have presented an alternative computing platform for performing ion channel simulations, besides the known methods of writing codes in programming languages. With the ease of varying the different parameters in the channel's vestibule and the ability of incorporating surface charges, we have shown the wide-ranging possibilities of using a device simulator for ion channel simulations. Our simulated results closely agree with the experimental data, validating our model.
https://www.sciencedirect.com/science/article/abs/pii/S0169260706002276
Talk two electro dynamics and ions in chemistryBob Eisenberg
The universal nature of electrodynamics and the strength of the electric field needs to be incoporated into chemical theory and thinking. The law of mass action for example is incompatible with continuity of current and thus with Maxwell's equations. Maxwell's equations are accurate from unimaginably small to unimaginably large dimensions with immeasurable accuracy. Violations of Maxwell's equations have large effects because the electric field is so large. Methods are shown to incorporate these realities into chemical descriptions.
Saturation of ions in channels and solutions a fermi-poisson treatment 11-19-...Bob Eisenberg
The main effect of the finite size of ions is the saturation of concentration. Here we use a Fermi like distribution to deal with that saturation and show that we can describe ions in calcium channels, gramicdin, and in bulk solutions with some accuracy.
Saturation of ions in channels and solutions a Fermi-Poisson treatment 11-23-...Bob Eisenberg
Ions in water, and in and near channels, proteins, nucleic acids, and electrodes are difficult to analyze, because everything interacts with everything else through the electric field and through the steric exclusion of ions and water. Ions and water have their own space and cannot overlap significantly. Excluded volume has almost always been treated by enforcing force laws that prevent overlap. Such treatments are difficult to compute because of the singularity of the forces and the need for three dimensions. Here we take a different approach and enforce a Fermi like distribution of the entropy of mixtures of spheres of any size, derived by J.-L. Liu. We show that this approach fits the complex properties of calcium channels, and the properties of gramicdin channels, computed from their full three dimensional structure. Using the simplest shell treatment of hydration, we successfully compute the activity (free energy per mole) curves of pure calcium and sodium chloride solutions. The Fermi-Poisson approach uses the full consistency of its mathematics to replace the computation of repulsive forces. It may prove to be good enough to detail with experimental data in three dimensions difficult to deal with accurately in any other way.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
On the Possibility of Manipulating Lightwaves via Active Electric Chargescclarbl
‧ Can TEM waves be affected by the presence of electric charges?
‧ We’ve seen role of passive charges → dipoles → dielectrics
‧ Can EM waves/ lights be manipulated meaningfully by
active charges instead?
‧ Exact solution in the presence of still and moving charges
→ useful?
‧ E. T. Whittaker’s two potential general solution → useful?
‧ Feynman’s versatile formula → intuitive and useful?
‧ Scope reduction to steady-state → effect of interfacial & surface active charges
‧ Experiments & results
Maxwell's equations can be written without a dielectric constant. They are then universal and exact. They are also useful because they imply a universal and exact conservation of total current (including the displacement current). Kirchhoff's current law for circuits then also becomes universal and exact.
Maxwell's Equations can be written without a dielectric constant.
They then imply conservation of total current as a universal and exact physical law. In circuits they imply a generalization of Kirchhoff's current law that is universal and exact
More Related Content
Similar to Talk device approach to biology march 29 1 2015
Bio-Molecular Engineering is the Future of Molecular BiologyBob Eisenberg
Bio-Molecular Engineering is the Future of Molecular Biology: Now that we have large numbers of excellent structures, we molecular biologists must turn to studying how they work. That is the task of BioMolecular Engineering that uses almost the same tools as classical membrane biophysics. Both treat systems as devices, with inputs, outputs and power supplies, that ONLY function with flow, away from equilibrium.
Talk multiscale analysis of ionic solutions is unavoidableBob Eisenberg
Ions in channels and solutions control most living functions. Analysis in atomic detail is needed, but so is prediction of functions on the macroscopic scale. Computational electronics has solved similar issues and we all benefit from the computational devices it provides us. These slides show how a similar approach can be used, and is necessary in my view, for ions solutions and biological systems, most notably in ion channels
Molecular Mean Field Theory of ions in Bulk and ChannelsBob Eisenberg
Life and most of chemistry occurs in ionic solutions, but ionic solutions have only recently been recognized as the complex fluids that they are. The molecular view shows ions interacting with surrounding water and nearby ions. Everything is correlated in a complex way because ions and water have diameters comparable to their interaction length. The molecular scale shows only a small part of the correlation enforced by electrodynamics. Current defined as Maxwell did to include the ethereal current is exactly conserved, and therefore correlated, over all scales reaching to macroscopic boundary conditions some 10^9× larger than atoms crucial in batteries and nerve cells.
Jinn Liang Liu and I have built a molecular field theory PNPB Poisson Nernst Planck Bikerman that deals with water as molecules and describes local interactions with a steric potential that depends on the volume fraction of molecules and voids between them. The correlations of electrodynamics are described by a fourth-order differential operator that gives (as outputs) ion-ion and ion-water correlations; the dielectric response (permittivity) of ionic solutions; and the polarization of water molecules, all using a single correlation length parameter. The theory fits experimental data on activity and differential capacitance in ionic solutions of varying composition and content, including mixtures. Potassium channels, Gramicidin, L-type calcium channels, and the Na/Ca transporter are computed in three dimensions from structures in the Protein Data Bank.
Numerical analysis faces challenges
Geometric singularities of molecular surfaces
strong electric fields (100 mV/nm) and resulting exponential nonlinearities, and the
enormous concentrations (> 10 M) often found where ions are important, for example, near electrodes in batteries, in ion channels, and in active sites of proteins.
Wide ranging concentrations of Ca^(2+) in (> 10M) and near (10^(-2) to 10^(-8)M) almost every protein in biological cells make matters worse.
Challenges have been overcome using methods developed over many decades by the large community that works on the computational electronics of semiconductors.
What is different about life? it is inherited oberwolfach march 7 1 2018Bob Eisenberg
What is different about life? Why do life sciences require different science and mathematics? I address these issues starting from the obvious: all of life is inherited from genes. Twenty thousand genes of say 30 atoms each control an animal of ~1e25 atoms. How is that possible? Answer: the structures of life form a hierarchy of devices that allow handfuls of atoms to control everything. A nerve signal involves meters of nerve but is controlled by a few atoms. Indeed, potassium and sodium differ only in the diameter of the atoms. Life depends on this difference in diameter. Sodium and potassium are otherwise identical. The task of the biological scientist is first to identify the hierarchy of devices and what they do. Then we want to know how the devices work. We want to understand life well enough to improve its devices, in disease and technology.
