Simple biological controllers drive the evolution of soft modes

Arvind Murugan; Christopher Joel Russo; David Pincus; Kabir Husain; Rama Ranganathan

REVIEW 5 major objections 7 minor 1 cited by

Simple biological controllers drive the evolution of soft modes

T0 review · 5 major / 7 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Selection for homeostasis in a high-dimensional network can create a soft mode that a low-dimensional controller then senses and acts on, which is why simple controllers like cAMP or (p)ppGpp can work.

desk verdict New idea about why simple controllers work—soft modes as a byproduct of selection for homeostasis—but the evolutionary simulations rest on a fitness function that may not penalize the costs of slowness. read the letter →

arxiv 2507.11973 v1 pith:KU3BV5MI submitted 2025-07-16 physics.bio-ph

Christopher Joel Russo , Kabir Husain , Rama Ranganathan , David Pincus , Arvind Murugan This is my paper · ORCID

classification physics.bio-ph

keywords integralfeedbackcontrolsoftmodesdimensionalityreductionhomeostasisevolutionarydynamicsmutationalrobustnessyeastknockoutcollectionstressresponse

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Simple biological controllers — low-dimensional integral feedback loops such as cAMP and (p)ppGpp — appear to regulate networks with thousands of components. This paper argues that they can do so because selection for homeostasis itself drives the controlled network to evolve a soft mode: one direction in state space that relaxes far more slowly than all others. Once such a mode gap exists, any environmental perturbation pushes the system mostly along that soft mode, so a controller that senses and acts on that single direction can restore homeostasis. The theory predicts that such controllers should buffer mutational perturbations as well as environmental ones, and that knocking the controller out should make the response to diverse environments lower-dimensional rather than higher. Both predictions are checked against yeast fitness and transcriptomic data.

What carries the argument

The mode gap $\lambda/\lambda_0$ between the slowest mode and all other modes is the object that carries the argument, together with the effective rank of the ensemble of perturbation effects. A large mode gap lowers the effective dimensionality of how environmental perturbations move the system, so a low-dimensional integral feedback controller that projects the state onto one vector and acts along one vector can cancel the dominant slow mode. The paper's analytic result is that optimal sensing and action vectors align with the soft mode, reducing the residual perturbation to equation 14.

What would settle it

Measure the relaxation time of a network after a perturbation in systems evolved under a simple controller: if imposing a fitness penalty proportional to recovery time prevents the mode gap from evolving, or if a measured soft mode carries a clear fitness cost in the organism's natural environment, the claim that homeostasis alone selects for soft modes would be falsified.

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Extended reading notes

Core claim

The central claim is that a mode gap is not a fixed property of the network but an evolved consequence of having to be regulated by a controller with fewer measurements than the system has dimensions. In the linearized model, a system with a single slow mode $\lambda_0$ and faster modes $\lambda$ is controlled by sensing along one vector $\vec{s}$ and acting along one vector $\vec{a}$. In the limit of a large mode gap $\lambda/\lambda_0$, the optimal sensing and action vectors align with the slowest eigenvector, and the normalized effect of a perturbation reduces to $\sqrt{\sum_{i\neq 0}(\mu_i^2+\sigma_i^2)} \big/ \sqrt{\sum_{i\neq 0}(\mu_i^2+\sigma_i^2)+(\lambda/\lambda_0)^2(\mu_0^2+\sigma_0^2)}$, meaning the soft mode is cancelled and only the fast modes contribute. The same soft mode channels environmental and mutational perturbations, so a controller selected for environmental robustness also buffers mutations. In simulations, evolution with low controller complexity produces a mode gap; evolution with high complexity does not.

Load-bearing premise

The evolutionary simulations score fitness only by how close the system stays to its fixed point on average, ignoring any cost of slow recovery, instability margins, or controller effort; if slow relaxation itself is costly, selection may not produce the large mode gap on which the predictions depend.

