Navigation driven by bidirectional information transmission between sensing and actuation

Avishek Das; Pieter Rein ten Wolde

REVIEW 2 major objections 3 minor 53 references

Navigation driven by bidirectional information transmission between sensing and actuation

T0 review · 2 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Navigation performance in shallow gradients is governed by two information flows alone.

desk verdict The spatial BEST is wrong as printed, but the temporal result and E. coli test are strong enough to warrant a careful revision. read the letter →

arxiv 2607.26798 v2 pith:46FZLDEH submitted 2026-07-29 physics.bio-ph cond-mat.softcond-mat.stat-mechq-bio.MN

Avishek Das , Pieter Rein ten Wolde This is my paper · ORCID

classification physics.bio-phcond-mat.softcond-mat.stat-mechq-bio.MN

keywords chemotaxistransferentropynavigationperformancesensory-motorfeedbackstochasticcontrolE.coliBehavioralEquationofState

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

The paper tries to establish that a cell's navigation performance in shallow gradients is fully determined by how much information flows from the sensory input to the sensory output and back from the output through actuation to the future input, not by the specific gains, noises, or rates of the underlying biochemical circuitry. For both spatial and temporal sensing, the authors derive exact equalities, called Behavioral Equations of State (BESTs), connecting normalized performance to feedforward and feedback transfer entropies plus the relative speed of sensing and actuation. If true, this means information transmission is the organizing principle for stochastic navigation, and a simple data collapse should be observable across mutants and cell types. The authors support the claim with analytical solution of two minimal models and parameter-free simulation of E. coli chemotaxis.

What carries the argument

The central objects are the feedforward and feedback transfer-entropy rates, defined over full signal trajectories rather than single time points (multi-step transfer entropy). The spatial-sensing derivation uses stochastic control theory with spectral factorization of power spectra to obtain causal prediction variances; the temporal-sensing derivation combines path-measure transformation formulas with a perturbation expansion of stochastic filtering equations, valid to second order in the actuator gain. For the nonlinear E. coli test, transfer entropies are computed exactly by the TE-PWS (path-weight sampling) algorithm.

What would settle it

Measure P, T_FF, T_FB and rho in cells with a clearly multi-exponential velocity autocorrelation under shallow-gradient, weak-actuation conditions. If their normalized performance deviates from P/P0 = 4[rho/(1+rho)] sqrt(T_FF T_FB) while T_FF and T_FB are correctly computed from full trajectories, the universality claim is refuted. Equivalently, find two navigators with the same T_FF, T_FB and rho but different elementary parameters whose performance differs.

Watch

Extended reading notes

Core claim

Stochastic navigation in shallow gradients is claimed to obey a Behavioral Equation of State (BEST): performance is fully determined by two history-dependent information flows—feedforward transfer entropy T_FF (sensory input to output) and feedback transfer entropy T_FB (output through actuation to future input)—independent of gain, noise, or actuation strength. For temporal sensing, P/P0 = 4[rho/(1+rho)] sqrt(T_FF) sqrt(T_FB), rho = sensory speed / velocity relaxation rate; for spatial sensing, an analogous equality (Eq. 3) holds. These equalities are derived analytically in two minimal models and verified in E. coli chemotaxis simulations without fitting.

Load-bearing premise

The E. coli test assumes the cell's velocity fluctuations are fully captured by a single exponential decay timescale H; cells with multi-timescale velocity dynamics may not obey the BEST.

Editorial extensions

If this is right

The BEST predicts a data collapse: cells or mutants with different sensory gain, noise, or actuation strength should fall on the same performance-versus-information curve in shallow gradients.
In this regime, navigation can be improved only by increasing feedforward or feedback information or, for temporal sensing, the relative sensing speed rho; elementary parameters matter only through these flows.
Too much feedback information degrades performance, implying an optimal actuator gain—found analytically for spatial sensing and by simulation (around 4 nats) for E. coli—so actuator design must balance responding to signal versus sensory noise.
Single-step transfer entropy is insufficient; any empirical test of the BEST must use history-dependent, trajectory-based transfer entropy.
The same principle may extend to other feedback-driven biological functions such as homeostasis and immune response, as the paper's closing discussion suggests.

