I’m in Luxembourg, and I’ll be blogging a bit about this workshop:
• Dynamics, Thermodynamics and Information Processing in Chemical Networks, 13-16 June 2017, Complex Systems and Statistical Mechanics Group, University of Luxembourg. Organized by Massimiliano Esposito and Matteo Polettini.
I’ll do it in the comments!
I explained the idea of this workshop here:
The first talk:
• Luca Peliti, On the value of information in gambling, evolution and thermodynamics.
I’m fond of Kelly’s work, where he showed that you can double your money if you can get people to bet on a topic where you know one bit of information that they don’t.
• Wikipedia, Kelly criterion.
I don’t know what ‘substitution load’ is.
I’ve been familiar with the analogy Peliti is explaining—the analogy between how Maxwell’s demon can extract extra work by knowing some information, and how Kelly’s gambler can win bets by knowing some ‘inside information’—for some time now. He says it’s due to Vinkler et al in 2015 and Rivoire in 2015. So, I missed the boat.
Peliti went on to cover a lot of very interesting material that’s new to me, e.g. the analogue of the Jarzynski equality for population dynamics.
I hear he’ll put his slides on the conference website; they contain a lot of cool references at the end. I’ll link to them here when they’re up. If I forget, post a comment to remind me!
Here’s one interesting reference:
• T. J. Kobayashi and Y. Sughiyama, Fluctuation relations of fitness and information in population dynamics, Phys. Rev. Lett. 115 (2015), 238102.
Next:
• Hong Qian, The Mathematical Foundation of a landscape theory for living matter and life.
A cool-looking paper:
• Yi-An Ma and Hong Qian, A thermodynamic theory of ecology: Helmholtz theorem for Lotka-Volterra equation, extended conservation law, and stochastic predator-prey dynamics, Proceedings of the Royal Society A 471 (2015), 20150456.
Hong Qian said that Jan Maas has worked on writing Markov processes in terms of gradient flow with respect to the Wasserstein metric on the space of probability distributions (a metric that I don’t yet understand, apparently). I should read this:
• Jan Maas, Gradient flows of the entropy for finite Markov chains.
For ‘motifs’ in genetic regulatory networks, see:
• Uri Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, Chapman, 2006.
Enrico Carlon is talking about one of these: the heterodimer auto-repression loop (or HAL) is one of several simple motifs that gives rise to oscillatory behavior. You can think of it as a chemical reaction network and write down its rate equation: a set of first-order differential equations.
• Enrico Carlon, A robust and flexible pulse-generating genetic module.
Here’s a paper on it:
• B. Lannoo, E. Carlon and M. Lefranc, The heterodimer auto-repression loop: a robust and flexible pulse-generating genetic module.
E. Yeger-Lotem has written a couple of papers in 2003-4 looking for the HAL motif in nature.
Another talk by someone I know, whose work I like a lot, in part because it combines chemical reaction theory with graph rewrite theory:
• Christoph Flamm, How to find mechanisms in large reaction networks? (Part 1.)
After this will come a second part:
• Daniel Merkle, Exploration and analysis of chemical spaces. (Part 2.)
Merkle is speaking. This is the first talk I’ve seen where someone argues strongly for the usefulness of category theory, then explains the definition of pushouts, and then illustrates it with examples from organic chemistry! Good thing I’d explained the definition of ‘category’ earlier in the day! Double-pushout graph rewriting applied to chemistry, and implemented in software that creates pictures of molecules using TikZ:
• Jakob L. Andersen, Christoph Flamm, Daniel Merkle, Peter F. Stadler, A software package for chemically inspired graph transformation.
I’m listening to this talk now:
• Thomas Ouldridge, The thermodynamics of persistent information in biochemical systems.
One thing I like is that he considers some simple reaction networks as models of the concepts he’s studying. One of them is this:
X + ATP
X* + ADP
X*
X + P
This is simple enough that I can imagine understanding it! He shows how the rate equation for this is “the same as” (or can be mapped to, in some way that deserves investigation) the rate equation for a rate equation for a more abstract reaction network for data copying.
Some papers on this work:
• Thomas McGrath, Nick S. Jones, Pieter Rein ten Wolde, Thomas E. Ouldridge, Biochemical machines for the interconversion of mutual information and work, Physical Review Letters 118 (2017).
• Thomas E. Ouldridge, Christopher C. Govern, Pieter Rein ten Wolde, Thermodynamics of computational copying in biochemical systems, Physical Review X 7 (2017).
