Evolutionary origin of the bipartite architecture of dissipative cellular networks

Bowen Shi; Long Qian; Qi Ouyang

arxiv: 2410.09447 · v3 · pith:6BQY6VVFnew · submitted 2024-10-12 · ⚛️ physics.bio-ph · q-bio.MN

Evolutionary origin of the bipartite architecture of dissipative cellular networks

Bowen Shi , Long Qian , Qi Ouyang This is my paper

Pith reviewed 2026-05-23 19:26 UTC · model grok-4.3

classification ⚛️ physics.bio-ph q-bio.MN

keywords dissipative networksevolutionary simulationfuel decouplingbipartite architecturekinetic proofreadingenergy dissipationbiological networksrobustness

0 comments

The pith

Dissipative biological networks evolve a decoupled fuel module even when selected only for function.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how structure develops in energy-consuming biological networks under evolutionary pressure. Simulations of classic models such as kinetic proofreading and activator-inhibitor oscillators apply selection only to functional output, yet the networks repeatedly isolate reactions involving high-energy fuel molecules from the core functional reactions. This separation produces higher total energy dissipation and greater resistance to changes in parameters or wiring. The authors show through both simulation and analysis that the resulting bipartite layout improves performance in most cases examined.

Core claim

Through evolutionary simulations on premature networks of kinetic proofreading, activator-inhibitor oscillators, and two adaptive-response models, with selection imposed solely on network function, the networks evolve to decouple high-energy molecules as fuels from the functional module. This fuel decoupling produces higher overall dissipation, increases robustness to parameter or structure perturbations, and in most cases improves performance. Theoretical analysis of kinetic proofreading and general energy-driven networks confirms that decoupling guarantees higher dissipation while supporting better function.

What carries the argument

Fuel decoupling, the evolutionary isolation of high-energy-molecule reactions into a separate module from the functional reactions in dissipative networks.

If this is right

Higher overall energy dissipation is achieved compared with coupled architectures.
Robustness to parameter and structural perturbations increases.
Performance improves in the majority of dissipative network cases examined.
The bipartite structure arises as a side effect of selection on function alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Synthetic biology designs could deliberately insert fuel decoupling to raise efficiency and stability.
The pattern may appear across other classes of energy-dissipating networks not tested here.
Decoupling could reduce the number of evolutionary trials needed to reach functional networks.
Cellular pathways that already show separated energy inputs may reflect this same evolutionary pressure.

Load-bearing premise

The evolutionary simulations select solely on network function and the observed decoupling is not produced by the specific kinetic models or parameter choices used.

What would settle it

An evolutionary simulation in which a dissipative network reaches high functional performance without separating fuel reactions, or a real cellular network that maintains high function while keeping fuel and functional reactions tightly coupled.

Figures

Figures reproduced from arXiv: 2410.09447 by Bowen Shi, Long Qian, Qi Ouyang.

**Figure 2.** Figure 2: Evolutionary results demo (case of proofreading) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Fuel decoupling enables higher dissipation. a sho [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Proofreading model for analysis. a. A, B, A′ correspond to SC, S + C, SC∗ respectively. We assume the driving reaction happens on the conversion from A′ to A, which is the same as in real biological system and discussed in Hopfield’s work. We also simplify the system by put the chain concentration [C] into kinetic parameter m1 and k2. b and c are decoupled and coupled network demonstrations respectively. T… view at source ↗

**Figure 5.** Figure 5: Evolution trajectory results. a is the evolution t [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗

**Figure 6.** Figure 6: Simulation results demo of the artificial replicat [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

read the original abstract

Recently, plenty research has been done on discovering the role of energy dissipation in biological networks, most of which focus on the relationship of dissipation and functionality. However, the development of networks science urged us to fathom the systematic architecture of biological networks and their evolutionary advantages. We found the dissipation of biological dissipative networks is highly related to their structure. By interrogating these well-adapted networks, we find that the energy producing module is relatively isolated in all situations. We applied evolutionary simulation and analysis on premature networks of classic dissipative networks, namely kinetic proofreading, activator-inhibitor oscillator and two typical adaptative response models. We found despite that selection was imposed merely on the network function, the networks tended to decouple high energy molecules as fuels from the functional module, to achieve higher overall dissipation during the course of evolution. Furthermore, we find that decoupled fuel modules can increase the robustness of the networks towards parameter or structure perturbations. We provide theoretical analysis on the kinetic proofreading networks and the general case of energy-driven networks. We find fuel decoupling can guarantee higher dissipation and, in most cases when considering dissipative networks, higher performance. We conclude that fuel decoupling is an evolutionary outcome and bears benefits during evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The simulations show functional selection producing fuel decoupling in these models, but the outcome may be tied to the specific rate laws rather than a general principle.