Reading between the lines

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

If the BEST holds broadly, navigation performance could be monitored non-invasively by measuring two information flows from trajectory data, turning information into a practical diagnostic for chemotaxis and other sensorimotor loops.
The different scaling with feedforward information (linear for spatial, square-root for temporal) suggests that trajectory statistics alone could reveal which sensing strategy a cell uses, without requiring morphological measurements.
The optimal feedback information found in E. coli simulations implies a possible evolutionary pressure on actuator gain; one could test whether wild-type cells sit near this optimum by measuring feedback information across many strains and conditions.
The single-exponential velocity assumption is a natural place to generalize: cells with several motility timescales may require a multi-timescale BEST with rho replaced by a spectrum of ratios.

Share X Bluesky LinkedIn Reddit HN

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

The headline in your report is right: this is a novel and potentially important framework. The idea that navigation performance in the linear regime can be expressed as a function of feedforward and feedback multi-step transfer entropies alone—without any reference to the elementary parameters—is genuinely new. The temporal-sensing BEST (Eq. 7), P/P0 = 4[ρ/(1+ρ)]√TFF√TFB, is a clean result, and the E. coli simulation shows a collapse with no fitted parameters. That is real evidence and deserves credit.

The soft spots are real, though, and one of them is load-bearing. Equation 3, the spatial-sensing BEST, cannot be correct as printed. As TFB → 0, the bracket diverges as 1/√TFB, so the right-hand side diverges while the performance must vanish when the actuator gain goes to zero. Direct substitution from Eq. 1 in the same small-TFF limit gives P/P0 = 2 TFF √((2TFB+1)^2−1)/(2TFB+1)^2, which reduces to 4 TFF√TFB for weak feedback and TFF/TFB for strong feedback—the bounds that Eq. 4 claims to derive from Eq. 3. So the printed equality is internally inconsistent; the formula appears to have a typo in the bracket. This error sits in the first central result of the paper, and it cannot be waved away. If the authors produce the correct expression, the framework may stand; but as submitted, the spatial claim is not supported.

Other concerns are less severe but worth stating. The full temporal perturbation derivation is in an SI that is not included, and the Methods acknowledge the expressions were developed with ChatGPT/Claude and independently verified. That is not disqualifying, but I would need to see the calculations to believe the second-order perturbation theory. The E. coli test selects parameter values whose velocity autocorrelation is a single exponential, then defines H from that; that makes the test less universal than the abstract implies. The normalization of transfer entropies also looks inconsistent across sections, which matters because the BEST relations depend on those dimensionless definitions.

The authors are honest about the regime restrictions: they state shallow gradients, weak actuation, and the need for fast sensing in steeper gradients. So this is not an overreach in the discussion; the problem is the technical error in Eq. 3 and the missing SI.

My take: the paper deserves a serious referee, not a desk reject. The temporal result and the E. coli test are strong enough to warrant a careful round. But the referee needs to demand the correct form of Eq. 3 (or an explanation for the divergence), the SI, and a fuller treatment of the H-selection. I would not cite this version in my own work until the spatial relation is fixed.

Referee Report

2 major / 3 minor

Summary. The paper develops two analytic minimal models of stochastic cellular navigation—spatial and temporal sensing—and claims that in the linear-response regime of shallow gradients, navigation performance is fully determined by the feedforward and feedback transfer entropies T_FF and T_FB. These 'Behavioral Equations of State' (BESTs) are stated as Eq. (3) for spatial sensing and Eq. (7) for temporal sensing. The temporal-sensing BEST is tested against stochastic simulations of E. coli chemotaxis using the exact TE-PWS algorithm, and the authors report agreement without fitting or scaling parameters. The paper also argues that single-step transfer entropy is insufficient and discusses an optimal feedback information in the spatial model.

