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.
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.
Talk device approach to biology march 29 1 2015Bob 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.
Dr. AVS Suresh, MD, DM, ECMO, Consultant Hemato-Oncologist, Chief Scientific Officer & Director, ClinSync, on the man-made as well as other kind of EMF radiation.
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
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.
Talk device approach to biology march 29 1 2015Bob 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.
Dr. AVS Suresh, MD, DM, ECMO, Consultant Hemato-Oncologist, Chief Scientific Officer & Director, ClinSync, on the man-made as well as other kind of EMF radiation.
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
Study on Transmission Probabilities for Some Rectangular Potential Barriersijtsrd
In this research, we apply the time independent Schroedinger equation for a particle moving in one dimensional potential barrier of finite width and height. We study the two cases which corresponds to the particle energies being respectively larger and smaller than the potential barrier. Then, we calculate transmission coefficient T as a function of particle energy E for a potential barrier by changing the barrier height V0 and width L using Propagation Matrix Method. If we keep the barrier width constant and varying the height, we see that the passing limit is shifting towards the higher energies when barrier height is increased. If we keep the barrier height constant and change the barrier width, we see significance change in oscillations. Aye Than Kyae | Htay Yee | Thida Win | Aye Aye Myint | Kyaw Kyaw Naing "Study on Transmission Probabilities for Some Rectangular Potential Barriers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26813.pdfPaper URL: https://www.ijtsrd.com/physics/other/26813/study-on-transmission-probabilities-for-some-rectangular-potential-barriers/aye-than-kyae
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.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
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journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
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.
Study on Transmission Probabilities for Some Rectangular Potential Barriersijtsrd
In this research, we apply the time independent Schroedinger equation for a particle moving in one dimensional potential barrier of finite width and height. We study the two cases which corresponds to the particle energies being respectively larger and smaller than the potential barrier. Then, we calculate transmission coefficient T as a function of particle energy E for a potential barrier by changing the barrier height V0 and width L using Propagation Matrix Method. If we keep the barrier width constant and varying the height, we see that the passing limit is shifting towards the higher energies when barrier height is increased. If we keep the barrier height constant and change the barrier width, we see significance change in oscillations. Aye Than Kyae | Htay Yee | Thida Win | Aye Aye Myint | Kyaw Kyaw Naing "Study on Transmission Probabilities for Some Rectangular Potential Barriers" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd26813.pdfPaper URL: https://www.ijtsrd.com/physics/other/26813/study-on-transmission-probabilities-for-some-rectangular-potential-barriers/aye-than-kyae
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.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
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.
The public trial lecture presented by Mohammadreza Nematollahi on 8th of October 2014 at Norwegian University of Science and Technology. The theoretical models and the experimental progress of highly mismatched alloys, as well as their optoelectronic applications are covered.
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
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.
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
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'.
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 .
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
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.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
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.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...
What is different about life? it is inherited oberwolfach march 7 1 2018
1. 1
Life is Different: it is inherited
Oberwolfach Workshop, February 2018
Bob Eisenberg
Department of Applied Mathematics
Illinois Institute of Technology
Department of Physiology and Biophysics
Rush University
Chicago USA
u
2. Page 2
Oberwolfach Workshop 1809
The Mathematics of Mechanobiology and Cell Signaling
25 February – 3 March 2018
Organizers:
Davide Ambrosi, Milano Italy
Chun Liu, State College PA USA
Matthias Röger, Dortmund Germany
Angela Stevens, Münster Germany
at the Mathematisches Forschungsinstitut Oberwolfach.
3. 3
Thanks to Chun Liu
柳 春
For a very special
Friendship
and
Collaboration!
4. Page 4
Life is special because it is
inherited from a tiny number
of atoms
And the central question of biology is
How is this possible?
7. Page 7
How can a few thousand atoms
conceivably control 1025 atoms?
8. 8
Experimental Evidence:
A few atoms make a
BIG Difference
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
Current Voltage relation determined by
John Tang
in Bob Eisenberg’s Lab
Ompf
G119D
Glycine G
replaced by
Aspartate D
9. Page 9
How can a few thousand atoms
conceivably control 1025 atoms?
Traditional Statistical Mechanics says this is impossible!