Editorial extensions

If this is right

If selection for homeostasis creates soft modes, then low-dimensional controllers in biology are not a design puzzle: they are a signature of evolutionary pressure on the controlled network.
Environmental and mutational robustness should be correlated: genes that buffer many environmental conditions should buffer many mutations, as observed in the yeast knockout data.
Knocking out a controller that listens to a soft mode should expose that mode, making the transcriptomic response to diverse stresses more stereotyped and lower-dimensional.
Soft modes can evolve purely for dimensionality reduction, without any direct function such as allostery, giving an evolutionary origin for low-dimensional structure observed across biological scales.
The theory connects to cryptic genetic variation and global epistasis: mutations buffered along a soft mode hide their effects until the controller is compromised.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the same mechanism could explain why 'capacitor' proteins like Hsp90 buffer both environmental and genetic perturbations, if they sit on the soft mode of the proteostasis network.
Beyond the paper: a direct experimental test would measure the relaxation spectrum of a metabolic or signaling network before and after selection under a simple controller, looking for the slowest eigenvalue to split from the rest only when the controller is low-dimensional.
Beyond the paper: the framework suggests that deliberately engineering a large mode gap in a synthetic host network could make a simple controller effective, reducing the need for complex multi-input regulatory circuits.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

This one is worth your time, but read it with the supplement missing in mind. The new idea is genuinely new: if a controller is constrained to sense and act on a low-dimensional projection, selection for homeostasis can itself favor a soft (slow) mode, because the controller then cancels most of the perturbation by sitting on that mode. That is distinct from earlier soft-mode explanations that require the mode to have a direct function like allostery or internal modeling.

The analytic model is the strongest part. Equation 14 is a clean, closed-form expression showing how a mode gap reduces the normalized perturbation effect, and the benefit grows with system dimensionality. The dual-buffering prediction—genes that buffer environmental perturbations should also buffer mutations—is crisp, and the check against the yeast GxG/GxE datasets is a genuine use of public data with no obvious parameter fitting. The Tpk123 result is suggestive but qualitative.

Now the soft spots. The biggest one is the evolutionary claim. The only direct evidence that selection creates the mode gap is the in-silico evolution in Section A, and the fitness function there penalizes only the time-averaged residual deviation from the fixed point. A soft mode makes the unregulated response slow and hypersensitive; any fitness cost of slowness, instability, or fragility would work against the selection pressure you identify. The paper does not analyze this trade-off. That does not kill the idea, but it leaves the central arrow from 'selection for homeostasis' to 'emergent soft mode' undefended. Second, large parts of the derivations, the simulation protocol, and the statistical tests are in a supplement that is not present in the arXiv version. That blocks auditing and reproduction. Third, the dual-buffering plot (Fig. 4d) has no error bars and is correlational; minor but should be fixed.

Overall: the analytic mechanism is solid as a conditional statement, and the framing is worth having in the literature. But the paper overstates what the simulations establish. I'd send it to peer review only after the supplement is provided and the fitness-cost objection is addressed. If you read it, start with Section B and the yeast analysis, and take the t-SNE with a grain of salt.

Referee Report

5 major / 7 minor

Summary. The paper develops a theory of low-dimensional integral-feedback control in high-dimensional biological networks, arguing that selection for homeostasis with a simple, low-dimensional controller drives the evolution of a dynamical soft mode. The analytic model (Eqs. 11-14) is intended to show that a large mode gap lets a one-dimensional controller align with the slow mode and reduce the normalized impact of environmental perturbations. In-silico evolution simulations (Fig. 2) are reported to show that selection with a k=1 controller increases the mode gap. The authors then derive two empirical predictions: controllers that buffer environmental perturbations also buffer mutational perturbations (tested with yeast GxG/GxE data), and knocking out such a controller decreases the dimensionality of environmental responses (tested with kinase-inhibition transcriptomics). The central conceptual claim is interesting, but the manuscript currently leaves the simulation protocol, the analytic derivations, and the details of the empirical significance tests in an absent supplement, and the empirical figures lack statistical support.

