The single-celled green algae
with its two flagella-microtubule-based structures of equal and constant lengths-is the canonical model organism for studying size control of organelles. Experiments ...have identified motor-driven transport of tubulin to the flagella tips as a key component of their length control. Here we consider a class of models whose key assumption is that proteins responsible for the intraflagellar transport (IFT) of tubulin are present in limiting amounts. We show that the limiting-pool assumption is insufficient to describe the results of severing experiments, in which a flagellum is regenerated after it has been severed. Next, we consider an extension of the limiting-pool model that incorporates proteins that depolymerize microtubules. We show that this 'active disassembly' model of flagellar length control explains in quantitative detail the results of severing experiments and use it to make predictions that can be tested in experiments.
Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing ...budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This "antenna mechanism" involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control.
Microtubule-based cytoskeletal structures aid in cell motility, cell polarization, and intracellular transport. These functions require a coordinated effort of regulatory proteins which interact with ...microtubule cytoskeleton distinctively. In-vitro experiments have shown that free tubulin can repair nanoscale damages of microtubules created by severing proteins. Based on this observation, we theoretically analyze microtubule severing as a competition between the processes of damage spreading and tubulin-induced repair. We demonstrate that this model is in quantitative agreement with in-vitro experiments and predict the existence of a critical tubulin concentration above which severing becomes rare, fast, and sensitive to concentration of free tubulin. We show that this sensitivity leads to a dramatic increase in the dynamic range of steady-state microtubule lengths when the free tubulin concentration is varied, and microtubule lengths are controlled by severing. Our work demonstrates how synergy between tubulin and microtubule-associated proteins can bring about specific dynamical properties of microtubules.
•Past experiments show tubulin repairing severing protein-induced damages on microtubules•Theoretical analysis describes severing as a contest between damage spreading and repair•Model predicts a regime where severing probability is sensitive to tubulin concentration•Varying free tubulin dramatically changes steady-state microtubule lengths
Biological sciences; Cell biology
Cells contain elaborate and interconnected networks of protein polymers, which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles and ...controls dynamic changes in cell polarity, shape, and movement. Many of these processes require tight control of the size and shape of cytoskeletal structures, which is achieved despite rapid turnover of their molecular components. Here we review mechanisms by which cells control the size of filamentous cytoskeletal structures, from the point of view of simple quantitative models that take into account stochastic dynamics of their assembly and disassembly. Significantly, these models make experimentally testable predictions that distinguish different mechanisms of length control. Although the primary focus of this review is on cytoskeletal structures, we believe that the broader principles and mechanisms discussed herein will apply to a range of other subcellular structures whose sizes are tightly controlled and are linked to their functions.
Single-class closed queueing networks, consisting of infinite-server and single-server queues with exponential service times and probabilistic routing, admit product-from solutions. Such solutions, ...although seemingly tractable, are difficult to characterize explicitly for practically relevant problems due to the exponential combinatorial complexity of its normalization constant (partition function). In “A Probabilistic Approach to Growth Networks,” Jelenković, Kondev, Mohapatra, and Momčilović develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. From a methodological perspective, a fundamental feature of the proposed approach is that it provides exact results for order-one probabilities, even though the analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.
Widely used closed product-form networks have emerged recently as a primary model of stochastic growth of subcellular structures, for example, cellular filaments. The baseline bio-molecular model is equivalent to a single-class closed queueing network, consisting of single-server and infinite-server queues. Although this model admits a seemingly tractable product-form solution, explicit analytical characterization of its partition function is difficult due to the large-scale nature of bio-molecular networks. To this end, we develop a novel methodology, based on a probabilistic representation of product-form solutions and large-deviations concentration inequalities, which identifies distinct operating regimes and yields explicit expressions for the marginal distributions of queue lengths. The parameters of the derived distributions can be computed from equations involving large-deviations rate functions, often admitting closed-form algebraic expressions. From a methodological perspective, a fundamental feature of our approach is that it provides exact results for order-one probabilities, even though our analysis involves large-deviations rate functions, which characterize only vanishing probabilities on a logarithmic scale.
Supplemental Material:
The e-companion is available at
https://doi.org/10.1287.opre.2021.2195
.
Actin cables are linear cytoskeletal structures that serve as tracks for myosin-based intracellular transport of vesicles and organelles in both yeast and mammalian cells. In a yeast cell undergoing ...budding, cables are in constant dynamic turnover yet some cables grow from the bud neck toward the back of the mother cell until their length roughly equals the diameter of the mother cell. This raises the question: how is the length of these cables controlled? Here we describe a novel molecular mechanism for cable length control inspired by recent experimental observations in cells. This "antenna mechanism" involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. We compute the probability distribution of cable lengths as a function of several experimentally tuneable parameters such as the formin-binding affinity of Smy1 and the concentration of myosin motors delivering Smy1. These results provide testable predictions of the antenna mechanism of actin-cable length control.
How the size of micrometer-scale cellular structures such as the mitotic spindle, cytoskeletal filaments, the nucleus, the nucleolus, and other non-membrane bound organelles is controlled despite a ...constant turnover of their constituent parts is a central problem in biology. Experiments have implicated the limiting-pool mechanism: structures grow by stochastic addition of molecular subunits from a finite pool until the rates of subunit addition and removal are balanced, producing a structure of well-defined size. Here, we consider these dynamics when multiple filamentous structures are assembled stochastically from a shared pool of subunits. Using analytical calculations and computer simulations, we show that robust size control can be achieved only when a single filament is assembled. When multiple filaments compete for monomers, filament lengths exhibit large fluctuations. These results extend to three-dimensional structures and reveal the physical limitations of the limiting-pool mechanism of size control when multiple organelles are assembled from a shared pool of subunits.
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•The limiting-pool mechanism of size control successfully assembles one structure of a well defined size•Multiple structures assembled from a common limiting pool exhibit large size fluctuations•Assembly of multiple structures exhibits three characteristic timescales
While the limiting-pool mechanism can control the size of an individual sub-cellular structure, it fails to control the sizes of multiple structures that are all competing for the same pool of subunits.
Cells contain elaborate and interconnected networks of protein polymers which make up the cytoskeleton. The cytoskeleton governs the internal positioning and movement of vesicles and organelles, and ...controls dynamic changes in cell polarity, shape and movement. Many of these processes require tight control of the size and shape of these cytoskeletal structures. A key question in cell biology is how these structures maintain a particular size and shape despite the rapid turnover of their components. In this thesis I show that the emerging mechanisms by which cells control and regulate the size of filamentous cytoskeletal structures can be classified using key parameters related to their assembly and disassembly kinetics. First, I examine quantitative models based on these specific molecular mechanisms of length control and make experimentally testable predictions that can be used to distinguish different mechanisms of length-control. Second, I study the length control of actin cables in budding yeast cells. Inspired by recent experimental observations in cells, I propose a novel antenna mechanism for cable length control which involves three key proteins: formins, which polymerize actin, Smy1 proteins, which bind formins and inhibit actin polymerization, and myosin motors, which deliver Smy1 to formins, leading to a length-dependent actin polymerization rate. My results provide testable predictions of the antenna mechanism of actin-cable length control. Next I consider the question of how different sized structures can co-exist in the same cytoplasm while making use of the same building blocks. Using theory, I discover limitations imposed by physics on the finite monomer pool as a mechanism of size control and conclude that additional length control mechanisms are required if a cell is to maintain multiple structures. While the primary focus of this thesis is on cytoskeletal structures, the broader principles and mechanisms discussed herein will apply to a range of other subcellular structures whose sizes are tightly controlled and are linked to their functions.
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