𝑨 𝒙, 𝒕 ≡ 𝒂 𝒙, 𝒕
where 𝒓 𝟐 = 𝒙 𝟐 + 𝒚 𝟐 + 𝒛 𝟐 and
𝑾 𝒙 = 𝑵𝒆
−
𝒓 𝟐
𝑹 𝟐
𝑹 specifies the radius of the small spherical volume over which the
spatial average takes place.
= 𝑾 𝒙′ 𝒂 𝒙 − 𝒙′, 𝒕 𝒅 𝟑 𝒙′
10. Page 10
How can a few thousand atoms
conceivably control 1025 atoms?
The thousand atoms of one gene occupy say 10-27 m3
The volume of a person might be 1m3
Volume of Canada, USA 𝒐𝒓China 1m high is 1013 m3
Fraction of space of a gene is about 10-27
Fraction of Space of One Person in Canada is 10-13
1 m3 has no effect in Canada
1 gene should have no effect
11. Page 11
How can a few thousand atoms
conceivably control 1025 atoms?
Biological Answer:
Structure: a Hierarchy of Devices
Physical Answer:
Electrodynamics: Strong and Universal
inside atoms to stars
Another talk*
another day!
*Eisenberg, Oriols, and Ferry. 2017. Dynamics of Current, Charge, and Mass.
Molecular Based Mathematical Biology 5:78-115
arXiv https://arxiv.org/abs/1708.07400.
12. 12
Everyone knows Biology
is made of
Structures
Working hypothesis:
The Structures
make
Devices
that span the scales
14. Page 14
How can a few thousand atoms
conceivably control 1025 atoms?
ANSWER:
by forming a
HIERARCHY of DEVICES
15. Page 15
Different Kind of Averaging
in Device
Definition of a Device
Output is Perfectly Correlated with Input
Averaging in a Device Creates a Perfectly Correlated* Replica of the Input
𝑨 𝒙, 𝒕 ≡ 𝒂 𝒙, 𝒕
≠ 𝒅 𝟑
𝒙′ 𝑾(𝒙′
)𝒂(𝒙 − 𝒙′, 𝒕)
Not equal
Precise
stochastic
definition
*Coherence function of Device = 1.0
Coherence function in general =
𝑷 𝒙𝒚 𝒇
𝑷 𝒙𝒙 𝒇 𝑷 𝒚𝒚 𝒇
;
𝑷 𝒙𝒚; 𝑷 𝒛𝒛 = cross, self-power spectral density
= estimator of
19. 19
Real Biological System
A Nerve Cell is a Hierarchy of Devices
Cell Body, Dendrites, Axon, Terminals
Example:
Bob, I would not put it
that way…..
Andrew Huxley with his mentor
Alan Hodgkin
20. 20
Nerve Signal is the propagating ‘Action Potential’,
a waveform in x and t
Purely Local Theory is Impossible
because the phenomena involves
centimeter scales, as well as
Angstroms.
All atom Molecular Dynamics
is impossible because ~1023 atoms
are involved
Atomic Properties of the Voltage
Sensor are coupled to the
macroscopic electric field a
centimeter away. The electric field
controls the sensor; the sensor
controls the electric field.
That is how propagation works!
24. 24
Vargas, E., Yarov-Yarovoy, V., Khalili-Araghi, F., Catterall, W. A., Klein, M. L., Tarek, M., Lindahl, E., Schulten, K., Perozo, E., Bezanilla, F. & Roux, B.
An emerging consensus on voltage-dependent gating from computational modeling and molecular dynamics simulations.
The Journal of General Physiology 140, 587-594 (2012).
Emerging Consensus ….
Voltage Sensor Structure
(NOT conduction channel)
25. 25
Vargas, E., Yarov-Yarovoy, V., Khalili-Araghi, F., Catterall, W. A., Klein, M. L., Tarek, M., Lindahl, E., Schulten, K., Perozo, E., Bezanilla, F. & Roux, B.
An emerging consensus on voltage-dependent gating from computational modeling and molecular dynamics simulations.
The Journal of General Physiology 140, 587-594 (2012).
Emerging Consensus ….