Significance. If the central claim holds, the paper offers a generic, scale-independent mechanism for low-dimensional structure in biology and provides a new evolutionary explanation for soft modes that does not require assigning a direct function to the slow mode. The theory is not fit to the yeast data, and the predictions are falsifiable; the use of two large public datasets is a strength. However, the current verification is incomplete: the evolutionary result and the analytic formulas cannot be audited without the supplement, and the empirical dual-buffering and dimensionality claims rest on figures without error bars or quantitative tests. The conceptual contribution is substantial enough to justify a major revision rather than rejection.

major comments (5)

[Section A, Eqs. (4)-(6), Fig. 2c] The central evolutionary claim—that selection for homeostasis with a k=1 controller increases the mode gap—rests entirely on the in-silico evolution, but the fitness function is only described verbally as a normalized, time-averaged residual deviation, and the simulated annealing protocol, parameter ranges, and initial conditions are deferred to a supplement that is not present in this version. Without the explicit fitness function and protocol, the result cannot be audited or reproduced. This is load-bearing because the analytic theory in Section B shows only the benefit of a pre-existing mode gap, not that selection creates it.
[Section B, Eqs. (12)-(14)] The main analytic results—the solution for δx in Eq. (12), the claim that the optimal sensing and action vectors satisfy α=β=1 in the large-gap limit, and the normalized perturbation effect in Eq. (14)—are stated without derivation, with all details referred to the supplement. Since the supplement is absent, the reader cannot verify the central formula or the assumptions under which the optimality claim holds. Please include the derivations in an appendix or provide the supplement.
[Section A, fitness in Eqs. (4)-(5)] The fitness cost only penalizes the residual deviation from the fixed point and does not include costs that a soft mode should naturally incur: slow unregulated recovery, reduced stability margins, hypersensitivity to perturbations (Eq. 8), and potential metabolic or fragility costs. Because a soft mode is by definition slow, a time-averaged deviation cost may or may not favor it depending on the averaging window and the controller dynamics; this trade-off is not analyzed. This is a load-bearing gap, since the reported increase in mode gap could be an artifact of a fitness function that ignores the costs of slowness.
[Section C2, Fig. 4d] The dual-buffering empirical claim is supported only by cumulative histograms without error bars, confidence intervals, or significance tests. The criterion for identifying significant negative GxE and GxG interactions is stated to be the same as in the original studies, but the details are deferred to the missing supplement, so the threshold and multiplicity correction cannot be assessed. As presented, the figure does not quantitatively establish that genes buffering 6-7 environmental conditions buffer significantly more mutations than genes buffering 1-2 conditions.
[Section D, Fig. 5d-f] The dimensionality-decrease prediction is tested by visual inspection of t-SNE plots and by average distances in t-SNE space. t-SNE is a nonlinear embedding that can produce apparent clustering even in high-dimensional data and is not a measure of intrinsic dimensionality. To support the claim, the authors should report a quantitative dimensionality measure on the gene-expression matrices, such as effective rank or the variance explained by principal components, together with uncertainty estimates and a statistical test.

minor comments (7)

[Section A, first paragraph] The text says selection 'leads to a reduction in the system's mode gap—the ratio of the second and first eigenmodes λ1/λ0,' but Fig. 2c shows an increase in mode gap, and the later theory consistently uses a large λ/λ0 as the beneficial regime. Please correct this apparent contradiction.
[Section B] In the sentence 'in the limit of a large mode gap λ/λ >>1,' the ratio should be λ/λ0 >> 1.
[Section C1, Eqs. (15)-(16)] The slow mode is denoted λ0 in Section B but λ1 in Eqs. (15)-(16), and the condition 'λ1 >> λ_i>1' is undefined. Please use consistent indexing and explicit inequalities.
[Section C2] 'Rapmycin' should be 'Rapamycin,' and the sentence 'mTOR is buffering over the effect of over 400 knockouts' is ungrammatical and should be rewritten.
[Fig. 4d caption] The caption does not state whether the curves are cumulative distribution functions or what the sample sizes are for each bin; please add a legend, sample sizes, and error bars or at least counts.
[Fig. 2 caption] The caption uses 'm nodes' and 'k random and independent combinations' with variables that are not defined in the main text; please align the caption notation with Eqs. (4)-(6).
[Section B, parameterization of s and a] The sensing and action vectors are restricted to the span of the slow mode and the mean perturbation direction; the text should state explicitly that the optimality claim for α=β=1 is within this restricted family of controllers.