Significance. The idea that bidirectional information transmission provides a system-independent equation of state for navigation is conceptually appealing and, if correct, yields an experimentally testable data collapse across cell types and mutants. The temporal-sensing derivation uses a controlled perturbation theory and is corroborated by exact numerical simulations, and the E. coli test is a strong, falsifiable validation. However, the spatial-sensing BEST as printed in Eq. (3) is mathematically inconsistent, which calls into question the associated claims about optimal feedback information. The overall framework remains significant, but the spatial-sensing leg of the paper requires correction.

major comments (2)

[§'Performance depends solely on bidirectional information transmission', Eq. (3)] Eq. (3) is internally inconsistent and contradicts the model. As T_FB→0 (J→0), the bracket diverges because of the term 1/sqrt((2T_FB+1)^2-1) ~ 1/(2√T_FB), while the performance P must vanish when actuation is turned off. Direct substitution of T_FF and T_FB into Eq. (1) in the small-k limit gives P/P0 = 4 T_FF√T_FB, which is precisely the first bound in Eq. (4) and the expression used in the Discussion for spatial sensing. Thus Eq. (3) is not the shallow-gradient limit of the model. The derived optimum T*_FB=(√2−1)/2 and the non-monotonic curve in Fig. 3A are artifacts of this erroneous expression and must be revised.
[Materials and Methods, 'Nonlinear perturbation theory...'] The temporal-sensing BEST (Eq. (7)) rests on a second-order perturbation expansion of stochastic Riccati equations. The Methods state that the full derivation is provided in the SI, but the SI is not included in the manuscript. The authors also disclose that the expressions were obtained with AI assistance and independently verified. Because Eq. (7) is a central result, the derivation must be available for review; without it, the analytic content of the temporal BEST cannot be fully verified, although the final expression matches the numerical simulations in Fig. 4C.

minor comments (3)

[E. coli section, 'BEST predicts chemotaxis in E. coli'] The definition of a single velocity correlation timescale H relies on choosing parameters for which the velocity autocorrelation function is a single exponential. This restricts the test to a subset of navigators; the universal claim for multi-timescale velocity dynamics is not tested. The authors should state this scope condition more prominently.
[Equation (3) vicinity] The printed definitions of T_FF and T_FB contain garbled mathematical expressions ('[p 1 + (2Gk/H2)(Dv/Df )1/2 −1]/2'); they should be typeset unambiguously.
[Performance depends solely on bidirectional information transmission, p.5] The sentence 'Eq. 1 shows that in shallow gradients, navigation is controlled by bidirectional information flow alone' is imprecise: Eq. (1) is written in elementary parameters; the information-only statement follows only after substitution. Please clarify the wording.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the BEST relations are derived relations between model outputs and tested against an external E. coli simulation; no prediction reduces to its own input.

full rationale

The central derivations are not circular. The transfer entropies T_FF and T_FB are not defined in terms of the performance P; they are computed from the stochastic models as separate observables, while P is an independent performance metric (inverse positional variance for spatial sensing, mean drift for temporal sensing). Eliminating the elementary parameters between the performance expression and the transfer-entropy expressions is a legitimate derivation of an equation of state, not a fit or a self-definition. The genuinely independent test is the E. coli agent-based simulation: T_FF, T_FB, and rho are measured from the simulation with TE-PWS and by the J=0 velocity autocorrelation, whereas P is measured directly, and the authors state the data follow the BEST 'without any fitting or scaling parameters.' No prediction parameter is adjusted to force the comparison. The paper's explicit selection of E. coli parameter values for which the velocity autocorrelation is a single exponential is a scope restriction on the universality claim, but it is not circular. The self-citations (TE-PWS [24], ML-PWS [33], and background work) are methodological or contextual; TE-PWS is an exact numerical algorithm, not the target relation, and no uniqueness theorem from the authors is imported to forbid alternatives. The apparent divergence of Eq. 3 as T_FB→0, if confirmed, is a mathematical inconsistency in the spatial-sensing claim rather than an equivalence between the claim and its inputs; it does not raise the circularity score. The Methods note that analytical expressions were derived with LLM assistance and verified by the authors is a provenance statement, not a circularity mechanism.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central derivation has no fitted free parameters: the BEST is obtained by eliminating the elementary parameters of the minimal models. The main assumptions are the standard Gaussian linear-system framework, the weak-nonlinearity perturbation regime, the restriction to shallow gradients, and the single-exponential velocity decorrelation for E. coli. No new physical entities are introduced.

