REVIEW 2 major objections 5 minor 30 references
Acceleration of enzymatic reactions due to nearby inactive binding sites
T0 review · 2 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read This paper argues that an allosterically coupled, non-catalytic binding site near an enzyme's active site can increase the steady-state reaction rate, by storing fuel for release after a reaction or by blocking substrate escape before…
desk verdict Clean theoretical result with a rigorous analytical core and a provisional quantitative headline; deserves review but the numerical optimization should be pinned down. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is a three-site master-equation model: a catalytic site that binds substrate with rate $r_+$, releases it with rate $r_-$, and reacts with rate $k_r$; a coarse-grained bridging site that mediates exchange with a molecule reservoir; and an auxiliary site whose binding and release rates switch between $h_\pm$ and $\tilde h_\pm$ depending on whether the catalytic site is occupied. This state-dependent switching is the allosteric coupling that makes acceleration possible, and the comparison model is obtained by setting the auxiliary entry rates to zero. The load-bearing identity is the closed-form formula for $\Delta J_{\rm cat}$, whose sign is controlled by the simple factor $(r_- - r_+) [h_+\tilde h_- - Q\tilde h_+ h_-]$; the same structure determines which mechanism operates and which rates are optimal.
What would settle it
A single-molecule experiment on an inert site engineered near a catalytic site could settle it: the model predicts zero current change when the inert site's binding rates are identical in the occupied and empty catalytic states, and it predicts a sign change in $\Delta J_{\rm cat}$ when $r_- - r_+$ crosses zero; observing acceleration under state-independent inert-site kinetics would falsify the mechanism.
Extended reading notes
Core claim
The paper's central result is an exact expression for the change in steady-state catalytic current caused by adding an inert auxiliary site: $\Delta J_{\rm cat} = B r_+ (r_- - r_+) [h_+ \tilde h_- - Q \tilde h_+ h_-]$, where $B$ and $Q$ are positive quantities built from the other rates. Because $B>0$ and $Q>0$, the sign of the effect is fixed by the product of two factors, and this yields two distinct regimes. When $r_- > r_+$ and $Q < h_+\tilde h_-/(\tilde h_+ h_-)$, the auxiliary site works by blocking: it releases a stored molecule into the bridging region while the catalytic site is occupied, making escape of the substrate less likely. When $r_- < r_+$ and the inequality is reversed, the auxiliary site works by storage: it holds a fuel molecule while the catalytic site is busy and releases it as soon as the site empties, shortening the wait for the next substrate. The paper identifies the optimal transition rates in each regime and shows that relaxing the single-occupancy assumption for the bridging region weakens blocking but leaves storage largely intact.
Load-bearing premise
The whole effect depends on the auxiliary site's binding and release rates changing when the catalytic site becomes occupied or empty; without that allosteric sensing, the inert site can neither store fuel at the right moment nor block escape.
Editorial extensions
If this is right
- If the allosteric coupling exists, adding an auxiliary site raises the steady-state turnover without adding any new molecular entry pathway from the reservoir and without changing the catalytic step itself.
- The analytically derived sign condition gives a direct parameter-space test for when an inert site helps rather than hurts: acceleration requires $(r_- - r_+)[h_+\tilde h_- - Q\tilde h_+ h_-] > 0$.
- Optimal auxiliary-site rates sit at the boundaries of the allowed range, so maximal acceleration is achieved by making the site switch sharply between capture and release depending on the active site's occupancy.
- In this model the storage mechanism's gain is at most about 15%, while blocking can multiply the relative current by up to 2.89 when fuel is scarce; enlarging the bridging region weakens blocking but leaves storage nearly unchanged.
- The largest absolute gains occur when the fuel arrival rate is comparable to the reaction rate, neither when the system is starved of fuel nor when it is saturated.
Reading between the lines
- The paper leaves implicit that the 15% storage ceiling is a property of the single-auxiliary-site, single-occupancy model, not a fundamental bound; several inert sites around one active site should add independent storage channels, so real gains could be larger.
