Time and length scales of autocrine signals in three dimensions

A model of autocrine signaling in cultures of suspended cells is developed on the basis of the effective medium approximation. The fraction of autocrine ligands, the mean and distribution of distances traveled by paracrine ligands before binding, as well as the mean and distribution of the ligand lifetime are derived. Interferon signaling by dendritic immune cells is considered as an illustration.Comment: 15 page

Mutual Repression enhances the Steepness and Precision of Gene Expression Boundaries

Embryonic development is driven by spatial patterns of gene expression that determine the fate of each cell in the embryo. While gene expression is often highly erratic, embryonic development is usually exceedingly precise. In particular, gene expression boundaries are robust not only against intrinsic noise from gene expression and protein diffusion, but also against embryo-to-embryo variations in the morphogen gradients, which provide positional information to the differentiating cells. How development is robust against intra- and inter-embryonic variations is not understood. A common motif in the gene regulation networks that control embryonic development is mutual repression between pairs of genes. To assess the role of mutual repression in the robust formation of gene expression patterns, we have performed large-scale stochastic simulations of a minimal model of two mutually repressing gap genes in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only mutual repression between hb and kni, but also the stochastic and cooperative activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni. Our analysis reveals that mutual repression can markedly increase the steepness and precision of the gap gene expression boundaries. In contrast to spatial averaging and cooperative gene activation, mutual repression thus allows for gene-expression boundaries that are both steep and precise. Moreover, mutual repression dramatically enhances their robustness against embryo-to-embryo variations in the morphogen levels. Finally, our simulations reveal that gap protein diffusion plays a critical role not only in reducing the width of gap gene expression boundaries via spatial averaging, but also in repairing patterning errors that could arise due to the bistability induced by mutual repression.Comment: 29 pages, 9 figures, supporting text with 9 supporting figures; accepted for publication in PLoS Comp. Bio

Bistability and Oscillations in the Huang-Ferrell Model of MAPK Signaling

Physicochemical models of signaling pathways are characterized by high levels of structural and parametric uncertainty, reflecting both incomplete knowledge about signal transduction and the intrinsic variability of cellular processes. As a result, these models try to predict the dynamics of systems with tens or even hundreds of free parameters. At this level of uncertainty, model analysis should emphasize statistics of systems-level properties, rather than the detailed structure of solutions or boundaries separating different dynamic regimes. Based on the combination of random parameter search and continuation algorithms, we developed a methodology for the statistical analysis of mechanistic signaling models. In applying it to the well-studied MAPK cascade model, we discovered a large region of oscillations and explained their emergence from single-stage bistability. The surprising abundance of strongly nonlinear (oscillatory and bistable) input/output maps revealed by our analysis may be one of the reasons why the MAPK cascade in vivo is embedded in more complex regulatory structures. We argue that this type of analysis should accompany nonlinear multiparameter studies of stationary as well as transient features in network dynamics

Magnetic and dielectric properties of multiferroic Eu0.5Ba0.25Sr0.25TiO3 ceramics

Dielectric and magnetic properties of Eu0.5Ba0.25Sr0.25TiO3 are investigated between 10 K and 300 K in the frequency range from 10 Hz to 100 THz. A peak in permittivity revealed near 130 K and observed ferroelectric hysteresis loops prove the ferroelectric order below thistemperature. The peak in permittivity is given mainly by softening of the lowest frequency polar phonon (soft mode revealed in THz and IR spectra) that demonstrates displacive character of the phase transition. Room-temperature X-ray diffraction analysis reveals cubic structure, but the IR reflectivity spectra give evidence of a lower crystal structure, presumably tetragonal I4/mcm with tilted oxygen octahedra as it has been observed in EuTiO3. The magnetic measurements show that the antiferromagnetic order occurs below 1.8 K. Eu0.5Ba0.25Sr0.25TiO3 has three times lower coercive field than Eu0.5Ba0.5TiO3, therefore we propose this system for measurements of electric dipole moment of electron.Comment: Phase Transitions, in pres

Quantifying the Gurken morphogen gradient in Drosophila oogenesis

Quantitative information about the distribution of morphogens is crucial for understanding their effects on cell-fate determination, yet it is difficult to obtain through direct measurements. We have developed a parameter estimation approach for quantifying the spatial distribution of Gurken, a TGFα-like EGFR ligand that acts as a morphogen in Drosophila oogenesis. Modeling of Gurken/EGFR system shows that the shape of the Gurken gradient is controlled by a single dimensionless parameter, the Thiele modulus, which reflects the relative importance of ligand diffusion and degradation. By combining the model with genetic alterations of EGFR levels, we have estimated the value of the Thiele modulus in the wild-type egg chamber. This provides a direct characterization of the shape of the Gurken gradient and demonstrates how parameter estimation techniques can be used to quantify morphogen gradients in development

Self-similar dynamics of morphogen gradients

We discovered a class of self-similar solutions in nonlinear models describing the formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differention in developing tissues. These models account for diffusion and self-induced degration of locally produced chemical signals. When production starts, the signal concentration is equal to zero throughout the system. We found that in the limit of infinitely large signal production strength the solution of this problem is given by the product of the steady state concentration profile and a function of the diffusion similarity variable. We derived a nonlinear boundary value problem satisfied by this function and used a variational approach to prove that this problem has a unique solution in a natural setting. Using the asymptotic behavior of the solutions established by the analysis, we constructed these solutions numerically by the shooting method. Finally, we demonstrated that the obtained solutions may be easily approximated by simple analytical expressions, thus providing an accurate global characterization of the dynamics in an important class of non-linear models of morphogen gradient formation. Our results illustrate the power of analytical approaches to studying nonlinear models of biophysical processes.Comment: 17 pages, 5 figure

Gene Regulation by MAPK Substrate Competition

SummaryDeveloping tissues are patterned by coordinated activities of signaling systems, which can be integrated by a regulatory region of a gene that binds multiple transcription factors or by a transcription factor that is modified by multiple enzymes. Based on a combination of genetic and imaging experiments in the early Drosophila embryo, we describe a signal integration mechanism that cannot be reduced to a single gene regulatory element or a single transcription factor. This mechanism relies on an enzymatic network formed by mitogen-activated protein kinase (MAPK) and its substrates. Specifically, anteriorly localized MAPK substrates, such as Bicoid, antagonize MAPK-dependent downregulation of Capicua, a repressor that is involved in gene regulation along the dorsoventral axis of the embryo. MAPK substrate competition provides a basis for ternary interaction of the anterior, dorsoventral, and terminal patterning systems. A mathematical model of this interaction can explain gene expression patterns with both anteroposterior and dorsoventral polarities

Temporal ordering and registration of images in studies of developmental dynamics

Abstract Dynamics of developmental progress is commonly reconstructed from imaging snapshots of chemical or mechanical processes in fixed embryos. As a first step in these reconstructions, snapshots must be spatially registered and ordered in time. Currently, image registration and ordering is often done manually, requiring a significant amount of expertise with a specific system. However, as the sizes of imaging data sets grow, these tasks become increasingly difficult, especially when the images are noisy and the examined developmental changes are subtle. To address these challenges, we present an automated approach to simultaneously register and temporally order imaging data sets. The approach is based on vector diffusion maps, a manifold learning technique that does not require a priori knowledge of image features or a parametric model of the developmental dynamics. We illustrate this approach by registering and ordering data from imaging studies of pattern formation and morphogenesis in three different model systems. We also provide software to aid in the application of our methodology to other experimental data sets