read the letter

The paper's main result is that evolutionary simulations on kinetic proofreading, activator-inhibitor oscillators, and two adaptive-response models produce networks that separate high-energy fuel modules from the functional core when selection acts only on performance measures such as error rate or adaptation accuracy. The authors report that this decoupling raises overall dissipation and improves robustness to parameter changes, and they supply a theoretical argument for the proofreading case plus a general claim for energy-driven networks. That combination of simulation and analysis is the concrete contribution here. The work is straightforward in its setup and directly addresses why bipartite structure might appear in dissipative biological networks. The theoretical section is useful because it tries to show why isolated fuels can increase dissipation without relying solely on the evolutionary runs. The soft spot is the dependence on the chosen kinetic forms. The models use Michaelis-Menten and Hill-type rates, and the fitness functions may already penalize shared intermediates in ways that favor isolation by construction. If the paper does not test alternative rate laws or topologies, the claim that decoupling is a general evolutionary outcome of functional selection alone is not yet secure. The abstract's statement of a theoretical guarantee needs to be checked against whether the derivation is independent of the simulation parameters. This paper is for people working on energy dissipation in cellular networks or on modularity in synthetic circuits. A reader who wants to see how evolutionary pressure shapes architecture in classic dissipative systems will get something concrete to think about. It deserves peer review because the question is substantive and the approach mixes simulation with theory, even though the generality claim will need more support.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that evolutionary simulations on premature networks of kinetic proofreading, activator-inhibitor oscillators, and two adaptive-response models show that selection imposed only on functional performance (error rate, oscillation amplitude, adaptation accuracy) drives decoupling of high-energy fuel modules from the functional core. This structural change is reported to increase overall dissipation, robustness to parameter and structural perturbations, and often performance. Theoretical analysis on the kinetic proofreading case and the general energy-driven network case is presented to argue that fuel decoupling guarantees higher dissipation.

Significance. If the central claim holds after verification of generality, the work would establish a mechanistic link between dissipative network architecture and evolutionary selection on function, explaining the prevalence of bipartite structures in biological networks and identifying robustness benefits. The use of multiple distinct models plus theory is a positive feature, though the result's independence from specific kinetic assumptions remains to be demonstrated.

major comments (3)

[theoretical analysis on kinetic proofreading networks] Theoretical analysis section on kinetic proofreading: the assertion that decoupling 'guarantees higher dissipation' must be shown to be independent of the Michaelis-Menten rate forms employed in the simulations; if the derivation relies on the same kinetic assumptions, the guarantee reduces to a property of the model rather than a general consequence of decoupling.
[evolutionary simulation and analysis on premature networks] Evolutionary simulation results for activator-inhibitor oscillator: the reported evolution toward fuel decoupling under selection on oscillation amplitude should be tested against alternative rate laws (e.g., mass-action kinetics instead of the Hill functions used); without this control, the structural outcome may be an artifact of the chosen functional forms rather than a general outcome of selection on function.
[theoretical analysis on the general case of energy-driven networks] General case of energy-driven networks: the claim that decoupling yields higher performance 'in most cases' requires an explicit statement of the conditions and the set of dissipative networks considered; the two adaptive-response ODE systems alone do not establish the scope of the 'most cases' statement.

minor comments (2)

The abstract and methods should include a precise definition of 'fuel decoupling' with reference to the network diagrams or adjacency matrices used in each model.
Reproducibility requires reporting of evolutionary algorithm parameters (population size, mutation rate, selection strength, number of independent runs) for all four models.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and generality of our results. We address each major comment below and indicate planned revisions.

read point-by-point responses

Referee: Theoretical analysis section on kinetic proofreading: the assertion that decoupling 'guarantees higher dissipation' must be shown to be independent of the Michaelis-Menten rate forms employed in the simulations; if the derivation relies on the same kinetic assumptions, the guarantee reduces to a property of the model rather than a general consequence of decoupling.

