The physics of cellulose biosynthesis : polymerization and self-organization, from plants to bacteria

This thesis deals with many different biological problems concerning cellulose biosynthesis. Cellulose is made by all plants, and therefore it is probably the most abundant organic compound on Earth. Aside from being the primary building material for plants, this biopolymer is of great economic importance globally because it is the major constituent of cotton (over 94%) and wood (over 50%). Moreover, according to how it is treated, cellulose can be used to make paper, film, explosives, and plastics, in addition to having many other industrial uses. The paper in this book, for example, contains cellulose, as do some of the clothes we are wearing.In addition to higher plants, cellulose is synthesized by a number of bacterial species, algae, lower eukaryotes (tunicates), and the slime mold Dictyostelium. The function of cellulose in these different groups of organisms reflects the diverse role associated with this simple structural polysaccharide. Whereas it is possible for some organisms, specifically bacteria, to survive in absence of cellulose synthesis, it may not be true for most vascular plant cells. As such, the importance of cellulose in the life of a plant cannot be overemphasized since it not only provides the necessary strength to resist the turgor pressure in plant cells, but also has a distinct role in maintaining the size, shape and differentiation of most plant cells.The aim of this thesis is to investigate, by mean of theoretical methods, coupled to simulation techniques, the polymerization, crystallization, and self-organization mechanism of this universal distributed polysaccharide, in different biological systems.We start in Chapter 2 with a general description of the chemical and mechanical features of the cellulose microfibrils (CMFs), the crystalline form of cellulose in nature. After a brief overview on the biogenesis of the CMFs in the plant cells we proceed focusing on two of the most important cellulose producer entities: the plant cells and the Acetobacter cells.The first part of the thesis, therefore, is concerned with all the aspects related to cellulose biosynthesis in the cell-wall of plant cells. We begin in Chapter 3 with a detailed investigation on the self-assembly mechanism of the Cellulose Synthase Complex (CSC) in higher plants, the hexagonal Rosette CSC: based on the known experimental evidences regarding the internal structure of this protein, we are able to build a theoretical scheme to characterize the interactions among the CSC subunits; then, by mean of a Monte Carlo algorithm, we implement this interaction scheme in a simulation that document step by step the formation of the hexagonal enzyme. Our model is able to explain the assembly of many types of CSCs, like the hexagonal Rosettes of plants as well as the linear CSCs present in bacteria and the clusters that form in the cell wall of some algae.After having clarified the formation of the Rosette CSC structure, we shift our attention to its motion in the plasma membrane of plant cell. In Chapter 4 we present a biophysical model that unravels the force generating mechanism underlying the propulsion of the Rosette CSC: the model identifies polymerization and crystallization as driving forces, and elucidates the role of polymer flexibility and membrane elasticity as force transducers. On the basis of our model and appropriate values for the relevant physical constants, we obtain a theoretical estimate for the velocity of the CSC that is in agreement with the experimental value. To have a proof a principle of the proposed mechanism, we have also developed a stochastic simulation that reproduces the movement of the Rosette CSC in the fluid membrane of the plant cell.The last issue related to plant cells cellulose is the formulation of a mathematical model to analyze the building of cell wall architecture (Chapter 5). The highly regular textures observed in cell walls reflect the spatial organization of the cellulose CMFs. Based on a geometrical hypothesis proposed earlier, we formulate a model that describes the space-time evolution of the density of Rosette CSCs in the plasma membrane of plant cell. The trajectories of the Rosettes are assumed to be governed by an optimal packing constraint of the CMFs that couples the direction of motion to the density of the CSCs. Our model is based on a relatively small numbers of variables that can be tuned to obtain most of the cell wall textures that have been found experimentally. Moreover, we demonstrate that it is also robust against a number of perturbations and noise effects.The second part of the thesis is focused on the cellulose-producing Acetobacter cells, which live at the air-liquid interface and which exhibit a peculiar motion during the cellulose polymerization process. The mechanism of formation as well as the structure of the bacterial cellulose has been studied extensively in recent decades. The cellulose product appears as a long ribbon, composed of many CMFs, which extends parallel to the longitudinal axis of the cell, and which is synthesized by a linear array of particles placed along the axis of the bacterial rod. Goal of this chapter (Chapter 6) is to correlate the peculiar motion of Acetobacter with an hydrodynamic effect caused by the interactions between the cellulose CMFs and the fluid in which they are immersed. To further assess the correctness of our model, in the last part of the thesis we implement a Brownian Dynamics simulation that is able to reproduce the main features of this particular bacterial motion.With this work we hope to contribute in elucidating some key questions, both regarding the cell biology of plants as well as concerning the physics of interacting filaments and complex macromolecular assemblies.