arXiv subjects

Thomas Gregor

Publications and source records attributed to Thomas Gregor.

29 records · Page 2Linked to original sources

arXiv2016

Optimal decoding of information from a genetic network

Gene expression levels carry information about signals that have functional significance for the organism. Using the gap gene network in the fruit fly embryo as an example, we show how this information can be decoded, building a dictionary that translates expression levels into a map of implied positions. The optimal decoder makes use of graded variations in absolute expression level, resulting in positional estimates that are precise to ~1% of the embryo's length. We test this optimal decoder by analyzing gap gene expression in embryos lacking some of the primary maternal inputs to the network. The resulting maps are distorted, and these distortions predict, with no free parameters, the positions of expression stripes for the pair-rule genes in the mutant embryos.

q-bio.MN↗

arXiv2015

Only accessible information is useful: insights from gradient-mediated patterning

Information theory is gaining popularity as a tool to characterize performance of biological systems. However, information is commonly quantified without reference to whether or how a system could extract and use it; as a result, information-theoretic quantities are easily misinterpreted. Here we take the example of pattern-forming developmental systems which are commonly structured as cascades of sequential gene expression steps. Such a multi-tiered structure appears to constitute sub-optimal use of the positional information provided by the input morphogen because noise is added at each tier. However, the conventional theory fails to distinguish between the total information in a morphogen and information that can be usefully extracted and interpreted by downstream elements. We demonstrate that quantifying the information that is _accessible_ to the system naturally explains the prevalence of multi-tiered network architectures as a consequence of the noise inherent to the control of gene expression. We support our argument with empirical observations from patterning along the major body axis of the fruit fly embryo. Our results exhibit the limitations of the standard information-theoretic characterization of biological signaling and illustrate how they can be resolved.

q-bio.MN↗

arXiv2014

Multiscale modeling of oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales -- from biochemical networks within individual cells to spatially structured cellular populations. Here, we present a family of multiscale models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cAMP used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various pre-processing modules. We use this family of models to study spatially unstructured populations by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then extend our models to include spatial structure and show how they naturally give rise to spiral waves. Our models exhibit a wide range of novel phenomena including a density dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

q-bio.CB↗

arXiv2014

From Intracellular Signaling to Population Oscillations: Bridging Scales in Collective Behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems we know that behavioral changes in the individual constituents of a collectively-behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network and its effects at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.

physics.bio-ph↗

arXiv2014

Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework

The concept of positional information is central to our understanding of how cells in a multicellular structure determine their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an information-theoretic definition in the context of developmental gene expression patterns and examine which features of expression patterns increase or decrease positional information. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with single cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

physics.bio-ph↗

arXiv2013

Maternal origins of developmental reproducibility

Cell fate decisions in multicellular organisms are precisely coordinated, leading to highly reproducible macroscopic outcomes of developmental processes. The origins of this reproducibility can be found at the molecular level during the earliest stages of development when spatial patterns of morphogen (form-generating) molecules emerge reproducibly. However, the initial conditions for these early stages are determined by the female during oogenesis, and it is unknown whether reproducibility is passed on to the zygote or whether it is reacquired by the zygote. Here we examine the earliest reproducible pattern in the Drosophila embryo, the Bicoid protein gradient. Using a unique combination of absolute molecule counting techniques, we show that it is generated from a highly controlled source of mRNA molecules that is reproducible from embryo to embryo to within ~8%. This occurs in a perfectly linear feed-forward process: changes in the female's gene dosage lead to proportional changes in the mRNA and protein counts in the embryo. In this setup, noise is kept low in the transition from one molecular species to another, allowing the female to precisely deposit the same absolute number of mRNA molecules in each embryo and therefore confer reproducibility to the Bicoid pattern. Our results indicate that the reproducibility of the morphological structures that emerge in the embryo originates during oogenesis when all initial patterning signals are controlled with precision similar to what we observe for the Bicoid pattern.

q-bio.MN↗

arXiv2013

Precision and reproducibility of macroscopic developmental patterns

Developmental processes in multicellular organisms occur far from equilibrium, yet produce complex patterns with astonishing reproducibility. We measure the precision and reproducibility of bilaterally symmetric fly wings across the natural range of genetic and environmental conditions and find that wing patterns are specified with identical spatial precision and are reproducible to within a single cell width. The early fly embryo operates at a similar degree of reproducibility, suggesting that the overall spatial precision of morphogenesis in Drosophila performs at the single cell level, arguably the physical limit of what a biological system can achieve.

q-bio.TO↗

arXiv2013

Morphogenesis at criticality?