- A direct experimental signature follows from the model: in the storage regime the auxiliary site should be occupied preferentially when the catalytic site is occupied, while in the blocking regime the bridging site should be filled when the catalytic site is occupied, so single-molecule occupancy statistics could classify the mechanism.
- Because the current change is proportional to a difference between a cycle affinity and a conditional-occupancy ratio, one can view the acceleration as fueled by information about the active site; testing whether faster acceleration requires more dissipation in the auxiliary-site switching would connect this model to the thermodynamics of sensing.
- The model suggests that engineering an inert binding site whose affinity is mechanically coupled to the catalytic site's occupancy could be a practical way to accelerate a reaction without altering the chemistry of the active site itself.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper studies a seven-rate Markov model of a catalytic site equipped with a nearby inactive 'auxiliary' binding site, connected to the catalytic site through a coarse-grained bridging region. The auxiliary site's binding and unbinding rates depend on whether the catalytic site is occupied, modeling allosteric coupling. The steady-state catalytic current is compared to that of a reference model without the auxiliary site. The authors derive an exact expression for the current difference, factor it as ΔJ = B r+ (r− − r+) [h+ τh− − Q τh+ h−] with B,Q>0, and thus identify two parameter regimes (r−>r+ with Q < h+τh−/(τh+h−), and r−<r+ with Q > that ratio) in which the current is enhanced. They then compute rates that maximize the current difference and the relative current difference, using analytic monotonicity arguments for the auxiliary-site rates and numerical optimization for the remaining rates. The maximizing rates motivate two mechanisms: 'blocking' of escape from the occupied catalytic site, and 'storage' of substrate for release when the catalytic site empties. The model is then generalized to allow up to m molecules in the bridging region.
Significance. If the conclusions hold, the paper provides a simple and general kinetic mechanism by which non-catalytic binding sites can accelerate enzymatic turnover, with potential relevance to molecular motors such as RecBCD. The analytical factorization in Eq. (6) and the proof that B,Q>0 are rigorous and constitute a strong, self-contained existence result: the auxiliary site enhances the current in well-defined regions of parameter space. The authors are careful to restrict the model so that the enhancement is not a trivial consequence of additional entry pathways or changed catalytic rates, and they explicitly acknowledge the limitations of the allosteric-coupling assumption and the speculative biological implications. However, the quantitative headline (up to 15% for the storage mechanism, and the factor 2.89 for blocking in the relative measure) rests on numerical optimization in Sec. V B that is not proven to be global. The mechanism identification in Sec. VI is inferred from these optimizing rates, so the quantitative significance is currently provisional.
major comments (2)
- [Sec. V B, Tables I and II; abstract] The abstract states that the storage mechanism can accelerate the reaction by up to 15%, and Sec. VI assigns the mechanisms solely on the basis of the optimizing rates listed in Tables I and II. However, Sec. V B explicitly states that there is no analytical proof that the numerical optima for r± and k− are global. Since the objective functions depend on seven rates and the paper does not provide a certified global optimizer or a proof of convexity/monotonicity in the remaining variables, the reported maxima could be local. This concern is load-bearing: the 'up to 15%' bound and the storage-versus-blocking attribution would change if a different parameter set achieved a larger objective. The authors should either provide a rigorous global optimization (for example, by exploiting monotonicity or by using interval/global methods) or clearly reword the claims to state that the reported values correspond to candidate maxima found by local search, and adjust the abstract accordingly.
- [Sec. VII] The same global-optimality issue affects the generalized model with m=2,3,4 molecules in the bridging region. The optimization is purely numerical, and the mechanisms are again inferred from the optimizing rates. The trends in Fig. 4 are plausible, but because the underlying optima are unverified, the qualitative statement that the blocking mechanism degrades with increasing m while storage persists is not fully established. Adding a robustness analysis (e.g., showing that the reported values are stable under multiple starting points or perturbations) would strengthen this section.
minor comments (5)
- [Sec. VIII and abstract] The allosteric coupling between the auxiliary site and the catalytic site is a load-bearing modeling assumption, as the authors themselves note in Sec. VIII when they state that direct evidence of coupling would be needed for biological applications. The abstract would benefit from stating explicitly that the acceleration is conditional on this coupling, rather than implying it is an unconditional property of inactive nearby sites.
