TY - THES AB - Synthesis of proteins – translation – is a fundamental process of life. Quantitative studies anchor translation into the context of bacterial physiology and reveal several mathematical relationships, called “growth laws,” which capture physiological feedbacks between protein synthesis and cell growth. Growth laws describe the dependency of the ribosome abundance as a function of growth rate, which can change depending on the growth conditions. Perturbations of translation reveal that bacteria employ a compensatory strategy in which the reduced translation capability results in increased expression of the translation machinery. Perturbations of translation are achieved in various ways; clinically interesting is the application of translation-targeting antibiotics – translation inhibitors. The antibiotic effects on bacterial physiology are often poorly understood. Bacterial responses to two or more simultaneously applied antibiotics are even more puzzling. The combined antibiotic effect determines the type of drug interaction, which ranges from synergy (the effect is stronger than expected) to antagonism (the effect is weaker) and suppression (one of the drugs loses its potency). In the first part of this work, we systematically measure the pairwise interaction network for translation inhibitors that interfere with different steps in translation. We find that the interactions are surprisingly diverse and tend to be more antagonistic. To explore the underlying mechanisms, we begin with a minimal biophysical model of combined antibiotic action. We base this model on the kinetics of antibiotic uptake and binding together with the physiological response described by the growth laws. The biophysical model explains some drug interactions, but not all; it specifically fails to predict suppression. In the second part of this work, we hypothesize that elusive suppressive drug interactions result from the interplay between ribosomes halted in different stages of translation. To elucidate this putative mechanism of drug interactions between translation inhibitors, we generate translation bottlenecks genetically using in- ducible control of translation factors that regulate well-defined translation cycle steps. These perturbations accurately mimic antibiotic action and drug interactions, supporting that the interplay of different translation bottlenecks partially causes these interactions. We extend this approach by varying two translation bottlenecks simultaneously. This approach reveals the suppression of translocation inhibition by inhibited translation. We rationalize this effect by modeling dense traffic of ribosomes that move on transcripts in a translation factor-mediated manner. This model predicts a dissolution of traffic jams caused by inhibited translocation when the density of ribosome traffic is reduced by lowered initiation. We base this model on the growth laws and quantitative relationships between different translation and growth parameters. In the final part of this work, we describe a set of tools aimed at quantification of physiological and translation parameters. We further develop a simple model that directly connects the abundance of a translation factor with the growth rate, which allows us to extract physiological parameters describing initiation. We demonstrate the development of tools for measuring translation rate. This thesis showcases how a combination of high-throughput growth rate mea- surements, genetics, and modeling can reveal mechanisms of drug interactions. Furthermore, by a gradual transition from combinations of antibiotics to precise genetic interventions, we demonstrated the equivalency between genetic and chemi- cal perturbations of translation. These findings tile the path for quantitative studies of antibiotic combinations and illustrate future approaches towards the quantitative description of translation. AU - Kavcic, Bor ID - 8657 SN - 2663-337X TI - Perturbations of protein synthesis: from antibiotics to genetics and physiology ER - TY - JOUR AB - Antibiotics that interfere with translation, when combined, interact in diverse and difficult-to-predict ways. Here, we explain these interactions by “translation bottlenecks”: points in the translation cycle where antibiotics block ribosomal progression. To elucidate the underlying mechanisms of drug interactions between translation inhibitors, we generate translation bottlenecks genetically using inducible control of translation factors that regulate well-defined translation cycle steps. These perturbations accurately mimic antibiotic action and drug interactions, supporting that the interplay of different translation bottlenecks causes these interactions. We further show that growth laws, combined with drug uptake and binding kinetics, enable the direct prediction of a large fraction of observed interactions, yet fail to predict suppression. However, varying two translation bottlenecks simultaneously supports that dense traffic of ribosomes and competition for translation factors account for the previously unexplained suppression. These results highlight the importance of “continuous epistasis” in bacterial physiology. AU - Kavcic, Bor AU - Tkačik, Gašper AU - Bollenbach, Tobias ID - 8250 JF - Nature