Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative

Chemist’s View Ion ChannelsProteins with a Hole All Atoms View Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative ~30 Å Figure by Raimund Dutzler

ION CHANNELS: Proteins with a Hole Channels form a class of Biological Systemsthat can be analyzed with Physics as Usual Physics-Mathematics-Engineering are the proper language for Ion Channels in my opinion

Ion Channels can be analyzed with Physics as Usual along with Biology as Usual “Why think? . . . Exhaustively experiment. Then, think” Claude Bernard Appropriate when nothing was known of Inverse Problems! Cited inThe Great Influenza, John M. Barry, Viking Penguin Group 2004

Channels control flow in and out of cells ION CHANNELS as Biological Objects ~5 µm

Ion Channels are the Main Molecular Controllers“Valves”ofBiological Function ~30 Å Figure by Raimund Dutzler

ION CHANNELS as Physical Devices Channels control flow of Charged Spheres Channels have Simple Invariant Structure on the biological time scale. Why can’t we predict the movement of Charged Spheres through a Hole?

Ion channels have Selectivity. K channel selects K+ over Na+ by ~104. Ion channelsGate/Switchin response to pH, voltage, chemical species and mechanical force from conducting to nonconducting state. Ion channelshaveVERY Large Charge Densities critical to I-V characteristics and selectivity (and gating?) Ion channels allowMutations that modify conductance, selectivity, and function. Ion channels are Device Elementsthat self-assemble into perfectly reproducible arrays. Ion channelsformTemplatesfor design of bio-devices and biosensors. ~30Å Physical Characteristics of Ion ChannelsNatural Nanodevices Figure by Raimund Dutzler

ION CHANNELS asTechnological Objects Channels Control Macroscopic Flow with Atomic Resolution

Ion Channelsare Important Enough to be Worth the Effort

Goal: Predict Function From Structure given Fundamental Physical Laws

Current in One Channel Molecule is a Random Telegraph Signal

Voltage Step Applied Here (+ 80 mV; 1M KCl) Gating: Opening of Porin Trimer John TangRush Medical Center

Single Channel Currents have little variance John TangRush Medical Center

Conflict of Interest Lipid Bilayer SetupRecordings from a Single Molecule Axopatch

Patch clampand Bilayer apparatus clamp ion concentrations in the baths and thevoltageacross membranes. PatchClamp Setup Recordings from One Molecule

OmpF KCl 1M 1M || G119D KCl 1M 1M || G119D KCl0.05 M 0.05M || ompF KCl0.05 M 0.05M || Current depends on Bilayer Setup Voltagein baths Concentrationin baths Fixed Chargeon channel protein John TangRush Medical Center

OmpF KCl 1M 1M || OmpF CaCl2 1M 1M || Current depends on type of ionSelectivity John TangRush Medical Center Bilayer Setup

Structures… Location of charges are known with atomic precision (~0.1 Å) in favorable cases.

G119D Ompf Charge Mutation in Porin Structure determined by x-ray crystallography in Tilman Schirmer’s lab Figure by Raimund Dutzler

But … What are the Fundamental Physical ‘Laws’?

Verbal Models Are Popular with Biologists but Inadequate

James Clerk Maxwell “I carefully abstain from asking molecules where they start… I only count them…., avoiding all personal enquiries which would only get me into trouble.” Royal Society of London, 1879, Archives no. 188 In Maxwell on Heat and Statistical Mechanics, Garber, Brush and Everitt, 1995

I fear Biologists indulge themselves with verbal models of molecules where Maxwell abstained

Verbal Models areVagueandDifficult to Test

Verbal Modelslead to Interminable Argument and Interminable Investigation

thus,to Interminable Funding

and so Verbal Models Are Popular

Can Molecular Simulationsserve as “Fundamental Physical Laws”? Only if they count correctly !

It is very difficult for Molecular Dynamics to count well enough to reproduce ConservationLaws(e.g., of number, energy) Concentration (i.e., number density) or activity Energy of Electric Field Ohm’s ‘law’(in simple situations) Fick’s ‘law’(in simple situations) Fluctuationsin number density (e.g., entropy)

Can Molecular Simulations serve as “Fundamental Physical Laws”? Only if Calibrated!

