Editor's synthesis & decision
Minor RevisionRevision requests
- Provide a more explicit discussion comparing your dissipative model to alternative mechanisms (e.g., receptor heterogeneity or complex feedback loops) to justify why your model is the most parsimonious explanation for the observed asymmetry.
- Clarify the criteria used to define the 'two-state' switching regime and the 'ultra-switchable' parameter space, specifically addressing whether the phase boundaries are sharp or represent crossovers in the finite-size limit.
- Include a sensitivity analysis or expanded discussion on how the simplified three-state kinetic cycle and the 6x6 lattice geometry might influence the quantitative results and the robustness of the identified switching paths.
- Temper the speculative claims regarding the 'Mpemba effect' and ensure that the functional 'desirability' of the ultra-switchable state is framed as a hypothesis rather than a derived optimality.
Where this could be published
At its current quality
Selective biophysics and physical biology journals
- Physical Review E
- Biophysical Journal
- PLOS Computational Biology
Then you could realistically aim for
Broad-audience flagship journals
- Nature Communications
- eLife
- PNAS
The current work is well-suited for specialized biophysics venues, but with a more rigorous treatment of alternative mechanisms and clearer validation of the model's parameter space, it becomes competitive for broader-audience journals. The most important improvement is providing a more robust justification for the uniqueness of your mechanism. This is guidance, not a guarantee; please perform a live literature search to ensure your findings remain novel.
edited by model: gemini-flash-lite-latest
Reviewer comments — reproduced in full, unabridged
Reviewer 1
gemini-flash-lite-latestThis manuscript presents a nonequilibrium lattice model of the Escherichia coli chemosensory array to investigate how dissipative chemical cycles and cooperative coupling influence signaling dynamics. The authors demonstrate that the experimentally observed asymmetric switching between active and inactive states is a consequence of time-reversal symmetry breaking driven by ATP hydrolysis. Furthermore, they show that this dissipation allows the system to overcome fundamental speed-sensitivity trade-offs, providing a potential functional advantage for cellular sensing. The work is technically sound, uses appropriate stochastic simulation methods, and provides a clear, physically motivated explanation for observed biological phenomena. It represents a solid contribution to the biophysics of nonequilibrium systems and is well-suited for a specialist journal.
Strengths
- Provides a clear, physically grounded explanation for the experimentally observed asymmetric switching in E. coli chemoreceptor arrays.
- Uses a well-justified nonequilibrium lattice model that integrates dissipative reaction cycles with cooperative coupling.
- Demonstrates how dissipation can relieve fundamental speed-sensitivity trade-offs, offering a compelling functional hypothesis for the observed dynamics.
- The analysis of the 'ultra-switchable' parameter regime provides a concrete, testable prediction for future experiments.
Weaknesses
- The model relies on a coarse-grained three-state cycle that may oversimplify the complex phosphorylation pathway, as acknowledged by the authors.
- The connection between the model's parameters and specific biological molecular rates is somewhat abstract, requiring significant future work to map onto experimental data.
- The discussion on the 'Mpemba effect' in the context of chemosensory response is speculative and lacks a direct experimental path for validation.
Detailed comments
The authors state that 'the observed asymmetric switching dynamics can only be explained by an interplay between the dissipative reactions within individual core units and the cooperative coupling between neighboring units.' While the model successfully reproduces this asymmetry, the claim that it 'can only be explained' by this specific interplay is strong. It would be beneficial to clarify whether alternative mechanisms, such as non-Markovian dynamics or hidden variables in the phosphorylation cycle, have been ruled out or if the authors' model is simply the most parsimonious explanation.
Regarding the link to experimental data, the authors note that 'the remaining asymmetry observed in the experiments may be accounted for by considering the dephosphorylation reaction, neglected in our simulations.' Given that this accounts for a significant portion (10%) of the observed asymmetry, the manuscript would be strengthened by a more explicit discussion of how the inclusion of the full dephosphorylation cycle might alter the phase diagram or the identified 'ultra-switchable' regions. Does the current simplification potentially bias the conclusions regarding the required dissipation level?
The authors claim that 'dissipation enables sensitive and rapid signaling response by relieving the speed-sensitivity trade-off.' This is a central conclusion of the paper. However, the trade-off analysis in Figure 4 relies on specific choices for the effective barrier shift. It would be helpful if the authors could provide more justification for why these specific parameter ranges are biologically relevant to the E. coli chemotaxis system, rather than just theoretically interesting.