Communications SN - 2041-1723 TI - Mechanisms of drug interactions between translation-inhibiting antibiotics VL - 11 ER - TY - GEN AB - Combining drugs can improve the efficacy of treatments. However, predicting the effect of drug combinations is still challenging. The combined potency of drugs determines the drug interaction, which is classified as synergistic, additive, antagonistic, or suppressive. While probabilistic, non-mechanistic models exist, there is currently no biophysical model that can predict antibiotic interactions. Here, we present a physiologically relevant model of the combined action of antibiotics that inhibit protein synthesis by targeting the ribosome. This model captures the kinetics of antibiotic binding and transport, and uses bacterial growth laws to predict growth in the presence of antibiotic combinations. We find that this biophysical model can produce all drug interaction types except suppression. We show analytically that antibiotics which cannot bind to the ribosome simultaneously generally act as substitutes for one another, leading to additive drug interactions. Previously proposed null expectations for higher-order drug interactions follow as a limiting case of our model. We further extend the model to include the effects of direct physical or allosteric interactions between individual drugs on the ribosome. Notably, such direct interactions profoundly change the combined drug effect, depending on the kinetic parameters of the drugs used. The model makes additional predictions for the effects of resistance genes on drug interactions and for interactions between ribosome-targeting antibiotics and antibiotics with other targets. These findings enhance our understanding of the interplay between drug action and cell physiology and are a key step toward a general framework for predicting drug interactions. AU - Kavcic, Bor AU - Tkačik, Gašper AU - Bollenbach, Tobias ID - 7673 T2 - bioRxiv TI - A minimal biophysical model of combined antibiotic action ER - TY - JOUR AB - Organisms cope with change by taking advantage of transcriptional regulators. However, when faced with rare environments, the evolution of transcriptional regulators and their promoters may be too slow. Here, we investigate whether the intrinsic instability of gene duplication and amplification provides a generic alternative to canonical gene regulation. Using real-time monitoring of gene-copy-number mutations in Escherichia coli, we show that gene duplications and amplifications enable adaptation to fluctuating environments by rapidly generating copy-number and, therefore, expression-level polymorphisms. This amplification-mediated gene expression tuning (AMGET) occurs on timescales that are similar to canonical gene regulation and can respond to rapid environmental changes. Mathematical modelling shows that amplifications also tune gene expression in stochastic environments in which transcription-factor-based schemes are hard to evolve or maintain. The fleeting nature of gene amplifications gives rise to a generic population-level mechanism that relies on genetic heterogeneity to rapidly tune the expression of any gene, without leaving any genomic signature. AU - Tomanek, Isabella AU - Grah, Rok AU - Lagator, M. AU - Andersson, A. M. C. AU - Bollback, Jonathan P AU - Tkačik, Gašper AU - Guet, Calin C ID - 7652 IS - 4 JF - Nature Ecology & Evolution SN - 2397-334X TI - Gene amplification as a form of population-level gene expression regulation VL - 4 ER - TY - GEN AB - There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but interacting sites are embedded in a liquid droplet of proteins which condenses out of the surrounding solution. We argue that droplet-mediated interactions can account for crucial features of gene regulation only if the droplet is poised at a non-generic point in its phase diagram. We explore a minimal model that embodies this idea, show that this model has a natural mechanism for self-tuning, and suggest direct experimental tests. AU - Bialek, William AU - Gregor, Thomas AU - Tkačik, Gašper ID - 7552 T2 - arXiv:1912.08579 TI - Action at a distance in transcriptional regulation ER - TY - JOUR AB - In developing organisms, spatially prescribed cell identities are thought to be determined by the expression levels of multiple genes. Quantitative tests of this idea, however, require a theoretical framework capable of exposing the rules and precision of cell specification over developmental time. We use the gap gene network in the early fly embryo as an example to show how expression levels of the four gap genes can be jointly decoded into an optimal specification of position with 1% accuracy. The decoder correctly predicts, with no free parameters, the dynamics of pair-rule expression patterns at different developmental time points and in various mutant backgrounds. Precise cellular identities are thus available at the earliest stages of development, contrasting the prevailing view of positional information being slowly refined across successive layers of the patterning network. Our results suggest that developmental enhancers closely approximate a mathematically optimal decoding strategy. AU - Petkova, Mariela D. AU - Tkacik, Gasper AU - Bialek, William AU - Wieschaus, Eric