- [Eq. (12)] The notation for the conditional probability in Eq. (12) has an ambiguity: the denominator should be written as Σ_b Π̄(n_c n_b) to make the sum over the bridging occupation clear.
- [Sec. V A] The analytic derivation of the optimal auxiliary rates is only sketched; for example, the calculation for τh− is said to be essentially the same as for h+, but not shown explicitly. A few more intermediate steps would improve readability and help readers verify the monotonicity claims.
- [Sec. V B and Appendix C] The paper does not provide the numerical code or a detailed description of the optimization algorithm (method, tolerance, number of starting points), which limits reproducibility of Tables I–VI and the figures. Supplying code or at least a precise numerical protocol would be useful.
- [Throughout] There are minor typographical and formatting issues, such as 'Underl ying' in the Sec. II heading and 'Zananiri et. al.' in the introduction; these should be corrected.
Circularity Check
No circularity: the central result follows from the paper's own master equation, and the proposed mechanisms are post-hoc interpretations of optimized rates rather than fitted inputs.
full rationale
The central claim that an auxiliary site can accelerate the steady-state current is derived analytically from the model's master equation. Equation (6) gives the exact factorization ΔJcat = B r+ (r− − r+) [h+ h̃− − Q h̃+ h−], with B and Q positive for all positive rates (Appendix B), so the two acceleration regimes in Eqs. (7) and (8) are algebraic sign conditions on the paper's own transition rates. The optimal auxiliary-site rates in Sec. V A follow from monotonicity, e.g., Eq. (9) with M > 0, and the remaining numerical optimizations in Sec. V B maximize the same explicit expression. The 'blocking' and 'storage' mechanisms in Sec. VI are interpretations of the optimizing rates and of steady-state conditional probabilities; they are not inserted into the equations as fitted parameters or as constraints that force the outcome. No experimental data are fitted, no external benchmark is claimed, and the quoted accelerations (up to 15%, factor 2.89) are properties of the stated model. The only self-citation ([24], Bogod and Rahav) concerns a different polymer-copying discrimination problem and is not load-bearing. The allosteric coupling is an explicit modeling assumption, not a hidden reuse of the result. Therefore no circular step can be exhibited, and the derivation is self-contained.
Assumptions & free parameters
free parameters (3)
- Rate bounds [hmin, hmax] = [1,100] =
1, 100
- kr = 10 =
10
- Fuel concentration k+rho0 values =
1, 10, 100
assumptions (7)
- domain assumption Each zone (catalytic, auxiliary, bridging, reservoir) is coarse-grained to a site with at most one molecule, so the system has eight many-particle states.
- domain assumption The auxiliary site is connected only to the bridging site, not to the reservoir or active site, and does not alter existing transition rates.
- domain assumption The rates of entering and leaving the auxiliary site depend on whether the catalytic site is occupied (h+ and h- vs tilde h+ and tilde h-).
- domain assumption The chemical reaction at the active site is completely irreversible with rate kr.
- domain assumption The reservoir is well-mixed with constant fuel concentration rho0, molecules enter at rate k+rho0 and leave at rate k-.
- ad hoc to paper Transition rates are bounded to the interval [1,100], with kr=10 fixed.
- standard math The probabilities of many-particle states evolve according to a linear master equation.
