--- _id: '7553' abstract: - lang: eng text: Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximum-entropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We demonstrate the applicability of our framework using data from the visual cortex, and argue that the flexibility it affords is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems. acknowledgement: The authors thank Dario Ringach for providing the V1 receptive fields and Olivier Marre for providing the retinal receptive fields. W.M. was funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 754411. M.H. was funded in part by Human Frontiers Science grant no. HFSP RGP0032/2018. article_processing_charge: No author: - first_name: Wiktor F full_name: Mlynarski, Wiktor F id: 358A453A-F248-11E8-B48F-1D18A9856A87 last_name: Mlynarski - first_name: Michal full_name: Hledik, Michal id: 4171253A-F248-11E8-B48F-1D18A9856A87 last_name: Hledik - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Gašper full_name: Tkačik, Gašper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkačik orcid: 0000-0002-6699-1455 citation: ama: Mlynarski WF, Hledik M, Sokolowski TR, Tkačik G. Statistical analysis and optimality of neural systems. Neuron. 2021;109(7):1227-1241.e5. doi:10.1016/j.neuron.2021.01.020 apa: Mlynarski, W. F., Hledik, M., Sokolowski, T. R., & Tkačik, G. (2021). Statistical analysis and optimality of neural systems. Neuron. Cell Press. https://doi.org/10.1016/j.neuron.2021.01.020 chicago: Mlynarski, Wiktor F, Michal Hledik, Thomas R Sokolowski, and Gašper Tkačik. “Statistical Analysis and Optimality of Neural Systems.” Neuron. Cell Press, 2021. https://doi.org/10.1016/j.neuron.2021.01.020. ieee: W. F. Mlynarski, M. Hledik, T. R. Sokolowski, and G. Tkačik, “Statistical analysis and optimality of neural systems,” Neuron, vol. 109, no. 7. Cell Press, p. 1227–1241.e5, 2021. ista: Mlynarski WF, Hledik M, Sokolowski TR, Tkačik G. 2021. Statistical analysis and optimality of neural systems. Neuron. 109(7), 1227–1241.e5. mla: Mlynarski, Wiktor F., et al. “Statistical Analysis and Optimality of Neural Systems.” Neuron, vol. 109, no. 7, Cell Press, 2021, p. 1227–1241.e5, doi:10.1016/j.neuron.2021.01.020. short: W.F. Mlynarski, M. Hledik, T.R. Sokolowski, G. Tkačik, Neuron 109 (2021) 1227–1241.e5. date_created: 2020-02-28T11:00:12Z date_published: 2021-04-07T00:00:00Z date_updated: 2024-03-06T14:22:51Z day: '07' department: - _id: GaTk doi: 10.1016/j.neuron.2021.01.020 ec_funded: 1 external_id: isi: - '000637809600006' intvolume: ' 109' isi: 1 issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://doi.org/10.1101/848374 month: '04' oa: 1 oa_version: Preprint page: 1227-1241.e5 project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Neuron publication_status: published publisher: Cell Press quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/can-evolution-be-predicted/ record: - id: '15020' relation: dissertation_contains status: public scopus_import: '1' status: public title: Statistical analysis and optimality of neural systems type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 109 year: '2021' ... --- _id: '7422' abstract: - lang: eng text: Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green’s Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green’s functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present “eGFRD2,” a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions. article_number: '054108' article_processing_charge: No article_type: original author: - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Joris full_name: Paijmans, Joris last_name: Paijmans - first_name: Laurens full_name: Bossen, Laurens last_name: Bossen - first_name: Thomas full_name: Miedema, Thomas last_name: Miedema - first_name: Martijn full_name: Wehrens, Martijn last_name: Wehrens - first_name: Nils B. full_name: Becker, Nils B. last_name: Becker - first_name: Kazunari full_name: Kaizu, Kazunari last_name: Kaizu - first_name: Koichi full_name: Takahashi, Koichi last_name: Takahashi - first_name: Marileen full_name: Dogterom, Marileen last_name: Dogterom - first_name: Pieter Rein full_name: ten Wolde, Pieter Rein last_name: ten Wolde citation: ama: Sokolowski TR, Paijmans J, Bossen L, et al. eGFRD in all dimensions. The Journal of Chemical Physics. 