Ion Channel Simulations for Potassium, Sodium, Calcium, and Chloride Channels...Iowa State University
Computer simulations of realistic ion channel structures have always been challenging and a subject of rigorous study. Simulations based on continuum electrostatics have proven to be computationally cheap and reasonably accurate in predicting a channel's behavior. In this paper we discuss the use of a device simulator, SILVACO, to build a solid-state model for KcsA channel and study its steady-state response. SILVACO is a well-established program, typically used by electrical engineers to simulate the process flow and electrical characteristics of solid-state devices. By employing this simulation program, we have presented an alternative computing platform for performing ion channel simulations, besides the known methods of writing codes in programming languages. With the ease of varying the different parameters in the channel's vestibule and the ability of incorporating surface charges, we have shown the wide-ranging possibilities of using a device simulator for ion channel simulations. Our simulated results closely agree with the experimental data, validating our model.
https://www.sciencedirect.com/science/article/abs/pii/S0169260706002276
Talk two electro dynamics and ions in chemistryBob Eisenberg
The universal nature of electrodynamics and the strength of the electric field needs to be incoporated into chemical theory and thinking. The law of mass action for example is incompatible with continuity of current and thus with Maxwell's equations. Maxwell's equations are accurate from unimaginably small to unimaginably large dimensions with immeasurable accuracy. Violations of Maxwell's equations have large effects because the electric field is so large. Methods are shown to incorporate these realities into chemical descriptions.
Saturation of ions in channels and solutions a fermi-poisson treatment 11-19-...Bob Eisenberg
The main effect of the finite size of ions is the saturation of concentration. Here we use a Fermi like distribution to deal with that saturation and show that we can describe ions in calcium channels, gramicdin, and in bulk solutions with some accuracy.
Saturation of ions in channels and solutions a Fermi-Poisson treatment 11-23-...Bob Eisenberg
Ions in water, and in and near channels, proteins, nucleic acids, and electrodes are difficult to analyze, because everything interacts with everything else through the electric field and through the steric exclusion of ions and water. Ions and water have their own space and cannot overlap significantly. Excluded volume has almost always been treated by enforcing force laws that prevent overlap. Such treatments are difficult to compute because of the singularity of the forces and the need for three dimensions. Here we take a different approach and enforce a Fermi like distribution of the entropy of mixtures of spheres of any size, derived by J.-L. Liu. We show that this approach fits the complex properties of calcium channels, and the properties of gramicdin channels, computed from their full three dimensional structure. Using the simplest shell treatment of hydration, we successfully compute the activity (free energy per mole) curves of pure calcium and sodium chloride solutions. The Fermi-Poisson approach uses the full consistency of its mathematics to replace the computation of repulsive forces. It may prove to be good enough to detail with experimental data in three dimensions difficult to deal with accurately in any other way.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
On the Possibility of Manipulating Lightwaves via Active Electric Chargescclarbl
‧ Can TEM waves be affected by the presence of electric charges?
‧ We’ve seen role of passive charges → dipoles → dielectrics
‧ Can EM waves/ lights be manipulated meaningfully by
active charges instead?
‧ Exact solution in the presence of still and moving charges
→ useful?
‧ E. T. Whittaker’s two potential general solution → useful?
‧ Feynman’s versatile formula → intuitive and useful?
‧ Scope reduction to steady-state → effect of interfacial & surface active charges
‧ Experiments & results
Similar to Talk device approach to biology march 29 1 2015 (20)
Maxwell's equations can be written without a dielectric constant. They are then universal and exact. They are also useful because they imply a universal and exact conservation of total current (including the displacement current). Kirchhoff's current law for circuits then also becomes universal and exact.
Maxwell's Equations can be written without a dielectric constant.
They then imply conservation of total current as a universal and exact physical law. In circuits they imply a generalization of Kirchhoff's current law that is universal and exact
Core Maxwell Equations are Scary April 11, 2021Bob Eisenberg
When the Maxwell equations are written without a dielectric constant, they are universal and exact, for biological and technological applications, from inside atoms to between stars. Dielectric and polarization phenomena need then to be described by stress strain relations for charge, that show how charge redistributes when the electric field is changed, in each system of interest.
Conservation of total current (including the ethereal displacement current 휺_ퟎ 흏퐄∕흏풕) is then as exact as the Maxwell equations themselves and independent of any property of matter. It is a consequence of the Lorentz invariance of the elementary charge, a property of all locally inertial systems, described by the theory of relativity.
Exact Conservation of Total Current allows a redefinition of Kirchhoff’s current law that is itself exact. In unbranched systems like circuit components or ion channels, conservation of total current becomes equality. Spatial dependence of total current disappears in that case. Hopping phenomena disappear. Spatial Brownian motion disappears. The infinite variation of a Brownian model of thermal noise becomes the zero spatial variation of total current. Maxwell’s Core Equations become a perfect (spatial) low pass filter.
An Exact and Universal theory of Electrodynamics is a scary challenge to scientists like me, trained to be skeptical of all sweeping claims to perfection.
Thermostatics vs. electrodynamics preprints 10.20944.v1Bob Eisenberg
Thermodynamics has been the foundation of many models of biological and technological systems. But thermodynamics is static and is misnamed. A more suitable name is thermostatics.
Thermostatics does not include time as a variable and so has no velocity, flow or friction. Indeed, as usually formulated, thermostatics does not include boundary conditions. Devices require boundary conditions to define their input and output. They usually involve flow and friction. Thermostatics is an unsuitable foundation for understanding technological and biological devices. A time dependent generalization of thermostatics that might be called thermal dynamics is being
developed by Chun Liu and collaborators to avoid these limitations. Electrodynamics is not restricted like thermostatics, but in its classical formulation involves drastic assumptions about polarization and an over-approximated dielectric constant. Once the Maxwell equations are rewritten without a dielectric constant, they are universal and exact. Conservation of total current,including displacement current, is a restatement of the Maxwell equations that leads to dramatic simplifications in the understanding of one dimensional systems, particularly those without branches, like the ion channel proteins of biological membranes and the two terminal devices of electronic systems. The Brownian fluctuations of concentrations and fluxes of ions become the spatially independent total current, because the displacement current acts as an unavoidable low pass filter, a consequence of the Maxwell equations for any material polarization. Electrodynamics and thermal dynamics together form a suitable foundation for models of technological and biological systems.
Maxwell equations without a polarization field august 15 1 2020Bob Eisenberg
Electrodynamics is almost always written using a polarization vector field to describe the response of matter to an electric field, or more specifically, to describe the change in distribution of charges as an electric field is applied or changed. This approach does not allow unique specification of a polarization field from measurements of the electric and magnetic fields and electrical current.