Voltage Sensor Structure
(NOT conduction channel)
27. 27
Physiologists§
Mistakenly call a Saturating distribution
‘Boltzmann’
e.g., Bezanilla, Villalba-Galea J. Gen. Physiol (2013) 142: 575
𝑸 𝑽 =
𝑸 𝒎𝒂𝒙
𝟏 + 𝒆𝒙𝒑 −𝑸 𝒎𝒂𝒙 𝑽 − 𝑽 𝟏 𝟐 𝒌 𝑩 𝑻
Physicists: Saturation Fermi distribution
Boltzmann* distribution does NOT saturate.
Boltzmann is exponential, like 𝒆𝒙𝒑 −𝑽 𝒌 𝑩 𝑻 .
*Boltzmann (1904) Lectures on Gas Theory, Berkeley
§ p.503 of Hodgkin and Huxley. 1952.
‘Quantitative description ...’ J. Physiol. 117:500-544.
Bezanilla. How membrane proteins sense voltage Nature Rev Mol Cell Biol (2008) 9, 323
Fermi Distribution
not Boltzmann
Arginines
Internal Dissolved Ions
𝑲+, 𝒐𝒓𝒈𝒂𝒏𝒊𝒄𝒔−
External Dissolved Ions
𝑵𝒂+ 𝑪𝒍−
Dissolved
Ions
𝑲+, 𝒐𝒓𝒈𝒂𝒏𝒊𝒄𝒔−
External Dissolved Ions
𝑵𝒂+ 𝑪𝒍−
Voltage Clamp
= Test Potential
Voltage
Clamp
=0
Holding
Potential
Current 𝐈 𝐦
to maintain test potential
Holding
Potenti
al
Test Potentials
Holding
Potenti
al
Test
Potentials
𝐈 𝐦
28. Perhaps the first
Consistent Model of a Protein Machine
made by a conformation change
28
Francisco Bezanilla
Chun Liu
柳 春
Allen Tzyy-Leng Horng
洪子倫
Bob Eisenberg
29. Figure 1. Geometric configuration of the reduced mechanical model.
Voltage sensor works by charge injection through a fluid dielectric of side
chains, attachments of arginines to the S4 segment.
intracellular
extracellular
Voltage Sensor
works by
Charge Injection
through a fluid dielectric of side chains,
not yet fully known. More work needed!
31. 31
𝐸 = 𝑘 𝐵 𝑇 𝑐𝑖 𝑙𝑜𝑔𝑐𝑖 −
𝜀0 𝜀𝑟
2𝑎𝑙𝑙 𝑖
∇𝜙 2
+ 𝑧𝑖 𝑒
𝑎𝑙𝑙 𝑖
𝑐𝑖 𝜙 + ( 𝑉𝑖 + 𝑉𝑏 )
𝑎𝑟𝑔𝑖𝑛𝑖𝑛𝑒𝑠
𝑐𝑖
𝑉
+
𝑔𝑖𝑗
2
𝑐𝑖 𝑐𝑗
𝑎𝑟𝑔𝑖𝑛𝑖𝑛𝑒𝑠 𝑖,𝑗
𝑑𝑉,
Variational Formulation
EnVarA
because
‘Everything’ interacts with ‘Everything Else’
through the electric field and often through steric interactions of Pauli exclusion principle
Poisson Equation and Transport equation are DERIVED, not assumed from variations like
𝛿𝐸
𝛿𝜙
= 0,
so cross terms are always consistent, i.e., satisfy all equations with one set of parameters.
32. 30
Defining Laws
Charge Creates Electric Field
−
1
𝐴
𝑑
𝑑𝑧
Γ𝐴
𝑑𝜙
𝑑𝑧
=
𝑖=1
𝑁
𝑧𝑖 𝑐𝑖 , 𝑖 = Na, Cl, 1, 2, 3, 4
Transport of Mass
𝜕𝑐 𝑖
𝜕𝑡
+ 1
𝐴
𝜕
𝜕𝑧
𝐴𝐽𝑖 = 0, 𝑖 =Na, Cl, 1,2,3,4
33. 33
𝑽𝒊 𝒛, 𝒕 = 𝑲(𝒛 − 𝒛𝒊 + 𝒁 𝑺𝟒(𝒕) ) 𝟐
,
where K is the spring constant, zi is the fixed anchoring position of the spring for each arginine ci
on S4, 𝑍 𝑆4(𝑡) is the center-of-mass z position of S4 by treating S4 as a rigid body.
