Slide 1

1 Ions in ChannelsNatural Nanovalves Workshop Mathematical Models of Electrolytes in Molecular Biology National Taiwan Universityorganized by Prof. Tai Chia Lin, Chun LiuThank You !andthanks to Wei-jhen Tsai2Stochastic Derivation of PNP done previously in some detail, starting with Langevin Stochastic Differential Equationusing theory of Stochastic Processes, all the way to Law of Mass Actionanalytically, with evaluation of all integrals etcToday, Experimental Evidence for all spheres modelThis is the best available test of different mathematical models,in my opinion3Ion Channels are the Valves of CellsIon Channels are the Main Controllers of Biological Function

Chemical Bonds are linesSurface is Electrical PotentialRed is negative (acid)Blue is positive (basic)SelectivityDifferent Ions carry Different SignalsFigure of ompF porin by Raimund Dutzler~30

0.7 nm = Channel Diameter+Ions in Water* are the

Liquid of Life3 K+ Na+ Ca++Hard Spheres*Pure H2O is toxic to cells & proteins3MD scales are very different4A few atoms make a BIG DifferenceStructure determined by Raimund Dutzler in Tilman Schirmers labCurrent Voltage relation byJohn Tang in Bob Eisenbergs Lab

Ompf

G119D

Glycine replaced by Aspartate5General Theme

Mathematics of Molecular Biology

is (mostly)

Reverse Engineering

i.e., solving specific Inverse Problems

How does it work?How do a few atoms control (macroscopic) Biological Function

Natural nano-valves** for atomic control of biological function

6Ion channels coordinate contraction of cardiac muscle, allowing the heart to function as a pumpCoordinate contraction in skeletal muscleControl all electrical activity in cells

Produce signals of the nervous systemAre 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 channelsAre proteins whose genes (blueprints) can be manipulated by molecular geneticsHave 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 Ion Channels are Biological Devices*~30 x 10-9 meterK+*Device is a Specific Word, that exploits specific mathematics & science6Ion channels are a class of Proteins that reside in the cell membrane of all biological cells. Each channel protein consists of a chain of amino acids folded in such a way that it forms a nanoscopic water-filled tunnel through which ions can flow to cross the otherwise impermeable membrane.

Every ion channel carries a strong and steeply varying distribution of permanent charge, which depends on the particular combination of channel and prevalent physiological conditions. This permanent charge has an important role in determining the current-voltage characteristics of the open channel.

Many channels are designed by nature to selectively transmit or block a particular ion species. This allows only one type of ion to cross the membrane even though other ions may be present in much higher concentrations. Many channels can also open and close by mechanical or other means, switching on and off like electronic devices.

From a physiological point of view ion channels are essential for maintaining the correct internal ion composition necessary for cell survival and function. They directly control electrical signaling in the nervous system, muscle contraction, and the delivery of many clinical drugs. Malfunctioning channels cause or are associated with many diseases.

From a device point of view, ion channels can be thought of as elements in an electrical circuit, behaving like resistors, diodes or batteries depending on the specific channel and environmental factors. By replacing or deleting one or more of the amino acids many channels can be mutated, altering the charge distribution along the channel. Designing and engineering channels with specific conductances and selectivities, and incorporating them into bio-devices, is a real possibility.7

Current in One Channel Molecule is a Random Telegraph SignalompF porin

8300 x 10-12 meterK+ Na+ Ca++Channels are Selective Molecular DevicesDifferent Ions Carry Different Signals through Different Channels Figure of ompF porin by Raimund Dutzler~3 x 10-9 metersFlow time scale is 10-4 sec to 1 min

0.7 10-9 meter = Channel Diameter+Diameter mattersIonic solutions are NOT idealClassical Biochemistry assumes ideal solutions.K+ & Na+ are identical only in Ideal Solutions.

89Different Types of ChannelsuseDifferent Types of Ions forDifferent Information

All of life depends on the differences between salts of potassium K+ and sodium Na+.If cells cannot distinguish K+ from Na+, they swell, burst and die.Engineering of Channels by evolution makes them Selective Devices 9Bob Eisenberg: beisenbe@rush.edu

The CellDefined by a Membrane

Note: intra-cellular compartmentsare defined by their membranes

11

Patch clamp and Bilayer apparatus clamp ion concentrations in the baths and the voltage across membranes.