assumptions (5)

standard math The spatial-sensing model trajectories are Gaussian distributed because the dynamics are linear (Eqs. 12-14).
Used to justify the transfer entropy rate formula in Eq. 15.
domain assumption In the temporal-sensing model, the conditional distributions P(f(t)|v[-inf,t]) and P(v(t)|f[-inf,t]) are Gaussian because each equation is linear in the conditioned variable.
Needed for the stochastic Riccati equations (Eqs. 24-25).
domain assumption The perturbation expansion in the actuator gain J is valid to second order; the model is stable only for small J.
Temporal-sensing theory is restricted to weak actuation; large J leads to runaway positive feedback.
domain assumption The shallow-gradient linear-response regime is the scope of the BEST; steeper gradients introduce an additional variable rho (Eq. 5).
The paper explicitly restricts the universal claim to shallow gradients.
domain assumption The E. coli model (Eqs. 8-11) with parameters from [38] faithfully represents E. coli chemotaxis, and the selected parameters yield a single-exponential velocity autocorrelation defining H.
Underlies the E. coli test; parameter selection is described in the section 'BEST predicts chemotaxis in E. coli'.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Navigation driven by bidirectional information transmission between sensing and actuation." pith.science (2026). https://pith.science/paper/46FZLDEH

@misc{pith2026260726798,
  author       = {Pith},
  title        = {Pith review of: Navigation driven by bidirectional information transmission between sensing and actuation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/46FZLDEH}},
  note         = {Machine review of arXiv:2607.26798}
}

read the original abstract

A wide variety of biological functions are driven by feedback between sensing and actuation. A paradigmatic example is cellular navigation. During navigation, the sensory system maps the environmental input signal onto a sensory output, which then drives an actuation response, changing the future sensory input. How the accuracy of this bidirectional information transmission controls navigation is not currently understood. Here, we study how information controls navigation by analytically solving two generic models that describe two major classes of biological navigators: spatial- and temporal-sensing cells. We find that, in the linear-response regime of shallow gradients, navigation performance is fully determined by the strengths and timescales of bidirectional information transmission, without any explicit dependence on the elementary parameters of the navigator. We call these relations Behavioral Equations of State (BESTs): equalities that map information to function in a system-independent way. BESTs predict an experimentally testable data collapse for the performance of navigators with different sensing and actuation parameters. We test the validity of our theory by performing stochastic simulations of chemotaxis of the bacterium Escherichia coli, computing transfer entropies exactly with the TE-PWS algorithm. The observed performance obeys the BEST without fitting or scaling parameters. Thus, our theory identifies bidirectional information transmission between sensing and actuation as an organizing principle for navigation.

Figures

Figures reproduced from arXiv: 2607.26798 by the authors.

**Figure 1.** FIG. 1. Bidirectional information transmission drives navigation. (A) The chemoattractant concentration is the sensory input [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** FIG. 2. Performance in spatial sensing depends on all elementary parameters. (A) Schematic illustration of the minimal model [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. In the spatial-sensing model, navigation performance [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: FIG. 4. In the temporal-sensing model, navigation performance is controlled by bidirectional information transmission. (A) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: FIG. 5. BEST predicts [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

53 extracted references · 50 canonical work pages

[1]

C. E. Cressler, D. C. Metz, D. A. C. Van Oordt, and A. L. Graham, Immunological feedback loops generate parasite persistence thresholds that explain variation in infection duration, Proceedings of the Royal Society B: Biological Sciences291, 20240934 (2024)

work page 2024
[2]

Meijers, D

M. Meijers, D. Ruchnewitz, J. Eberhardt, M. Luksza, and M. L¨ assig, Population immunity predicts evolution- ary trajectories of sars-cov-2, Cell186, 5151 (2023)

work page 2023
[3]

Pezzotta and J

A. Pezzotta and J. Briscoe, Optimal control of gene regu- latory networks for morphogen-driven tissue patterning, Cell Systems14, 940 (2023)

work page 2023
[4]

O’Shaughnessy, T

L. O’Shaughnessy, T. Izawa, I. Masai, J. W. Shaevitz, and G. J. Stephens, Dynamics of dominance in interact- ing zebrafish, PRX Life2, 043006 (2024)

2024
[5]

E. Ziv, I. Nemenman, and C. H. Wiggins, Optimal signal processing in small stochastic biochemical networks, PloS one2, e1077 (2007)

work page 2007
[6]