Circularity Check

1 steps flagged · score 2.0 of 10

No material circularity: analytic results are derived in-paper and empirical tests are external and unfitted; only a minor framing self-citation (refs 11–12) is self-referential.

other [Introduction / Results A — soft-mode definitional framing via refs [9–12] and [11]]
"That the mode is soft means that arbitrary perturbations will tend to push the system along that mode [9–12]. ... A slow mode [11] is also a soft mode – when arbitrarily perturbed, the system tends to move along this mode, making it easier for a simple controller to detect and correct deviations."

Ref [11] (Russo, Husain & Murugan, Annual Review of Biophysics 54, 2024) is the present paper's own review by three of its authors, and ref [12] (Husain & Murugan 2020) is co-authored by the senior author; the soft-mode frame through which the manuscript is presented is therefore self-citational. This is minor and not load-bearing: the text defines a soft mode directly ('a mode that relaxes slowly'), the analytic results (Eqs. 7–14) are derived with in-paper mathematics, and the empirical tests use external datasets. Score contribution is 2 (one minor self-citation) rather than genuine circularity.

full rationale

The central derivations are self-contained and the empirical tests are not fitted. Section B derives the optimal-control result in-paper: minimizing ⟨||δx||⟩ over the sensing/action parameters α, β (Eqs. 11–12) gives alignment with the slow mode and, for large mode gap, the normalized residual of Eq. 14. This is a conditional calculation (given a mode gap λ/λ0, a low-dimensional integral controller is more effective); it is not a fit, and no parameter anywhere in the paper is tuned to make the yeast GxG/GxE or Tpk123 results come out. The evolutionary arrow (selection creates the soft mode) rests on the in-silico evolution of Results A, whose fitness is the residual deviation normalized by the overall stiffness (Eqs. 4–5). That normalization is a modeling choice that removes the direct penalty a soft mode would otherwise carry — a small λ0 inflates the uncontrolled response δx = J^{-1}δe (Eq. 8) — so the evolutionary claim is weaker than advertised if slow recovery or fragility carries fitness cost; but this is a limitation (flagged here), not a circular reduction: the mode gap is an emergent output of the simulated-annealing protocol, not the fitness itself. Reproducibility of this central simulation is limited because the exact fitness function and protocol are deferred to a supplement not provided in this version ('see supplement'). The paper also candidly acknowledges that evolutionary-origin explanations may be indistinguishable ('It may in fact not be possible to distinguish between these, since one leads to the others'). Self-citations (refs 11–12) appear only as definitional framing for soft modes and do not carry the derivations or the data analysis. Verdict: no significant circularity; score 2 reflects one minor non-load-bearing self-citation.

Assumptions & free parameters 4 free parameters · 7 assumptions · 0 invented entities

The paper introduces no new physical or molecular entities. Its conceptual novelty is an evolutionary role for soft modes, but the soft mode itself is a pre-existing dynamical concept. The load-bearing assumptions are the spectral ansatz, linearization, Gaussian environment, the fitness definition, and the operational definition of buffering.

free parameters (4)

Mode gap λ/λ0 = scanned over 1-100 in analytic model; emergent in simulations
The fitness-benefit function (eq. 14) is evaluated as a function of this gap; it is not measured from experiment, so the quantitative predictions are conditional on the chosen range.
Controller sensing/action orientation parameters α, β = optimized; α=β=1 in the large-gap limit
The paper restricts s and a to the span of the slow mode and mean perturbation direction and then optimizes them; this is a variational choice, not a fit to data.
Integral and proportional controller gains k_i, k_p (c_i, c_p) = not reported numerically
These gains appear in eqs. 2, 3, 6, 11; the paper does not specify values used in simulations, so the stability regime underlying eq. 12 is not auditable.
Network interaction parameters k_ab and K_ab = evolved by MCMC simulated annealing
These define the modeled gene network and are the degrees of freedom selection acts on; the paper does not report the parameter ranges or evolution protocol in the preprint, so the landscape explored is unspecified.

