Jeff Canfield's Science Wish List:

Summary:

• Below is a list of science problems that I would like someone to solve.
• If you decide to pursue any of these ideas, have seen them done already, or would like my help with them, please e-mail me to let me know.
• If any of these ideas prove valuable to you (patents, publications, fame, fortune, etc.), appropriate acknowledgment, citation, co-authorship, etc. would be appreciated.
• Some references cited below are the following:
  • [1] My Ph.D. Thesis entitled "Approaching Magnetic Field Effects in Biology Using the Radical Pair Mechanism":
    • If this is not available at your library, please ask your library's science selector to order a copy to put on the shelves there.
  • [2] "A Perturbation Theory Treatment of Oscillating Magnetic Fields in the Radical Pair Mechanism"
    by J. M. Canfield, R. L. Belford, P. G. Debrunner, and K. J. Schulten in Chemical Physics vol.182 no.1 pp.1-18 April 15 1994.
  • [3] "A Perturbation Treatment of Oscillating Magnetic Fields in the Radical Pair Mechanism using the Liouville Equation"
    by J. M. Canfield, R. L. Belford, P. G. Debrunner, and K. Schulten in Chemical Physics vol.195 no.1-3 pp.59-69 June 1 1995.
  • [4] "Calculations of Earth-Strength Steady and Oscillating Magnetic Field Effects in Coenzyme B₁₂ Radical Pair Systems"
    by J. M. Canfield, R. L. Belford, and P. G. Debrunner in Molecular Physics vol.89 no.3 pp.889-930 Oct.20 1996.

Theory:

• Examine Appendix A of [1] and prove that k_S Φ_ST(t) = 3 k_T Φ_TS(t) holds quite generally, even when k_S differs from k_T.
• Adapt the method in [3] to calculate the time-dependence of the singlet-to-triplet yield Φ_ST(t) for general k_S and k_T:
  • Appendix E of [1] has some discussion of this.
• Find ways to extend the applicability of the perturbation expansion in [3] to explore a broader range of magnetic fields:
  • The method seems very stable and in 1995 did calculations out to 12th order in a reasonable timeframe. Modern computers should do more.
  • "From useful algorithms for slowly convergent series to physical predictions based on divergent perturbative expansions"
    in Physics Reports vol.446 no.1-3 July 2007 pp.1-96 might help.
  • Would some sort of renormalization help?
  • Pade Approximation might help:
    • Wikipedia has a brief article about this technique with some useful references.
    • See Chapters 7 and 8 of Bender and Orszag's "Advanced Mathematical Methods For Scientists and Engineers", 1978, ISBN=0-07-004452-X too.
    • "Numerical Recipes in C" 2nd Edition, 1992, ISBN=0-521-43108-5 on p.202 says the following about Pade Approximation:
      • "There is, in general, no way to tell how accurate it is, or how far out in x it can usefully be extended.
        It is a powerful, but in the end still mysterious, technique."
    • It seems that many people use Pade Approximation, but is its reliability really known?
    • How can you tell its accuracy or when its results can be trusted when you have no other methods available for comparison?
    • What if you base your Pade Approximation on a perturbation series out to 12th order, but a key behavior does not begin until 16th order?
    • Please examine the equations in [2] and pp.26,165 of [1] to see if they are a special class whose convergence properties are known.
• Explore what happens when one replaces the discrete frequencies in [2] and [3] with finite-bandwidth signals:
  • Finite-bandwidth signals (like Gaussians or Lorentzians vs. frequency) are more realistic than the δ-function frequency distributions used in [2] and [3].
  • Fig.6 and the 2nd order term in eq.48 of [2] show that the effect of multiple oscillating magnetic fields is not just the sum of the effects of individual oscillating magnetic fields:
    • Can this nonlinearity let a finite-bandwidth low-amplitude signal be more effective than a similar-amplitude signal at a single discrete frequency?
    • How should one normalize the two types of signals to make an appropriate comparison?
  • At first glance, one could simply replace the sums over discrete frequencies with integrals over a range of frequencies:
    • Should one also replace the sums over discrete phases with integrals over a range of phases?
    • Should the phase depend on the frequency?
  • What would be a good way to represent finite-bandwidth noise signals?
  • Appendix F of [1] has some discussion useful for this.
• Explore what happens when W-H_jj is near zero in the denominators of terms in Equations (6.32) and (6.33) of [1]:
  • Will the effective 2×2 matrix in Equation (6.21) of [1] still be a good approximation?
  • Harold Salwen may have written a paper about this after 1995:
    • Ref.146 in [1] is Physical Review v.99 n.4 1955 pp.1274-1286 (Aug.15, 1955) by H. Salwen.
    • The general technique might be called degenerate Wigner perturbation theory.
    • The non-degenerate version might have been done independently by Lennard-Jones, Brillouin, and Wigner:
      • Wigner may have published his work on this in a Hungarian journal written in English.
• Develop better density functional theory (DFT) methods for obtaining g-tensors, hyperfine couplings A, or exchange interactions J for radical pair systems.
• Develop better mixed Quantum Mechanics / Molecular Mechanics (QM/MM) methods, especially ones that can treat
  homolytic bond cleavage, free radical formation and recombination, electron and nuclear spins, and singlet/triplet states:
  • The DFTB method is along these lines:
    • Henryk Witek is working to parameterize all 92 elements for this method.
    • Stephan Irle has done some interesting calculations using this method.
• Find ways to lengthen electron spin relaxation times T₁ and T₂ in biological radical pair systems at 20-40 degrees C in Earth-strength magnetic fields:
  • T₁ and T₂ should approach each other as the applied magnetic field approaches zero.
  • Is T₁=T₂=50μsec or more attainable? If so, how? If not, why not?
  • What are the maximum attainable T₁ and T₂?
  • What type of microenvironment would favor long electron spin relaxation times T₁ and T₂?
    • Living cells are very inhomogeneous and many parts do not behave like simple solutions.
    • Light-sensitive organelles have many layers. Would that help?
    • Would being near microfilaments, fibers, ribbons, or tangled structures help?
      • β-amyloid proteins can form many different microstructures like these.
    • Would being in a tightly-packed structure with restricted or low-dimensional diffusion help?
    • Enzymes that use free radicals tend to isolate these free radicals to protect from unwanted side reactions:
      • Would this isolation extend relaxation times?
    • Mitochondria, chloroplasts, ribosomes, membranes, bones, etc. all provide special microenvironments:
      • Would any of these help?
  • Below are some interesting references along these lines:
    • "Spin relaxation of radicals in low and zero magnetic field"
      by M.V.Fedin, P.A.Purtov, and E.G.Bagryanskaya in J. Chem. Phys. vol.118 no.1 Jan 1, 2003 pp.192-201.
    • "Zero-Field Spin Dynamics and Relaxation"
      by Yu A. Serebrennikov, pp.47-99 in Advances in Magnetic and Optical Resonance vol.17 Academic Press, Inc. 1992.
    • "Zero-field magnetic resonance of the photo-excited triplet state of pentacene at room temperature"
      by T-C Yang, D J Sloop, S I Weissman, and T-S Lin in J. Chem. Phys. vol.113 no.24 Dec.22, 2000 pp.11194-11201.
    • "Enhanced Signal Intensities Obtained by Out-of-Phase Rapid-Passage EPR for Samples with Long Electron Spin Relaxation Times"
      by J R Harbridge, G A Rinard, R W Quine, S S Eaton, and G R Eaton in Journal of Magnetic Resonance vol.156 pp.41-51 2002:
      • This group has done many studies of electron spin relaxation times over a broad range of magnetic fields.
      • This particular paper reports room temperature electron spin relaxation times T₁=200µsec and T₂=35-200µsec.