Many polarization fields will produce the same electric and magnetic fields, and current, because only the divergence of the polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. Models of structures that produce polarization cannot be uniquely determined from electrical measurements for the same reason. Models must describe charge distribution not just distribution of polarization to be unique.
I propose a different approach, using a different paradigm to describe field dependent charge, i.e., to describe the phenomena of polarization. I propose an operational definition of polarization that has worked well in biophysics where a field dependent, time dependent polarization provides the gating current that makes neuronal sodium and potassium channels respond to voltage. The operational definition has been applied successfully to experiments for nearly fifty years. Estimates of polarization have been computed from simulations, models, and theories using this definition and they fit experimental data quite well.
I propose that the same operational definition be used to define polarization charge in experiments, models, computations, theories, and simulations of other systems. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’.
The classical polarization field need not enter into that treatment at all.
Molecular Mean-Field Theory of Ionic Solutions: a Poisson-Nernst-Planck-Biker...Bob Eisenberg
We have developed a molecular mean-field theory — fourth-order Poisson-
Nernst-Planck-Bikerman theory — for modeling ionic and water flows in biological ion channels
by treating ions and water molecules of any volume and shape with interstitial voids,
polarization of water, and ion-ion and ion-water correlations. The theory can also be used to
study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel
cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc.
The theory can compute electric and steric energies from all atoms in a protein and all ions
and water molecules in a channel pore while keeping electrolyte solutions in the extra- and
intracellular baths as a continuum dielectric medium with complex properties that mimic
experimental data. The theory has been verified with experiments and molecular dynamics
data from the gramicidin A channel, L-type calcium channel, potassium channel, and
sodium/calcium exchanger with real structures from the Protein Data Bank. It was also
verified with the experimental or Monte Carlo data of electric double-layer differential capacitance
and ion activities in aqueous electrolyte solutions. We give an in-depth review of
the literature about the most novel properties of the theory, namely, Fermi distributions of
water and ions as classical particles with excluded volumes and dynamic correlations that
depend on salt concentration, composition, temperature, pressure, far-field boundary conditions
etc. in a complex and complicated way as reported in a wide range of experiments.
The dynamic correlations are self-consistent output functions from a fourth-order differential
operator that describes ion-ion and ion-water correlations, the dielectric response (permit2
tivity) of ionic solutions, and the polarization of water molecules with a single correlation
length parameter.
1. INTRODUCTION
Water and ions give life. Their electrostatic and kinetic interactions play essential roles
in biological and chemical systems such as DNA, proteins, ion channels, cell membranes,
Hsinchu maxwell talk january 7 1 2020 for uploadBob Eisenberg
Applying the Maxwell equations to mitochondria seems a hopeless task: there is so much complexity. But computers and their chips are nearly as complicated. Design of circuits is done every day by uncounted numbers of engineers and scientists, thanks to Kirchoff's Current Law, which is a conservation law in one dimensional (branched) systems of devices. Kirchoff's current law conserves flux, not current in its usual derivation. But Maxwell's equations do not conserve flux; they conserve total current. Total current J equals flux plus displacement current J+ eps_0 partial E/partial t . Maxwell's definition of current allows circuit laws to be applied to complex systems of devices, over a wide range of times and conditions. Channels and enzymes are devices because they localize current flow. Channels and enzymes can be analyzed by the methods of circuit theory, for that reason.
Lens as an Osmotic Pump, a Bidomain Model. DOI: 10.13140/RG.2.2.25046.80966Bob Eisenberg
The lens of the eye has no blood vessels to interfere with vision. The lens is far too large for diffusion to provide food and clear wastes.
Experimental, theoretical and computational work has shown that the lens supports its own microcirculation. It is an osmotic pump that implements what physiologists have long believed “Convection provides what diffusion cannot.”
We introduce a general (non-electro-neutral) model that describes the steady-state relationships among ion fluxes, water flow and electric field inside cells, and in the narrow extracellular spaces within the lens.
Using asymptotic analysis, we derive a simplified model exploiting the numerical values of physiological parameters. The model reduces to first generation ‘circuit’ models and shows the basis of computer simulations too large to easily understand. The full model helps resolve paradoxes that have perplexed molecular biologists: crucial physiological properties do not depend as expected on the permeability of the lens interior (to water flow).
Updating maxwell with electrons and charge version 6 aug 28 1Bob Eisenberg
Maxwell’s equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on the electric field. Charge was induced and polarization was described by a single dielectric constant.
Electrons, permanent charge, and polarization are important when matter is involved. Polarization of matter cannot be described by a single dielectric constant ε_(r )with reasonable realism today when applications involve 10^(-10) sec. Only vacuum is well described by a single dielectric constant ε_(0 ).
Here, Maxwell's equations are rewritten to include permanent charge and any type of polarization. Rewriting is in one sense petty, and in another sense profound, in either case presumptuous. Either petty or profound, rewriting confirms the legitimacy of electrodynamics that includes permanent charge and realistic polarization. One cannot be sure that a theory of electrodynamics without electrons or (permanent, field independent) charge (like Maxwell’s equations as he wrote them) would be legitimate or not. After all a theory cannot calculate the fields produced by charges (for example electrons) that are not in the theory at all!
After updating,
1) Maxwell’s equations seem universal and exact.
2) Polarization must be described explicitly to use Maxwell’s equations in applications.
3) Conservation of total current (including ε_0 ∂E⁄∂t) becomes exact, independent of matter, allowing precise definition of electromotive force EMF in circuits.
4) Kirchhoff’s current law becomes as exact as Maxwell’s equations themselves.
5) Conservation of total current needs to be satisfied in a wide variety of systems where it has not traditionally received much attention.
6) Classical chemical kinetics is seen to need revision to conserve current.
The name PNP was introduced by Eisenberg and Chen because it has important physical meaning beyond being the first letters of Poisson-Nernst-Planck. PNP also means Positive-Negative-Positive, the signs of majority current carriers in different regions of a PNP bipolar transistor. PNP transistors are two diodes in series PN + NP that rectify by changing the shape of the electric field. Transistors can function as quite different types of nonlinear devices by changing the shape of the electric field. Those realities motivated Eisenberg and Chen to introduce the name PNP.
The pun “PNP = Poisson-Nernst-Planck = Positive-Negative-Positive” has physical content. It suggests that Poisson-Nernst-Planck systems like open ionic channels should not be assumed to have constant electric fields. The electric field should be studied and computed because its change of shape is likely to be important in the function of biological systems, as it is in semiconductor systems.