𝑍 𝑆4(𝑡) follows the motion of equation based on spring-mass system:
Conformation Change of Arginines is Described by an Elastic System
35. Page 35
Figure 9. (a) Time courses of subtracted gating current [A1] with voltage rising
from -90mV to V mV at t=10, holds on till t=150, and drops back to -90mV,
where V=-62, -50, … -8 mV. (b) τ2 versus V compared with experiment [7].
Fitting Data
36. Page 36
Figure 3. (a) QV curve and comparison with [7]. Steady-state distributions for Na, Cl
and arginines at (b) V=-90mV, (c) V=-48mV, (d) V=-8mV.
Fitting Data
37. 37
Ions
Electric
Field
Current is Conserved
OUTPUT
Current including 𝜺 𝟎 𝑬 𝒕
INPUT
Voltage
Clamp
t
Conservation of Current is an
Important Constraint.
Rate Models of Chemical Kinetics;
Molecular Dynamics
do not conserve current
A different talk
40. 40
Classical cable theory of transmission lines,
telegrapher’s equations, Kelvin, Hodgkin, Noble,
including 3D-cable theory, ~10 papers, e.g.,
Eisenberg and Johnson. 1970. Three dimensional electrical
field problems in physiology. Prog. Biophys. Mol. Biol. 20:1-65
Barcilon, Cole, Eisenberg. 1971. Singular Perturbation …
SIAM J. Appl. Math. 21:339-354.
Another talk, another time!
Channels + lipid capacitance
Poisson Equation
41. How do ions move through channels?
>75 papers since 1986
41
42. 42
Working Hypothesis
bio-speak:
Crucial Biological Adaptation is
Crowded Ions and Side Chains
Biology occurs in concentrated >0.3 M
mixtures of spherical charges
NOT IDEAL AT ALL
Poisson Boltzmann does NOT fit data!!
Solutions are extraordinarily concentrated >10M where
they are most important, near DNA, enzyme active sites, and channels
and
electrodes of batteries and electrochemical cells.
Solid NaCl is 37M
43. 43
Solutions are Extraordinarily Concentrated
>10M Solid NaCl is 37M
where they are most important,
DNA,
enzyme active sites,
channels and
electrodes
of batteries and electrochemical cells
44. 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
44
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
45. Crowded Active Sites
in 573 Enzymes
45
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
46. Charge-Space Competition
46
More than 35 papers are available at
ftp://ftp.rush.edu/users/molebio/Bob_Eisenberg/reprints
Monte Carlo Methods
Dezső Boda Wolfgang NonnerDoug Henderson Bob Eisenberg
47. 47
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
||
Evidence
RyR
(start)
48. 48
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
49. 49
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
||
Evidence
RyR
(start)
50. Poisson Fermi Approach to Ion
Channels
50
.
劉晉良
Jinn-Liang Liu
discovered role of
SATURATION
Bob Eisenberg helped with applications
51. Motivation
Natural Description of Crowded Charge
is a
Fermi Distribution
designed to describe saturation
Simulating saturation by interatomic repulsion (Lennard Jones)
is a significant mathematical challenge
to be side-stepped if possible
51
52. Motivation
Largest Effect
of
Crowded Charge
is
Saturation
important
in channels, DNA, enzymes, and
electrochemical devices in general
Saturation cannot be described at all by classical Poisson Boltzmann
approach and is described in a (wildly) uncalibrated way
by present day Molecular Dynamics
52
53. 53
Liu, Eisenberg. 2018. Journal of chemical physics 148:054501 also arXiv:1801.03470
.
Calibration in Bulk Solution: New Result
54. 54
Individual activity coefficients of 2:1 electrolytes.
Comparison of PF results with experimental
data [26] on i = Pos2+ (cation) and Neg− (anion) activity coefficients γi in various [PosNeg2]
from 0 to 1.5 M.
Calibration in Bulk Solution:
New Result
55. Na Channel
55
Signature of Cardiac Calcium Channel CaV1.n
Anomalous* Mole Fraction (non-equilibrium)
Liu & Eisenberg (2015) Physical Review E 92: 012711
*Anomalous because CALCIUM CHANNEL IS A SODIUM CHANNEL at [CaCl2] 10-3.4
Ca2+ is conducted for [Ca2+] > 10-3.4, but Na+ is conducted for [Ca2+] <10-3.
