Limits on Biological Size Regulation and Biochemical Sensing

Abstract

Living systems function reliably and reproducibly, despite intrinsic variability at the molecular level. In this thesis, we investigate three specific biological models and limits on their performance, given intrinsic variability. We first consider limits to the precision of cell division size, which is typically found to vary for a given cell type in a constant environment by about 10-20%. To understand the origin of this level of variability, we introduce a phenomenological, stochastic model which includes both growth rate noise and size sensor noise. Using our modeling framework, together with previously published E. coli growth data, we directly quantify the amplitudes of two uncorrelated noise sources which can together explain most of E. coli's division size variability: growth noise and expression noise of the putative size-sensor protein FtsZ. In accounting for both of these sources of noise, our model makes a previously unappreciated connection between the biological problem of size variability and the classical theory of Kalman filtering. Our model generates testable predictions for possible experiments that could tune the level of size variability. We use a similar phenomenological approach, inspired by ideas from control theory and Kalman filtering, to understand limits on the precision of organ size. In Drosophila, it has been observed that stochastic variations during development, at the level of individual organs, account for variation in adult organ sizes at the level of about 1%. To understand this level of variability, we consider a feedback model of growth control in which a size estimator controls the approach of organ size to a target final size. Our model quantifies how growth noise and sensing noise set the scale of final size variability. It also quantifies how mean final size depends on model parameters, and thereby suggests experimental perturbations which could probe candidate mechanisms of growth control. Finally we consider limits on biochemical sensing in confined domains. The precision of biochemical sensing is inherently limited because of the random, diffusive arrival of discrete ligand molecules. Our results quantify how confinement effects, sensor size, and sensor placement correct well-understood scaling relations for biochemical sensors in infinite domains of diffusion.