A systems biology approach to axis formation during early zebrafish embryogenesis: from biophysical measurements to model inference

During early embryogenesis, secreted proteins dictate the body plan of developing individuals. The resulting patterns are thought to be imposed by a graded distribution of molecular signals. To this day, it is not fully understood how signaling gradients are formed, maintained and adjusted to body sizes of differently sized individuals. This dissertation aims to provide new insights into the biophysical underpinnings of signal molecule gradients of early embryonic patterning and propose novel mechanisms that allow for scale-invariant patterning. Two of the most important parameters controlling the range and shape of signaling gradients are the rate at which signaling molecules decay and diffuse. Despite their importance, such biophysical parameters have not been measured or have only been assessed under simplified assumptions or contexts for most developmental systems. In this dissertation I present two assays and specialized software packages that allow the assessment of these parameters in living zebrafish embryos. I then demonstrate how these tools can be used to answer long-standing questions in early embryogenesis, such as how the dorsal-ventral axis is formed. This thesis provides evidence suggesting, in contrast to current hypotheses, that the dorsal-ventral axis is formed by a simple source-sink mechanism. Moreover, I show how to use mathematical modeling equipped with parameters estimated from the biophysical measurements to describe scale-invariant patterning during germ layer patterning in zebrafish development. My model, together with a rigorous multidimensional parameter screen fitted in normal and articially size-reduced embryos, was able to identify a new mechanism that allows for scaling of the germ layers in differently-sized embryos with realistic parameter congurations. In summary, this dissertation outlines how a systems biology approach can play a crucial role to advance the understanding of classical open questions in developmental biology

Stochastic modelling of animal movement using intermittent search patterns

In a world that is changing rapidly due to anthropogenic disturbances, an understanding of animal behaviour is key to the protection and restoration of endangered populations. Animal movement is strongly correlated to changes in the environment and constrained by physiology. Intermittent search patterns are compositions of different movement modes enabling a forager to switch from smaller intensive search steps to large extensive search steps mostly used for relocation. In this thesis, we extend previous modelling approaches for intermittent search patterns and test these extensions on optimal foraging strategies with respect to various definitions of search efficiency incorporating costs of metabolism and locomotion. We show that intermittent search patterns appear to be optimal mainly if there is either a penalty on larger steps such as a decrease in perceptual radius or predation success rate, if the global prey density is low enough to force the predator to relocate between patches or individuals, or if the prey distribution is sparse. We also show that optimal foraging strategies are especially efficient if one movement mode is more advantageous with respect to the defined search efficiency than another, resulting in a larger difference between the optimal and worst strategies. Relocation phases are the heart of intermittent search patterns. We thus also show how predators might optimize their encounter rate during relocation (extensive search mode) phases moving along more erratic trajectories. In the second part of this thesis, we focus on how we can measure the spatial heterogeneity of prey and what this tells us about encounter rates and the chances that tagged prey items are caught. We present a novel metric that enables relative prediction of encounter rates and hitting probabilities for sparse environments by taking the initial location of prey into account. However, since measuring the location of all prey may be difficult in real world experiments, we also provide a method that uses tools developed in our optimal foraging study to estimate possible ranges for encounter rates and hitting probabilities when a set of movement and environment parameters are unknown.Arts and Sciences, Irving K. Barber School of (Okanagan)Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)Graduat

Measuring Protein Stability in Living Zebrafish Embryos Using Fluorescence Decay After Photoconversion (FDAP)

Protein stability influences many aspects of biology, and measuring the clearance kinetics of proteins can provide important insights into biological systems. In FDAP experiments, the clearance of proteins within living organisms can be measured. A protein of interest is tagged with a photoconvertible fluorescent protein, expressed in vivo and photoconverted, and the decrease in the photoconverted signal over time is monitored. The data is then fitted with an appropriate clearance model to determine the protein half-life. Importantly, the clearance kinetics of protein populations in different compartments of the organism can be examined separately by applying compartmental masks. This approach has been used to determine the intra- and extracellular half-lives of secreted signaling proteins during zebrafish development. Here, we describe a protocol for FDAP experiments in zebrafish embryos. It should be possible to use FDAP to determine the clearance kinetics of any taggable protein in any optically accessible organism

Scale-invariant patterning by size-dependent inhibition of Nodal signalling

Individuals can vary substantially in size, but the proportions of their body plans are often maintained. We generated smaller zebrafish by removing 30% of their cells at the blastula stages and found that these embryos developed into normally patterned individuals. Strikingly, the proportions of all germ layers adjusted to the new embryo size within 2 hours after cell removal. As Nodal–Lefty signalling controls germ-layer patterning, we performed a computational screen for scale-invariant models of this activator–inhibitor system. This analysis predicted that the concentration of the highly diffusive inhibitor Lefty increases in smaller embryos, leading to a decreased Nodal activity range and contracted germ-layer dimensions. In vivo studies confirmed that Lefty concentration increased in smaller embryos, and embryos with reduced Lefty levels or with diffusion-hindered Lefty failed to scale their tissue proportions. These results reveal that size-dependent inhibition of Nodal signalling allows scale-invariant patterning.This work was supported by EMBO (M.A.-C., L.M. and P.M.) and HFSP (P.M.) long-term fellowships, the NSF Graduate Research Fellowship Program (K.W.R.), NIH grant GM56211 (A.F.S.), and funding from the Max Planck Society, ERC Starting Grant 637840 and HFSP Career Development Award CDA00031/2013-C (P.M.)

Quantitative diffusion measurements using the open-source software PyFRAP

Fluorescence Recovery After Photobleaching (FRAP) and inverse FRAP (iFRAP) assays can be used to assess the mobility of fluorescent molecules. These assays measure diffusion by monitoring the return of fluorescence in bleached regions (FRAP), or the dissipation of fluorescence from photoconverted regions (iFRAP). However, current FRAP/iFRAP analysis methods suffer from simplified assumptions about sample geometry, bleaching/photoconversion inhomogeneities, and the underlying reaction-diffusion kinetics. To address these shortcomings, we developed the software PyFRAP, which fits numerical simulations of three-dimensional models to FRAP/iFRAP data and accounts for bleaching/photoconversion inhomogeneities. Using PyFRAP we determined the diffusivities of fluorescent molecules spanning two orders of magnitude in molecular weight. We measured the tortuous effects that cell-like obstacles exert on effective diffusivity and show that reaction kinetics can be accounted for by model selection. These applications demonstrate the utility of PyFRAP, which can be widely adapted as a new extensible standard for FRAP analysis