Eric Smith is talking now. He mentioned that kappa is supposed to be an extensible language for systems biology. Worth looking into!
It’s the first part of a two-part talk:
• Eric Smith and Supriya Krishnamurthy, Stochastic chemical reaction networks in the Doi-Peliti representation: scaling, moment hierarchies, and duality under the non-equiilbrium work relations and their generalizations.
Eric Smith says “There is a native notion of the fluctuation-dissipation theorem built into Doi’s 2-field formalism”, citing Kamenev. This “2-field formalism” is the path integral approach to the chemical master equation.
Stefan Schuster is talking about “elementary flux modes” in reaction networks. Here’s the talk abstract:
• Stefan Schuster, Jan Ewald, Maximilian Fichtner, Severin Sasso and Christoph Kaleta, Modelling the link between lipid and carbohydrate metabolism in various species.
Schuster defined an elementary mode of a chemical reaction network as “a minimal set of enzymes that can operate at steady state with all irreversible reactions used in the appropriate direction, with enzymes weighted by the relative flux they carry”. A more mathematical-sounding definition would help me a lot, and I’m sure one exists! I believe we’ve got a (directed multi)graph and we’re looking for a basis of the space of 1-chains obeying some property. There may be an assumption that all reactions involve an enzyme, meaning that they’re of the form
or perhaps
or
for some species
the enzyme.
However they’re defined, the elementary modes are unique up to scaling, and they form a spanning set for some interesting vector space.
Here’s my attempt to formalize the idea. I fear I’m leaving out some important details.
A reaction network has a finite set of species
, a finite set of reactions
and source and target maps
The change in species due to a reaction
is
, and there is a linear map
usually called the stochiometric matrix defined by the equation
(Here I’m thinking of any element of
as a linear combination of elements of
, which form a basis; then I’m defining
by its action on these basis elements.)
A flux mode is an element
for which
So, it’s a sum of reactions that, taken together, ‘don’t do anything’—it leaves the number of species of each sort unchanged.
An elementary flux mode is a flux mode
that’s minimal, meaning there’s no nonzero flux mode
with
Here I’m using the obvious partial order on flux modes, where
iff
for each species 
I fear I’m leaving out some issues regarding enzymes: the reaction network I’m discussing might formally contain a reaction
but really ‘secretly’ this reaction could be
This wouldn’t significantly change the concept of flux mode, because the amount of the enzyme
is unchanged, but in applications of flux modes we might want to know which flux modes are allowed if we put a constraint on how much of the enzyme
is available.
Perhaps we should model this by a set
of enzymes and a map
saying how much of each enzyme is involved in each reaction.
Schuster describes how elementary mode analysis has been used to study an interesting question: can fatty acids be transformed into glucose? Humans can’t do it using the reactions that convert glucose into fatty acids, but green plants, fungi, many bacteria (including E. coli) and nematodes can do it. That’s because they have the ‘glyoxylate shunt’.
Can humans convert fatty acids into sugar using some more complicated mechanism. Yes! – at least in principle. They’re very complicated: molecules need to cross the mitochondrial membrane three times! And yet, it seems they may be used by people playing soccer (for example), and by the Inuit, who eat a diet high in fat and low in sugar.
If you count fatty acids with n carbon atoms, excluding ‘allenic’ ones (those with two neighboring double bonds, which are rare in nature) and ignoring cis/trans isomerism, you get the Fibonacci series!
Our paper on this stuff just got accepted, and it should appear soon:
• John Baez and Blake Pollard, A compositional framework for reaction networks, to appear in Reviews in Mathematical Physics.
But thanks to the arXiv, you don’t have to wait: beat the rush, click and download now!
Blake and I gave talks about this stuff in Luxembourg this June, at a nice conference called Dynamics, thermodynamics and information processing in chemical networks. So, if you’re the sort who prefers talk slides to big scary papers, you can look at those:
• John Baez, The mathematics of open reaction networks.
• Blake Pollard, Black-boxing open reaction networks.
The University of Southern Denmark wants to hire several postdocs who will use category theory to design enzymes. This sounds like a wonderful job for people who like programming, chemistry and categories—and especially double pushout rewriting. The application deadline is 20 March 2020. The project is described here and the official job announcement is here.
I’ve seen Christoph Flamm, Daniel Merkle, Peter Sadler give talks on this project in Luxembourg, and it’s really fascinating. They’re using double pushout rewriting (as shown in the picture above) and other categorical techniques to design sequences of chemical reactions that accomplish desired tasks.