Ca Channel
57. ‘Law’ of Mass Action
including
Interactions
From Bob Eisenberg p. 1-6, in this issue
Variational
Approach
EnVarA
1
2- 0E
6 7 8 6 7 8
r r
x u
Conservative Dissipative
Chun Liu
柳 春
58. 58
Energetic Variational Approach
allows
accurate computation of
Flow and Interactions
in Complex Fluids like Liquid Crystals
Engineering needs Calibrated Theories and
Simulations
Engineering Devices almost always use flow
Classical theories and Molecular Dynamics
have difficulties with flow, interactions,
and complex fluids
59. 59
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
r r
x u
Action Integral, after pullback Rayleigh Dissipation FunctionAction 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
Field Theory of Ionic Solutions: Liu, Ryham, Hyon, Eisenberg
Allows boundary conditions and flow
Deals Consistently with Interactions of Components
Composite
Variational Principle
Shorthand for Euler Lagrange process
with respect to
r
x
Shorthand for Euler Lagrange process
with respect to
r
u
60. 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
r r%
1 4 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 4 3
,
= = , ,
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
r r%
6 4 4 4 4 4 4 4 4 4 4 44 7 4 4 4 4 4 4 4 4 4 4 4 48
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
60
61. 61
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
r r
r r
r r
r r
r r
r r
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
62. 62
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
Ρ
0idJ
dx
ex
*
x
x x ln xi
i i iz e kT
1 2 3
Finite Size
Special Chemistry
Chemical Potential
Thermal Energy
Valence
Proton charge
Permanent Charge of Protein
Doping of Semiconductor
Cross sectional Area
Flux Diffusion Coefficient
Number Densities
Dielectric Coefficient
valence
proton charge
Not in Semiconductor
( )i x
63. All we have to do is
Solve them!
with Boundary Conditions
defining
Charge Carriers
ions, holes, quasi-electrons
Geometry
63
65. Page 65
out inJ J
k f k b kJ l k C l k C
6 44 7 4 48 6 44 7 4 48
Unidirectional Efflux Unidirectional Infflux
eft ightL R
f
b
k
k
L R
*but potential profile must be computed by solving electrostatics problem.
Complex coupled nonlinearities are in the electric field!!!
Solution
is a
Chemical Reaction*
exactly
66. 66
Solution* of PNP Equation
*MATHEMATICS
This solution was actually DERIVED
from several conditional probability measures by
ANALYTICAL integrations
No approximations, no numerics
Eisenberg, Klosek, & Schuss (1995) J. Chem. Phys. 102, 1767-1780
Eisenberg, B. (2000) in Biophysics Textbook On Line "Channels, Receptors, and Transporters"
Eisenberg, B. (2011). Chemical Physics Letters 511: 1-6
Simple formulas are
available for the
probabilities
{
Unidirectional Efflux Unidirectional I
ConditionalDiffusion ChannelSource
ProbabilityVelocity LengthConcentration
6 4 4 44 7 4 4 4 48
1 4 2 4 31 2 3
1 4 4 2 4 4 3
k k
k k
k
D D
CR LJ R L RC L Prob Prob
Rate Constant
nfflux
6 4 4 44 7 4 4 4 48
67. Page 67
Please do not be deceived
by the eventual simplicity of Results.
This took >2 years!
Solution
was actually
DERIVED
with explicit formulae
for probability measures
from a
Doubly Conditioned Stochastic Process
involving
Analytical Evaluation
of
Multidimensional Convolution Integrals
Eisenberg, Klosek, & Schuss (1995) J. Chem. Phys. 102, 1767-1780
Eisenberg, B. (2000) in on-line textbook of USA Biophysical Society, DeFelice editor.
Eisenberg, B. (2011) Chemical Physics Letters 511: 1-6
68. All we have to do is
Solve them!
Don’t Despair
Semiconductor
Technology has
Already Done That!
68
69. 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 formulas are possible
Weishi Liu University of Kansas
70. Device converts Input to Output by a simple ‘law’
70
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
