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 - 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
TI - Coevolution of transcription factors and their binding sites in sequence space
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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - JOUR
AB - Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state-dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie’s Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.
AU - Bod’Ová, Katarína
AU - Mitchell, Gabriel
AU - Harpaz, Roy
AU - Schneidman, Elad
AU - Tkacik, Gasper
ID - 406
IS - 3
JF - PLoS One
TI - Probabilistic models of individual and collective animal behavior
VL - 13
ER -
TY - JOUR
AB - Temperate bacteriophages integrate in bacterial genomes as prophages and represent an important source of genetic variation for bacterial evolution, frequently transmitting fitness-augmenting genes such as toxins responsible for virulence of major pathogens. However, only a fraction of bacteriophage infections are lysogenic and lead to prophage acquisition, whereas the majority are lytic and kill the infected bacteria. Unless able to discriminate lytic from lysogenic infections, mechanisms of immunity to bacteriophages are expected to act as a double-edged sword and increase the odds of survival at the cost of depriving bacteria of potentially beneficial prophages. We show that although restriction-modification systems as mechanisms of innate immunity prevent both lytic and lysogenic infections indiscriminately in individual bacteria, they increase the number of prophage-acquiring individuals at the population level. We find that this counterintuitive result is a consequence of phage-host population dynamics, in which restriction-modification systems delay infection onset until bacteria reach densities at which the probability of lysogeny increases. These results underscore the importance of population-level dynamics as a key factor modulating costs and benefits of immunity to temperate bacteriophages
AU - Pleska, Maros
AU - Lang, Moritz
AU - Refardt, Dominik
AU - Levin, Bruce
AU - Guet, Calin C
ID - 457
IS - 2
JF - Nature Ecology and Evolution
TI - Phage-host population dynamics promotes prophage acquisition in bacteria with innate immunity
VL - 2
ER -
TY - JOUR
AB - A central goal in theoretical neuroscience is to predict the response properties of sensory neurons from first principles. To this end, “efficient coding” posits that sensory neurons encode maximal information about their inputs given internal constraints. There exist, however, many variants of efficient coding (e.g., redundancy reduction, different formulations of predictive coding, robust coding, sparse coding, etc.), differing in their regimes of applicability, in the relevance of signals to be encoded, and in the choice of constraints. It is unclear how these types of efficient coding relate or what is expected when different coding objectives are combined. Here we present a unified framework that encompasses previously proposed efficient coding models and extends to unique regimes. We show that optimizing neural responses to encode predictive information can lead them to either correlate or decorrelate their inputs, depending on the stimulus statistics; in contrast, at low noise, efficiently encoding the past always predicts decorrelation. Later, we investigate coding of naturalistic movies and show that qualitatively different types of visual motion tuning and levels of response sparsity are predicted, depending on whether the objective is to recover the past or predict the future. Our approach promises a way to explain the observed diversity of sensory neural responses, as due to multiple functional goals and constraints fulfilled by different cell types and/or circuits.
AU - Chalk, Matthew J
AU - Marre, Olivier
AU - Tkacik, Gasper
ID - 543
IS - 1
JF - PNAS
TI - Toward a unified theory of efficient, predictive, and sparse coding
VL - 115
ER -
TY - DATA
AB - This package contains data for the publication "Nonlinear decoding of a complex movie from the mammalian retina" by Deny S. et al, PLOS Comput Biol (2018).
The data consists of
(i) 91 spike sorted, isolated rat retinal ganglion cells that pass stability and quality criteria, recorded on the multi-electrode array, in response to the presentation of the complex movie with many randomly moving dark discs. The responses are represented as 648000 x 91 binary matrix, where the first index indicates the timebin of duration 12.5 ms, and the second index the neural identity. The matrix entry is 0/1 if the neuron didn't/did spike in the particular time bin.
(ii) README file and a graphical illustration of the structure of the experiment, specifying how the 648000 timebins are split into epochs where 1, 2, 4, or 10 discs were displayed, and which stimulus segments are exact repeats or unique ball trajectories.
(iii) a 648000 x 400 matrix of luminance traces for each of the 20 x 20 positions ("sites") in the movie frame, with time that is locked to the recorded raster. The luminance traces are produced as described in the manuscript by filtering the raw disc movie with a small gaussian spatial kernel.
AU - Deny, Stephane
AU - Marre, Olivier
AU - Botella-Soler, Vicente
AU - Martius, Georg S
AU - Tkacik, Gasper
ID - 5584
KW - retina
KW - decoding
KW - regression
KW - neural networks
KW - complex stimulus
TI - Nonlinear decoding of a complex movie from the mammalian retina
ER -
TY - DATA
AB - Mean repression values and standard error of the mean are given for all operator mutant libraries.