Spatial patterns in the early fruit fly embryo emerge from a network of interactions among transcription factors, the gap genes, driven by maternal inputs. Such networks can exhibit many qualitatively different behaviors, separated by critical surfaces. At criticality, we should observe strong correlations in the fluctuations of different genes around their mean expression levels, a slowing of the dynamics along some but not all directions in the space of possible expression levels, correlations of expression fluctuations over long distances in the embryo, and departures from a Gaussian distribution of these fluctuations. Analysis of recent experiments on the gap genes shows that all these signatures are observed, and that the different signatures are related in ways predicted by theory. While there might be other explanations for these individual phenomena, the confluence of evidence suggests that this genetic network is tuned to criticality.

q-bio.MN↗

arXiv2011

Positional information, in bits

Cells in a developing embryo have no direct way of "measuring" their physical position. Through a variety of processes, however, the expression levels of multiple genes come to be correlated with position, and these expression levels thus form a code for "positional information." We show how to measure this information, in bits, using the gap genes in the Drosophila embryo as an example. Individual genes carry nearly two bits of information, twice as much as expected if the expression patterns consisted only of on/off domains separated by sharp boundaries. Taken together, four gap genes carry enough information to define a cell's location with an error bar of ~1% along the anterior-posterior axis of the embryo. This precision is nearly enough for each cell to have a unique identity, which is the maximum information the system can use, and is nearly constant along the length of the embryo. We argue that this constancy is a signature of optimality in the transmission of information from primary morphogen inputs to the output of the gap gene network.

q-bio.MN↗

arXiv2010

Quantifying the Bicoid morphogen gradient in living fly embryos

In multicellular organisms, patterns of gene expression are established in response to gradients of signaling molecules. During fly development in early Drosophila embryos, the Bicoid (Bcd) morphogen gradient is established within the first hour after fertilization. Bcd acts as a transcription factor, initiating the expression of a cascade of genes that determine the segmentation pattern of the embryo, which serves as a blueprint for the future adult organism. A robust understanding of the mechanisms that govern this segmentation cascade is still lacking, and a new generation of quantitative measurements of the spatio-temporal concentration dynamics of the individual players of this cascade are necessary for further progress. Here we describe a series of methods that are meant to represent a start of such a quantification using Bcd as an example. We describe the generation of a transgenic fly line expressing a Bcd-eGFP fusion protein, and we use this line to carefully analyze the Bcd concentration dynamics and to measure absolute Bcd expression levels in living fly embryos using two-photon microscopy. These experiments have proven to be a fruitful tool generating new insights into the mechanisms that lead to the establishment and the readout of the Bcd gradient. Generalization of these methods to other genes in the Drosophila segmentation cascade is straightforward and should further our understanding of the early patterning processes and the architecture of the underlying genetic network structure.

q-bio.QM↗

arXiv2007

The role of input noise in transcriptional regulation

Even under constant external conditions, the expression levels of genes fluctuate. Much emphasis has been placed on the components of this noise that are due to randomness in transcription and translation; here we analyze the role of noise associated with the inputs to transcriptional regulation, the random arrival and binding of transcription factors to their target sites along the genome. This noise sets a fundamental physical limit to the reliability of genetic control, and has clear signatures, but we show that these are easily obscured by experimental limitations and even by conventional methods for plotting the variance vs. mean expression level. We argue that simple, global models of noise dominated by transcription and translation are inconsistent with the embedding of gene expression in a network of regulatory interactions. Analysis of recent experiments on transcriptional control in the early Drosophila embryo shows that these results are quantitatively consistent with the predicted signatures of input noise, and we discuss the experiments needed to test the importance of input noise more generally.

q-bio.MN↗