assumptions (7)

standard math Eigen-decomposition and inverse of the Jacobian J_x; effective-rank entropy formula (Roy and Vetterli 2007).
Used to relate δx = J_x^{-1} δe_env and to define dimensionality; no independent derivation needed.
domain assumption Linearization about the fixed point is valid for the perturbation amplitudes considered.
The analytic solution (eqs. 8,12) treats δx as small; nonlinear saturation or bifurcations are not considered.
ad hoc to paper The Jacobian spectrum has one slow mode λ0 and N-1 equal fast modes λ.
This spectral ansatz is the basis for eqs. 10,13,14; real networks have a continuum of eigenvalues, and the paper does not prove this structure is generic.
ad hoc to paper Sensing and action vectors are unit vectors confined to the span of the slow mode and the mean perturbation direction.
Eqs. a=βv0+sqrt(1-β²) μ and s=αv0+sqrt(1-α²) μ restrict the controller optimization; a controller with access to any direction could behave differently.
domain assumption Environmental perturbations are Gaussian with mean μ and covariance σ²I.
The expectation values in eqs. 13-14 and effective ranks are computed for this ensemble; real stress ensembles may be correlated or non-Gaussian.
domain assumption A gene buffers a perturbation if it has many significant negative non-additive interactions, as defined in the original yeast studies.
The empirical dual-buffering test inherits the significance thresholds and interaction-calling model of Costanzo 2016/2021; the exact adaptation is in the omitted supplement.
domain assumption Tpk123/cAMP-PKA acts as a low-dimensional integral feedback controller in yeast.
Section D interprets Tpk123 inhibition as controller knockout; no dynamical characterization of Tpk123 as an integral controller is provided.

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Pith. "Pith review of Simple biological controllers drive the evolution of soft modes." pith.science (2026). https://pith.science/paper/KU3BV5MI

@misc{pith2026250711973,
  author       = {Pith},
  title        = {Pith review of: Simple biological controllers drive the evolution of soft modes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KU3BV5MI}},
  note         = {Machine review of arXiv:2507.11973}
}

read the original abstract

Biological systems, with many interacting components, face high-dimensional environmental fluctuations, ranging from diverse nutrient deprivations to toxins, drugs, and physical stresses. Yet, many biological control mechanisms are `simple' -- they restore homeostasis through low-dimensional representations of the system's high-dimensional state. How do low-dimensional controllers maintain homeostasis in high-dimensional systems? We develop an analytically tractable model of integral feedback for complex systems in fluctuating environments. We find that selection for homeostasis leads to the emergence of a soft mode that provides the dimensionality reduction required for the functioning of simple controllers. Our theory predicts that simple controllers that buffer environmental perturbations (e.g., stress response pathways) will also buffer mutational perturbation, an equivalence we test using experimental data across ~5000 strains in the yeast knockout collection. We also predict, counterintuitively, that knocking out a simple controller will \emph{decrease} the dimensionality of the response to environmental change; we outline transcriptomics tests to validate this. Our work suggests an evolutionary origin of soft modes whose function is for dimensionality reduction in and of itself rather than direct function like allostery, with implications ranging from cryptic genetic variation to global epistasis.

Figures

Figures reproduced from arXiv: 2507.11973 by the authors.

**Figure 1.** FIG. 1. (a) Low-dimensional controllers – controllers that project the high-dimensional state of the organism and the environ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** FIG. 2. Selection for environmental robustness in a system with a low complexity controller leads to the evolution of a [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. (a) In systems with no significant mode gap, relaxation trajectories are diverse, and perturbations push the system in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. Slow modes allow controllers of environmental perturbations to also buffer mutational perturbations (dual buffering). [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. Slow modes imply that knocking out a controller will, counterintuitively, reduce the dimensionality of an environmental [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

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Works this paper leans on

44 extracted references · 43 canonical work pages · cited by 1 Pith paper

[1]

This dual ability to buffer environmental stressors as well as mutations has been noted since the 1990s in the case of the heat shock system in Drosophila [25, 26]

Theory Our model of slow mode mediated response to environ- mental challenges in living systems predicts dual buffer- ing – mechanisms that buffer environmental perturba- tions should also buffer mutational perturbations. This dual ability to buffer environmental stressors as well as mutations has been noted since the 1990s in the case of the heat shock s...

work page
[2]

A library of yeast strains with all non-essential gene knockouts had previously been assembled [28]

