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Banerjee B, Das D. Effects of bursty synthesis in organelle biogenesis. Math Biosci 2024; 370:109156. [PMID: 38346665 DOI: 10.1016/j.mbs.2024.109156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Revised: 01/31/2024] [Accepted: 02/03/2024] [Indexed: 02/16/2024]
Abstract
A fundamental question of cell biology is how cells control the number of organelles. The processes of organelle biogenesis, namely de novo synthesis, fission, fusion, and decay, are inherently stochastic, producing cell-to-cell variability in organelle abundance. In addition, experiments suggest that the synthesis of some organelles can be bursty. We thus ask how bursty synthesis impacts intracellular organelle number distribution. We develop an organelle biogenesis model with bursty de novo synthesis by considering geometrically distributed burst sizes. We analytically solve the model in biologically relevant limits and provide exact expressions for the steady-state organelle number distributions and their means and variances. We also present approximate solutions for the whole model, complementing with exact stochastic simulations. We show that bursts generally increase the noise in organelle numbers, producing distinct signatures in noise profiles depending on different mechanisms of organelle biogenesis. We also find different shapes of organelle number distributions, including bimodal distributions in some parameter regimes. Notably, bursty synthesis broadens the parameter regime of observing bimodality compared to the 'non-bursty' case. Together, our framework utilizes number fluctuations to elucidate the role of bursty synthesis in producing organelle number heterogeneity in cells.
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Affiliation(s)
- Binayak Banerjee
- Department of Biological Sciences, Indian Institute of Science Education and Research Kolkata, Nadia 741 246, West Bengal, India
| | - Dipjyoti Das
- Department of Biological Sciences, Indian Institute of Science Education and Research Kolkata, Nadia 741 246, West Bengal, India.
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2
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Amiri KP, Kalish A, Mukherji S. Robustness and Universality in Organelle Size Control. PHYSICAL REVIEW LETTERS 2023; 130:018401. [PMID: 36669211 PMCID: PMC10316456 DOI: 10.1103/physrevlett.130.018401] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 11/07/2022] [Indexed: 06/15/2023]
Abstract
One of the grand challenges in cellular biophysics is understanding the precision with which cells assemble and maintain subcellular structures. Organelle sizes, for example, must be flexible enough to allow cells to grow or shrink them as environments demand yet be maintained within homeostatic limits. Despite identification of molecular factors that regulate organelle sizes we lack insight into the quantitative principles underlying organelle size control. Here we show experimentally that cells can robustly control average fluctuations in organelle size. By demonstrating that organelle sizes obey a universal scaling relationship we predict theoretically, our framework suggests that organelles grow in random bursts from a limiting pool of building blocks. Burstlike growth provides a general biophysical mechanism by which cells can maintain on average reliable yet plastic organelle sizes.
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Affiliation(s)
| | - Asa Kalish
- Department of Physics, Washington University in St. Louis
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Yadav A, Vagne Q, Sens P, Iyengar G, Rao M. Glycan processing in the Golgi: optimal information coding and constraints on cisternal number and enzyme specificity. eLife 2022; 11:76757. [PMID: 35175197 PMCID: PMC9154746 DOI: 10.7554/elife.76757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2022] [Accepted: 01/31/2022] [Indexed: 11/13/2022] Open
Abstract
Many proteins that undergo sequential enzymatic modification in the Golgi cisternae are displayed at the plasma membrane as cell identity markers. The modified proteins, called glycans, represent a molecular code. The fidelity of this glycan code is measured by how accurately the glycan synthesis machinery realises the desired target glycan distribution for a particular cell type and niche. In this paper, we construct a simplified chemical synthesis model to quantitatively analyse the tradeoffs between the number of cisternae, and the number and specificity of enzymes, required to synthesize a prescribed target glycan distribution of a certain complexity to within a given fidelity. We find that to synthesize complex distributions, such as those observed in real cells, one needs to have multiple cisternae and precise enzyme partitioning in the Golgi. Additionally, for fixed number of enzymes and cisternae, there is an optimal level of specificity (promiscuity) of enzymes that achieves the target distribution with high fidelity. The geometry of the fidelity landscape in the multidimensional space of the number and specificity of enzymes, inter-cisternal transfer rates, and number of cisternae, provides a measure for robustness and identifies stiff and sloppy directions. Our results show how the complexity of the target glycan distribution and number of glycosylation enzymes places functional constraints on the Golgi cisternal number and enzyme specificity.