AU - Igler, Claudia
AU - Lagator, Mato
AU - Tkacik, Gasper
AU - Bollback, Jonathan P
AU - Guet, Calin C
ID - 5585
TI - Data for the paper Evolutionary potential of transcription factors for gene regulatory rewiring
ER -
TY - DATA
AB - Supporting material to the article
STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH
boundscoli.dat
Flux Bounds of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium.
polcoli.dat
Matrix enconding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium,
obtained from the soichiometric matrix by standard linear algebra (reduced row echelon form).
ellis.dat
Approximate Lowner-John ellipsoid rounding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium
obtained with the Lovasz method.
point0.dat
Center of the approximate Lowner-John ellipsoid rounding the polytope of the E. coli catabolic core model iAF1260 in a glucose limited minimal medium
obtained with the Lovasz method.
lovasz.cpp
This c++ code file receives in input the polytope of the feasible steady states of a metabolic network,
(matrix and bounds), and it gives in output an approximate Lowner-John ellipsoid rounding the polytope
with the Lovasz method
NB inputs are referred by defaults to the catabolic core of the E.Coli network iAF1260.
For further details we refer to PLoS ONE 10.4 e0122670 (2015).
sampleHRnew.cpp
This c++ code file receives in input the polytope of the feasible steady states of a metabolic network,
(matrix and bounds), the ellipsoid rounding the polytope, a point inside and
it gives in output a max entropy sampling at fixed average growth rate
of the steady states by performing an Hit-and-Run Monte Carlo Markov chain.
NB inputs are referred by defaults to the catabolic core of the E.Coli network iAF1260.
For further details we refer to PLoS ONE 10.4 e0122670 (2015).
AU - De Martino, Daniele
AU - Tkacik, Gasper
ID - 5587
KW - metabolic networks
KW - e.coli core
KW - maximum entropy
KW - monte carlo markov chain sampling
KW - ellipsoidal rounding
TI - Supporting materials "STATISTICAL MECHANICS FOR METABOLIC NETWORKS IN STEADY-STATE GROWTH"
ER -
TY - JOUR
AB - We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed on a bounded domain and its transport and diffusion coefficients vanish on the domain's boundary. We first argue that, despite this degeneracy, the standard no-flux boundary condition is valid. We derive the weak formulation of the problem and prove the existence and uniqueness of its solutions by constructing the corresponding contraction semigroup on a suitable function space. Then, we prove that for the parameter regime with high enough mutation rate the problem exhibits a positive spectral gap, which implies exponential convergence to equilibrium.Next, we provide a simple derivation of the so-called Dynamic Maximum Entropy (DynMaxEnt) method for approximation of observables (moments) of the Fokker-Planck solution, which can be interpreted as a nonlinear Galerkin approximation. The limited applicability of the DynMaxEnt method inspires us to introduce its modified version that is valid for the whole range of admissible parameters. Finally, we present several numerical experiments to demonstrate the performance of both the original and modified DynMaxEnt methods. We observe that in the parameter regimes where both methods are valid, the modified one exhibits slightly better approximation properties compared to the original one.
AU - Bodova, Katarina
AU - Haskovec, Jan
AU - Markowich, Peter
ID - 607
JF - Physica D: Nonlinear Phenomena
TI - Well posedness and maximum entropy approximation for the dynamics of quantitative traits
VL - 376-377
ER -
TY - JOUR
AB - Although cells respond specifically to environments, how environmental identity is encoded intracellularly is not understood. Here, we study this organization of information in budding yeast by estimating the mutual information between environmental transitions and the dynamics of nuclear translocation for 10 transcription factors. Our method of estimation is general, scalable, and based on decoding from single cells. The dynamics of the transcription factors are necessary to encode the highest amounts of extracellular information, and we show that information is transduced through two channels: Generalists (Msn2/4, Tod6 and Dot6, Maf1, and Sfp1) can encode the nature of multiple stresses, but only if stress is high; specialists (Hog1, Yap1, and Mig1/2) encode one particular stress, but do so more quickly and for a wider range of magnitudes. In particular, Dot6 encodes almost as much information as Msn2, the master regulator of the environmental stress response. Each transcription factor reports differently, and it is only their collective behavior that distinguishes between multiple environmental states. Changes in the dynamics of the localization of transcription factors thus constitute a precise, distributed internal representation of extracellular change. We predict that such multidimensional representations are common in cellular decision-making.
AU - Granados, Alejandro
AU - Pietsch, Julian
AU - Cepeda Humerez, Sarah A
AU - Farquhar, Isebail
AU - Tkacik, Gasper
AU - Swain, Peter
ID - 281
IS - 23
JF - PNAS
TI - Distributed and dynamic intracellular organization of extracellular information
VL - 115
ER -
TY - JOUR
AB - Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains.
AU - Botella Soler, Vicent
AU - Deny, Stephane
AU - Martius, Georg S
AU - Marre, Olivier
AU - Tkacik, Gasper
ID - 292
IS - 5
JF - PLoS Computational Biology
TI - Nonlinear decoding of a complex movie from the mammalian retina
VL - 14
ER -
TY - JOUR
AB - The hanging-drop network (HDN) is a technology platform based on a completely open microfluidic network at the bottom of an inverted, surface-patterned substrate. The platform is predominantly used for the formation, culturing, and interaction of self-assembled spherical microtissues (spheroids) under precisely controlled flow conditions. Here, we describe design, fabrication, and operation of microfluidic hanging-drop networks.
AU - Misun, Patrick
AU - Birchler, Axel
AU - Lang, Moritz
AU - Hierlemann, Andreas
AU - Frey, Olivier
ID - 305
JF - Methods in Molecular Biology
TI - Fabrication and operation of microfluidic hanging drop networks
VL - 1771
ER -