Calibrated Molecular Dynamics may be possible Pair Correlation Function in Bulk Solution • MD without Periodic Boundary Conditions─ HNC HyperNetted Chain Saraniti Lab, IIT: Aboud, Marreiro, Saraniti & Eisenberg

Calibrated Molecular Dynamics may be possible Pair Correlation Function in Bulk Solution • MD without Periodic Boundary Conditions BioMOCA─ Equilibrium Monte Carlo (ala physical chemistry) van der Straaten, Kathawala, Trellakis, Eisenberg & Ravaioli

Calibrated MD may be possible,even in aGramicidin channel 16 Na+ single channel currents Molecular Dynamics without Periodic Boundary Conditions BioMOCA Simulations 235ns to 300ns, totaling 4.3 μs.Mean I = 3.85 pA, 24 Na+ crossings per 1 μs van der Straaten, Kathawala, Trellakis, Eisenberg & Ravaioli

Until Mathematics of Simulations is availablewe take anEngineering Approach Essence of Engineering is knowing What Variables to Ignore! WC Randels quoted in Warner IEEE Trans CT 48:2457 (2001)

What variables should we ignore when we make low resolution models? How can we tell when a model is helpful? Use the scientific method Guess and Check! Intelligent Guesses are MUCH more efficient Sequence of unintelligent guesses may not converge! (e.g., Rate/State theory of channels/proteins)

Use the scientific method Guess and Check! Intelligent Guesses are MUCH more efficient When theory works, need few checks ‘guesses’ are almost as good as experiments. in Mechanical Engineering, Electricity, Computer Science, Hydrodynamics,

Use Theory of Inverse Problemsto replace or optimize “Guess and Check” 1) Measure only what can be measured (e.g.,not two resistors in parallel). 2) Measure what determines important parameters. 3) Use efficient estimators. 4) Use estimators with known bias 5) no matter what the theory, Be clever in estimation

Channels are only Holes Why can’t we have a fully successful theory? Must know physical basis to make a good theory Physical Basis of Gating is not known Physical Basis of Permeation is known, in my opinion.

Proteins Bristle with Charge Cohn (1920’s) & Edsall (1940’s) Ion Channels are no exception We start with Electrostaticsbecause of biology

Many atoms in a protein have Permanent Charge ~1e Permanent charge is the (partial) charge on the atom when the local electric field is zero. Active Sites in Proteins haveMany Charges in a Small Place

Atom Charge in Arginine Atom Charge (units /e) N −0.40 H 0.25 C_a 0.10 C_b 0.00 C_g 0.00 C_d 0.10 N_e −0.40 H_e 0.30 C_z 0.50 NH_1 −0.45 HH_11 0.35 HH_12 0.35 NH_2 −0.45 HH_21 0.35 HH_22 0.35 C 0.60 O −0.55 according toCHARMM Average Magnitude 0.32

Active Sites of Proteins are VeryCharged e.g. 7 charges ~ 20 M net charge = 1.2×1022 cm-3 1 nM Selectivity Filters and Gates of Ion Channels are Active Sites

Start with electrostatics because Small Charge in Small Places Large Potentials* Vat psec times;dielectric constant = 2 mVat µsec times; dielectric constant =80 1 charge gives in a Sphere of diameter 14 Å *500 µvolt has significant effect on IV curve

We start without quantum chemistry*(onlyat first) *i.e., delocalization of orbitals of outer electrons

Although we start with electrostatics We will soon add Physical Models of Chemical Effects

It is appropriate to be skepticalof analysis in which the only chemistry is physical But give me a chance, ask I will be in Linz for a week! (thanks to Heinz!) Or email beisenbe@rush.edu for the papers

Very Different from TraditionalStructuralBiologywhich, more or less, ignores Electrostatics

Lowest resolution theory that includes Electrostatics and Flux is (probably) Poisson-Nernst-Planck (PNP) PNP, Gouy-Chapman, (nonlinear) Poisson-Boltzmann, Debye-Hückel, are fraternal twins or siblings with similar resolution

Chemical Bonds are lines Surface is Electrical Potential Red is positive Blue is negative