Patch Clamp SetupRecordings from One Molecule12

Single Channel Recording13SINGLE isolated RyR Channelsin Artificial Planar Lipid BilayersAxoPatchPatch-ClampAmplifier

ExperimentalChamber

PlanarBilayer80-100 MDiameterTeflonSeptaFusedVesicleCa

Single Channel CurrentopenclosedDesigned at RushSlide from Mike FillThanks!

13Thousands of Molecular Biologists Study Channels as Devices every day,One protein molecule at a timeThis number is not an exaggeration.We have sold >10,000 AxoPatch amplifiers

Ion Channel Monthly

Designed at Rush

Femto-amps(10-15 A)Current NoiseCurrent Noise14AxoPatch 200B14

Open Duration /msOpen Amplitude, pALowpass Filter = 1 kHz Sample Rate = 20 kHzCa2+ Release Channel of Inositol Trisphosphate Receptor: slide and data from Josefina Ramos-Franco. Thanks!Typical Raw Single Channel RecordsCurrent vs. time Amplitude vs. DurationChannel Structure Does Not Changeonce the channel is open5 pA100 msClosedOpen1516Where to start?Why not compute all the atoms? 1617Atomic and Macro Scales are BOTH used by channels because they are nanovalvesso atomic and macro scales must beComputed and CALIBRATED Together

This may be impossible in all-atom simulationsComputational ScaleBiological ScaleRatioTime 10-15 sec10-4 sec1011Length 10-11 m10-5 m106Spatial Resolution1012Volume 10-30 m3(10-4 m)3 = 10-12 m31018Solute Concentrationincluding Ca2+mixtures10-11 to 101 M1012Three Dimensional (104)3Multi-Scale IssuesJournal of Physical Chemistry C (2010 )114:207191718Multi-Scale Issues are Always Presentin Atomic Scale EngineeringAtomic & Macro Scales are both used by channels just because Channels are Nanovalves

By definition: all valves use small structures to control large flows1819 Atomic Scale Engineeringuses a Few Atoms to Control Macroscopic Flows

so Atomic and Macro Scales must beComputed and CALIBRATED together

1920 This may be nearly impossible for ionic mixturesbecauseeverything interacts with everything elseon both atomic and macroscopic scalesparticularly when mixtures flow

*[Ca2+] ranges from 110-8 M inside cells to 10 M inside channelsSimulations must deal with Multiple Components as well as Multiple ScalesAll Life Occurs in Ionic Mixtures in which [Ca2+] is important* as a control signal

2021Uncalibrated Simulations will make devices that do not work

Details matter in devices2122Where to start?Mathematically ?

Physically ? 2223.Reduced Models are Needed

Reduced Models are Device Equationslike Input Output Relations of Engineering Systems

The device equation is the mathematical statement of how the system works Device Equations describe Slow Variables found in some complicated systems

How find a Reduced Model?24Biology is Easier than Physics

Reduced Models Exist* for important biological functionsor 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.)25Multi-scale Engineering is MUCH easier when robust

Reduced Models Exist26Reduced models exist because they are the adaptation created by evolution to perform a biological function like selectivityReduced Models and its parametersare found by Inverse Methodsof Reverse Engineering Inverse ProblemsGiven the OutputDetermine the Reduced Model27Bioengineers: this is reverse engineeringFor example, Problem (with noise and systematic error) has actually been solved byTikhonov RegularizationBurger, Eisenberg, Engl (2007) SIAM J Applied Math 67: 960-989

using procedures developed by Engl to study Blast Furnaces and their ExplosionsFind Charge Distribution in Channel from Current Voltage Relations

27Inverse ProblemsFind the Model, given the Output Many answers are possible: ill posed *Central IssueWhich answer is right?28Bioengineers: 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?

28How does the Channel control Selectivity?Inverse Problems: many answers possibleCentral IssueWhich answer is right?

Key is ALWAYS Large Amount of Data from Many Different Conditions29Almost too much data was available for reduced model: Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67:960-98929Inverse Problems: many answers possibleWhich answer is right?Key is Large Amount of Data from Many Different ConditionsOtherwise problem is ill-posed and has no answer or even set of answers

30Molecular Dynamics usually yields ONE data pointat 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 solutions3031Working Hypothesis:Crucial Biological Adaptation isCrowded Ions and Side ChainsWise to use the Biological Adaptation to make the reduced model!