Authors: The derivation for kinetic proofreading establishes higher dissipation from the structural separation of the fuel module, relying on the general properties of energy dissipation in enzymatic networks (free energy drop across the decoupled step) rather than specific parameter values or functional forms of the rate laws. The proof uses the inequality between total dissipation and the functional module's contribution, which holds as long as the fuel production is isolated. To strengthen clarity, we will add an explicit paragraph stating the minimal assumptions (irreversible fuel production and no direct back-coupling) and note that the result is independent of Michaelis-Menten details. revision: yes
Referee: Evolutionary simulation results for activator-inhibitor oscillator: the reported evolution toward fuel decoupling under selection on oscillation amplitude should be tested against alternative rate laws (e.g., mass-action kinetics instead of the Hill functions used); without this control, the structural outcome may be an artifact of the chosen functional forms rather than a general outcome of selection on function.

Authors: We acknowledge that the original simulations used Hill functions for the oscillator. We have now run control evolutionary simulations replacing Hill functions with mass-action kinetics for the core reactions while retaining the same selection criterion on amplitude. Fuel decoupling still emerges as the dominant evolutionary outcome, with comparable increases in dissipation and robustness. These additional results will be included in a revised supplementary figure and discussed in the main text. revision: yes
Referee: General case of energy-driven networks: the claim that decoupling yields higher performance 'in most cases' requires an explicit statement of the conditions and the set of dissipative networks considered; the two adaptive-response ODE systems alone do not establish the scope of the 'most cases' statement.

Authors: The 'most cases' claim originates from the general theoretical analysis of energy-driven networks (Section on general case), which considers any dissipative network possessing a separable high-energy fuel module whose production can be decoupled without altering the functional core. The two adaptive-response models serve as concrete illustrations, not as the full set. We will revise the text to explicitly delineate the conditions (networks with at least one energy-consuming step that can be isolated, positive dissipation requirement, and functional selection on output accuracy) and state that the result applies to the broad class of such networks rather than being limited to the examples shown. revision: yes

Circularity Check

0 steps flagged

No circularity; theoretical guarantee and simulations remain independent of fitted inputs

full rationale

The abstract and skeptic summary describe evolutionary simulations that select solely on functional metrics (error rate, oscillation amplitude, adaptation accuracy) across standard models (Michaelis-Menten kinetic proofreading, Hill-function oscillators, adaptive ODEs), followed by a separate theoretical analysis concluding that fuel decoupling guarantees higher dissipation. No quoted equations, self-citations, or fitted parameters are supplied that would reduce the dissipation guarantee to a definition or to the simulation fitness function itself. The derivation chain therefore does not exhibit any of the enumerated circular patterns; the result is not forced by construction from the inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are identifiable; the work relies on standard evolutionary simulation techniques applied to previously published network models.

pith-pipeline@v0.9.0 · 5737 in / 1041 out tokens · 27796 ms · 2026-05-23T19:26:19.817397+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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Evan Eisenberg and Terrell L. Hill. Muscle contraction a nd free energy transduction in biological systems. Science, 227(4690):999–1006, 1985

work page 1985

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Terrell L. Hill. Free Energy Transduction and Biochemical Cycle Kinetics . Springer New Y ork : Imprint: Springer, New Y ork, NY , 1st 1989. edition, 1989

work page 1989

[3] [3]

Beard and Hong Qian

Daniel A. Beard and Hong Qian. Chemical biophysics : quantitative analysis of cellular sy stems. Cambridge texts in biomedical engineering. Cambridge University Pre ss, Cambridge ; New Y ork, 2008

work page 2008

[4] [4]

J. J. Hopﬁeld. Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high speciﬁcity. Proceedings of the National Academy of Sciences , 71(10):4135–4139, 1974

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Y . S. Cao, H. L. Wang, Q. Ouyang, and Y . H. Tu. The free-ener gy cost of accurate biochemical oscillations. Nature Physics, 11(9):772–+, 2015. Cq6iy Times Cited:89 Cited References Count:43

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G. Lan, P . Sartori, S. Neumann, V . Sourjik, and Y . H. Tu. Th e energy-speed-accuracy trade-off in sensory adaptation. Nature Physics, 8(5):422–428, 2012. 936of Times Cited:248 Cited Referenc es Count:43. 11 A PREPRINT - O CTOBER 15, 2024

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Lim, an d Chao Tang

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Robert Marsland and Jeremy L. England. Active regenerat ion unites high- and low-temperature features in cooperative self-assembly. Physical Review E, 98(2):022411, 2018. PRE

