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

Moth Mating: Modeling Female Pheromone Calling and Male Navigational Strategies to Optimize Reproductive Success

Male and female moths communicate in complex ways to search for and to select a mate. In a process termed calling, females emit small quantities of pheromones, generating plumes that spread in the environment. Males detect the plume through their antennae and navigate toward the female. The reproductive process is marked by female choice and male–male competition, since multiple males aim to reach the female but only the first can mate with her. This provides an opportunity for female selection on male traits such as chemosensitivity to pheromone molecules and mobility. We develop a mathematical framework to investigate the overall mating likelihood, the mean first arrival time, and the quality of the first male to reach the female for four experimentally observed female calling strategies unfolding over a typical one-week mating period. We present both analytical solutions of a simplified model as well as results from agent-based numerical simulations. Our findings suggest that, by adjusting call times and the amount of released pheromone, females can optimize the mating process. In particular, shorter calling times and lower pheromone titers at onset of the mating period that gradually increase over time allow females to aim for higher-quality males while still ensuring that mating occurs by the end of the mating period

Quantitative modeling of spatiotemporal systems: Simulation of biological systems and analysis of error metric effects on model fitting

Understanding the biophysical processes underlying biological and biotechnological processes is a prerequisite for therapeutic treatments and technological innovation. With the exponential growth of computational processing speed, experimental findings in these fields have been complemented by dynamic simulations of developmental signaling and genetic interactions. Models provide means to evaluate "emergent" properties of systems sometimes inaccessible by reductionist approaches, making them test beds for biological inference and technological refinement. The complexity and interconnectedness of biological processes pose special challenges to modelers; biological models typically possess a large number of unknown parameters relative to their counterparts in other physical sciences. Estimating these parameter values requires iterative testing of parameter values to find values that produce low error between model and data. This is a task whose length grows exponentially with the number of unknown parameters. Many biological systems require spatial representation (i.e., they are not well-mixed systems and change over space and time). Adding spatial dimensions complicates parameter estimation by increasing computational time for each model evaluation. Defining error for model-data comparison is also complicated on spatial domains. Different metrics compare different features of data and simulation, and the desired features are dependent on the underlying research question. This dissertation documents the modeling, parameter estimation, and simulation of two spatiotemporal modeling studies. Each study addresses an unanswered research question in the respective experimental system. The former is a 3D model of a nanoscale amperometric glucose biosensor; the model was used to optimize the sensor's design for improved sensitivity to glucose. The latter is a 3D model of the developmental gap gene system that helps establish the bodyplan of Drosophila melanogaster; I wished to determine if the embryo's geometry alone was capable of accounting for observed spatial distributions of gap gene products and to infer feasible genetic regulatory networks (GRNs) via parameter estimation of the GRN interaction terms. Simulation of the biosensor successfully predicted an optimal electrode density on the biosensor surface, allowing us to fabricate improved biosensors. Simulation of the gap gene system on 1D and 3D embryonic demonstrated that geometric effects were insufficient to produce observed distributions when simulated with previously reported GRNs. Noting the effects of the error definition on the outcome of parameter estimation, I conclude with a characterization of assorted error definitions (objective functions), describe data characteristics to which they are sensitive, and end with a suggested procedure for objective function selection. Choice of objective function is important in parameter estimation of spatiotemporal system models in varied biological and biotechnological disciplines

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

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

Effects of Carbon Nanotube-Tethered Nanosphere Density on Amperometric Biosensing: Simulation and Experiment

Nascent nanofabrication approaches are being applied to reduce electrode feature dimensions from the microscale to the nanoscale, creating biosensors that are capable of working more efficiently at the biomolecular level. The development of nanoscale biosensors has been driven largely by experimental empiricism to date. Consequently, the precise positioning of nanoscale electrode elements is typically neglected, and its impact on biosensor performance is subsequently overlooked. Herein, we present a bottom-up nanoelectrode array fabrication approach that utilizes low-density and horizontally oriented single-walled carbon nanotubes (SWCNTs) as a template for the growth and precise positioning of Pt nanospheres. We further develop a computational model to optimize the nanosphere spatial arrangement and elucidate the trade-offs among kinetics, mass transport, and charge transport in an enzymatic biosensing scenario. Optimized model variables and experimental results confirm that tightly packed Pt nanosphere/SWCNT nanobands outperform low-density Pt nanosphere/SWCNT arrays in enzymatic glucose sensing. These computational and experimental results demonstrate the profound impact of nanoparticle placement on biosensor performance. This integration of bottom-up nanoelectrode array templating with analysis-informed design produces a foundation for controlling and optimizing nanotechnology-based electrochemical biosensor performance