Multi-scale quantification of tissue behavior during amniote embryo axis elongation.

Embryonic axis elongation is a complex multi-tissue morphogenetic process responsible for the formation of the posterior part of the amniote body. How movements and growth are coordinated between the different posterior tissues (e.g. neural tube, axial and paraxial mesoderm, lateral plate, ectoderm, endoderm) to drive axis morphogenesis remain largely unknown. Here, we use quail embryos to quantify cell behavior and tissue movements during elongation. We quantify the tissue-specific contribution to axis elongation using 3D volumetric techniques, then quantify tissue-specific parameters such as cell density and proliferation. To study cell behavior at a multi-tissue scale, we used high-resolution 4D imaging of transgenic quail embryos expressing fluorescent proteins. We developed specific tracking and image analysis techniques to analyze cell motion and compute tissue deformations in 4D. This analysis reveals extensive sliding between tissues during axis extension. Further quantification of tissue tectonics showed patterns of rotations, contractions and expansions, which are consistent with the multi-tissue behavior observed previously. Our approach defines a quantitative and multi-scale method to analyze the coordination between tissue behaviors during early vertebrate embryo morphogenetic events.

A large number of receptors may reduce cellular response time variation.

Cells often have tens of thousands of receptors, even though only a few activated receptors can trigger full cellular responses. Reasons for the overabundance of receptors remain unclear. We suggest that, under certain conditions, the large number of receptors can result in a competition among receptors to be the first to activate the cell. The competition decreases the variability of the time to cellular activation, and hence results in a more synchronous activation of cells. We argue that, in simple models, this variability reduction does not necessarily interfere with the receptor specificity to ligands achieved by the kinetic proofreading mechanism. Thus cells can be activated accurately in time and specifically to certain signals. We predict the minimum number of receptors needed to reduce the coefficient of variation for the time to activation following binding of a specific ligand. Furthermore, we predict the maximum number of receptors so that the kinetic proofreading mechanism still can improve the specificity of the activation. These predictions fall in line with experimentally reported receptor numbers for multiple systems.

What the odor is not: Estimation by elimination.

Olfactory systems use a small number of broadly sensitive receptors to combinatorially encode a vast number of odors. We propose a method of decoding such distributed representations by exploiting a statistical fact: Receptors that do not respond to an odor carry more information than receptors that do because they signal the absence of all odorants that bind to them. Thus, it is easier to identify what the odor is not rather than what the odor is. For realistic numbers of receptors, response functions, and odor complexity, this method of elimination turns an underconstrained decoding problem into a solvable one, allowing accurate determination of odorants in a mixture and their concentrations. We construct a neural network realization of our algorithm based on the structure of the olfactory pathway.

Mechanistic insights from a quantitative analysis of pollen tube guidance.

BACKGROUND: Plant biologists have long speculated about the mechanisms that guide pollen tubes to ovules. Although there is now evidence that ovules emit a diffusible attractant, little is known about how this attractant mediates interactions between the pollen tube and the ovules. RESULTS: We employ a semi-in vitro assay, in which ovules dissected from Arabidopsis thaliana are arranged around a cut style on artificial medium, to elucidate how ovules release the attractant and how pollen tubes respond to it. Analysis of microscopy images of the semi-in vitro system shows that pollen tubes are more attracted to ovules that are incubated on the medium for longer times before pollen tubes emerge from the cut style. The responses of tubes are consistent with their sensing a gradient of an attractant at 100-150 mum, farther than previously reported. Our microscopy images also show that pollen tubes slow their growth near the micropyles of functional ovules with a spatial range that depends on ovule incubation time. CONCLUSIONS: We propose a stochastic model that captures these dynamics. In the model, a pollen tube senses a difference in the fraction of receptors bound to an attractant and changes its direction of growth in response; the attractant is continuously released from ovules and spreads isotropically on the medium. The model suggests that the observed slowing greatly enhances the ability of pollen tubes to successfully target ovules. The relation of the results to guidance in vivo is discussed.

Critical behavior of a model for catalyzed autoamplification.

We examine the critical behavior of a model of catalyzed autoamplification inspired by a common motif in genetic networks. Similar to models in the directed percolation (DP) universality class, a phase transition between an absorbing state with no copies of the autoamplifying species A and an active state with a finite amount of A occurs at the point at which production and removal of A are balanced. A suitable coordinate transformation shows that this model corresponds to one with three fields, one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field. Using stochastic simulations that account for discrete molecular copy numbers in one, two, and three dimensions, we show that this model has exponents that are distinct from previously studied reaction-diffusion systems, including the few with more than one field (unidirectionally coupled DP processes and the diffusive epidemic process). Thus the requirement of a catalyst changes the fundamental physics of autoamplification. Estimates for the exponents of the diffusive epidemic process in two dimensions are also presented.

Effects of receptor correlations on molecular information transmission.

Cells measure concentrations of external ligands by capturing ligand molecules with cell surface receptors. The numbers of molecules captured by different receptors co-vary because they depend on the same extrinsic ligand fluctuations. However, these numbers also counter-vary due to the intrinsic stochasticity of chemical processes because a single molecule randomly captured by a receptor cannot be captured by another. Such structure of receptor correlations is generally believed to lead to an increase in information about the external signal compared to the case of independent receptors. We analyze a solvable model of two molecular receptors and show that, contrary to this widespread expectation, the correlations have a small and negative effect on the information about the ligand concentration. Further, we show that measurements that average over multiple receptors are almost as informative as those that track the states of every individual one.

Director field model of the primary visual cortex for contour detection.

We aim to build the simplest possible model capable of detecting long, noisy contours in a cluttered visual scene. For this, we model the neural dynamics in the primate primary visual cortex in terms of a continuous director field that describes the average rate and the average orientational preference of active neurons at a particular point in the cortex. We then use a linear-nonlinear dynamical model with long range connectivity patterns to enforce long-range statistical context present in the analyzed images. The resulting model has substantially fewer degrees of freedom than traditional models, and yet it can distinguish large contiguous objects from the background clutter by suppressing the clutter and by filling-in occluded elements of object contours. This results in high-precision, high-recall detection of large objects in cluttered scenes. Parenthetically, our model has a direct correspondence with the Landau-de Gennes theory of nematic liquid crystal in two dimensions.

Field theoretic treatment of an effective action for a model of catalyzed autoamplification.

Reaction-diffusion models can exhibit continuous phase transitions in behaviors, and their dynamics at criticality often exhibit scalings with key parameters that can be characterized by exponents. While models with only a single field that transitions between absorbing and nonabsorbing states are well characterized and typically fall in the directed percolation universality class, the effects of coupling multiple fields remain poorly understood. We recently introduced a model which has three fields: one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field [Tchernookov, J. Chem. Phys. 130, 134906 (2009)]. Simulations suggested that this model is in a universality class distinct from other reaction-diffusion systems studied previously. Although the three fields give rise to interesting physics, they complicate analysis of the model with renormalization-group methods. Here, we show how to systematically simplify the action for this model such that analytical expressions for the exponents of this universality class can be obtained by standard means. We expect the approach taken here to be of general applicability in reaction-diffusion systems with coupled order parameters that display qualitatively different behaviors close to criticality.