Updating maxwell with electrons and charge Aug 2 2019Bob Eisenberg
Maxwell’s equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on the electric field. Charge was induced and polarization was described by a single dielectric constant.
Electrons, permanent charge, and polarization are important when matter is involved. Polarization of matter cannot be described by a single dielectric constant ε_(r )with reasonable realism today when applications involve 10^(-10) sec. Only vacuum is well described by a single dielectric constant ε_(0 ).
Here, Maxwell's equations are rewritten to include permanent charge and any type of polarization. Rewriting is in one sense petty, and in another sense profound, in either case presumptuous. Either petty or profound, rewriting confirms the legitimacy of electrodynamics that includes permanent charge and realistic polarization. One cannot be sure ahead of time that a theory of electrodynamics without electrons or (permanent, field independent) charge (like Maxwell’s equations as he wrote them) would be legitimate or not. After all a theory cannot calculate the fields produced by charges (for example electrons) that are not in the theory at all!
After updating,
Maxwell’s equations seem universal and exact.
Polarization must be described explicitly to use Maxwell’s equations in applications.
Conservation of total current (including ε_0 ∂E⁄∂t) becomes exact, independent of matter, allowing precise definition of electromotive force EMF in circuits.
Kirchhoff’s current law becomes as exact as Maxwell’s equations themselves.
Classical chemical kinetics is seen to need revision to conserve current.
Dielectric Dilemma 1901.10805 v2 feb 4 2019Bob Eisenberg
A dielectric dilemma faces scientists because Maxwell's equations are poor approximations as usually written, with a single dielectric constant. Maxwell's equations are then not accurate enough to be useful in many applications. The dilemma can be partially resolved by a rederivation of conservation of current, where current is defined now to include the epolarization of the vacuumf ..0 .......... Conserveration of current becomes Kirchoff's current law with this definition, in the one dimensional circuits of our electronic technology. With this definition, Kirchoff's laws are valid whenever Maxwell's equations are valid, explaining why those laws reliably describe circuits that switch in nanoseconds.
The action potential signal of nerve and muscle is produced by voltage sensitive channels that include a specialized device to sense voltage. Gating currents of the voltage sensor are now known to depend on the back-and-forth movements of positively charged arginines through the hydrophobic plug of a voltage sensor domain. Transient movements of these permanently charged arginines, caused by the change of transmembrane potential, further drag the S4 segment and induce opening/closing of ion conduction pore by moving the S4-S5 linker. The ion conduction pore is a separate device from the voltage sensor, linked (in an unknown way) by the mechanical motion and electric field changes of the S4-S5 linker. This moving permanent charge induces capacitive current flow everywhere. Everything interacts with everything else in the voltage sensor so everything must interact with everything else in its mathematical model, as everything does in the whole protein. A PNP-steric model of arginines and a mechanical model for the S4 segment are combined using energy variational methods in which all movements of charge and mass satisfy conservation laws of current and mass. The resulting 1D continuum model is used to compute gating currents under a wide range of conditions, corresponding to experimental situations. Chemical-reaction-type models based on ordinary differential equations cannot capture such interactions with one set of parameters. Indeed, they may inadvertently violate conservation of current. Conservation of current is particularly important since small violations (<0.01%) quickly (<< 10-6 seconds) produce forces that destroy molecules. Our model reproduces signature properties of gating current: (1) equality of on and off charge in gating current (2) saturating voltage dependence in QV curve and (3) many (but not all) details of the shape of gating current as a function of voltage.
Electricity plays a special role in our lives and life. Equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term the displacement current (of vacuum). Displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as Maxwell did, as the entire source of the curl of the magnetic field. We show how the Bohm formulation of quantum mechanics allows easy definition of current. We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. Matter does not behave the way physicists of the 1800's thought it does with a single dielectric constant, a real positive number independent of everything. Charge moves in enormously complicated ways that cannot be described in that way, when studied on time scales important today for electronic technology and molecular biology. Life occurs in ionic solutions in which charge moves in response to forces not mentioned or described in the Maxwell equations, like convection and diffusion. Classical derivations of conservation of current involve classical treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave that way, classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved exactly in any material no matter how complex the dielectric, polarization or conduction currents are. We believe models, simulations, and computations should conserve current on all scales, as accurately as possible, because physics conserves current that way. We believe models will be much more successful if they conserve current at every level of resolution, the way physics does.
Electricity is different august 16 1 2016 with doiBob Eisenberg
Charges are everywhere because most atoms are charged. Chemical bonds are formed by electrons with their charge. Charges move and interact according to Maxwell's equations in space and in atoms where the equations of electrodynamics are embedded in Schrödinger's equation as the potential. Maxwell's equations are universal, valid inside atoms and between stars from times much shorter than those of atomic motion (0.1 femtoseconds) to years (32 mega-seconds). Maxwell's equations enforce the conservation of current. Analysis shows that the electric field can take on whatever value is needed to ensure conservation of current. The properties of matter rearrange themselves to satisfy Maxwell's equations and conservation of current. Conservation of current is as universal as Maxwell's equations themselves. Yet equations of electrodynamics find little place in the literature of material physics, chemistry, or biochemistry. Kinetic models of chemistry and Markov treatments of atomic motion are ordinary differential equations in time and do not satisfy conservation of current unless modified significantly. Systems at equilibrium, without macroscopic flow, have thermal fluctuating currents that are conserved according to the Maxwell equations although their macroscopic averages are zero. The macroscopic consequences of atomic scale fluctuating thermal currents are not known but are likely to be substantial because of the nonlinear interactions in systems like these, in which 'everything interacts with everything else'.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Seminar of U.V. Spectroscopy by SAMIR PANDASAMIR PANDA
Spectroscopy is a branch of science dealing the study of interaction of electromagnetic radiation with matter.
Ultraviolet-visible spectroscopy refers to absorption spectroscopy or reflect spectroscopy in the UV-VIS spectral region.
Ultraviolet-visible spectroscopy is an analytical method that can measure the amount of light received by the analyte.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
8. 8
Biology is made of
Devices
and they are Multiscale
Hodgkin’s Action Potential
is the
Ultimate Biological Device
from
Input from Synapse
Output to Spinal Cord
Ultimate
Multiscale
Device
from
Atoms to Axons
Ångstroms to Meters
9. Device
Amplifier
Converts an Input to an Output
by a simple ‘law’
an algebraic equation
9
out gain in
gain
V g V
g
constantpositive real number,like12
Vin Vout
Gain
Power
Supply
110 v
10. Device
converts an
Input to an Output
by a simple ‘law’
10
out gain inV g V
DEVICE IS USEFUL
because it is
ROBUST and TRANSFERRABLE
ggain is Constant !!
