BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Robert Eisenberg (Rush University\, Illinois Institute of Technolo gy) DTSTART:20200520T150000Z DTEND:20200520T160000Z DTSTAMP:20260423T005836Z UID:GSMMA/4 DESCRIPTION:Title: Io ns in channels and bulk: mathematics and molecular biology\nby Robert Eisenberg (Rush University\, Illinois Institute of Technology) as part of Global Seminar on Mathematical Modeling and Applications\n\n\nAbstract\nLi fe and most of chemistry occurs in ionic solutions\, but ionic solutions h ave only recently been recognized as the complex fluids that they are. The molecular view shows ions interacting with surrounding water and nearby i ons. Everything is correlated in a complex way because ions and water have diameters comparable to their interaction length. The molecular scale sho ws only a small part of the correlation enforced by electrodynamics. Curre nt defined as Maxwell did to include the ethereal current is exactly conse rved\, and therefore correlated\, over all scales reaching to macroscopic boundary conditions some 1e9 larger than atoms crucial in batteries and n erve cells.\n

\n\n Jinn Liang Liu and I have built a molecular fiel d theory PNPB Poisson Nernst Planck Bikerman that deals with water as mole cules and describes local interactions with a steric potential that depend s on the volume fraction of molecules and voids between them. The correlat ions of electrodynamics are described by a fourth-order differential opera tor that gives (as outputs) ion-ion and ion-water correlations\; the diele ctric response (permittivity) of ionic solutions\; and the polarization of water molecules\, all using a single correlation length parameter. The th eory fits experimental data on activity and differential capacitance in io nic solutions of varying composition and content\, including mixtures. Pot assium channels\, Gramicidin\, L-type calcium channels\, and the Na/Ca tra nsporter are computed in three dimensions from structures in the Protein D ata Bank.\n

\n\nNumerical analysis faces challenges: \n
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  1. Geometric singularities of molecular surfaces
    2. \n
  2. strong electr ic fields (100 mV/nm) and resulting exponential nonlinearities\, and the < /li>\n
  3. enormous concentrations (> 10 M) often found where ions are i mportant\, for example\, near electrodes in batteries\, in ion channels\, and in active sites of proteins.
    4. \n
  4. Wide ranging concentrations of 1e-1 to 1e-8 M in and near almost every protein in biological cells ma ke matters worse.
    5. \n
\n\nChallenges have been overcome using meth ods developed over many decades by the large community that works on the c omputational electronics of semiconductors.\n\nmeeting ended\n LOCATION:https://researchseminars.org/talk/GSMMA/4/ END:VEVENT END:VCALENDAR