Thermodynamic analysis of bacterial metabolism

[Horowitz, Arie]

Dear Colleagues,

I am new to the metabolism field. I was advised to contact the community via this address by Dr. Robert Giessman, with whom I have been corresponding about the usage of the TECRDB repository. 

I am a cell biologist with training in theoretical and numerical approaches in biomechanics (CV attached). I have recently been interested in thermodynamic analysis of the cell as a means to establish a theoretical/causal basis to this discipline (see attached paper). The cellular systems I pick for analysis are those that have been measured adequately to serve as input. My published paper is an example of the analysis I perform, but it can differ from one system to another, depending on its attributes.

Bacterial metabolism measurements afford the test of a relatively recent non-equilibrium formulation named maximum caliber (MaxCal), where, instead of states, which are suited for equilibrium but not for its absence, the attribute of interest is entropy production. Under MaxCal, the trajectory that maximizes entropy production is selected over others - hence the maximum conduit caliber analogy. This methodology is suitable for modeling the cell because living systems are out of equilibrium and hypothesized to maintain stability by favoring maximum export of entropy to their environment. 

Though the analysis of E coli metabolism is ongoing, it occurred to me that the predictions of this approach could be tested by an experimental group. Such a test would probably amount to standard measurements of E coli enzymatic activities. We would then be able to submit a collaborative manuscript that would contain not only theory but also experimental backing. That would be a more rigorous and significant manuscript. 

This is obviously very preliminary. Nevertheless, I would appreciate your responses. I will respond promptly to all inquiries.

Best regards,

Arie 

[Elad Noor]

Dear Arie,

You raise some very good points, and although I have some basic background in thermodynamics of chemical reactions, I am less familiar with its more advance topics and non-equilibrium theories (including Onsager reciprocity).

Therefore, I might have misunderstood some of what you wrote and will be happy to stand corrected.

In any case, the idea of chemical pathways maximizing entropy production has been discussed in the past and I think there is some (debatable) evidence that it might not always be the case in metabolism.

For example, the work of Niebel et al. (https://doi.org/10.1038/s42255-018-0006-7) seems to show phenomenologically that there is an upper limit on the Gibbs energy dissipation rate in some cases.

Regardless of their conclusions, perhaps their dataset could be used for testing your hypothesis as well?

And a more general question, is Onsager reciprocity somehow related to the so called "flux-force" relationship discussed by Beard & Qian (https://doi.org/10.1371/journal.pone.0000144)?

All the best,

Elad

[First Name]

Dear Elad,

Sorry for my belated reply (there was no email alert) and thank you for taking the time to respond and for the link to Niebel et al. The maximization of entropy production is, of course, an assumption. However, even if there are exceptions to the notion that cellular dynamics maximizes entropy production, there are robust theoretical arguments in its favor. My analysis addresses non-equilibrium thermodynamics using a theorem that derives the dynamics of the system from the assumption that path (instead of state in equilibrium) entropies are maximized (while complying with the measured average fluxes). The parallelism between the biological and the methodological assumption is too attractive to dismiss.

I have only glanced at this interesting paper and noted the type of model they use. Naturally, the choice of the model determines the outcome. I'll have to read it to form an opinion. The authors did not measure fluxes but calculated them from the model's assumptions. In contrast, my analysis is based on measured (or estimated in compliance with measured fluxes) fluxes and Gibbs free energies. It appears that their dataset is insufficient for the type of analysis I am running.

Generalized "forces" and fluxes are some of the basic concepts in thermodynamics. To someone who is not familiar with the field, perhaps an analogy with voltage and current would explain it. Onsager's as well as numerous other theorems use them to model thermodynamic systems in a manner similar to the modeling of electrical circuits. 

I'll get back to you after I read Niebel's paper both on this forum and individually. Thank you again for reaching out.

Arie 

[Ronan M.T. Fleming]

Dear Arie,

the attached paper introduces maximisation of unidirectional path
entropy in biochemical networks. There was a workshop on that topic
earlier this year as others have found similar methods to increase
predictive capacity: https://www.entroflux.com
In the meantime, we expended a lot of effort to experimentally
validate that maximisation of unidirectional path entropy performed
better in terms of predictive capacity than several other objectives
(https://www.biorxiv.org/content/10.1101/2021.06.30.450562v2, to
appear Comm Biol).

From my perspective, the open question is what the correct prior is
when maximising unidirectional path entropy. What is correct may well
depend on the amount of data one has in each modelling situation.

Regards,

Ronan

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--
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Mr. Ronan MT Fleming B.V.M.S. Dip. Math. Ph.D.
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Associate Professor,
Digital Metabolic Twin Center, www.digitalmetabolictwin.org
School of Medicine,
University of Galway.
Ireland.
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Coordinator of the Horizon Europe project "Reconstruction and
Computational Modelling for Inherited Metabolic Diseases" (Recon4IMD)
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Peer-reviewed publications: https://goo.gl/FZPG23
Mobile: +353 852 109 806
Github: @rmtfleming
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