Help understanding external magnetic field sensitivity of radical pair reaction rate Two recent papers have been published on magnetoreception in birds. In this case it is the ability of the birds to sense the direction of the Earth's magnetic field potentially for navigation. 


Expression patterns of cryptochrome genes in avian retina suggest involvement of Cry4 in light-dependent magnetoreception Atticus Pinzon-Rodriguez, Staffan Bensch, Rachel Muheim J. R. Soc. Interface 2018 15 20180058; DOI: 10.1098/rsif.2018.0058. Published 28 March 2018
Double-Cone Localization and Seasonal Expression Pattern Suggest a Role in Magnetoreception for European Robin Cryptochrome 4 Günther, Anja et al.
Current Biology , Volume 28 , Issue 2 , 211 - 223.e4


The idea has been around a long time; cf A Biomagnetic Sensory Mechanism Based on Magnetic Field Modulated Coherent Electron Spin Motions Zeitschrift fur Physikalishe Chemie Neue Folge, Bd. 111, S. 1-5, (1978)

The two new papers address the role of something called "radical pairs", two molecules, each with an unpaired electron. The large molecules are in the retina and tend to have a preferred orientation with respect to the curved retina, and they also appear to affect the perceived intensity of blue light. This causes a modulation of light sensitivity across the retina dependent on the direction of the magnetic field with respect to the direction of the local normal vector of the retina.

The modulation of the reaction rate by the magnetic field direction has to do with singlet vs triplet states and quantum coherence, but I only say that because I've tried to read Cryptochrome and Magnetic Sensing by the Theoretical and Computational Biophysics Group at U. Illinois, Urbana-Champagne, as well as this Science Alert.

Are there simpler examples of the sensitivity of the reaction rate of "radical pairs" to the orientation of a magnetic field? Perhaps two atoms or two small molecules? Or does this phenomenon generally occur only in large, complex molecules?



below: "This is how a bird might see magnetic fields. (Theoretical and Computational Biophysics/UofI)" From ScienceAlert.
(This is really a comment but  has become too long)
There are many examples of  triplet states in magnetic fields as studied by electron paramagnetic resonance (ESR or EPR) experiments. See chapter 8 'Introduction to Magnetic Resonance' by Carrington &amp; McLachlan. It is an old book but does contain all you need to know. (A paper I happen to know showing magnetic field effects is Hyde et al. Chemical Physics v151,p239 1991 but there must be many others if you search)

As to the bird experiments, eqn 1 of the paper by Schulten et al. as described in your question describes the situation: scheme copied below. 

$$\begin{align}
(D^*&amp;+A)\leftrightharpoons \;^1(^2A^-+\;^2D^+) \stackrel{B}\leftrightharpoons \; ^3(^2A^-+\;^2D^+)\to \;^3T\\ &amp;\downarrow\\ &amp;\;^1X \end{align}$$

What it seems is necessary is (a) The reaction starts with a light induced electron transfer from excited donor $D^*$ to a nearby molecule that is the acceptor $A$. (b) The singlet state $^1(^2A^-+\;^2D^+) $ species produced has energy levels that cross those of one of the  of $m_I=\pm 1$ levels of the triplet states $^3(^2A^-+\;^2D^+) $ three levels at some value of the magnetic field $B$ and so singlet to triplet crossing occurs($^1$). (c) This enables the yield of products $^3T$ to $^1X$ to vary as the value of the magnetic field varies as the animal moves. (d) The protein has to be fixed relative to the bird otherwise this will not work. (This is the 'anisotropy' mentioned)  Being fixed could simply mean being in a cell membrane in one part of the retina. (e) Somehow the ratio of products has to be able to be distinguished.  Clearly this mechanism clearly will not work at night. 

So all in all a complicated mechanism, involving subtle processes, and this makes it very interesting.



($^1$) In a molecule as the triplet often differs significantly in energy from the singlet a huge magnetic field is needed to reach the S-T crossing point, but in pairs of molecule the interaction is very small and so the energy difference is v small also. This is advantageous as then small magnetic fields can cause S-T crossing. (Normally the singlet is above the triplet in energy, unlike the in figure, but the crossing is clear nonetheless)

also see Can magnetic fields affect a chemical reaction?