Mehta, S

P. Mehta, S. Goyal, T. Long, B. L. Bassler, and N. S. Wingreen, Information processing and signal integration in bacterial quorum sensing, Molecular systems biology 5, MSB200979 (2009)

work page 2009
[7]

Likewise, varying the gradient strength changes the feedforward informationT FF, and thereby changes the performance as predicted by Eq. 7. This strongly sug- gests that the Behavioral Equation of State, Eq. 7, cap- tures a general principle for temporal-sensing stochastic navigators in the regime of shallow gradients and weak actuation, independent of th...

work page 2020
[8]

J. O. Dubuis, G. Tkaˇ cik, E. F. Wieschaus, T. Gregor, and W. Bialek, Positional information, in bits, Proceedings of the National Academy of Sciences110, 16301 (2013)

work page 2013

Show all 53 references

[9]

Tostevin and P

F. Tostevin and P. R. Ten Wolde, Mutual information be- tween input and output trajectories of biochemical net- works, Physical review letters102, 218101 (2009)

2009
[10]

Cheong, A

R. Cheong, A. Rhee, C. J. Wang, I. Nemenman, and A. Levchenko, Information transduction capacity of noisy biochemical signaling networks, science334, 354 (2011)

2011
[11]

Voliotis, R

M. Voliotis, R. M. Perrett, C. McWilliams, C. A. McAr- dle, and C. G. Bowsher, Information transfer by leaky, heterogeneous, protein kinase signaling systems, Pro- ceedings of the National Academy of Sciences111, E326 (2014)

2014
[12]

Selimkhanov, B

J. Selimkhanov, B. Taylor, J. Yao, A. Pilko, J. Albeck, A. Hoffmann, L. Tsimring, and R. Wollman, Accurate information transmission through dynamic biochemical signaling networks, Science346, 1370 (2014)

2014
[13]

A. A. Granados, J. M. Pietsch, S. A. Cepeda-Humerez, I. L. Farquhar, G. Tkaˇ cik, and P. S. Swain, Distributed and dynamic intracellular organization of extracellular information, Proceedings of the National Academy of Sci- ences115, 6088 (2018)

2018
[14]

A. J. Tjalma, V. Galstyan, J. Goedhart, L. Slim, N. B. Becker, and P. R. Ten Wolde, Trade-offs between cost and information in cellular prediction, Proceedings of the National Academy of Sciences120, e2303078120 (2023)

2023
[15]

H. H. Mattingly, K. Kamino, J. Ong, R. Kottou, T. Emonet, and B. B. Machta, E. coli chemosensing accu- racy is not limited by stochastic molecule arrivals, Nature Physics , 1 (2026)

2026
[16]

Mattingly, K

H. Mattingly, K. Kamino, B. Machta, and T. Emonet, Escherichia coli chemotaxis is information limited, Na- ture physics17, 1426 (2021)

2021
[17]

Marshall, Specificity of receptor tyrosine kinase sig- naling: transient versus sustained extracellular signal- regulated kinase activation, Cell80, 179 (1995)

C. Marshall, Specificity of receptor tyrosine kinase sig- naling: transient versus sustained extracellular signal- regulated kinase activation, Cell80, 179 (1995). 14

1995
[18]

J. E. Purvis and G. Lahav, Encoding and decoding cel- lular information through signaling dynamics, Cell152, 945 (2013)

2013
[19]

J. H. Levine, Y. Lin, and M. B. Elowitz, Functional roles of pulsing in genetic circuits, Science342, 1193 (2013)

2013
[20]

J. E. Segall, S. M. Block, and H. C. Berg, Temporal com- parisons in bacterial chemotaxis., Proceedings of the Na- tional Academy of Sciences83, 8987 (1986)

1986
[21]

H. C. Berg and E. M. Purcell, Physics of chemoreception, Biophysical journal20, 193 (1977)

1977
[22]

Schreiber, Measuring information transfer, Physical review letters85, 461 (2000)

T. Schreiber, Measuring information transfer, Physical review letters85, 461 (2000)

2000
[23]