Cite this review
Pith. "Pith review of Acceleration of enzymatic reactions due to nearby inactive binding sites." pith.science (2026). https://pith.science/paper/RIYOJQK5
@misc{pith2026250101662,
author = {Pith},
title = {Pith review of: Acceleration of enzymatic reactions due to nearby inactive binding sites},
year = {2026},
howpublished = {\url{https://pith.science/paper/RIYOJQK5}},
note = {Machine review of arXiv:2501.01662}
}
read the original abstract
Many biological molecular motors and machines are driven by chemical reactions that occur in specific catalytic sites. We study whether the arrival of molecules to such an active site can be accelerated by the presence of a nearby inactive site. Our approach is based on comparing the steady-state current in simple models to reference models without an inactive site. We identify two parameter regimes in which the reaction is accelerated. We then find the transition rates that maximize this acceleration, and use them to determine the underlying mechanisms in each region. In the first regime, the inactive site stores a molecule in order to release it following a reaction, when the neighboring catalytic site is empty. In the second regime, the inactive site releases a molecule when the catalytic site is full, in order to impede the molecules from leaving the active site before they react. For the storage mechanism, which is more likely to be biologically relevant, the acceleration can reach up to 15%, depending on parameters.
Figures
Figures from the paper (1 more)
Reference graph
Works this paper leans on
-
[1]
O. G. Berg, R. B. Winter, and P. H. Von Hippel, Diffusion-driven mechanisms of protein translocation on nucleic acids. 1. models and theory, Biochemistry 20, 6929 (1981)
work page 1981
-
[2]
M. Slutsky and L. A. Mirny, Kinetics of protein-dna interaction: facilitated target location in sequence- dependent potential, Biophysical journal 87, 4021 (2004)
work page 2004
-
[3]
S. E. Halford and J. F. Marko, How do site-specific dna-binding proteins find their targets?, Nucleic acids research 32, 3040 (2004)
work page 2004
-
[4]
U. Gerland, J. D. Moroz, and T. Hwa, Physical constraints and functional characteristics of transcrip- tion factor–dna interaction, Proceedings of the National Academy of Sciences 99, 12015 (2002)
work page 2002
-
[5]
A. A. Shvets, M. P. Kochugaeva, and A. B. Kolomeisky, Mechanisms of protein search for targets on dna: theoretical insights, Molecules 23, 2106 (2018)
work page 2018
- [6]
-
[7]
V. Alex et al., Speed-selectivity paradox in the protein search for targets on dna: Is it real or not?, (2013)
work page 2013
-
[8]
O. G. Berg and P. H. von Hippel, Diffusion-controlled macromolecular interactions, Annual review of biophysics and biophysical chemistry 14, 131 (1985). 18 m k+ρ0 r∗ + r∗ − k∗ − h∗ − h∗ + ˜h∗ − ˜h∗ + 1 1 100 1 13.5 100 1 1 100 10 100 1 11.3 100 1 1 100 100 100 3.22 100 100 1 1 100 2 1 100 1 13.8 29.4 1 1 100 10 100 1 15.7 100 1 1 100 100 100 18.1 100 100 ...
work page 1985
Show all 30 references
-
[9]
Shin and A
J. Shin and A. B. Kolomeisky, Surface-assisted dynamic search processes, The Journal of Physical Chemistry B 122, 2243 (2018)
2018
-
[10]
M. M. Misiura, A. M. Berezhkovskii, S. M. Bezrukov, and A. B. Kolomeisky, Surface-facilitated trapping by active sites: From catalysts to viruses, The Journal of Chemical Physics 155 (2021)
2021
-
[11]
H. C. Berg and E. M. Purcell, Physics of chemoreception, Biophysical journal 20, 193 (1977)
1977
-
[12]
Hartich, A
D. Hartich, A. C. Barato, and U. Seifert, Sensory capacity: An information theoretical measure of the performance of a sensor, Physical Review E 93, 022116 (2016)
2016
-
[13]
Malaguti and P
G. Malaguti and P. R. Ten Wolde, Theory for the optimal detection of time-varying signals in cellular sensing systems, Elife 10, e62574 (2021). 19 m k+ρ0 r∗ + r∗ − k∗ − h∗ − h∗ + ˜h∗ − ˜h∗ + 1 1 100 1 18.8 100 1 1 100 10 100 1 21.8 100 1 1 100 100 100 13.5 100 100 1 1 100 2 1 ...