11. Device
Amplifier
Converts an Input to an Output
11
Power is needed
Non-equilibrium, with flow
Displaced Maxwellian
of velocities
Provides Flow
Input, Output, Power Supply
are at
Different Locations
Spatially non-uniform boundary conditions
Vin Vout
Gain
Power
Supply
110 v
12. Device converts Input to Output by a simple ‘law’
12
Device is ROBUST and TRANSFERRABLE
because it uses POWER and has complexity!
Dotted lines outline: current mirrors (red); differential amplifiers (blue);
class A gain stage (magenta); voltage level shifter (green); output stage (cyan).
Circuit Diagram of common 741 op-amp: Twenty transistors needed to make linear robust device
INPUT
Vin(t)
OUTPUT
Vout (t)
Power Supply
Dirichlet Boundary Condition
independent of time
and everything else
Power Supply
Dirichlet Boundary Condition
independent of time
and everything else
13. 13
How Describe a Device?
Not by its circuit diagram
Not by its atomic structure
but by its
Device Equation !!
14. 14
How Describe Biological Devices?
Engineering is about Device Equations
P.S. I do not know the answer. But I know how to begin, …. I think.
15. 15
Biological Question
How do a few atoms control
(macroscopic)
Device Function ?
Mathematics of Molecular Biology
is about
How the device works
In mathspeak:
Solving Inverse Problems
16. 16
A few atoms make a
BIG Difference
Current Voltage relation determined by
John Tang
in Bob Eisenberg’s Lab
Ompf
G119D
Glycine G
replaced by
Aspartate D
OmpF
1M/1M
G119D
1M/1M
G119D
0.05M/0.05M
OmpF
0.05M/0.05M
Structure determined by
Raimund Dutzler
in Tilman Schirmer’s lab
18. Natural nano-valves** for atomic control of biological function
18
Ions channels coordinate contraction of cardiac muscle,
allowing the heart to function as a pump
Coordinate contraction in skeletal muscle
Control all electrical activity in cells
Produce signals of the nervous system
Are involved in secretion and absorption in all cells:
kidney, intestine, liver, adrenal glands, etc.
Are involved in thousands of diseases and many
drugs act on channels
Are proteins whose genes (blueprints) can be
manipulated by molecular genetics
Have structures shown by x-ray crystallography in
favorable cases
Can be described by mathematics in some cases
*nearly pico-valves: diameter is 400 – 900 x 10-12 meter;
diameter of atom is ~200 x 10-12 meter
Ions in Channels: Biological Devices, Diodes*
~30 x 10-9 meter
K
+
*Device is a Specific Word,
that exploits
specific mathematics & science
20. Nonner & Eisenberg
Side Chains are Spheres
Channel is a Cylinder
Side Chains are free to move within Cylinder
Ions and Side Chains are at free energy minimum
i.e., ions and side chains are ‘self organized’,
‘Binding Site” is induced by substrate ions
‘All Spheres’ Model
22. 22
Ions in Channels
and
Ions in Bulk Solutions
are
Complex Fluids
like liquid crystals of LCD displays
All atom simulations of complex fluid are
particularly challenging because
‘Everything’ interacts with ‘everything’ else
on atomic& macroscopic scales
23. 23
20
Learned from Doug Henderson, J.-P. Hansen, Stuart Rice, among others…Thanks!
Ions
in a solution are a
Highly Compressible Plasma
Central Result of Physical Chemistry
although the
Solution is Incompressible
Free energy of an ionic solution is mostly determined by the
Number density of the ions.
Density varies from 10-11 to 101M
in typical biological system of proteins, nucleic acids, and channels.
24. 24
Energetic Variational Approach
EnVarA
Chun Liu, Rolf Ryham, and Yunkyong Hyon
Mathematicians and Modelers: two different ‘partial’ variations
written in one framework, using a ‘pullback’ of the action integral
1
2 0
E
'' Dissipative'Force'Conservative Force
x u
Action Integral, after pullback Rayleigh Dissipation Function
Field Theory of Ionic Solutions: Liu, Ryham, Hyon, Eisenberg
Allows boundary conditions and flow
Deals Consistently with Interactions of Components
Composite
Variational Principle
Euler Lagrange Equations
Shorthand for Euler Lagrange process
with respect to x
Shorthand for Euler Lagrange process
with respect tou
25. 2
,
= , = ,
i i i
B i i j j
B i
i n p j n p
D c c
k T z e c d y dx
k T c
=
Dissipative
,
= = , ,
0
, , =
1
log
2 2
i
B i i i i i j j
i n p i n p i j n p
c
k T c c z ec c d y dx
d
dt
Conservative
Hard Sphere
Terms
Permanent Charge of proteintime
ci number density; thermal energy; Di diffusion coefficient; n negative; p positive; zi valence; ε dielectric constantBk T
Number Density
Thermal Energy
valence
proton charge
Dissipation Principle
Conservative Energy dissipates into Friction
= ,
0
2
1
22
i i
i n p
z ec
Note that with suitable boundary conditions
25
26. 26
1
2 0
E
'' Dissipative'Force'Conservative Force
x u
is defined by the Euler Lagrange Process,
as I understand the pure math from Craig Evans
which gives
Equations like PNP
BUT
I leave it to you (all)
to argue/discuss with Craig
about the purity of the process
when two variations are involved
Energetic Variational Approach
EnVarA
27. 27
PNP (Poisson Nernst Planck) for Spheres
Eisenberg, Hyon, and Liu
12
,
14
12
,
14
12 ( ) ( )
= ( )
| |
6 ( ) ( )
( ) ,
| |
n n n nn n
n n n n
B
n p n p
p
a a x yc c
D c z e c y dy
t k T x y
a a x y
c y dy
x y
Nernst Planck Diffusion Equation
for number density cn of negative n ions; positive ions are analogous
Non-equilibrium variational field theory EnVarA
Coupling Parameters
Ion Radii
=1
or( ) =
N
i i
i
z ec i n p
0ρ
Poisson Equation
Permanent Charge of Protein
Number Densities
Diffusion Coefficient
Dielectric Coefficient
valence
proton charge
Thermal Energy
28. All we have to do is
Solve it/them!
with boundary conditions
defining
Charge Carriers
ions, holes, quasi-electrons
Geometry
28
30. Dirk Gillespie
Dirk_Gillespie@rush.edu
Gerhard Meissner, Le Xu, et al,
not Bob Eisenberg
More than 120 combinations of solutions & mutants
7 mutants with significant effects fit successfully
Best Evidence is from the
RyR Receptor
31. 31
1. Gillespie, D., Energetics of divalent selectivity in a calcium channel: the ryanodine receptor
case study. Biophys J, 2008. 94(4): p. 1169-1184.