Sourjik and H

V. Sourjik and H. C. Berg, Receptor sensitivity in bac- terial chemotaxis, Proceedings of the National Academy of Sciences99, 123 (2002)

2002
[24]

Cluzel, M

P. Cluzel, M. Surette, and S. Leibler, An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells, Science287, 1652 (2000)

2000
[25]

Das and P

A. Das and P. R. Ten Wolde, Exact computation of trans- fer entropy with path weight sampling, Physical Review Letters135, 107404 (2025)

2025
[26]

P. N. Devreotes and S. H. Zigmond, Chemotaxis in eu- karyotic cells: a focus on leukocytes and dictyostelium, Annual review of cell biology4, 649 (1988)

1988
[27]

Kaizu, W

K. Kaizu, W. De Ronde, J. Paijmans, K. Takahashi, F. Tostevin, and P. R. Ten Wolde, The berg-purcell limit revisited, Biophysical journal106, 976 (2014)

2014
[28]

Malaguti and P

G. Malaguti and P. R. Ten Wolde, Theory for the opti- mal detection of time-varying signals in cellular sensing systems, Elife10, e62574 (2021)

2021
[29]

T. E. Ouldridge, C. C. Govern, and P. R. ten Wolde, Thermodynamics of computational copying in biochemi- cal systems, Physical Review X7, 021004 (2017)

2017
[30]

Celani and M

A. Celani and M. Vergassola, Bacterial strategies for chemotaxis response, Proceedings of the National Academy of Sciences107, 1391 (2010)

2010
[31]

N. W. Frankel, W. Pontius, Y. S. Dufour, J. Long, L. Hernandez-Nunez, and T. Emonet, Adaptability of non-genetic diversity in bacterial chemotaxis, Elife3, e03526 (2014)

2014
[32]

Taute, S

K. Taute, S. Gude, S. Tans, and T. Shimizu, High- throughput 3d tracking of bacteria on a standard phase contrast microscope, Nature communications6, 8776 (2015)

2015
[33]

Sourjik, A

V. Sourjik, A. Vaknin, T. S. Shimizu, and H. C. Berg, In vivo measurement by fret of pathway activity in bacterial chemotaxis, inMethods in enzymology, Vol. 423 (Elsevier,
[34]

Reinhardt, G

M. Reinhardt, G. Tkaˇ cik, and P. R. t. Wolde, Ml-pws: Estimating the mutual information between experimen- tal time series using neural networks, arXiv preprint arXiv:2508.16509 (2025)

2025
[35]

E. A. Korobkova, T. Emonet, H. Park, and P. Cluzel, Hidden stochastic nature of a single bacterial motor, Physical review letters96, 058105 (2006)

2006
[36]

C. C. Govern and P. R. Ten Wolde, Optimal resource allocation in cellular sensing systems, Proceedings of the National Academy of Sciences111, 17486 (2014)

2014
[37]

N. B. Becker, A. Mugler, and P. R. Ten Wolde, Optimal prediction by cellular signaling networks, Physical review letters115, 258103 (2015)

2015
[38]

Chetrite, M

R. Chetrite, M. Rosinberg, T. Sagawa, and G. Tarjus, Information thermodynamics for interacting stochastic systems without bipartite structure, Journal of Statis- tical Mechanics: Theory and Experiment2019, 114002 (2019)

2019
[39]

J. Long, S. W. Zucker, and T. Emonet, Feedback between motion and sensation provides nonlinear boost in run- and-tumble navigation, PLoS computational biology13, e1005429 (2017)

2017
[40]

Flores, T

M. Flores, T. S. Shimizu, P. R. ten Wolde, and F. Tostevin, Signaling noise enhances chemotactic drift of e. coli, Physical review letters109, 148101 (2012)

2012
[41]

Moor and C

A.-L. Moor and C. Zechner, Dynamic information trans- fer in stochastic biochemical networks, Physical Review Research5, 013032 (2023)

2023
[42]

K. J. ˚Astr¨ om,Introduction to stochastic control theory (Courier Corporation, 2012)

2012
[43]

T. S. Shimizu, Y. Tu, and H. C. Berg, A modular gradient-sensing network for chemotaxis in escherichia coli revealed by responses to time-varying stimuli, Molec- ular systems biology6, MSB201037 (2010)