2021
-
[14]
G. Lan, P. Sartori, S. Neumann, V. Sourjik, and Y. Tu, The energy–speed–accuracy trade-off in sensory adaptation, Nature physics 8, 422 (2012)
2012
-
[15]
Mehta and D
P. Mehta and D. J. Schwab, Energetic costs of cellular computation, Proceedings of the National Academy of Sciences 109, 17978 (2012)
2012
-
[16]
Sartori, L
P. Sartori, L. Granger, C. F. Lee, and J. M. Horowitz, Thermodynamic costs of information processing in sensory adaptation, PLoS computational biology 10, e1003974 (2014)
2014
-
[17]
C. C. Govern and P. R. ten Wolde, Energy dissipation and noise correlations in biochemical sensing, Physical review letters 113, 258102 (2014). 20
2014
-
[18]
J. J. Hopfield, Kinetic proofreading: A new mechanism for reducing errors in biosynthetic pro- cesses requiring high specificity, Proceedings of the National Academy of Sciences 71, 4135 (1974), https://www.pnas.org/doi/pdf/10.1073/pnas.71.10.4135
1974 doi
-
[19]
Ninio, Kinetic amplification of enzyme discrimination, Biochimie 57, 587 (1975)
J. Ninio, Kinetic amplification of enzyme discrimination, Biochimie 57, 587 (1975)
1975
-
[20]
C. H. Bennett, The thermodynamics of computation—a review, International Journal of Theoretical Physics 21, 905–940 (1982)
1982
-
[21]
J. M. R. Parrondo, J. M. Horowitz, and T. Sagawa, Thermodynamics of information, Nature Physics 11, 131 (2015)
2015
-
[22]
Andrieux and P
D. Andrieux and P. Gaspard, Nonequilibrium generation of information in copolymer- ization processes, Proceedings of the National Academy of Sciences 105, 9516 (2008), https://www.pnas.org/doi/pdf/10.1073/pnas.0802049105
2008 doi
-
[23]
Sartori and S
P. Sartori and S. Pigolotti, Kinetic versus energetic discrimination in biological copying, Phys. Rev. Lett. 110, 188101 (2013)
2013
-
[24]
Bogod and S
I. Bogod and S. Rahav, Kinetic discrimination of a polymerase in the presence of obstacles, Phys. Rev. E 95, 042408 (2017)
2017
-
[25]
J. M. Poulton and T. E. Ouldridge, Edge-effects dominate copying thermodynamics for finite-length molecular oligomers, New Journal of Physics 23, 063061 (2021)
2021
-
[26]
Berx and K
J. Berx and K. Proesmans, Universal thermodynamic bounds on the fano factor of discriminatory networks with unidirectional transitions, Europhysics Letters 145, 51001 (2024)
2024
-
[27]
Zananiri, S
R. Zananiri, S. Mangapuram Venkata, V. Gaydar, D. Yahalom, O. Malik, S. Rudnizky, O. Kleifeld, A. Kaplan, and A. Henn, Auxiliary atp binding sites support dna unwinding by recbcd, Nature com- munications 13, 1806 (2022)
2022
-
[28]
Moretto, M
L. Moretto, M. Uˇ saj, O. Matusovsky, D. E. Rassier, R. Friedman, and A. M ˚ ansson, Multistep or- thophosphate release tunes actomyosin energy transduction, Nature communications 13, 4575 (2022)
2022
-
[29]
Hartich, A
D. Hartich, A. C. Barato, and U. Seifert, Stochastic thermodynamics of bipartite systems: transfer entropy inequalities and a maxwell’s demon interpretation, Journal of Statistical Mechanics: Theory and Experiment 2014, P02016 (2014)
2014
-
[30]
J. M. Horowitz and M. Esposito, Thermodynamics with continuous information flow, Phys. Rev. X 4, 031015 (2014)
2014
Reviewed August 10, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.