2. Gillespie, D. and D. Boda, Anomalous Mole Fraction Effect in Calcium Channels: A Measure
of Preferential Selectivity. Biophys. J., 2008. 95(6): p. 2658-2672.
3. Gillespie, D. and M. Fill, Intracellular Calcium Release Channels Mediate Their Own
Countercurrent: Ryanodine Receptor. Biophys. J., 2008. 95(8): p. 3706-3714.
4. Gillespie, D., W. Nonner, and R.S. Eisenberg, Coupling Poisson-Nernst-Planck and Density
Functional Theory to Calculate Ion Flux. Journal of Physics (Condensed Matter), 2002. 14: p.
12129-12145.
5. Gillespie, D., W. Nonner, and R.S. Eisenberg, Density functional theory of charged, hard-
sphere fluids. Physical Review E, 2003. 68: p. 0313503.
6. Gillespie, D., Valisko, and Boda, Density functional theory of electrical double layer: the
RFD functional. Journal of Physics: Condensed Matter, 2005. 17: p. 6609-6626.
7. Gillespie, D., J. Giri, and M. Fill, Reinterpreting the Anomalous Mole Fraction Effect. The
ryanodine receptor case study. Biophysical Journal, 2009. 97: p. pp. 2212 - 2221
8. Gillespie, D., L. Xu, Y. Wang, and G. Meissner, (De)constructing the Ryanodine Receptor:
modeling ion permeation and selectivity of the calcium release channel. Journal of Physical
Chemistry, 2005. 109: p. 15598-15610.
9. Gillespie, D., D. Boda, Y. He, P. Apel, and Z.S. Siwy, Synthetic Nanopores as a Test Case for
Ion Channel Theories: The Anomalous Mole Fraction Effect without Single Filing. Biophys. J.,
2008. 95(2): p. 609-619.
10. Malasics, A., D. Boda, M. Valisko, D. Henderson, and D. Gillespie, Simulations of calcium
channel block by trivalent cations: Gd(3+) competes with permeant ions for the selectivity
filter. Biochim Biophys Acta, 2010. 1798(11): p. 2013-2021.
11. Roth, R. and D. Gillespie, Physics of Size Selectivity. Physical Review Letters, 2005. 95: p.
247801.
12. Valisko, M., D. Boda, and D. Gillespie, Selective Adsorption of Ions with Different Diameter
and Valence at Highly Charged Interfaces. Journal of Physical Chemistry C, 2007. 111: p.
15575-15585.
13. Wang, Y., L. Xu, D. Pasek, D. Gillespie, and G. Meissner, Probing the Role of Negatively
Charged Amino Acid Residues in Ion Permeation of Skeletal Muscle Ryanodine Receptor.
Biophysical Journal, 2005. 89: p. 256-265.
14. Xu, L., Y. Wang, D. Gillespie, and G. Meissner, Two Rings of Negative Charges in the
Cytosolic Vestibule of T Ryanodine Receptor Modulate Ion Fluxes. Biophysical Journal, 2006.
90: p. 443-453.
32. Samsó et al, 2005, Nature Struct Biol 12: 539
32
• 4 negative charges D4899
• Cylinder 10 Å long, 8 Å diameter
• 13 M of charge!
• 18% of available volume
• Very Crowded!
• Four lumenal E4900 positive
amino acids overlapping D4899.
• Cytosolic background charge
RyR
Ryanodine Receptor redrawn in part from Dirk Gillespie, with thanks!
Zalk, et al 2015 Nature 517: 44-49.
All Spheres Representation
33. 33
Solved by DFT-PNP (Poisson Nernst Planck)
DFT-PNP
gives location
of Ions and ‘Side Chains’
as OUTPUT
Other methods
give nearly identical results
DFT (Density Functional Theory of fluids, not electrons)
MMC (Metropolis Monte Carlo))
SPM (Primitive Solvent Model)
EnVarA (Energy Variational Approach)
Non-equil MMC (Boda, Gillespie) several forms
Steric PNP (simplified EnVarA)
Poisson Fermi (replacing Boltzmann distribution)
34. 34
Nonner, Gillespie, Eisenberg
DFT/PNP vs Monte Carlo Simulations
Concentration Profiles
Misfit
Different Methods give
Same Results
NO adjustable
parameters
35. The model predicted an AMFE for Na+/Cs+ mixtures
before it had been measured
Gillespie, Meissner, Le Xu, et al
62 measurements
Thanks to Le Xu!
Note
the
Scale
Mean
±
Standard
Error of
Mean
2% error
Note
the
Scale
38. Theory fits Mutation with Zero Charge
Gillespie et al
J Phys Chem 109 15598 (2005)
Protein charge density
wild type* 13M
Solid Na+Cl- is 37M
*some wild type curves not shown, ‘off the graph’
0M in D4899
Theory Fits Mutant
in K + Ca
Theory Fits Mutant
in K
Error < 0.1 kT/e
1 kT/e
1 kT/e
39. Calcium Channel of the Heart
39
More than 35 papers are available at
ftp://ftp.rush.edu/users/molebio/Bob_Eisenberg/reprints
Dezső Boda Wolfgang NonnerDoug Henderson
40. 40
Mutants of ompF Porin
Atomic Scale
Macro Scale
30 60
-30
30
60
0
pA
mV
LECE (-7e)
LECE-MTSES- (-8e)
LECE-GLUT- (-8e)ECa
ECl
WT (-1e)
Calcium selective
Experiments have ‘engineered’ channels (5 papers) including
Two Synthetic Calcium Channels
As density of permanent charge increases, channel becomes calcium selective
Erev ECa in 0.1M 1.0 M CaCl2 ; pH 8.0
Unselective
Natural ‘wild’ Type
built by Henk Miedema, Wim Meijberg of BioMade Corp. Groningen, Netherlands
Miedema et al, Biophys J 87: 3137–3147 (2004); 90:1202-1211 (2006); 91:4392-4400 (2006)
MUTANT ─ Compound
Glutathione derivatives
Designed by Theory
||
41. Nonner & Eisenberg
Side Chains are Spheres
Channel is a Cylinder
Side Chains are free to move within Cylinder
Ions and Side Chains are at free energy minimum
i.e., ions and side chains are ‘self organized’,
‘Binding Site” is induced by substrate ions
‘All Spheres’ Model
42. 42
Ion Diameters
‘Pauling’ Diameters
Ca++
1.98 Å
Na+ 2.00 Å
K+ 2.66 Å
‘Side Chain’ Diameter
Lysine K 3.00 Å
D or E 2.80 Å
Channel Diameter 6 Å
Parameters are Fixed in all calculations
in all solutions for all mutants
Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie
‘Side Chains’ are Spheres
Free to move inside channel
Snap Shots of Contents
Crowded Ions
6Å
Radial Crowding is Severe
Experiments and Calculations done at pH 8
43. 43
Dielectric Protein
Dielectric Protein
6 Å
μ μmobile ions mobile ions=
Ion ‘Binding’ in Crowded Channel
Classical Donnan Equilibrium of Ion Exchanger
Side chains move within channel to their equilibrium position of minimal free energy.