2019;150(5). doi:10.1063/1.5064867 apa: Sokolowski, T. R., Paijmans, J., Bossen, L., Miedema, T., Wehrens, M., Becker, N. B., … ten Wolde, P. R. (2019). eGFRD in all dimensions. The Journal of Chemical Physics. AIP Publishing. https://doi.org/10.1063/1.5064867 chicago: Sokolowski, Thomas R, Joris Paijmans, Laurens Bossen, Thomas Miedema, Martijn Wehrens, Nils B. Becker, Kazunari Kaizu, Koichi Takahashi, Marileen Dogterom, and Pieter Rein ten Wolde. “EGFRD in All Dimensions.” The Journal of Chemical Physics. AIP Publishing, 2019. https://doi.org/10.1063/1.5064867. ieee: T. R. Sokolowski et al., “eGFRD in all dimensions,” The Journal of Chemical Physics, vol. 150, no. 5. AIP Publishing, 2019. ista: Sokolowski TR, Paijmans J, Bossen L, Miedema T, Wehrens M, Becker NB, Kaizu K, Takahashi K, Dogterom M, ten Wolde PR. 2019. eGFRD in all dimensions. The Journal of Chemical Physics. 150(5), 054108. mla: Sokolowski, Thomas R., et al. “EGFRD in All Dimensions.” The Journal of Chemical Physics, vol. 150, no. 5, 054108, AIP Publishing, 2019, doi:10.1063/1.5064867. short: T.R. Sokolowski, J. Paijmans, L. Bossen, T. Miedema, M. Wehrens, N.B. Becker, K. Kaizu, K. Takahashi, M. Dogterom, P.R. ten Wolde, The Journal of Chemical Physics 150 (2019). date_created: 2020-01-30T10:34:36Z date_published: 2019-02-07T00:00:00Z date_updated: 2023-09-06T14:59:28Z day: '07' department: - _id: GaTk doi: 10.1063/1.5064867 external_id: arxiv: - '1708.09364' isi: - '000458109300009' intvolume: ' 150' isi: 1 issue: '5' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1708.09364 month: '02' oa: 1 oa_version: Preprint publication: The Journal of Chemical Physics publication_identifier: eissn: - 1089-7690 issn: - 0021-9606 publication_status: published publisher: AIP Publishing quality_controlled: '1' status: public title: eGFRD in all dimensions type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 150 year: '2019' ... --- _id: '7606' abstract: - lang: eng text: We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and maximum a posteriori decodes (most probable signals given channel output). As part of our derivation, we describe the key properties of the distribution of signals, channel outputs and decodes, that minimizes equivocation and maximizes mutual information. This work addresses a problem in data analysis, where mutual information between signals and decodes is sometimes used to lower bound the mutual information between signals and channel outputs. Our result provides a corresponding upper bound. article_number: '8989292' article_processing_charge: No author: - first_name: Michal full_name: Hledik, Michal id: 4171253A-F248-11E8-B48F-1D18A9856A87 last_name: Hledik - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Gašper full_name: Tkačik, Gašper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkačik orcid: 0000-0002-6699-1455 citation: ama: 'Hledik M, Sokolowski TR, Tkačik G. A tight upper bound on mutual information. In: IEEE Information Theory Workshop, ITW 2019. IEEE; 2019. doi:10.1109/ITW44776.2019.8989292' apa: 'Hledik, M., Sokolowski, T. R., & Tkačik, G. (2019). A tight upper bound on mutual information. In IEEE Information Theory Workshop, ITW 2019. Visby, Sweden: IEEE. https://doi.org/10.1109/ITW44776.2019.8989292' chicago: Hledik, Michal, Thomas R Sokolowski, and Gašper Tkačik. “A Tight Upper Bound on Mutual Information.” In IEEE Information Theory Workshop, ITW 2019. IEEE, 2019. https://doi.org/10.1109/ITW44776.2019.8989292. ieee: M. Hledik, T. R. Sokolowski, and G. Tkačik, “A tight upper bound on mutual information,” in IEEE Information Theory Workshop, ITW 2019, Visby, Sweden, 2019. ista: Hledik M, Sokolowski TR, Tkačik G. 2019. A tight upper bound on mutual information. IEEE Information Theory Workshop, ITW 2019. Information Theory Workshop, 8989292. mla: Hledik, Michal, et al. “A Tight Upper Bound on Mutual Information.” IEEE Information Theory Workshop, ITW 2019, 8989292, IEEE, 2019, doi:10.1109/ITW44776.2019.8989292. short: M. Hledik, T.R. Sokolowski, G. Tkačik, in:, IEEE Information Theory Workshop, ITW 2019, IEEE, 2019. conference: end_date: 2019-08-28 location: Visby, Sweden name: Information Theory Workshop start_date: 2019-08-25 date_created: 2020-03-22T23:00:47Z date_published: 2019-08-01T00:00:00Z