Adriana T. Dawes

During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within and between cells. Here, we develop and present a model-independent ordinary differential equation (ODE) framework for analyzing pattern formation in a homogeneous cell array. In contrast to traditional approaches that focus on specific equations, our method relies solely on general assumptions about global intercellular communication (between cells) and qualitative properties of local intracellular biochemical signaling (within cells). Prior work has shown that global intercellular communication networks alone determine the possible emergent patterns in a generic system. We build on these results by demonstrating that additional constraints on the local intracellular signaling network lead to a single stable pattern which depends on the qualitative features of the network. Our framework enables the prediction of cell fate patterns with minimal modeling assumptions, and provides a powerful tool for inferring unknown interactions within signaling networks by analyzing tissue-level patterns.

Centrosomes are critical organelles associated with the nucleus, consisting of a pair of centrioles surrounded by a cloud of pericentriolar material. They serve as key nucleation sites for microtubule arrays and are essential for positioning the nucleus prior to cell division, but mechanisms for ensuring proper centrosome positioning are not well understood. Previous research has identified asymmetries in microtubule arrays nucleated by centrosomes prior to cell division, including during the first cell cycle in Caenorhabditis elegans, as playing a critical role in centrosome positioning, however the origin of this asymmetry remains unclear. To explore potential sources of centrosome asymmetry, we developed a mathematical model of centrosome maturation, distinct from prior models by not presuming any inherent symmetry or asymmetry. We determined model parameters using in vivo data on the recruitment and recovery of GFP-tagged AIR-1 (Aurora kinase A) in early C. elegans embryos, enabling precise parameter estimation. Our results reveal an intrinsic asymmetry in centrosome dynamics that highlights the potential for variability in physical centrosome characteristics. These dynamics produce highly consistent microtubule arrays, independent of specific structural details. These findings offer novel insights into centrosome behavior and positioning during cell division and early embryonic development.

During development, precise cellular patterning is essential for the formation of functional tissues and organs. These patterns arise from conserved signaling networks that regulate communication both within and between cells. Here, we develop and present a model-independent ordinary differential equation (ODE) framework for analyzing pattern formation in a homogeneous cell array. In con trast to traditional approaches that focus on specific equations, our method relies solely on general assumptions about global intercellular communication (between cells) and qualitative properties of local intracellular biochemical signal ing (within cells). Prior work has shown that global intercellular communication networks alone determine the possible emergent patterns in a generic system. We build on these results by demonstrating that additional constraints on the local intracellular signaling network lead to a single stable pattern which depends on the qualitative features of the network. Our framework enables the prediction of cell fate patterns with minimal modeling assumptions, and provides a powerful tool for inferring unknown interactions within signaling networks by analyzing tissue-level patterns. Mathematics Subject Classification: 34A34, 24C14, 34C23, 92C15, 92C40, 92C42

Mathematical models of complex systems rely on parameter values to produce a desired behavior. As mathematical and computational models increase in complexity, it becomes correspondingly difficult to find parameter values that satisfy system constraints. We propose a Markov Chain Monte Carlo (MCMC) approach for the problem of constrained model parameter generation by designing a Markov chain that efficiently explores a model’s parameter space. We demonstrate the use of our proposed methodology to analyze responses of a newly constructed bistability-constrained model of protein phosphorylation to perturbations in the underlying protein network. Our results suggest that parameter generation for constrained models using MCMC provides powerful tools for modeling-aided analysis of complex natural processes.

A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares time series data relies on a pairwise distance between trajectories, and the choice of distance measure determines the accuracy and speed of the time series comparison. This paper introduces an optimal transport type distance for comparing time series trajectories that are allowed to lie in spaces of different dimensions and/or with differing numbers of points possibly unequally spaced along each trajectory. The construction is based on a modified Gromov–Wasserstein distance optimization program, reducing the problem to a Wasserstein distance on the real line. The resulting program has a closed-form solution and can be computed quickly due to the scalability of the one-dimensional Wasserstein distance. We discuss theoretical properties of this distance measure, and empirically demonstrate the performance of the proposed distance on several datasets with a range of characteristics commonly found in biologically relevant data. We also use our proposed distance to demonstrate that averaging oscillatory time series trajectories using the recently proposed Fused Gromov–Wasserstein barycenter retains more characteristics in the averaged trajectory when compared to traditional averaging, which demonstrates the applicability of Fused Gromov–Wasserstein barycenters for biological time series. Fast and user friendly software for computing the proposed distance and related applications is provided. The proposed distance allows fast and meaningful comparison of biological time series and can be efficiently used in a wide range of applications.

Mathematical models of natural processes rely on parameter values to produce scientifically meaningful simulation behaviour such as bistability or oscillations. Frequently, the parameter values cannot be estimated from experimental data and have to be randomly selected and then evaluated whether they satisfy system constraints. Evaluating these constraints for a randomly chosen vector of parameter values can be computationally very costly, preventing efficient learning of the model parameter space. We propose a novel application of a Markov chain methodology to generate a large number of parameter vectors for high-dimensional models with potentially complicated parameter space structures. The method is based on a modification of the Metropolis-Hastings algorithm which learns the parameter space as the chain progresses, reducing unnecessary evaluations of model constraints and resulting in many working parameter vectors that generate a desired model behaviour. We show that the method outperforms commonly used parameter generating schemes in terms of speed and accuracy of parameter space learning. Further, we demonstrate how the learned parameter space can be used to identify bistability mechanisms in a model of protein phosphorylation. The method can be applied to any mathematical or computational models for efficient parameter generation and discovery of underlying parameter space structure.

Centrosomes serve as a site for microtubule nucleation and these microtubules will grow and interact with the motor protein dynein at the cortex. The position of the centrosomes determines where the mitotic spindle will develop across all cell types. Centrosome positioning is achieved through dynein and microtubule-mediated force generation. The mechanism and regulation of force generation during centrosome positioning are not fully understood. Centrosome and pronuclear movement in the first cell cycle of the Caenorhabditis elegans early embryo undergoes both centration and rotation prior to cell division. The proteins LET-99 and GPB-1 have been postulated to have a role in force generation associated with pronuclear centration and rotation dynamics. When the expression of these proteins is perturbed, pronuclear positioning exhibits a movement defect characterized by oscillatory ("wobble") behavior of the pronuclear complex (PNC). To determine if this movement defect is due to an effect on cortical dynein distribution, we utilize RNAi-mediated knockdown of LET-99 and GPB-1 to induce wobble and assay for any effects on GFP-tagged dynein localization in the early C. elegans embryo. To compare and quantify the movement defect produced by the knockdown of LET-99 and GPB-1, we devised a quantification method that measures the strength of wobble ("wobble metric") observed under these experimental conditions. Our quantification of pronuclear complex dynamics and dynein localization shows that loss of LET-99 and GPB-1 induces a similar movement defect which is independent of cortical dynein localization in the early C. elegans embryo.