TY - JOUR AB - 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. AU - Mlynarski, Wiktor F AU - Hledik, Michal AU - Sokolowski, Thomas R AU - Tkačik, Gašper ID - 7553 IS - 7 JF - Neuron TI - Statistical analysis and optimality of neural systems VL - 109 ER - TY - JOUR AB - 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. AU - Sokolowski, Thomas R AU - Paijmans, Joris AU - Bossen, Laurens AU - Miedema, Thomas AU - Wehrens, Martijn AU - Becker, Nils B. AU - Kaizu, Kazunari AU - Takahashi, Koichi AU - Dogterom, Marileen AU - ten Wolde, Pieter Rein ID - 7422 IS - 5 JF - The Journal of Chemical Physics SN - 0021-9606 TI - eGFRD in all dimensions VL - 150 ER - TY - CONF AB - 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. AU - Hledik, Michal AU - Sokolowski, Thomas R AU - Tkačik, Gašper ID - 7606 SN - 9781538669006 T2 - IEEE Information Theory Workshop, ITW 2019 TI - A tight upper bound on mutual information ER - TY - JOUR AB - 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. AU - Sokolowski, Thomas R AU - Walczak, Aleksandra AU - Bialek, William AU - Tkacik, Gasper ID - 1242 IS - 2 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Extending the dynamic range of transcription factor action by translational regulation VL - 93 ER - TY - JOUR AB - 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. AU - Recouvreux, Pierre AU - Sokolowski, Thomas R AU - Grammoustianou, Aristea AU - Tenwolde, Pieter AU - Dogterom, Marileen ID - 1244 IS - 7 JF - PNAS TI - Chimera proteins with affinity for membranes and microtubule tips polarize in the membrane of fission yeast cells VL - 113 ER - TY - JOUR AB - 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. AU - Sokolowski, Thomas R AU - Tkacik, Gasper ID - 1940 IS - 6 JF - Physical Review E Statistical Nonlinear and Soft Matter Physics TI - Optimizing information flow in small genetic networks. IV. Spatial coupling VL - 91 ER -