date_updated: 2024-03-06T14:22:51Z day: '01' department: - _id: GaTk doi: 10.1109/ITW44776.2019.8989292 ec_funded: 1 external_id: arxiv: - '1812.01475' isi: - '000540384500015' isi: 1 language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1812.01475 month: '08' oa: 1 oa_version: Preprint project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: IEEE Information Theory Workshop, ITW 2019 publication_identifier: isbn: - '9781538669006' publication_status: published publisher: IEEE quality_controlled: '1' related_material: record: - id: '15020' relation: dissertation_contains status: public scopus_import: '1' status: public title: A tight upper bound on mutual information type: conference user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 year: '2019' ... --- _id: '1242' abstract: - lang: eng text: A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other regulatory proteins. Intuitively, each mRNA molecule acts as an independent sensor of the input concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression. acknowledgement: "We thank T. Gregor, A. Prochaintz, and others for\r\nhelpful discussions. This work was supported in part by\r\nGrants No. PHY-1305525 and No. CCF-0939370 from the\r\nUS National Science Foundation and by the W.M. Keck\r\nFoundation. A.M.W. acknowledges the support by European\r\nResearch Council (ERC) Grant No. MCCIG PCIG10–GA-\r\n2011–303561. G.T. and T.R.S. were supported by Austrian\r\nScience Fund (FWF) Grant No. P28844S." article_number: '022404' author: - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Aleksandra full_name: Walczak, Aleksandra last_name: Walczak - first_name: William full_name: Bialek, William last_name: Bialek - first_name: Gasper full_name: Tkacik, Gasper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkacik orcid: 0000-0002-6699-1455 citation: ama: Sokolowski TR, Walczak A, Bialek W, Tkačik G. Extending the dynamic range of transcription factor action by translational regulation. Physical Review E Statistical Nonlinear and Soft Matter Physics. 2016;93(2). doi:10.1103/PhysRevE.93.022404 apa: Sokolowski, T. R., Walczak, A., Bialek, W., & Tkačik, G. (2016). Extending the dynamic range of transcription factor action by translational regulation. Physical Review E Statistical Nonlinear and Soft Matter Physics. American Institute of Physics. https://doi.org/10.1103/PhysRevE.93.022404 chicago: Sokolowski, Thomas R, Aleksandra Walczak, William Bialek, and Gašper Tkačik. “Extending the Dynamic Range of Transcription Factor Action by Translational Regulation.” Physical Review E Statistical Nonlinear and Soft Matter Physics. American Institute of Physics, 2016. https://doi.org/10.1103/PhysRevE.93.022404. ieee: T. R. Sokolowski, A. Walczak, W. Bialek, and G. Tkačik, “Extending the dynamic range of transcription factor action by translational regulation,” Physical Review E Statistical Nonlinear and Soft Matter Physics, vol. 93, no. 2. American Institute of Physics, 2016. ista: Sokolowski TR, Walczak A, Bialek W, Tkačik G. 2016. Extending the dynamic range of transcription factor action by translational regulation. Physical Review E Statistical Nonlinear and Soft Matter Physics. 93(2), 022404. mla: Sokolowski, Thomas R., et al. “Extending the Dynamic Range of Transcription Factor Action by Translational Regulation.” Physical Review E Statistical Nonlinear and Soft Matter Physics, vol. 93, no. 2, 022404, American Institute of Physics, 2016, doi:10.1103/PhysRevE.93.022404. short: T.R. Sokolowski, A. Walczak, W. Bialek, G. Tkačik, Physical Review E Statistical Nonlinear and Soft Matter Physics 93 (2016). date_created: 2018-12-11T11:50:54Z date_published: 2016-02-04T00:00:00Z date_updated: 2021-01-12T06:49:20Z day: '04' department: - _id: GaTk doi: 10.1103/PhysRevE.93.022404 intvolume: ' 93' issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1507.02562 month: '02' oa: 1 oa_version: Preprint project: - _id: 254E9036-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P28844-B27 name: Biophysics of information processing in gene regulation publication: Physical Review E Statistical Nonlinear and Soft Matter Physics publication_status: published publisher: American Institute of Physics publist_id: '6088' quality_controlled: '1' scopus_import: 1 status: public