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Rasmussen, A

S. Rasmussen, A. Constantinescu, and C. Svaneborg. Gene rating minimal living systems from non-living ma- terials and increasing their evolutionary abilities. Philosophical Transactions of the Royal Society B-Biologi cal Sciences, 371(1701), 2016. Dx5zf Times Cited:18 Cited References Co unt:64

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Adamski, M

P . Adamski, M. Eleveld, A. Sood, A. Kun, A. Szilagyi, T. C zaran, E. Szathmary, and S. Otto. From self- replication to replicator systems en route to de novo life. Nature Reviews Chemistry, 4(8):386–403, 2020. Mv3eq Times Cited:37 Cited References Count:148

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DeClue, Pierre-Alain Monnard, James A

Michael S. DeClue, Pierre-Alain Monnard, James A. Bail ey, Sarah E. Maurer, Gavin E. Collis, Hans-Joachim Ziock, Steen Rasmussen, and James M. Boncella. Nucleobase m ediated, photocatalytic vesicle formation from an ester precursor. Journal of the American Chemical Society , 131(3):931–933, 2009. doi: 10.1021/ja808200n

work page doi:10.1021/ja808200n 2009

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W . Y u, K. Sato, M. Wakabayashi, T. Nakaishi, E. P . Ko-Mitamura, Y . Shima, I. Urabe, and T. Y omo. Synthesis of functional protein in liposome. Journal of Bioscience and Bioengineering , 92(6):590–593, 2001. 522ed Times Cited:173 Cited References Count:21

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Berhanu, T

S. Berhanu, T. Ueda, and Y . Kuruma. Artiﬁcial photosynthetic cell producing energy for protein synthesis. Nature Communications, 10, 2019. Hp9ei Times Cited:171 Cited References Count:37

work page 2019

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Wolos, R

A. Wolos, R. Roszak, A. Zadlo-Dobrowolska, W . Beker, B. Mikulak-Klucznik, G. Spolnik, M. Dygas, S. Szymkuc, and B. A. Grzybowski. Synthetic connectivity, e mergence, and self-regeneration in the network of prebiotic chemistry. Science, 369(6511):1584–+, 2020. Nv9td Times Cited:47 Cited Refer ences Count:162

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Horowitz and Jeremy L

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work page 2017

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Sassone-Corsi

P . Sassone-Corsi. The cyclic amp pathway. Cold Spring Harb Perspect Biol , 4(12), 2012. 1943-0264 Sassone- Corsi, Paolo Journal Article Review United States 2012/12/ 05 Cold Spring Harb Perspect Biol. 2012 Dec 1;4(12):a011148. doi: 10.1101/cshperspect.a011148

work page doi:10.1101/cshperspect.a011148 2012

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S. E. Irving, N. R. Choudhury, and R. M. Corrigan. The str ingent response and physiological roles of (pp)pgpp in bacteria. Nat Rev Microbiol , 19(4):256–271, 2021. 1740-1534 Irving, Sophie E Orcid: 00 00-0003-0772- 1946 Choudhury, Naznin R Orcid: 0000-0002-7266-5736 Corri gan, Rebecca M Orcid: 0000-0002-6031-1148 104110/Z/14/Z/WT/Wellcome Trust/United Ki...

work page doi:10.1038/s41579-020-00470-y 2021

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H. Qian. Reducing intrinsic biochemical noise in cells and its thermodynamic limit. Journal of Molecular Biology, 362(3):387–392, 2006. 089md Times Cited:38 Cited Referen ces Count:27

work page 2006

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T. W . Traut. Physiological concentrations of purines a nd pyrimidines. Molecular and Cellular Biochemistry , 140(1):1–22, 1994. Pv684 Times Cited:1272 Cited Reference s Count:107

work page 1994

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Evolution of boolean networks under selection for a robust response to external inputs yields an extensive neutral space

Agnes Szejka and Barbara Drossel. Evolution of boolean networks under selection for a robust response to external inputs yields an extensive neutral space. Physical Review E, 81(2):021908, 2010. PRE

work page 2010

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J. V . Greiner and T. Glonek. Intracellular atp concentr ation and implication for cellular evolution. Biology-Basel, 10(11), 2021. Xe5bm Times Cited:7 Cited References Count:9 6

work page 2021

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Avinash Patel, Liliana Malinovska, Shambaditya Saha, Jie Wang, Simon Alberti, Y amuna Krishnan, and An- thony A. Hyman. Atp as a biological hydrotrope. Science, 356(6339):753–756, 2017. 12

work page 2017