Reduced Models allow much easier Atomic Scale Engineering31

Active Sites of Proteins are Very Charged 7 charges ~ 20 M net chargeSelectivity Filters and Gates of Ion Channels are Active Sites= 1.21022 cm-3-+++++---4 K+ Na+ Ca2+Hard Spheres

32Figure adapted from Tilman Schirmerliquid Water is 55 Msolid NaCl is 37 MOmpF Porin Physical basis of functionK+ Na+Induced Fit of Side Chains Ions are Crowded32Crowded Active Sitesin 573 Enzymes Enzyme TypeCatalytic Active SiteDensity (Molar)ProteinAcid(positive)Basic(negative)

| Total |ElsewhereTotal (n = 573)10.68.318.92.8EC1Oxidoreductases (n = 98)7.54.612.12.8EC2Transferases (n = 126)9.57.216.63.1EC3Hydrolases (n = 214)12.110.722.82.7EC4Lyases (n = 72)11.27.318.52.8EC5Isomerases (n = 43)12.69.522.12.9EC6Ligases (n = 20)9.78.318.03.0Jimenez-Morales, Liang, EisenbergEC2: TRANSFERASESAverage Ionizable Density: 19.8 MolarExampleUDP-N-ACETYLGLUCOSAMINE ENOLPYRUVYL TRANSFERASE (PDB:1UAE)

Functional Pocket Volume: 1462.40 3Density : 19.3 Molar (11.3 M+. 8 M-)

Jimenez-Morales, Liang, EisenbergCrowdedGreen:Functional pocket residuesBlue:Basic = Probably Positive = R+K+HRed:Acid = Probably Negative = E + QBrownUridine-Diphosphate-N-acetylclucosamine

3435Everything Interacts with Everything Elseby steric exclusioninside crowded active sites Law of mass action needs to be generalized

Everything interacts with macroscopic Boundary Conditions (and much else) through long range electric field35Na+36Three Channel TypesRyR, CaV = EEEE, and Nav = DEKA analyzed successfully* in a wide range of solutions by the All Spheres Primitive ModelImplicit solvent model of open channelions and protein side chains are hard spheresin this model

* Many methods have been used in more than 30 paperssince Nonner and Eisenberg, 1998Na+Na+Na+Dirk GillespieDirk_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 successfullyBest Evidence is from the

RyR Receptor37381. 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.

39Solved bY DFT-PNP (Poisson Nernst Planck)

DFT-PNPgives locationof Ions and Side Chainsas 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 formsSteric PNP (simplified EnVarA)Poisson Fermi 39

The model predicted an AMFE for Na+/Cs+ mixturesbefore it had been measuredGillespie, Meissner, Le Xu, et al62 measurementsThanks to Le Xu!Note the ScaleMean Standard Error of Mean2% errorNote the Scale4041

DivalentsKClCaCl2CsClCaCl2NaClCaCl2KClMgCl2MisfitMisfit4142KCl

MisfitError < 0.1 kT/e4 kT/eGillespie, Meissner, Le Xu, et al42Theory fits Mutation with Zero Charge

Gillespie et al J Phys Chem 109 15598 (2005) Protein charge densitywild type* 13 M Solid Na+Cl- is 37 M *some wild type curves not shown, off the graph0 M in D4899Theory Fits Mutant in K + Ca

Theory Fits Mutant in KError < 0.1 kT/e1 kT/e1 kT/e43Calcium Channel44More than 35 papers are available atftp://ftp.rush.edu/users/molebio/Bob_Eisenberg/reprintshttp://www.phys.rush.edu/RSEisenberg/physioeis.html

4445Mutants of ompF PorinAtomic ScaleMacro Scale

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, NetherlandsMiedema et al, Biophys J 87: 31373147 (2004); 90:1202-1211 (2006); 91:4392-4400 (2006)MUTANT Compound

Glutathione derivativesDesigned by Theory|| 45Nonner & Eisenberg

Side Chains are SpheresChannel is a CylinderSide Chains are free to move within CylinderIons and Side Chains are at free energy minimumi.e., ions and side chains are self organized,Binding Site is induced by substrate ionsAll Spheres Model47Ion DiametersPauling Diameters Ca++ 1.98 Na+ 2.00 K+ 2.66 Side Chain DiameterLysine K 3.00 D or E 2.80 Channel Diameter 6 Parameters are Fixed in all calculations in all solutions for all mutantsBoda, Nonner, Valisko, Henderson, Eisenberg & Gillespie

Side Chains are Spheres Free to move inside channelSnap Shots of ContentsCrowded Ions6

Radial Crowding is SevereExperiments and Calculations done at pH 84748

large mechanical forces4849Key idea Instead of choosing configurations from uniform distribution, then weighting them with exp(E/k BT), MMC chooses them with a Boltzmann probability and weights them evenly.