We compute the Tertiary Structure as the structure of minimal free energy.
Boda, Nonner, Valisko, Henderson, Eisenberg & Gillespie
Mobile
Anion
Mobile
Cation
Mobile
Cation
‘Side
Chain’
‘Side
Chain’
Mobile
Cation
Mobile
Cation
large mechanical forces
44. 44
Solved with Metropolis Monte Carlo
MMC Simulates Location of Ions
both the mean and the variance
Produces Equilibrium Distribution
of location
of Ions and ‘Side Chains’
MMC yields Boltzmann Distribution with correct Energy, Entropy and Free Energy
Other methods
give nearly identical results
DFT (Density Functional Theory of fluids, not electrons)
DFT-PNP (Poisson Nernst Planck)
MSA (Mean Spherical Approximation)
SPM (Primitive Solvent Model)
EnVarA (Energy Variational Approach)
Non-equil MMC (Boda, Gillespie) several forms
Steric PNP (simplified EnVarA)
Poisson Fermi
45. 45
Key Idea
produces enormous improvement in efficiency
MMC chooses configurations with Boltzmann probability and weights them evenly, instead
of choosing from uniform distribution and weighting them with Boltzmann probability.
Metropolis Monte Carlo
Simulates Location of Ions
both the mean and the variance
1) Start with Configuration A, with computed energy EA
2) Move an ion to location B, with computed energy EB
3) If spheres overlap, EB → ∞ and configuration is rejected
4) If spheres do not overlap, EB ≠ 0 and configuration may be accepted
(4.1) If EB < EA : accept new configuration.
(4.2) If EB > EA : accept new configuration with Boltzmann probability
MMC details
exp -A B BE E k T
49. 49
Challenge
from channologists
Walter Stühmer and Stefan Heinemann
Göttingen Leipzig
Max Planck Institutes
Can THEORY explain the MUTATION
Calcium Channel into Sodium Channel?
DEEA DEKA
Sodium
Channel
Calcium
Channel
50. 50
Ca Channel
log (Concentration/M)
0.5
-6 -4 -2
Na+
0
1
Ca2+
Charge -3e
Occupancy(number)
E
E
E
A
Monte Carlo simulations of Boda, et al
Same Parameters
pH 8
Mutation
Same Parameters
Mutation
EEEE has full biological selectivity
in similar simulations
Na Channel
Concentration/M
pH =8
Na+
Ca2+
0.004
0
0.002
0.05 0.10
Charge -1e
D
E
K
A
51. Nothing was Changed
from the
EEEA Ca channel
except the amino acids
51
Calculations and experiments done at pH 8
Calculated DEKA Na Channel
Selects
Ca 2+ vs. Na + and also K+ vs. Na+
52. 52
Size Selectivity is in the Depletion Zone
Depletion Zone
Boda, et al
[NaCl] = 50 mM
[KCl] = 50 mM
pH 8
Channel Protein
Na+ vs. K+ Occupancy
of the DEKA Na Channel, 6 Å
Concentration[Molar]
K+
Na+
Selectivity Filter
Na Selectivity
because 0 K+
in Depletion Zone
K+Na+
Binding Sites
NOT SELECTIVE
53. How?
Usually Complex Unsatisfying Answers*
How does a Channel Select Na+ vs. K+ ?
* Gillespie, D., Energetics of divalent selectivity in the ryanodine receptor.
Biophys J (2008). 94: p. 1169-1184
* Boda, et al, Analyzing free-energy by Widom's particle insertion method.
J Chem Phys (2011) 134: p. 055102-14
53Calculations and experiments done at pH 8
54. Simple
Independent§
Control Variables*
DEKA Na+ channel
54
Amazingly simple, not complex
for the most important selectivity property
of DEKA Na+ channels
Boda, et al
*Control variable = position of gas pedal or dimmer on light switch
§ Gas pedal and brake pedal are (hopefully) independent control variables
55. (1) Structure
and
(2) Dehydration/Re-solvation
emerge from calculations
Structure (diameter) controls Selectivity
Solvation (dielectric) controls Contents
*Control variables emerge as outputs
Control variables are not inputs
55
Diameter
Dielectric
constants
Independent Control Variables*
56. Structure (diameter) controls Selectivity
Solvation (dielectric) controls Contents
Control Variables emerge as outputs
Control Variables are not inputs
Monte Carlo calculations of the DEKA Na channel
56
57. Na+ vs K+ (size) Selectivity (ratio)
Depends on Channel Size,
not dehydration (not on Protein Dielectric Coefficient)*
57
Selectivity
for small ion
Na+ 2.00 Å
K+ 2.66 Å
*in DEKA Na channel
K+
Na+
Boda, et al
Small Channel Diameter Large
in Å
6 8 10
61. 61
Semiconductor PNP Equations
For Point Charges
i
i i i
d
J D x A x x
dx
Poisson’s Equation
Drift-diffusion & Continuity Equation
0
i i
i
d d
x A x e x e z x
A x dx dx
0idJ
dx
Chemical Potential
ex
*
x
x x ln xi
i i iz e kT
Finite Size
Special ChemistryThermal Energy
Valence
Proton charge
Permanent Charge of Protein
Cross sectional Area
Flux Diffusion Coefficient
Number Densities
( )i x
Dielectric Coefficient
valence
proton charge
Not in Semiconductor
62. Boundary conditions:
STRUCTURES of Ion Channels
STRUCTURES of semiconductor
devices and integrated circuits
62
All we have to do is
Solve it / them!
64. Semiconductor Devices
PNP equations describe many robust input output relations
Amplifier
Limiter
Switch
Multiplier
Logarithmic convertor
Exponential convertor
These are SOLUTIONS of PNP for different boundary conditions
with ONE SET of CONSTITUTIVE PARAMETERS
PNP of POINTS is
TRANSFERRABLE
Analytical - Numerical Analysis
should be attempted using techniques of
Weishi Liu University of Kansas
Tai-Chia Lin National Taiwan University & Chun Liu PSU
65. 65
DEVICE APPROACH IS FEASIBLE
Biology Provides the Data
Semiconductor Engineering Provides the Approach
Mathematics Provides the Tools
66. 66
Learn from
Mathematics of Ion Channels
solving specific
Inverse Problems
How does it work?