Empirical Results Two experimental studies collected high throughput fitness data on yeast grown subject to different kinds of mutational and environmental perturbations, shedding light on dual buffering in living cells [13, 14]. A library of yeast strains with all non-essential gene knockouts had previously been assembled [28]. In one experiment, this li...

work page 2016
[3]

Milo and R

R. Milo and R. Phillips,Cell biology by the numbers(Gar- land Science, 2015)

2015
[4]

C. Wu, R. Balakrishnan, N. Braniff, M. Mori, G. Man- zanarez, Z. Zhang, and T. Hwa, Cellular perception of growth rate and the mechanistic origin of bacterial growth law, Proceedings of the National Academy of Sci- ences119, e2201585119 (2022)

work page 2022
[5]

M. F. Traxler, S. M. Summers, H.-T. Nguyen, V. M. Zacharia, G. A. Hightower, J. T. Smith, and T. Conway, The global, ppgpp-mediated stringent response to amino acid starvation in escherichia coli, Molecular microbiol- ogy68, 1128 (2008)

work page 2008
[6]

L. U. Magnusson, A. Farewell, and T. Nystr¨ om, ppgpp: a global regulator in escherichia coli, Trends in microbi- ology13, 236 (2005)

work page 2005
[7]

Conrad, J

M. Conrad, J. Schothorst, H. N. Kankipati, G. Van Zee- broeck, M. Rubio-Texeira, and J. M. Thevelein, Nutrient sensing and signaling in the yeast saccharomyces cere- visiae, FEMS microbiology reviews38, 254 (2014)

work page 2014
[8]

J. M. Thevelein and J. H. De Winde, Novel sensing mech- anisms and targets for the camp–protein kinase a path- way in the yeast saccharomyces cerevisiae, Molecular mi- crobiology33, 904 (1999)

work page 1999

Show all 44 references

[9]

Gottesman, Trouble is coming: Signaling pathways that regulate general stress responses in bacteria, Journal of Biological Chemistry294, 11685 (2019)

S. Gottesman, Trouble is coming: Signaling pathways that regulate general stress responses in bacteria, Journal of Biological Chemistry294, 11685 (2019)

2019
[10]

C. H. Serezani, M. N. Ballinger, D. M. Aronoff, and M. Peters-Golden, Cyclic amp: master regulator of in- nate immune cell function, American journal of respira- tory cell and molecular biology39, 127 (2008)

2008
[11]

Bahar, On the functional significance of soft modes pre- dicted by coarse-grained models for membrane proteins, Journal of General Physiology135, 563 (2010)

I. Bahar, On the functional significance of soft modes pre- dicted by coarse-grained models for membrane proteins, Journal of General Physiology135, 563 (2010)

2010
[12]

Leo-Macias, P

A. Leo-Macias, P. Lopez-Romero, D. Lupyan, D. Zerbino, and A. R. Ortiz, An analysis of core deformations in pro- tein superfamilies, Biophysical journal88, 1291 (2005)

2005
[13]

C. J. Russo, K. Husain, and A. Murugan, Soft modes as a predictive framework for low-dimensional biological systems across scales, Annual Review of Biophysics54 (2024)

2024
[14]

Husain and A

K. Husain and A. Murugan, Physical constraints on epis- tasis, Molecular Biology and Evolution37, 2865 (2020)

2020
[15]

Costanzo, B

M. Costanzo, B. VanderSluis, E. N. Koch, A. Barysh- nikova, C. Pons, G. Tan, W. Wang, M. Usaj, J. Han- chard, S. D. Lee,et al., A global genetic interaction net- work maps a wiring diagram of cellular function, Science 353, aaf1420 (2016)

2016
[16]

Costanzo, J

M. Costanzo, J. Hou, V. Messier, J. Nelson, M. Rahman, B. VanderSluis, W. Wang, C. Pons, C. Ross, M. Uˇ saj, et al., Environmental robustness of the global yeast ge- netic interaction network, Science372, eabf8424 (2021)

2021
[17]

M. R. Mitchell, T. Tlusty, and S. Leibler, Strain analy- sis of protein structures and low dimensionality of me- chanical allosteric couplings, Proceedings of the National Academy of Sciences113, E5847 (2016)

2016
[18]