F. AU - Gregor, Thomas ID - 5945 IS - 4 JF - Cell TI - Optimal decoding of cellular identities in a genetic network VL - 176 ER - TY - JOUR AB - In this article it is shown that large systems with many interacting units endowing multiple phases display self-oscillations in the presence of linear feedback between the control and order parameters, where an Andronov–Hopf bifurcation takes over the phase transition. This is simply illustrated through the mean field Landau theory whose feedback dynamics turn out to be described by the Van der Pol equation and it is then validated for the fully connected Ising model following heat bath dynamics. Despite its simplicity, this theory accounts potentially for a rich range of phenomena: here it is applied to describe in a stylized way (i) excess demand-price cycles due to strong herding in a simple agent-based market model; (ii) congestion waves in queuing networks triggered by user feedback to delays in overloaded conditions; and (iii) metabolic network oscillations resulting from cell growth control in a bistable phenotypic landscape. AU - De Martino, Daniele ID - 6049 IS - 4 JF - Journal of Physics A: Mathematical and Theoretical TI - Feedback-induced self-oscillations in large interacting systems subjected to phase transitions VL - 52 ER - TY - JOUR AB - Sudden stress often triggers diverse, temporally structured gene expression responses in microbes, but it is largely unknown how variable in time such responses are and if genes respond in the same temporal order in every single cell. Here, we quantified timing variability of individual promoters responding to sublethal antibiotic stress using fluorescent reporters, microfluidics, and time‐lapse microscopy. We identified lower and upper bounds that put definite constraints on timing variability, which varies strongly among promoters and conditions. Timing variability can be interpreted using results from statistical kinetics, which enable us to estimate the number of rate‐limiting molecular steps underlying different responses. We found that just a few critical steps control some responses while others rely on dozens of steps. To probe connections between different stress responses, we then tracked the temporal order and response time correlations of promoter pairs in individual cells. Our results support that, when bacteria are exposed to the antibiotic nitrofurantoin, the ensuing oxidative stress and SOS responses are part of the same causal chain of molecular events. In contrast, under trimethoprim, the acid stress response and the SOS response are part of different chains of events running in parallel. Our approach reveals fundamental constraints on gene expression timing and provides new insights into the molecular events that underlie the timing of stress responses. AU - Mitosch, Karin AU - Rieckh, Georg AU - Bollenbach, Mark Tobias ID - 6046 IS - 2 JF - Molecular systems biology TI - Temporal order and precision of complex stress responses in individual bacteria VL - 15 ER - TY - JOUR AB - Mathematical models have been used successfully at diverse scales of biological organization, ranging from ecology and population dynamics to stochastic reaction events occurring between individual molecules in single cells. Generally, many biological processes unfold across multiple scales, with mutations being the best studied example of how stochasticity at the molecular scale can influence outcomes at the population scale. In many other contexts, however, an analogous link between micro- and macro-scale remains elusive, primarily due to the challenges involved in setting up and analyzing multi-scale models. Here, we employ such a model to investigate how stochasticity propagates from individual biochemical reaction events in the bacterial innate immune system to the ecology of bacteria and bacterial viruses. We show analytically how the dynamics of bacterial populations are shaped by the activities of immunity-conferring enzymes in single cells and how the ecological consequences imply optimal bacterial defense strategies against viruses. Our results suggest that bacterial populations in the presence of viruses can either optimize their initial growth rate or their population size, with the first strategy favoring simple immunity featuring a single restriction modification system and the second strategy favoring complex bacterial innate immunity featuring several simultaneously active restriction modification systems. AU - Ruess, Jakob AU - Pleska, Maros AU - Guet, Calin C AU - Tkačik, Gašper ID - 6784 IS - 7 JF - PLoS Computational Biology TI - Molecular noise of innate immunity shapes bacteria-phage ecologies VL - 15 ER - TY - GEN AU - Ruess, Jakob AU - Pleska, Maros AU - Guet, Calin C AU - Tkačik, Gašper ID - 9786 TI - Supporting text and results 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 - JOUR AB - Across diverse biological systems—ranging from neural networks to intracellular signaling and genetic regulatory networks—the information about changes in the environment is frequently encoded in the full temporal dynamics of the network nodes. A pressing data-analysis challenge has thus been to efficiently estimate the amount of information that these dynamics convey from experimental