Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors
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Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors Youngmin Park1
· Thomas G. Fai1,2
Received: 10 April 2020 / Accepted: 7 October 2020 © Society for Mathematical Biology 2020
Abstract We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in Fai et al. (Phys Rev Fluids 2:113601, 2017) to a fast–slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The model’s key parameters include: (1) the ratio of motors that prefer to push toward the head of the dendritic spine to the motors that prefer to push in the opposite direction, and (2) the viscous drag exerted on the vesicle by the spine constriction. We perform a numerical bifurcation analysis in these parameters and find that steady-state vesicle velocities appear and disappear through several saddle-node bifurcations. This process allows us to identify the region of parameter space in which multiple stable velocities exist. We show by direct calculations that there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio, at which there is a transition from unidirectional to bidirectional motion, consistent with experimental observations of vesicle trajectories in the literature. Keywords Neurophysiology · Cell physiology · Motor transport · Vesicle transport · Dendritic spines
1 Introduction Pyramidal neurons, the most ubiquitous type of neurons in the mammalian neocortex, each feature tens of thousands of excitatory convergent synaptic inputs. Most incoming
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Youngmin Park [email protected]
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Department of Mathematics, Brandeis University, Waltham, MA 02453, USA
2
Department of Mathematics and Volen Center for Complex Systems, Brandeis University, Waltham, MA 02453, USA 0123456789().: V,-vol
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Y. Park, T. G. Fai
synaptic signals terminate on submicron bulbs known as dendritic spines (Nimchinsky et al. 2002). Spines exhibit a significant degree of morphological plasticity (Kasai et al. 2010; Holtmaat and Svoboda 2009) with pathological spine formation implicated in disorders such as Autism spectrum disorder and Alzheimer’s disease (Penzes et al. 2011). Normal synaptic function, including the dynamic process of spine remodeling, requires intracellular transport for maintenance (da Silva et al. 2015). Micron-sized vesicles carrying surface proteins are squeezed through the submicron-sized neck, undergoing strong deformations before fusing with the spine head. Recent experiments have shown that movement is not always unidirectional (translocation), but includes no movement (corking), and rejection (Park et al. 2006; Wang et al. 2008). The mechanisms underlying these directional changes are not well understood. To understand this question in greater detail, we use two primary consid
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