J. W. Rocks, N. Pashine, I. Bischofberger, C. P. Goodrich, A. J. Liu, and S. R. Nagel, Designing allostery- inspired response in mechanical networks, Proceedings of the National Academy of Sciences114, 2520 (2017)

2017
[19]

Campitelli, T

P. Campitelli, T. Modi, S. Kumar, and S. B. Ozkan, The role of conformational dynamics and allostery in modu- lating protein evolution, Annual review of biophysics49, 267 (2020)

2020
[20]

Ravasio, S

R. Ravasio, S. M. Flatt, L. Yan, S. Zamuner, C. Brito, and M. Wyart, Mechanics of allostery: contrasting the induced fit and population shift scenarios, Biophysical journal117, 1954 (2019)

2019
[21]

A. S. Raman, K. I. White, and R. Ranganathan, Origins of allostery and evolvability in proteins: a case study, Cell166, 468 (2016)

2016
[22]

Friedlander, A

T. Friedlander, A. E. Mayo, T. Tlusty, and U. Alon, Evo- lution of bow-tie architectures in biology, PLoS compu- tational biology11, e1004055 (2015)

2015
[23]

Furusawa and K

C. Furusawa and K. Kaneko, Formation of dominant mode by evolution in biological systems, Physical Review E97, 042410 (2018)

2018
[24]

T.-M. Yi, Y. Huang, M. I. Simon, and J. Doyle, Ro- bust perfect adaptation in bacterial chemotaxis through integral feedback control, Proceedings of the National Academy of Sciences97, 4649 (2000)

2000
[25]

P. R. Somvanshi, A. K. Patel, S. Bhartiya, and K. Venkatesh, Implementation of integral feedback con- trol in biological systems, Wiley Interdisciplinary Re- views: Systems Biology and Medicine7, 301 (2015)

2015
[26]

Roy and M

O. Roy and M. Vetterli, The effective rank: A measure of effective dimensionality, in2007 15th European signal processing conference(IEEE, 2007) pp. 606–610

2007
[27]

S. L. Rutherford and S. Lindquist, Hsp90 as a capacitor for morphological evolution, Nature396, 336 (1998)

1998
[28]

Queitsch, T

C. Queitsch, T. A. Sangster, and S. Lindquist, Hsp90 as a capacitor of phenotypic variation, Nature417, 618 (2002)

2002
[29]

P. L. Yeyati and V. van Heyningen, Incapacitating the evolutionary capacitor: Hsp90 modulation of disease, Current opinion in genetics & development18, 264 (2008)

2008
[30]

Costanzo, A

M. Costanzo, A. Baryshnikova, J. Bellay, Y. Kim, E. D. Spear, C. S. Sevier, H. Ding, J. L. Koh, K. Toufighi, S. Mostafavi,et al., The genetic landscape of a cell, sci- ence327, 425 (2010)

2010
[31]

L. M. Ballou and R. Z. Lin, Rapamycin and mtor kinase inhibitors, Journal of chemical biology1, 27 (2008)

2008
[32]

K. Mace, J. Krakowiak, H. El-Samad, and D. Pincus, Multi-kinase control of environmental stress responsive transcription, PLoS One15, e0230246 (2020)

2020
[33]

M. Love, S. Anders, and W. Huber, Differential analysis of count data–the deseq2 package, Genome Biol15, 10 (2014)

2014
[34]

Van der Maaten and G

L. Van der Maaten and G. Hinton, Visualizing data using t-sne., Journal of machine learning research9(2008)

2008
[35]

Eckmann and T

J.-P. Eckmann and T. Tlusty, Dimensional reduction in complex living systems: Where, why, and how, BioEssays 43, 2100062 (2021)

2021
[36]

Raimondi, M

F. Raimondi, M. Orozco, and F. Fanelli, Deciphering the Deformation Modes Associated with Function Retention and Specialization in Members of the Ras Superfamily, Structure18, 402 (2010)

2010
[37]

A. V. Sastry, Y. Gao, R. Szubin, Y. Hefner, S. Xu, D. Kim, K. S. Choudhary, L. Yang, Z. A. King, and B. O. Palsson, The escherichia coli transcriptome mostly con- sists of independently regulated modules, Nature com- munications10, 5536 (2019). 13

