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

Biology is first of all a Descriptive Science Biology Involves Many Objects. The Devices and Machines of Biology must be Named and Described Then they can be understood by Physics as Usual

Biology is first of all a Descriptive Science Biology as Usual “Why think? . . . Exhaustively experiment. Then, think” Claude Bernard Cited inThe Great Influenza, John M. Barry, Viking Penguin Group 2004 Then,Physics as Usual

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

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

ION CHANNELS asTechnological Objects Channels Control Macroscopic Flowwith Atomic Resolution

Ion Channelsare Important Enough to be Worth the Effort

Goal: Predict Function From Structure given Fundamental Physical Laws

Goal in language of Physiology: Predict Function, from Structure, given Fundamental Physical Laws Goal, in language of engineers, Develop Device Equation!

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 Figure by Raimund Dutzler Structure determined by x-ray crystallography in Tilman Schirmer’s lab

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 use Verbal Models 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 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”? Simulations are Reliable Science when they are Calibrated Simulations are not Mathematics! (e.g., results depend on numerical procedures and round-off error)

Simulations are not Mathematics! Simulations are Reliable Science when they are Calibrated The computer should not be used in the ‘stand-alone’ mode quotation from J.D. Skufca, Analysis Still Matters, SIAM Review 46: 737 (2004) because results often depend on numerical procedures and round-off error

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

Can Molecular Simulations serve as “Fundamental Physical Laws”? What should be calibrated? I believe Thermodynamics of ions must be calibrated, i.e., activity = free energy per mole, which means the Pair Correlation Function according to classical Stat Mech

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)

Guess Cleverly! Without qualitative understanding,quantitative models can be onlyvague statements of thermodynamics. Qualitative Simulationshave an important role in Computational Biology

Goal in language of Physiology: Predict Function, from Structure, given Fundamental Physical Laws Goal, in language of engineers, Develop Device Equation!

Use Theory of Inverse Problems (Reverse Engineering) optimizes “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, Guess Cleverly!

Use the scientific method Guess and Check! When theory works, need few checks Computations (almost) equal experiments Structural Engineering Circuit Design Airplane Design Computer Design Can be done (almost) by theory,

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 Is the physical basis of permeation known?

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

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

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