What can Molecular Dynamics Tell us about how our proteins work?

1. What can Molecular Dynamics Tell us about how our proteins work?

2. Why not compute all the atoms?

3. What Molecular Dynamics can NOT tell us Some physical systems cannot be computed on an atomic scale Propagating Action Potential

4. Why not compute all the atoms? 1 mm length of a 10 µ diameter nerve has ~1013 atoms Action potential propagates meters

5. Why not compute all the atoms? Open Probability of one channel is changed by potential far away (1013 atoms away)

6. Maxwell’s Equationsare aboutConservation of Current A different talk! Conservation of Charge

7. Multi-Scale Issues Journal of Physical Chemistry C (2010 )114:20719, invited review Three Dimensional (104)3 Biological Scales Occur Together so must be Computed and CALIBRATED Together This may be impossible in simulations

8. Uncalibrated Simulations will make devices that do not work Details matter in devices

9. Three Dimensional (104)3 Biological Scales Occur Together so must be Computed and CALIBRATED Together

10. Once calibrated, Molecular Dynamics can tell us a great deal

11. ~30 Å James Clerk Maxwell “I only count molecules ….,avoiding all personal enquiries which would only get me into trouble.” Slightly rephrased from Royal Society of London, 1879, Archives no. 188 in Maxwell on Heat and Statistical Mechanics, Garber, Brush and Everitt, 1995 0.7 nm = Channel Diameter Figure of ompF porin by Raimund Dutzler

12. First Principle of Numerical Integration The larger the calculation, the more work done, the greater the error First Principle of Experimentation The more work done, the less the error

13. 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)

14. Multi-scale Issues Most of biology depends on trace concentrations of hormones and Ca ion

15. Difficulties for all atom calculations (nickname MD) 10-7 M Ca occurs in 55 M water for each Ca ion have 5.5 × 107 water molecules 1.65× 108 atoms need ~1000 calcium ions for statistics Must calculate 1.65 × 1011 atoms and all their interactions!

16. Difficulties for all-atom calculations Most of biology occurs in mixturesMD is calibrated in ZERO concentration MD of mixtures does not exist because calibration fails MD is designed for zero concentrations of pure monovalents

17. Force Fields are Calibrated Ignoring Interactions with ions but Chemically Specific Properties come from Interactionsin Ionic Solutions Life occurs in Interacting Solutions

18. MD force fields are calibrated in distilled water, using “free energy of formation” Membrane phenomena depend on the free energy per mole (activity, approximated sometimes by concentration) MD does not calculate activities very well

19. Force Fields must be RE-calibrated in each Biological Solutionto verify equilibrium potentials (chemical potentials) Fitting Real Experimentsrequires Accurate Chemical Potentials in mixtures Calibration is Hard Work

20. Summary Almost no MD calculations exist of divalents NO MD calculations exist of trace concentrations of ions NO MD calibrations exist of mixtures of ions

21. Simulations produce too many numbers 106 trajectories each 10-6 sec long, with 109 samples in each trajectory, in background of 1022 atoms

22. Simulations need a theory that Estimates Parameters (e.g., averages) Theories and Reduced Models are needed to create estimators. Theories and Models are Unavoidable!(in my opinion)

23. Where to start? Biologically? Structure? Molecular Dynamics?

24. . Reduced Models are Needed Reduced Models are Device Equations like 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?

25. Molecular Dynamics is a crucial component of a HIERARCHY OF MODELS

26. Molecular Dynamics is a crucial component of an hierarchy of models Molecular Dynamics today is QUALITATIVE Part of Structural Biology Help build the Reduced Model What moves? How much water?

27. Once calibrated Molecular Dynamics can become part of Quantitative Models

28. Biology is Easier than Physics Reduced Models Exist* for important biological functions or the Animal would not survive to reproduce *Evolution provides the existence theorems and uniqueness conditions so hard to find in theory of inverse problems. (Some biological systems  the human shoulder  are not robust, probably because they are incompletely evolved,i.e they are in a local minimum ‘in fitness landscape’ .I do not know how to analyze these. I can only describe them in the classical biological tradition.)

29. Reduced models exist because they are the adaptationcreated by evolution to perform a biological functionlike selectivity Reduced Models and its parameters are found by Inverse Methodsof Reverse Engineering Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67:960-989

30. Bioengineers:this is reverse engineering *Ill posed problems with too little data seem complex, even if they are not. Some of biology seems complex for that reason. The question is which ‘some’? Inverse Problems Find the Model, given the OutputMany answers are possible: ‘ill posed’ *Central Issue Which answer is right?

31. Almost too much data was available for reduced model: Burger, Eisenberg and Engl (2007) SIAM J Applied Math 67:960-989 How does theChannel control Selectivity? Inverse Problems: many answers possible Central Issue Which answer is right? Key is ALWAYS Large Amount of Data from Many Different Conditions

32. Molecular Dynamics usually yields ONE data point at one concentration MD is not yet well calibrated (i.e., for activity = free energy per mole) for Ca2+ or ionic mixtures like seawater or biological solutions Inverse Problems: many answers possible Which answer is right? Key is Large Amount of Data fromMany Different Conditions Otherwise problem is ‘ill-posed’ and has no answer or even set of answers

33. Working Hypothesis: Crucial Biological Adaptation is Crowded Ions and Side Chains Wise to use the Biological Adaptation to make the reduced model! Reduced Models allow much easier Atomic Scale Engineering

34. Active Sites of Proteins are Very Charged 7 charges ~ 20M net charge = 1.2×1022 cm-3 liquidWater is 55 Msolid NaCl is 37 M + + + + + - - - - Selectivity Filters and Gates of Ion Channels are Active Sites Physical basis of function OmpF Porin Hard Spheres Na+ Ions are Crowded K+ Ca2+ Na+ Induced Fit of Side Chains K+ 4 Å Figure adapted from Tilman Schirmer

35. Crowded Active Sitesin 573 Enzymes Jimenez-Morales,Liang, Eisenberg

36. Don’t worry! Crowded Charge is GOOD It enables SIMPLIFICATION by exploiting a biological fact (an adaptation) Charges are Crowded where they are important!

37. Where do we begin? Crowded Charge enables Dimensional Reduction* to a Device Equation Inverse Problem! Essence of Engineering is knowing What Variables to Ignore! WC Randels in Warner IEEE Trans CT 48:2457 (2001) *Dimensional reduction = ignoring some variables

38. What can Molecular Dynamics Tell us about how our proteins work?

39. Molecular Dynamics is a crucial component of a HIERARCHY OF MODELS Help build the Reduced Model What moves? How much water? Structural Parameters VOLUME Concentration of STRUCTURAL components Diffusion coefficient Dielectric coefficient (i.e., polarization)

40. Molecular Dynamics is a crucial component of a HIERARCHY OF MODELS