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In many cell types, mitochondria undergo extensive fusion and fission to form dynamic, responsive network structures that contribute to a number of homeostatic, metabolic, and signaling functions. The relationship between the dynamic interactions of individual mitochondrial units and the cell-scale network architecture remains an open area of study. In this work, we use coarse-grained simulations and approximate analytic models to establish how the network morphology is governed by local mechanical and kinetic parameters. The transition between fragmented structures and extensive networks is controlled by local fusion-to-fission ratios, network density, and geometric constraints. Similar fusion rate constants are found to account for the very different structures formed by mammalian networks (poised at the percolation transition) and well-connected budding yeast networks. Over a broad parameter range, the simulated network structures can be described by effective mean-field association constants that exhibit a nonlinear dependence on the microscopic nonequilibrium fusion, fission, and transport rates. Intermediate fusion rate constants are shown to result in the highest rates of network remodeling, with mammalian mitochondrial networks situated in a regime of high turnover. This spatially resolved modeling and simulation framework helps elucidate the emergence of cellular scale network structures, and allows for the quantitative extraction of microscopic kinetic parameters from past and future experimental data. Published by the American Physical Society2024 

The peripheral endoplasmic reticulum (ER) forms a dense, interconnected, and constantly evolving network of membrane-bound tubules in eukaryotic cells. While individual structural elements and the morphogens that stabilize them have been described, a quantitative understanding of the dynamic large-scale network topology remains elusive. We develop a physical model of the ER as an active liquid network, governed by a balance of tension-driven shrinking and new tubule growth. This minimalist model gives rise to steady-state network structures with density and rearrangement timescales predicted from the junction mobility and tubule spawning rate. Several parameter-independent geometric features of the liquid network model are shown to be representative of ER architecture in live mammalian cells. The liquid network model connects the timescales of distinct dynamic features such as ring closure and new tubule growth in the ER. Furthermore, it demonstrates how the steady-state network morphology on a cellular scale arises from the balance of microscopic dynamic rearrangements. 

The endoplasmic reticulum (ER) forms an interconnected network of tubules stretching throughout the cell. Understanding how ER functionality relies on its structural organization is crucial for elucidating cellular vulnerability to ER perturbations, which have been implicated in several neuronal pathologies. One of the key functions of the ER is enabling Ca ${}^{2+}$signaling by storing large quantities of this ion and releasing it into the cytoplasm in a spatiotemporally controlled manner. Through a combination of physical modeling and live-cell imaging, we demonstrate that alterations in ER shape significantly impact its ability to support efficient local Ca ${}^{2+}$releases, due to hindered transport of luminal content within the ER. Our model reveals that rapid Ca ${}^{2+}$release necessitates mobile luminal buffer proteins with moderate binding strength, moving through a well-connected network of ER tubules. These findings provide insight into the functional advantages of normal ER architecture, emphasizing its importance as a kinetically efficient intracellular Ca ${}^{2+}$delivery system. 

Abstract The function of many membrane-enclosed intracellular structures relies on release of diffusing particles that exit through narrow pores or channels in the membrane. The rate of release varies with pore size, density, and length of the channel. We propose a simple approximate model, validated with stochastic simulations, for estimating the effective release rate from cylinders, and other simple-shaped domains, as a function of channel parameters. The results demonstrate that, for very small pores, a low density of channels scattered over the boundary is sufficient to achieve substantial rates of particle release. Furthermore, we show that increasing the length of passive channels will both reduce release rates and lead to a less steep dependence on channel density. Our results are compared to previously-measured local calcium release rates from tubules of the endoplasmic reticulum, providing an estimate of the relevant channel density responsible for the observed calcium efflux. 

Macroautophagy is a homeostatic process required to clear cellular waste. Neuronal autophagosomes form constitutively in the distal tip of the axon and are actively transported toward the soma, with cargo degradation initiated en route. Cargo turnover requires autophagosomes to fuse with lysosomes to acquire degradative enzymes; however, directly imaging these fusion events in the axon is impractical. Here we use a quantitative model, parameterized and validated using data from primary hippocampal neurons, to explore the autophagosome maturation process. We demonstrate that retrograde autophagosome motility is independent of fusion and that most autophagosomes fuse with only a few lysosomes during axonal transport. Our results indicate that breakdown of the inner autophagosomal membrane is much slower in neurons than in nonneuronal cell types, highlighting the importance of this late maturation step. Together, rigorous quantitative measurements and mathematical modeling elucidate the dynamics of autophagosome–lysosome interaction and autophagosomal maturation in the axon. 

For many nuclear-encoded mitochondrial genes, mRNA localizes to the mitochondrial surface co-translationally, aided by the association of a mitochondrial targeting sequence (MTS) on the nascent peptide with the mitochondrial import complex. For a subset of these co-translationally localized mRNAs, their localization is dependent on the metabolic state of the cell, while others are constitutively localized. To explore the differences between these two mRNA types we developed a stochastic, quantitative model for MTS-mediated mRNA localization to mitochondria in yeast cells. This model includes translation, applying gene-specific kinetics derived from experimental data; and diffusion in the cytosol. Even though both mRNA types are co-translationally localized we found that the steady state number, or density, of ribosomes along an mRNA was insufficient to differentiate the two mRNA types. Instead, conditionally-localized mRNAs have faster translation kinetics which modulate localization in combination with changes to diffusive search kinetics across metabolic states. Our model also suggests that the MTS requires a maturation time to become competent to bind mitochondria. Our work indicates that yeast cells can regulate mRNA localization to mitochondria by controlling mitochondrial volume fraction (influencing diffusive search times) and gene translation kinetics (adjusting mRNA binding competence) without the need for mRNA-specific binding proteins. These results shed light on both global and gene-specific mechanisms that enable cells to alter mRNA localization in response to changing metabolic conditions.