title: Extending the dynamic range of transcription factor action by translational regulation type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 93 year: '2016' ... --- _id: '1244' abstract: - lang: eng text: Cell polarity refers to a functional spatial organization of proteins that is crucial for the control of essential cellular processes such as growth and division. To establish polarity, cells rely on elaborate regulation networks that control the distribution of proteins at the cell membrane. In fission yeast cells, a microtubule-dependent network has been identified that polarizes the distribution of signaling proteins that restricts growth to cell ends and targets the cytokinetic machinery to the middle of the cell. Although many molecular components have been shown to play a role in this network, it remains unknown which molecular functionalities are minimally required to establish a polarized protein distribution in this system. Here we show that a membrane-binding protein fragment, which distributes homogeneously in wild-type fission yeast cells, can be made to concentrate at cell ends by attaching it to a cytoplasmic microtubule end-binding protein. This concentration results in a polarized pattern of chimera proteins with a spatial extension that is very reminiscent of natural polarity patterns in fission yeast. However, chimera levels fluctuate in response to microtubule dynamics, and disruption of microtubules leads to disappearance of the pattern. Numerical simulations confirm that the combined functionality of membrane anchoring and microtubule tip affinity is in principle sufficient to create polarized patterns. Our chimera protein may thus represent a simple molecular functionality that is able to polarize the membrane, onto which additional layers of molecular complexity may be built to provide the temporal robustness that is typical of natural polarity patterns. acknowledgement: "We thank Sophie Martin, Ken Sawin, Stephen Huisman,\r\nand Damian Brunner for strains; Julianne\r\nTeapal, Marcel Janson, Sergio Rincon,\r\nand Phong Tran for technical assistance; Andrew Mugler and Bela Mulder for\r\ndiscussions; and Sander Tans, Phong Tran,\r\nand Anne Paoletti for critical reading\r\nof the manuscript. This work is part of the research program of the\r\n“\r\nStichting\r\nvoor Fundamenteel Onderzoek de Materie,\r\n”\r\nwhich is financially supported by\r\nthe\r\n“\r\nNederlandse organisatie voor Wete\r\nnschappelijk Onderzoek (NWO).\r\n”" author: - first_name: Pierre full_name: Recouvreux, Pierre last_name: Recouvreux - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Aristea full_name: Grammoustianou, Aristea last_name: Grammoustianou - first_name: Pieter full_name: Tenwolde, Pieter last_name: Tenwolde - first_name: Marileen full_name: Dogterom, Marileen last_name: Dogterom citation: ama: Recouvreux P, Sokolowski TR, Grammoustianou A, Tenwolde P, Dogterom M. Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells. PNAS. 2016;113(7):1811-1816. doi:10.1073/pnas.1419248113 apa: Recouvreux, P., Sokolowski, T. R., Grammoustianou, A., Tenwolde, P., & Dogterom, M. (2016). Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1419248113 chicago: Recouvreux, Pierre, Thomas R Sokolowski, Aristea Grammoustianou, Pieter Tenwolde, and Marileen Dogterom. “Chimera Proteins with Affinity for Membranes and Microtubule Tips Polarize in the Membrane of Fission Yeast Cells.” PNAS. National Academy of Sciences, 2016. https://doi.org/10.1073/pnas.1419248113. ieee: P. Recouvreux, T. R. Sokolowski, A. Grammoustianou, P. Tenwolde, and M. Dogterom, “Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells,” PNAS, vol. 113, no. 7. National Academy of Sciences, pp. 1811–1816, 2016. ista: Recouvreux P, Sokolowski TR, Grammoustianou A, Tenwolde P, Dogterom M. 2016. Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells. PNAS. 113(7), 1811–1816. mla: Recouvreux, Pierre, et al. “Chimera Proteins with Affinity for Membranes and Microtubule Tips Polarize in the Membrane of Fission Yeast Cells.” PNAS, vol. 113, no. 7, National Academy of Sciences, 2016, pp. 1811–16, doi:10.1073/pnas.1419248113. short: P. Recouvreux, T.R. Sokolowski, A. Grammoustianou, P. Tenwolde, M. Dogterom, PNAS 113 (2016) 1811–1816. date_created: 2018-12-11T11:50:55Z date_published: 2016-02-16T00:00:00Z date_updated: 2021-01-12T06:49:21Z day: '16' department: - _id: GaTk doi: 10.1073/pnas.1419248113 intvolume: ' 113' issue: '7' language: - iso: eng main_file_link: - open_access: '1' url: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4763754/ month: '02' oa: 1 oa_version: Submitted Version page: 1811 - 1816 publication: PNAS publication_status: published publisher: National Academy of Sciences publist_id: '6085' quality_controlled: '1' scopus_import: 1 status: public title: Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 113 year: '2016' ... --- _id: '1940' abstract: - lang: eng text: We typically think of cells as responding to external signals independently by regulating their gene expression levels, yet they often locally exchange information and coordinate. Can such spatial coupling be of benefit for conveying signals subject to gene regulatory noise? Here we extend our information-theoretic framework for gene regulation to spatially extended systems. As an example, we consider a lattice of nuclei responding to a concentration field of a transcriptional regulator (the "input") by expressing a single diffusible target gene. When input concentrations are low, diffusive coupling markedly improves information transmission; optimal gene activation functions also systematically change. A qualitatively new regulatory strategy emerges where individual cells respond to the input in a nearly step-like fashion that is subsequently averaged out by strong diffusion. While motivated by early patterning events in the Drosophila embryo, our framework is generically applicable to spatially coupled stochastic gene expression models. article_number: '062710' author: - first_name: Thomas R full_name: Sokolowski, Thomas R id: 3E999752-F248-11E8-B48F-1D18A9856A87 last_name: Sokolowski orcid: 0000-0002-1287-3779 - first_name: Gasper full_name: Tkacik, Gasper id: 3D494DCA-F248-11E8-B48F-1D18A9856A87 last_name: Tkacik orcid: 0000-0002-6699-1455 citation: ama: Sokolowski TR, Tkačik G. Optimizing information flow in small genetic networks. IV. Spatial coupling. Physical Review E Statistical Nonlinear and Soft Matter Physics. 2015;91(6). doi:10.1103/PhysRevE.91.062710 apa: Sokolowski, T. R., & Tkačik, G. (2015). Optimizing information flow in small genetic networks. IV. Spatial coupling. Physical Review E Statistical Nonlinear and Soft Matter Physics. American Institute of Physics. https://doi.org/10.1103/PhysRevE.91.062710 chicago: Sokolowski, Thomas R, and Gašper Tkačik. “Optimizing Information Flow in Small Genetic Networks. IV. Spatial Coupling.” Physical Review E Statistical Nonlinear and Soft Matter Physics. American Institute of Physics, 2015. https://doi.org/10.1103/PhysRevE.91.062710. ieee: T. R. Sokolowski and G. Tkačik, “Optimizing information flow in small genetic networks. IV. Spatial coupling,” Physical Review E Statistical Nonlinear and Soft Matter Physics, vol. 91, no. 6. American Institute of Physics, 2015. ista: Sokolowski TR, Tkačik G. 2015. Optimizing information flow in small genetic networks. IV. Spatial coupling. Physical Review E Statistical Nonlinear and Soft Matter Physics. 91(6), 062710. mla: Sokolowski, Thomas R., and Gašper Tkačik. “Optimizing Information Flow in Small Genetic Networks. IV. Spatial Coupling.” Physical Review E Statistical Nonlinear and Soft Matter Physics, vol. 91, no. 6, 062710, American Institute of Physics, 2015, doi:10.1103/PhysRevE.91.062710. short: T.R. Sokolowski, G. Tkačik, Physical Review E Statistical Nonlinear and Soft Matter Physics 91 (2015). date_created: 2018-12-11T11:54:49Z date_published: 2015-06-15T00:00:00Z date_updated: 2021-01-12T06:54:13Z day: '15' department: - _id: GaTk doi: 10.1103/PhysRevE.91.062710 intvolume: ' 91' issue: '6' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1501.04015 month: '06' oa: 1 oa_version: Preprint publication: Physical Review E Statistical Nonlinear and Soft Matter Physics publication_status: published publisher: American Institute of Physics publist_id: '5145' quality_controlled: '1' scopus_import: 1 status: public title: Optimizing information flow in small genetic networks. IV. Spatial coupling type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 91 year: '2015' ...