Comments on figures
- Figure 2B: The plot shows switching asymmetry as a function of J and epsilon. The white bins indicate regions where no two-state switching occurs. It is unclear if the boundary between the white region and the colored region is sharp or if it represents a crossover. Please clarify if this boundary is a true phase transition in the thermodynamic limit or a finite-size effect.
- Figure 3: The projection of trajectories onto the (N1, N-1) plane is a clever way to visualize the irreversibility. However, the caption mentions '8204 switching event pairs' for the lower triangle and '602 pairs of events' for the upper triangle. This large difference in sample size between the two conditions is concerning. Could the authors confirm that the observed asymmetry in paths is not an artifact of the lower sampling density in the reversible case?
- Figure 5C: The phase diagram shows a 'saddle-node bifurcation' that eliminates the barrier. The axes are (J - Jc, Delta EB). It is visually difficult to see the transition point for different Delta G values. Could the authors add a clearer indicator or a zoomed-in inset to show how the threshold Jth changes with Delta G?
Referee report rubric — reproduced exactly as submitted
Reviewer 2
gemini-3.1-flash-liteThis manuscript presents a nonequilibrium lattice model of the Escherichia coli chemosensory array, investigating how energy dissipation from the phosphorylation-dephosphorylation cycle influences collective dynamics and sensing performance. The authors demonstrate that the observed asymmetric switching between active and inactive states in single-cell FRET measurements is a direct consequence of time-reversal symmetry breaking driven by this dissipation. Furthermore, the model suggests that operating far from equilibrium allows the system to overcome fundamental speed-sensitivity trade-offs inherent in equilibrium sensing mechanisms. The work provides a coherent theoretical framework that integrates microscopic kinetic cycles with cooperative lattice interactions, offering a compelling explanation for experimental observations. Overall, the study is technically rigorous and provides a significant conceptual advance in understanding how nonequilibrium driving shapes biological signaling.
Strengths
- The model successfully bridges the gap between microscopic reaction kinetics (ATP-driven phosphorylation) and macroscopic lattice-level dynamics (cooperative switching).
- The identification of the switching time asymmetry as a signature of time-reversal symmetry breaking is a strong, well-supported conceptual insight.
- The analysis of the speed-sensitivity trade-off provides a clear, testable functional advantage for the observed nonequilibrium behavior.
Weaknesses
- The manuscript relies on a simplified three-state model for the kinase cycle, which may overlook more complex, multi-step phosphorylation dynamics that could contribute to the observed asymmetry.
- The connection to the 'Mpemba effect' in the Discussion is speculative and lacks a rigorous justification for why this specific analogy is appropriate for this system.
- The model assumes a square lattice for simplicity, and while the authors claim robustness, a more explicit discussion of how the hexagonal geometry of native arrays specifically influences the quantitative results would strengthen the work.
Detailed comments
The authors state that 'the observed asymmetric switching dynamics can only be explained by an interplay between the dissipative reactions within individual core units and the cooperative coupling between neighboring units.' While this is a compelling claim, the manuscript does not fully explore whether alternative mechanisms—such as heterogeneity in the receptor cluster composition or complex feedback loops not captured in the current model—could potentially produce similar asymmetries. To strengthen this, the authors should explicitly discuss why these alternative explanations are insufficient to account for the magnitude of the asymmetry observed in the Keegstra et al. data.
Regarding the 'ultra-switchable' region defined in Figure 5, the authors claim this is the 'most desirable' state for the cell. However, this optimality is asserted rather than derived from a fitness-based objective function. It would be beneficial for the authors to clarify if this 'desirability' is based on a specific biological hypothesis regarding the cell's need to respond rapidly to both attractants and repellents, or if it is merely a mathematical observation of the parameter space. A more nuanced discussion of the potential costs of maintaining such a state—such as metabolic expenditure or susceptibility to noise—would provide a more balanced view of the system's design principles.
Comments on figures
- Figure 2B and 2D: The white regions are labeled as lying below the critical coupling Jc with 'no two-state switching.' It is unclear from the plots whether the transition at Jc is sharp or if there is a region of crossover dynamics. The authors should clarify if the lack of switching is defined by a specific threshold in the dwell time distribution or a lack of bimodality in the activity histogram, and whether this boundary is sensitive to the finite lattice size (N=6x6) used in the simulations.
