Efficient Calculation of Steady State Probability Distribution for Stochastic Biochemical Reaction Network.

The Steady State (SS) probability distribution is an important quantity needed to characterize the steady state behavior of many stochastic biochemical networks. In this paper, we propose an efficient and accurate approach to calculating an approximate SS probability distribution from solution of the Chemical Master Equation (CME) under the assumption of the existence of a unique deterministic SS of the system. To find the approximate solution to the CME, a truncated state-space representation is used to reduce the state-space of the system and translate it to a finite dimension. The subsequent ill-posed eigenvalue problem of a linear system for the finite state-space can be converted to a well-posed system of linear equations and solved. The proposed strategy yields efficient and accurate estimation of noise in stochastic biochemical systems. To demonstrate the approach, we applied the method to characterize the noise behavior of a set of biochemical networks of ligand-receptor interactions for Bone Morphogenetic Protein (BMP) signaling. We found that recruitment of type II receptors during the receptor oligomerization by itself doesn\u27t not tend to lower noise in receptor signaling, but regulation by a secreted co-factor may provide a substantial improvement in signaling relative to noise. The steady state probability approximation method shortened the time necessary to calculate the probability distributions compared to earlier approaches, such as Gillespie\u27s Stochastic Simulation Algorithm (SSA) while maintaining high accuracy

Model-Based Analysis for Qualitative Data: An Application in Drosophila Germline Stem Cell Regulation.

Discovery in developmental biology is often driven by intuition that relies on the integration of multiple types of data such as fluorescent images, phenotypes, and the outcomes of biochemical assays. Mathematical modeling helps elucidate the biological mechanisms at play as the networks become increasingly large and complex. However, the available data is frequently under-utilized due to incompatibility with quantitative model tuning techniques. This is the case for stem cell regulation mechanisms explored in the Drosophila germarium through fluorescent immunohistochemistry. To enable better integration of biological data with modeling in this and similar situations, we have developed a general parameter estimation process to quantitatively optimize models with qualitative data. The process employs a modified version of the Optimal Scaling method from social and behavioral sciences, and multi-objective optimization to evaluate the trade-off between fitting different datasets (e.g. wild type vs. mutant). Using only published imaging data in the germarium, we first evaluated support for a published intracellular regulatory network by considering alternative connections of the same regulatory players. Simply screening networks against wild type data identified hundreds of feasible alternatives. Of these, five parsimonious variants were found and compared by multi-objective analysis including mutant data and dynamic constraints. With these data, the current model is supported over the alternatives, but support for a biochemically observed feedback element is weak (i.e. these data do not measure the feedback effect well). When also comparing new hypothetical models, the available data do not discriminate. To begin addressing the limitations in data, we performed a model-based experiment design and provide recommendations for experiments to refine model parameters and discriminate increasingly complex hypotheses

Analysis of Gap Gene Regulation in a 3D Organism-Scale Model of the Drosophila melanogaster Embryo

The axial bodyplan of Drosophila melanogaster is determined during a process called morphogenesis. Shortly after fertilization, maternal bicoid mRNA is translated into Bicoid (Bcd). This protein establishes a spatially graded morphogen distribution along the anterior-posterior (AP) axis of the embryo. Bcd initiates AP axis determination by triggering expression of gap genes that subsequently regulate each other's expression to form a precisely controlled spatial distribution of gene products. Reaction-diffusion models of gap gene expression on a 1D domain have previously been used to infer complex genetic regulatory network (GRN) interactions by optimizing model parameters with respect to 1D gap gene expression data. Here we construct a finite element reaction-diffusion model with a realistic 3D geometry fit to full 3D gap gene expression data. Though gap gene products exhibit dorsal-ventral asymmetries, we discover that previously inferred gap GRNs yield qualitatively correct AP distributions on the 3D domain only when DV-symmetric initial conditions are employed. Model patterning loses qualitative agreement with experimental data when we incorporate a realistic DV-asymmetric distribution of Bcd. Further, we find that geometry alone is insufficient to account for DV-asymmetries in the final gap gene distribution. Additional GRN optimization confirms that the 3D model remains sensitive to GRN parameter perturbations. Finally, we find that incorporation of 3D data in simulation and optimization does not constrain the search space or improve optimization results

Vibrational Photoacoustic Microscopy for Depth-resolved Bond-selective Imaging of Tissues and Organisms

We realize vibrational photoacoustic microscopy (VPA) using molecular excitation of overtone vibration and acoustic detection of the resultant pressure transients. We demonstrate 3-D VPA imaging of lipid-rich atherosclerotic plaques and lipid bodies in living Drosophila larvae by exciting 2nd overtone of the CH bond stretch around 8300 cm^(−1). Depth-resolved spectral analysis and a penetration depth of several mm are available

Label-Free Bond-Selective Imaging by Listening to Vibrationally Excited Molecules

We report the realization of vibrational photoacoustic (VPA) microscopy using optical excitation of molecular overtone vibration and acoustic detection of the resultant pressure transients. Our approach eliminates the tissue scattering problem encountered in near-infrared spectroscopy and enables depth-resolved signal collection. The 2nd overtone of the CH bond stretch around 8300  cm^(−1), where blood interference is minimal, is excited. We demonstrate 3D VPA imaging of lipid-rich atherosclerotic plaques by excitation from the artery lumen, and lipid storage in live Drosophila larvae, with millimeter-scale penetration depth

Vibrational Photoacoustic Microscopy for Depth-resolved Bond-selective Imaging of Tissues and Organisms

We realize vibrational photoacoustic microscopy (VPA) using molecular excitation of overtone vibration and acoustic detection of the resultant pressure transients. We demonstrate 3-D VPA imaging of lipid-rich atherosclerotic plaques and lipid bodies in living Drosophila larvae by exciting 2nd overtone of the CH bond stretch around 8300 cm^(−1). Depth-resolved spectral analysis and a penetration depth of several mm are available

Label-Free Bond-Selective Imaging by Listening to Vibrationally Excited Molecules

We report the realization of vibrational photoacoustic (VPA) microscopy using optical excitation of molecular overtone vibration and acoustic detection of the resultant pressure transients. Our approach eliminates the tissue scattering problem encountered in near-infrared spectroscopy and enables depth-resolved signal collection. The 2nd overtone of the CH bond stretch around 8300  cm^(−1), where blood interference is minimal, is excited. We demonstrate 3D VPA imaging of lipid-rich atherosclerotic plaques by excitation from the artery lumen, and lipid storage in live Drosophila larvae, with millimeter-scale penetration depth