data. Here we develop and evaluate decoding-based estimation methods to lower bound the mutual information about a finite set of inputs, encoded in single-cell high-dimensional time series data. For biological reaction networks governed by the chemical Master equation, we derive model-based information approximations and analytical upper bounds, against which we benchmark our proposed model-free decoding estimators. In contrast to the frequently-used k-nearest-neighbor estimator, decoding-based estimators robustly extract a large fraction of the available information from high-dimensional trajectories with a realistic number of data samples. We apply these estimators to previously published data on Erk and Ca2+ signaling in mammalian cells and to yeast stress-response, and find that substantial amount of information about environmental state can be encoded by non-trivial response statistics even in stationary signals. We argue that these single-cell, decoding-based information estimates, rather than the commonly-used tests for significant differences between selected population response statistics, provide a proper and unbiased measure for the performance of biological signaling networks. AU - Cepeda Humerez, Sarah A AU - Ruess, Jakob AU - Tkačik, Gašper ID - 6900 IS - 9 JF - PLoS computational biology TI - Estimating information in time-varying signals VL - 15 ER - TY - JOUR AB - The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain. AU - Lang, Moritz AU - Shkolnikov, Mikhail ID - 196 IS - 8 JF - Proceedings of the National Academy of Sciences TI - Harmonic dynamics of the Abelian sandpile VL - 116 ER - TY - JOUR AB - We theoretically study the shapes of lipid vesicles confined to a spherical cavity, elaborating a framework based on the so-called limiting shapes constructed from geometrically simple structural elements such as double-membrane walls and edges. Partly inspired by numerical results, the proposed non-compartmentalized and compartmentalized limiting shapes are arranged in the bilayer-couple phase diagram which is then compared to its free-vesicle counterpart. We also compute the area-difference-elasticity phase diagram of the limiting shapes and we use it to interpret shape transitions experimentally observed in vesicles confined within another vesicle. The limiting-shape framework may be generalized to theoretically investigate the structure of certain cell organelles such as the mitochondrion. AU - Kavcic, Bor AU - Sakashita, A. AU - Noguchi, H. AU - Ziherl, P. ID - 5817 IS - 4 JF - Soft Matter SN - 1744-683X TI - Limiting shapes of confined lipid vesicles VL - 15 ER - TY - THES AB - Single cells are constantly interacting with their environment and each other, more importantly, the accurate perception of environmental cues is crucial for growth, survival, and reproduction. This communication between cells and their environment can be formalized in mathematical terms and be quantified as the information flow between them, as prescribed by information theory. The recent availability of real–time dynamical patterns of signaling molecules in single cells has allowed us to identify encoding about the identity of the environment in the time–series. However, efficient estimation of the information transmitted by these signals has been a data–analysis challenge due to the high dimensionality of the trajectories and the limited number of samples. In the first part of this thesis, we develop and evaluate decoding–based estimation methods to lower bound the mutual information and derive model–based precise information estimates for biological reaction networks governed by the chemical master equation. This is followed by applying the decoding-based methods to study the intracellular representation of extracellular changes in budding yeast, by observing the transient dynamics of nuclear translocation of 10 transcription factors in response to 3 stress conditions. Additionally, we apply these estimators to previously published data on ERK and Ca2+ signaling and yeast stress response. We argue that this single cell decoding-based measure of information provides an unbiased, quantitative and interpretable measure for the fidelity of biological signaling processes. Finally, in the last section, we deal with gene regulation which is primarily controlled by transcription factors (TFs) that bind to the DNA to activate gene expression. The possibility that non-cognate TFs activate transcription diminishes the accuracy of regulation with potentially disastrous effects for the cell. This ’crosstalk’ acts as a previously unexplored source of noise in biochemical networks and puts a strong constraint on their performance. To mitigate erroneous initiation we propose an out of equilibrium scheme that implements kinetic proofreading. We show that such architectures are favored over their equilibrium counterparts for complex organisms despite introducing noise in gene expression. AU - Cepeda Humerez, Sarah A ID - 6473 KW - Information estimation KW - Time-series KW - data analysis SN - 2663-337X TI - Estimating information flow in single cells ER - TY - THES AB - Transcription factors, by binding to specific sequences on the DNA, control the precise spatio-temporal expression of genes inside a