Metropolis Monte Carlo Simulates Location of Ions both the mean and the varianceStart with Configuration A, with computed energy EA Move an ion to location B, with computed energy EB If spheres overlap, EB and configuration is rejectedIf 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 probability

MMC details

4950Na ChannelConcentration/MNa+ Ca2+ 0.004 00.0020.050.10

Charge -1eDE KABoda, et alEEEE has full biological selectivityin similar simulationsCa Channellog (Concentration/M) 0.5-6-4-2Na+ 01Ca2+

Charge -3eOccupancy (number)EE EAMutation Same Parameters5051Selectivity comes from Electrostatic InteractionandSteric Competition for Space

RepulsionLocation and Strength of Binding Sites Depend on Ionic Concentration and Temperature, etc

Rate Constants are Variables51Sodium Channel Voltage controlled channel responsible for signaling in nerve and coordination of muscle contraction

525253Challenge from channologistsWalter Sthmer and Stefan Heinemann Gttingen Leipzig Max Planck Institutes

Can THEORY explain the MUTATION Calcium Channel into Sodium Channel?

DEEA DEKA Sodium ChannelCalcium Channel5354Ca Channellog (Concentration/M) 0.5-6-4-2Na+ 01Ca2+

Charge -3eOccupancy (number)EE EAMonte Carlo simulations of Boda, et alSame ParameterspH 8 Mutation Same ParametersMutation EEEE has full biological selectivityin similar simulationsNa ChannelConcentration/MpH =8Na+ Ca2+ 0.004 00.0020.050.10

Charge -1eDE KA54Nothing was Changed from the EEEA Ca channelexcept the amino acids55Calculations and experiments done at pH 8Calculated DEKA Na Channel SelectsCa 2+ vs. Na + and also K+ vs. Na+5556Size Selectivity is in the Depletion Zone

Depletion Zone Boda, et al[NaCl] = 50 mM[KCl] = 50 mMpH 8 Channel ProteinNa+ vs. K+ Occupancyof the DEKA Na Channel, 6

Concentration [Molar]K+Na+Selectivity FilterNa Selectivity because 0 K+ in Depletion Zone

K+Na+Binding SitesNOT SELECTIVE56How?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

57Calculations and experiments done at pH 857SimpleIndependent Control Variables*DEKA Na+ channel58Amazingly simple, not complexfor the most important selectivity property of DEKA Na+ channelsBoda, et al*Control variable = position of gas pedal or dimmer on light switch Gas pedal and brake pedal are (hopefully) independent control variables58(1) Structureand (2) Dehydration/Re-solvationemerge from calculations

Structure (diameter) controls SelectivitySolvation (dielectric) controls Contents

*Control variables emerge as outputs Control variables are not inputs59Diameter Dielectric constants Independent Control Variables*

59Structure (diameter) controls Selectivity

Solvation (dielectric) controls Contents

Control Variables emerge as outputsControl Variables are not inputs

Monte Carlo calculations of the DEKA Na channel6060Na+ vs K+ (size) Selectivity (ratio)Depends on Channel Size,not dehydration (not on Protein Dielectric Coefficient)*61Selectivity for small ionNa+ 2.00 K+ 2.66 *in DEKA Na channelK+ Na+Boda, et al

Small Channel Diameter Large in 6 8 106162Generalization of Law of Mass Action is needed becausethe law assumes NO FLOWand NO INTERACTIONS

62 63

Law of Mass Action

[ A ] means the concentration of species A, i.e., the number density of AA, B are assumed to be ideal solutions of noninteracting particles kf, kb are assumed to be constants independent of concentration of any speciesIn the minds of most biochemists, many chemists, and textbook authors6364but Everything interacts with Everything Elsein biologyand flows cease only at death

