As a nonexpert, the dumb question is why we cannot conceive of coupling as resolution of kinetic energy into potential to achieve closest, cheapest, nearest stability. Coupling is nearest resolution of displacement from rest (to potential).

]]>• Jonathan Lorand and Alan Weinstein, Decomposition of (co)isotropic relations.

Lorand is working on a paper with Weinstein and Christian Herrman that delves deeper into these topics. I first met him at the ACT2018 school in Leiden, where we worked along with Blake Pollard, Fabrizio Genovese (shown below) and Maru Sarazola on biochemical coupling through emergent conservation laws. Right now he’s visiting UCR and working with me to dig deeper into these questions using symplectic geometry! This is a very tantalizing project that keeps on not quite working…

]]>It seems to work. There's one place where you still have ‘the two reactions in the above schema’ ambiguously.

I’m doing fine. I read all of the top-level posts here, even though I don’t comment much.

]]>The question we’re trying to address is: *what’s coupling?* Enzymes are important for speeding up certain reactions, and that’s crucial for coupling. But you could know everything about what enzymes you’ve got and how they interact with the reactants, and still not have a precise understanding of when coupling happens, when it does not happen, and more fundamentally what coupling *is*. Conversely, you could know nothing about the enzymes—just the rate constants for the reactions they catalyze—and still be able to figure out what coupling is and when it happens.

Don’t forget: we’re mathematicians, not chemists. There’s not a chance in hell that we’re going to discover anything new about specific enzymes and how they catalyze reactions. But we *do* have a chance of thinking about the rate equations of reaction networks and coming up with insights about what ‘coupling’ really is.

To me the most informative and valuable information would be about how the enzyme and the reactants interact, and about how/if the enzyme concentration changes.

]]>Hi there, long time no see! I hope you’re doing okay.

I accidentally left out the equations after “such as these.”

All your guesses about what I meant are right. In the PDF version of this paper I use equation numbers to refer to previous equations, and some of these problems go away. I think equation numbers work badly on this WordPress version of LaTeX, and they seem a bit stuffy for a blog article, but I’ll try ’em.

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