cell. However, this specificity is limited, leading to frequent incorrect binding of transcription factors that might have deleterious consequences on the cell. By constructing a biophysical model of TF-DNA binding in the context of gene regulation, I will first explore how regulatory constraints can strongly shape the distribution of a population in sequence space. Then, by directly linking this to a picture of multiple types of transcription factors performing their functions simultaneously inside the cell, I will explore the extent of regulatory crosstalk -- incorrect binding interactions between transcription factors and binding sites that lead to erroneous regulatory states -- and understand the constraints this places on the design of regulatory systems. I will then develop a generic theoretical framework to investigate the coevolution of multiple transcription factors and multiple binding sites, in the context of a gene regulatory network that performs a certain function. As a particular tractable version of this problem, I will consider the evolution of two transcription factors when they transmit upstream signals to downstream target genes. Specifically, I will describe the evolutionary steady states and the evolutionary pathways involved, along with their timescales, of a system that initially undergoes a transcription factor duplication event. To connect this important theoretical model to the prominent biological event of transcription factor duplication giving rise to paralogous families, I will then describe a bioinformatics analysis of C2H2 Zn-finger transcription factors, a major family in humans, and focus on the patterns of evolution that paralogs have undergone in their various protein domains in the recent past. AU - Prizak, Roshan ID - 6071 SN - 2663-337X TI - Coevolution of transcription factors and their binding sites in sequence space ER - TY - JOUR AB - Origin and functions of intermittent transitions among sleep stages, including short awakenings and arousals, constitute a challenge to the current homeostatic framework for sleep regulation, focusing on factors modulating sleep over large time scales. Here we propose that the complex micro-architecture characterizing the sleep-wake cycle results from an underlying non-equilibrium critical dynamics, bridging collective behaviors across spatio-temporal scales. We investigate θ and δ wave dynamics in control rats and in rats with lesions of sleep-promoting neurons in the parafacial zone. We demonstrate that intermittent bursts in θ and δ rhythms exhibit a complex temporal organization, with long-range power-law correlations and a robust duality of power law (θ-bursts, active phase) and exponential-like (δ-bursts, quiescent phase) duration distributions, typical features of non-equilibrium systems self-organizing at criticality. Crucially, such temporal organization relates to anti-correlated coupling between θ- and δ-bursts, and is independent of the dominant physiologic state and lesions, a solid indication of a basic principle in sleep dynamics. AU - Wang, Jilin W. J. L. AU - Lombardi, Fabrizio AU - Zhang, Xiyun AU - Anaclet, Christelle AU - Ivanov, Plamen Ch. ID - 7103 IS - 11 JF - PLoS Computational Biology SN - 1553-7358 TI - Non-equilibrium critical dynamics of bursts in θ and δ rhythms as fundamental characteristic of sleep and wake micro-architecture VL - 15 ER - TY - JOUR AB - Cells need to reliably sense external ligand concentrations to achieve various biological functions such as chemotaxis or signaling. The molecular recognition of ligands by surface receptors is degenerate in many systems, leading to crosstalk between ligand-receptor pairs. Crosstalk is often thought of as a deviation from optimal specific recognition, as the binding of noncognate ligands can interfere with the detection of the receptor's cognate ligand, possibly leading to a false triggering of a downstream signaling pathway. Here we quantify the optimal precision of sensing the concentrations of multiple ligands by a collection of promiscuous receptors. We demonstrate that crosstalk can improve precision in concentration sensing and discrimination tasks. To achieve superior precision, the additional information about ligand concentrations contained in short binding events of the noncognate ligand should be exploited. We present a proofreading scheme to realize an approximate estimation of multiple ligand concentrations that reaches a precision close to the derived optimal bounds. Our results help rationalize the observed ubiquity of receptor crosstalk in molecular sensing. AU - Carballo-Pacheco, Martín AU - Desponds, Jonathan AU - Gavrilchenko, Tatyana AU - Mayer, Andreas AU - Prizak, Roshan AU - Reddy, Gautam AU - Nemenman, Ilya AU - Mora, Thierry ID - 6090 IS - 2 JF - Physical Review E TI - Receptor crosstalk improves concentration sensing of multiple ligands VL - 99 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 cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of ‘entropy’, and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data. AU - De Martino, Andrea AU - De Martino, Daniele ID - 306 IS - 4 JF - Heliyon TI - An introduction to the maximum entropy approach and its application to inference problems in biology VL - 4 ER -