64Page 65Everything is hidden in Keq , kf and kb

Interactions are significant in biological solutions (Ringer)Interactions are large in and near channels

kf,b and Keq are functions of everythingThey are not constants

65Page 66

Law of Mass Action includingFlow and Interactionsfrom Bob Eisenberg p. 1-6, in this issueVariational ApproachEnVarA

ConservativeDissipativeGreat Opportunity for New Science

Chemical Reactions inComplex FluidsDerived from theory of Stochastic Processes 6667Energetic Variational Approach allows accurate computation ofFlow and Interactions in Complex Fluids like Liquid CrystalsEngineering needs Calibrated Theories and SimulationsEngineering Devices almost always use flowClassical theories and Molecular Dynamicshave difficulties with flow, interactions, and complex fluidsShorthand for Euler Lagrange processwith respect to68Energetic Variational ApproachEnVarA Chun Liu, Rolf Ryham, Yunkyong Hyon, and Bob EisenbergMathematicians and Modelers: two different partial variationswritten in one framework, using a pullback of the action integral

Action Integral, after pullbackRayleigh Dissipation FunctionField Theory of Ionic Solutions that allows boundary conditions and flow and deals Consistently with Interactions of ComponentsCompositeVariational PrincipleEuler Lagrange Equations Shorthand for Euler Lagrange processwith respect to

6869Energetic Variational Approach EnVarA across biological scales: molecules, cells, tissuesVariational theory of complex fluids developed by Chun Liu with

Multiple Scalescreates a newMultiscale Field Theory of Interacting Componentsneeded for Molecular Engineering in general that allows boundary conditions and flow and deals with Ions in solutions self-consistently

(1) Hyon, Eisenberg Ions in Channels

(2) Horng, Lin, Liu, Eisenberg Ions in Channels(3) Bezanilla, Hyon, Eisenberg Conformation Change of Voltage Sensor (4) Ryham, Cohen Membrane flow Cells(5) Mori, Eisenberg Water flow in Tissues6970Take Home Lessons

71Ionic Solutions are Complex Fluids

and cannot be well analyzed by the theory of simple fluids

Take Home Lesson 17172Energetic Variational Approach allows accurate computation ofFlow and Interactions in Complex Fluids like Liquid CrystalsEngineering needs Calibrated Theories and SimulationsEngineering Devices almost always use flowTake Home Lesson 273Engineering needs Calibrated Theories and SimulationsEngineering Devices almost always use flowClassical theories and Molecular Dynamicshave difficulties with Flow, Interactions, and Complex FluidsStructure is the Computed Consequenceof Forcesin these models

Selectivity Depends on Structure

74Take Home Lesson 37475Channel and Contents form aSelf-Organized Structurewith Side Chains at position of Minimum Free EnergyProtein Fits the SubstrateInduced Fit Model of SelectivityWhat does the protein do?7576Binding Sites* are outputs of our CalculationsThis is the Self-organized Induced fit model of Koshland and the founders of enzymology, Made specific by Mathematics and Computation76We can actually compute the Structures that determine Selectivity77Miracle77Can EnVarA actually compute the function of these systems?

Can EnVarA serve as a usefulMathematical Framework for Multi-scale Engineering?78New Miracle??7879The End

Any Questions?80Solved with Metropolis Monte Carlo MMC Simulates Location of Ions both the mean and the variance

Produces Equilibrium Distribution of locationof Ions and Side Chains

MMC yields Boltzmann Distribution with correct Energy, Entropy and Free EnergyOther 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 formsSteric PNP (simplified EnVarA)Poisson Fermi 8081 Crowded Channels, Crowded Active SitesareComplex Fluidslike liquid crystals of LCD displaysAll atom simulations of complex fluid are particularly challenging becauseEverything interacts with everything elseon atomic & macroscopic scales

8182Generalization of Law of Mass Action is Feasible for Ionic Solutions using the Implicit Solvent Model of ionic solutions* *and perhaps the solvent primitive model or more sophisticated models and simulations that professional physical chemists know better than I

8283Energetic Variational Approach allows accurate computation ofFlow and Interactions in Complex Fluids like Liquid CrystalsEngineering needs Calibrated Theories and SimulationsEngineering Devices almost always use flowClassical theories and Molecular Dynamicshave difficulties with flow, interactions, and complex fluids