2010
[44]

K. S. Chen, M. P. Leighton, D. A. Clark, and T. Emonet, A behavior-environment information loop drives sensory navigation, arXiv preprint arXiv:2607.26295 (2026)

2026 arXiv
[45]

J. R. Taylor and R. Stocker, Trade-offs of chemotactic foraging in turbulent water, Science338, 675 (2012)

2012
[46]

de Anna, A

P. de Anna, A. A. Pahlavan, Y. Yawata, R. Stocker, and R. Juanes, Chemotaxis under flow disorder shapes mi- crobial dispersion in porous media, Nature Physics17, 68 (2021)

2021
[47]

Saragosti, V

J. Saragosti, V. Calvez, N. Bournaveas, B. Perthame, A. Buguin, and P. Silberzan, Directional persistence of chemotactic bacteria in a traveling concentration wave, Proceedings of the National Academy of Sciences108, 16235 (2011)

2011
[48]

I. V. Girsanov, On transforming a certain class of stochas- tic processes by absolutely continuous substitution of measures, Theory of Probability & Its Applications5, 285 (1960)

1960
[49]

A. H. Jazwinski,Stochastic processes and filtering theory (Courier Corporation, 2007)

2007
[50]

M. W. Sneddon, W. Pontius, and T. Emonet, Stochastic coordination of multiple actuators reduces latency and improves chemotactic response in bacteria, Proceedings of the National Academy of Sciences109, 805 (2012)

2012
[51]

H. C. Berg and D. A. Brown, Chemotaxis in escherichia coli analysed by three-dimensional tracking, nature239, 500 (1972)

1972
[52]

Saragosti, P

J. Saragosti, P. Silberzan, and A. Buguin, Modeling e. coli tumbles by rotational diffusion. implications for chemotaxis, PloS one7, e35412 (2012)

2012
[53]

Taheri-Araghi, S

S. Taheri-Araghi, S. Bradde, J. T. Sauls, N. S. Hill, P. A. Levin, J. Paulsson, M. Vergassola, and S. Jun, Cell-size control and homeostasis in bacteria, Current biology25, 385 (2015)

2015

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [1]

C. E. Cressler, D. C. Metz, D. A. C. Van Oordt, and A. L. Graham, Immunological feedback loops generate parasite persistence thresholds that explain variation in infection duration, Proceedings of the Royal Society B: Biological Sciences291, 20240934 (2024)

work page 2024

[2] [2]

Meijers, D

M. Meijers, D. Ruchnewitz, J. Eberhardt, M. Luksza, and M. L¨ assig, Population immunity predicts evolution- ary trajectories of sars-cov-2, Cell186, 5151 (2023)

work page 2023

[3] [3]

Pezzotta and J

A. Pezzotta and J. Briscoe, Optimal control of gene regu- latory networks for morphogen-driven tissue patterning, Cell Systems14, 940 (2023)

work page 2023

[4] [4]

O’Shaughnessy, T

L. O’Shaughnessy, T. Izawa, I. Masai, J. W. Shaevitz, and G. J. Stephens, Dynamics of dominance in interact- ing zebrafish, PRX Life2, 043006 (2024)

2024

[5] [5]

E. Ziv, I. Nemenman, and C. H. Wiggins, Optimal signal processing in small stochastic biochemical networks, PloS one2, e1077 (2007)

work page 2007

[6] [6]

Mehta, S

P. Mehta, S. Goyal, T. Long, B. L. Bassler, and N. S. Wingreen, Information processing and signal integration in bacterial quorum sensing, Molecular systems biology 5, MSB200979 (2009)

work page 2009

[7] [7]

Likewise, varying the gradient strength changes the feedforward informationT FF, and thereby changes the performance as predicted by Eq. 7. This strongly sug- gests that the Behavioral Equation of State, Eq. 7, cap- tures a general principle for temporal-sensing stochastic navigators in the regime of shallow gradients and weak actuation, independent of th...

work page 2020

[8] [8]

J. O. Dubuis, G. Tkaˇ cik, E. F. Wieschaus, T. Gregor, and W. Bialek, Positional information, in bits, Proceedings of the National Academy of Sciences110, 16301 (2013)

work page 2013