2019
[38]

Schmidt, K

A. Schmidt, K. Kochanowski, S. Vedelaar, E. Ahrn´ e, B. Volkmer, L. Callipo, K. Knoops, M. Bauer, R. Aeber- sold, and M. Heinemann, The quantitative and condition- dependent escherichia coli proteome, Nature biotechnol- ogy34, 104 (2016)

2016
[39]

M. Lukk, M. Kapushesky, J. Nikkil¨ a, H. Parkinson, A. Goncalves, W. Huber, E. Ukkonen, and A. Brazma, A global map of human gene expression, Nature biotech- nology28, 322 (2010)

2010
[40]

Kinsler, K

G. Kinsler, K. Geiler-Samerotte, and D. A. Petrov, Fit- ness variation across subtle environmental perturbations reveals local modularity and global pleiotropy of adapta- tion, Elife9, e61271 (2020)

2020
[41]

Kashtan and U

N. Kashtan and U. Alon, Spontaneous evolution of mod- ularity and network motifs, Proceedings of the National Academy of Sciences102, 13773 (2005)

2005
[42]

K. Kaneko, Constructing universal phenomenology for biological cellular systems: an idiosyncratic review on evolutionary dimensional reduction, Journal of Statisti- cal Mechanics: Theory and Experiment2024, 024002 (2024)

2024
[43]

Halabi, O

N. Halabi, O. Rivoire, S. Leibler, and R. Ranganathan, Protein sectors: evolutionary units of three-dimensional structure, Cell138, 774 (2009)

2009
[44]

Masel, Cryptic genetic variation is enriched for poten- tial adaptations, Genetics172, 1985 (2006)

J. Masel, Cryptic genetic variation is enriched for poten- tial adaptations, Genetics172, 1985 (2006)

2006

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

This dual ability to buffer environmental stressors as well as mutations has been noted since the 1990s in the case of the heat shock system in Drosophila [25, 26]

Theory Our model of slow mode mediated response to environ- mental challenges in living systems predicts dual buffer- ing – mechanisms that buffer environmental perturba- tions should also buffer mutational perturbations. This dual ability to buffer environmental stressors as well as mutations has been noted since the 1990s in the case of the heat shock s...

work page

[2] [2]

A library of yeast strains with all non-essential gene knockouts had previously been assembled [28]

Empirical Results Two experimental studies collected high throughput fitness data on yeast grown subject to different kinds of mutational and environmental perturbations, shedding light on dual buffering in living cells [13, 14]. A library of yeast strains with all non-essential gene knockouts had previously been assembled [28]. In one experiment, this li...

work page 2016

[3] [3]

Milo and R

R. Milo and R. Phillips,Cell biology by the numbers(Gar- land Science, 2015)

2015

[4] [4]

C. Wu, R. Balakrishnan, N. Braniff, M. Mori, G. Man- zanarez, Z. Zhang, and T. Hwa, Cellular perception of growth rate and the mechanistic origin of bacterial growth law, Proceedings of the National Academy of Sci- ences119, e2201585119 (2022)

work page 2022

[5] [5]

M. F. Traxler, S. M. Summers, H.-T. Nguyen, V. M. Zacharia, G. A. Hightower, J. T. Smith, and T. Conway, The global, ppgpp-mediated stringent response to amino acid starvation in escherichia coli, Molecular microbiol- ogy68, 1128 (2008)

work page 2008

[6] [6]

L. U. Magnusson, A. Farewell, and T. Nystr¨ om, ppgpp: a global regulator in escherichia coli, Trends in microbi- ology13, 236 (2005)

work page 2005

[7] [7]

Conrad, J

M. Conrad, J. Schothorst, H. N. Kankipati, G. Van Zee- broeck, M. Rubio-Texeira, and J. M. Thevelein, Nutrient sensing and signaling in the yeast saccharomyces cere- visiae, FEMS microbiology reviews38, 254 (2014)

work page 2014

[8] [8]

J. M. Thevelein and J. H. De Winde, Novel sensing mech- anisms and targets for the camp–protein kinase a path- way in the yeast saccharomyces cerevisiae, Molecular mi- crobiology33, 904 (1999)

work page 1999