- Figure 3: The projection of trajectories onto the (N1, N-1) plane is a useful visualization. However, the 'irreversible limit' (lower triangle) shows trajectories that appear to collapse onto a narrow path. The authors should comment on whether this collapse is a consequence of the deterministic limit of the mean-field approximation or if it persists in the stochastic Gillespie simulations, and what this implies for the robustness of the switching mechanism to noise.
Referee report rubric — reproduced exactly as submitted
Reviewer 3
gemini-flash-lite-latestThis manuscript presents a nonequilibrium lattice model of the Escherichia coli chemosensory array, investigating how energy dissipation from the phosphorylation-dephosphorylation cycle influences collective signaling dynamics. The authors demonstrate that the observed asymmetric switching between active and inactive states, previously reported in single-cell FRET experiments, is a direct consequence of time-reversal symmetry breaking inherent in the dissipative lattice. Furthermore, the model suggests that dissipation enables the system to navigate speed-sensitivity trade-offs more effectively than equilibrium models, potentially operating near a nonequilibrium critical point. The work provides a robust theoretical framework for understanding how coupled, driven subunits in biological complexes achieve high-fidelity sensing. The study is technically sound, well-motivated by existing experimental literature, and offers a clear, mechanistic explanation for complex emergent behavior in a biological system.
Strengths
- The model successfully bridges the gap between microscopic dissipative reaction cycles and macroscopic lattice-level switching behavior.
- The use of the Gillespie algorithm to generate stochastic trajectories provides a rigorous basis for comparing simulation results with experimental dwell-time and switching-time distributions.
- The identification of 'ultra-switchable' regions in the parameter space provides a clear, testable hypothesis for how E. coli optimizes its response to diverse stimuli.
Weaknesses
- The manuscript relies on a simplified three-state model that may overlook more complex, multi-step kinetics present in the actual CheA-CheY phosphorylation pathway.
- The discussion of 'super-stable' states and their potential biological relevance remains speculative without direct experimental evidence of such states in vivo.
- The connection between the model's lattice size (N=6x6) and the actual size of native arrays is discussed, but the scaling behavior of switching asymmetry with system size is not fully explored.
Detailed comments
The authors claim that 'the observed asymmetric switching dynamics can only be explained by an interplay between the dissipative reactions within individual core units and the cooperative coupling between neighboring units.' While the model convincingly demonstrates that dissipation is necessary for the observed asymmetry, the assertion that it is the *only* explanation could be strengthened. It would be beneficial for the authors to explicitly discuss whether alternative, non-dissipative mechanisms—such as heterogeneous receptor populations or complex, non-linear feedback loops—could potentially produce similar asymmetric switching, and why the dissipative model is more parsimonious or physically consistent with current data.
Regarding the 'microscopic origin of asymmetric switching,' the authors state that 'depending on the direction of switching, transitions take distinct paths through the lattice space.' This is a compelling finding. However, the interpretation of Figure 3 would be improved if the authors provided a more granular analysis of the transition paths. Specifically, the text notes that 'trajectories toward the inactive state (red) tend to take paths through the lower left region of state space.' It is unclear if this path is a consequence of the specific parameterization of the three-state cycle or a fundamental property of the lattice coupling. A brief sensitivity analysis of these paths to variations in the transition rates (k1, k2, k3) would clarify whether this behavior is robust or highly dependent on the chosen kinetic rates.
Comments on figures
- Figure 2B and 2D: The plots show 'switching time asymmetry' and 'switching/dwell time ratio' as functions of J and epsilon. The white regions are described as having 'no two-state switching.' It is unclear from the figure or the text what the exact criterion for 'two-state switching' is. Are these regions defined by a specific threshold in the autocorrelation function or the dwell-time distribution? Please clarify the definition of the two-state regime to ensure the phase boundaries are reproducible.
- Figure 5C: The phase boundaries for 'two-state switching' and 'single-state' are plotted in the (Delta E_B, J)-plane. The text states that 'for epsilon > 0 (Delta G finite) the boundary has a finite asymptote J_th(Delta E_B) -> J_c+/- as Delta E_B -> +/- infinity.' The figure shows these boundaries, but the transition from the 'two-state' region to the 'single-state' region is shown as a sharp line. Given the stochastic nature of the Gillespie simulations, how were these boundaries determined? Are they based on the disappearance of a local minimum in the effective free energy, or on a specific statistical measure of the activity distribution?
Referee report rubric — reproduced exactly as submitted
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