Experiment:

• Study biological free radicals, especially radical pairs, to determine their g-tensors, hyperfine couplings A, exchange interactions J, inter-radical distances and orientations, lifetimes τ, and electron spin relaxation times T₁ and T₂:
  • Explore what happens to these parameters at 20-40 degrees C in Earth-strength magnetic fields.
  • Some enzymes contain very stable, long-lived free radicals. Others contain transient free radicals.
    • In [4], the most interesting things happen for radicals with lifetimes 50μsec or longer.
  • Many proteins contain free radical forms of amino acids. Some examples are glycyl, tryptophanyl, and tyrosyl radicals.
  • Many enzymes contain transition metals like cobalt, copper, iron, or molybdenum that have unpaired electrons and so behave like free radicals.
  • Superoxide dismutases (SOD), nitric oxide synthases (NOS), xanthine oxidase (XO), β-amyloid proteins, melanins, cryptochromes, radical SAM enzymes, B₁₂ enzymes, photosynthetic reaction centers, and DNA photolyases are all interesting systems:
    • Do any exchange-coupled radical pair species lurk in the EPR spectra of Cu-containing β-amyloid complexes?
  • The magnesium-dependent phosphorylation enzymes ATPase and phosphocreatine and phosphoglycerate kinase sound interesting.
• Find ways to lengthen electron spin relaxation times T₁ and T₂ in biological radical pair systems at 20-40 degrees C in Earth-strength magnetic fields:
  • See above for details.
• Explore the effects of Earth-strength magnetic fields on semiconductors, free radical polymerization, and biological radical pair systems:
  • Nature vol.453 15 May 2008 pp.387-390 discusses a model experimental system sensitive to Earth-strength magnetic fields.
  • The free radical photopolymerization of methyl methacrylate (MMA) behaves differently in Earth-strength versus 6400 G magnetic fields.

More About Jeff:

• UIUC Web Site
• Ohio State Web Site

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