How do a few atoms control
(macroscopic)
Biological Devices
67. 67
Biology is Easier than Physics
Reduced Models Exist*
for important biological functions
or the
Animal would not survive
to reproduce
*Evolution provides the existence theorems and uniqueness conditions
so hard to find in theory of inverse problems.
(Some biological systems the human shoulder are not robust,
probably because they are incompletely evolved,
i.e they are in a local minimum ‘in fitness landscape’ .
I do not know how to analyze these.
I can only describe them in the classical biological tradition.)
69. 69
Reduced models exist
because they are the
Adaptation
created by evolution
to perform a biological function
like selectivity
Reduced Models
and its parameters
are found by
Inverse Methods
73. 73
Ill posed problems
with too little data
Seem Complex
even if they are not
Some of biology seems complex
only because data is inadequate
Some* of biology is
amazingly
Simple
ATP as UNIVERSAL energy source
*The question is which ‘some’?
PS: Some of biology IS complex
74. Inverse Problems
Find the Model, given the Output
Many answers are possible: ‘ill posed’ *
Central Issue
Which answer is right?
74
Bioengineers: this is reverse engineering
*Ill posed problems with too little data
seem complex, even if they are not.
Some of biology seems complex for that reason.
The question is which ‘some’?
75. How does the
Channel control Selectivity?
Inverse Problems: many answers possible
Central Issue
Which answer is right?
Key is
ALWAYS
Large Amount of Data
from
Many Different Conditions
75
Almost too much data was available for reduced model:
Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67:960-989
76. Inverse Problems: many answers possible
Which answer is right?
Key is
Large Amount of Data from Many Different Conditions
Otherwise problem is ‘ill-posed’ and has no answer or even set of answers
76
Molecular Dynamics
usually yields
ONE data point
at one concentration
MD is not yet well calibrated
(i.e., for activity = free energy per mole)
for Ca2+ or ionic mixtures like seawater or biological solutions
77. 77
Working Hypothesis:
Crucial Biological Adaptation is
Crowded Ions and Side Chains
Wise to use the Biological Adaptation
to make the reduced model!
Reduced Models allow much easier Atomic Scale Engineering
78. 78
Working Hypothesis:
Crucial Biological Adaptation is
Crowded Ions and Side Chains
Biological Adaptation
GUARANTEES stable
Robust, Insensitive Reduced Models
Biological Adaptation ‘solves’ the Inverse Problem
79. 79
Working Hypothesis:
Biological Adaptation
of Crowded Charge
produces stable
Robust, Insensitive, Useful Reduced Models
Biological Adaptation
Solves
the
Inverse Problem
Provides Dimensional Reduction
81. Active Sites of Proteins are Very Charged
7 charges ~ 20M net charge
Selectivity Filters and Gates of Ion Channels
are
Active Sites
= 1.2×1022 cm-3
-
+ + + +
+
-
-
-
4 Å
K+
Na+
Ca2+
Hard Spheres
81
Figure adapted
from Tilman
Schirmer
liquid Water is 55 M
solid NaCl is 37 M
OmpF Porin
Physical basis of function
K+
Na+
Induced Fit
of
Side Chains
Ions are
Crowded
82. Crowded Active Sites
in 573 Enzymes
Enzyme Type
Catalytic Active Site
Density
(Molar)
Protein
Acid
(positive)
Basic
(negative)
| Total | Elsewhere
Total (n = 573) 10.6 8.3 18.9 2.8
EC1 Oxidoreductases (n = 98) 7.5 4.6 12.1 2.8
EC2 Transferases (n = 126) 9.5 7.2 16.6 3.1
EC3 Hydrolases (n = 214) 12.1 10.7 22.8 2.7
EC4 Lyases (n = 72) 11.2 7.3 18.5 2.8
EC5 Isomerases (n = 43) 12.6 9.5 22.1 2.9
EC6 Ligases (n = 20) 9.7 8.3 18.0 3.0
Jimenez-Morales, Liang, Eisenberg
89. 89
Computational
Scale
Biological
Scale Ratio
Time 10-15 sec 10-4 sec 1011
Length 10-11 m 10-5 m 106
Multi-Scale Issues
Journal of Physical Chemistry C (2010 )114:20719
DEVICES DEPEND ON FINE TOLERANCES
parts must fit
Atomic and Macro Scales are BOTH used by channels because
they are nanovalves
so atomic and macro scales must be
Computed and CALIBRATED Together
This may be impossible in all-atom simulations
90. 90
Computational
Scale
Biological
Scale Ratio
Spatial Resolution 1012
Volume 10-30 m3 (10-4 m)3 = 10-12 m3
1018
Three Dimensional (104)3
Multi-Scale Issues
Journal of Physical Chemistry C (2010 )114:20719
DEVICES DEPEND ON FINE TOLERANCES
parts must fit
Atomic and Macro Scales are BOTH used by channels because
they are nanovalves
so atomic and macro scales must be
Computed and CALIBRATED Together
This may be impossible in all-atom simulations
91. 91
Computational
Scale
Biological
Scale Ratio
Solute
Concentration
including Ca2+mixtures
10-11 to 101 M 1012
Multi-Scale Issues
Journal of Physical Chemistry C (2010 )114:20719
DEVICES DEPEND ON FINE TOLERANCES
parts must fit
Atomic and Macro Scales are BOTH used by channels because
they are nanovalves
so atomic and macro scales must be
Computed and CALIBRATED Together
This may be impossible in all-atom simulations
92. 92
This may be nearly impossible for ionic mixtures
because
‘everything’ interacts with ‘everything else’
on both atomic and macroscopic scales
particularly when mixtures flow
*[Ca2+] ranges from 1×10-8 M inside cells to 10 M inside channels
Simulations must deal with
Multiple Components
as well as
Multiple Scales
All Life Occurs in Ionic Mixtures
in which [Ca2+] is important* as a control signal
93. 93
Multi-Scale Issues
Journal of Physical Chemistry C (2010 )114:20719
DEVICES DEPEND ON FINE TOLERANCES
parts must fit
Atomic and Macro Scales are BOTH used by
channels because they are nanovalves
so atomic and macro scales must be
Computed and CALIBRATED
Together
This may be impossible in all-atom
simulations
95. Valves Control Flow
95
Classical Theory & Simulations
NOT designed for flow
Thermodynamics, Statistical Mechanics do not allow flow
Rate Models are inconsistent with Maxwell’s Eqn (Kirchoff Law)
(if rate constants are independent of potential)