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Affiliation(s)
| | - Quentin Vagne
- Laboratoire Physico Chimie Curie, Institut Curie, CNRS UMR168, Paris, France
| | - Pierre Sens
- Laboratoire Physico Chimie Curie, Institut Curie, CNRS UMR168, Paris, France
| | - Garud Iyengar
- Industrial Engineering and Operations Research, Columbia University, New York, United States
| | - Madan Rao
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences, Bangalore, India
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4
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Quiros DN, Nieto F, Mayorga LS. From cartoons to quantitative models in Golgi transport. Biol Cell 2020; 113:146-164. [PMID: 33275796 DOI: 10.1111/boc.202000107] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 11/29/2020] [Indexed: 11/29/2022]
Abstract
BACKGROUND Cell biology is evolving to become a more formal and quantitative science. In particular, several mathematical models have been proposed to address Golgi self-organisation and protein and lipid transport. However, most scientific articles about the Golgi apparatus are still using static cartoons that miss the dynamism of this organelle. RESULTS In this report, we show that schematic drawings of Golgi trafficking can be easily translated into an agent-based model using the Repast platform. The simulations generate an active interplay among cisternae and vesicles rendering quantitative predictions about Golgi stability and transport of soluble and membrane-associated cargoes. The models can incorporate complex networks of molecular interactions and chemical reactions by association with COPASI, a software that handles ordinary differential equations. CONCLUSIONS The strategy described provides a simple, flexible and multiscale support to analyse Golgi transport. The simulations can be used to address issues directly linked to the mechanism of transport or as a way to incorporate the complexity of trafficking to other cellular processes that occur in dynamic organelles. SIGNIFICANCE We show that the rules implicitly present in most schematic representations of intracellular trafficking can be used to build dynamic models with quantitative outputs that can be compared with experimental results.
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Affiliation(s)
- D Nicolas Quiros
- IHEM, Universidad Nacional de Cuyo, CONICET, Mendoza, Argentina.,Facultad de Ciencias Exactas y Naturales, Mendoza, Argentina
| | - Franco Nieto
- IHEM, Universidad Nacional de Cuyo, CONICET, Mendoza, Argentina
| | - Luis S Mayorga
- IHEM, Universidad Nacional de Cuyo, CONICET, Mendoza, Argentina.,Facultad de Ciencias Exactas y Naturales, Mendoza, Argentina
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Vagne Q, Vrel JP, Sens P. A minimal self-organisation model of the Golgi apparatus. eLife 2020; 9:47318. [PMID: 32755543 PMCID: PMC7406241 DOI: 10.7554/elife.47318] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/01/2019] [Accepted: 07/07/2020] [Indexed: 11/29/2022] Open
Abstract
The design principles dictating the spatio-temporal organisation of eukaryotic cells, and in particular the mechanisms controlling the self-organisation and dynamics of membrane-bound organelles such as the Golgi apparatus, remain elusive. Although this organelle was discovered 120 years ago, such basic questions as whether vesicular transport through the Golgi occurs in an anterograde (from entry to exit) or retrograde fashion are still strongly debated. Here, we address these issues by studying a quantitative model of organelle dynamics that includes: de-novo compartment generation, inter-compartment vesicular exchange, and biochemical conversion of membrane components. We show that anterograde or retrograde vesicular transports are asymptotic behaviors of a much richer dynamical system. Indeed, the structure and composition of cellular compartments and the directionality of vesicular exchange are intimately linked. They are emergent properties that can be tuned by varying the relative rates of vesicle budding, fusion and biochemical conversion.
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Affiliation(s)
- Quentin Vagne
- Center for Systems Biology Dresden, Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany
| | - Jean-Patrick Vrel
- Institut Curie, PSL Research University, CNRS, UMR 168, F-75005, Paris, France.,UPMC Univ Paris 06, CNRS, UMR 168, F-75005, Paris, France
| | - Pierre Sens
- Institut Curie, PSL Research University, CNRS, UMR 168, F-75005, Paris, France.,UPMC Univ Paris 06, CNRS, UMR 168, F-75005, Paris, France
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6
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Abstract
The Golgi apparatus has intrigued researchers since its discovery and despite the advances, there are still many open questions in regards to its shape and function. We propose a mechanical model of Golgi apparatus stack and explain its most elementary geometrical properties: the equilibrium number of cisternae, the stack size, and its general equilibrium shape. Combining both analytical and numerical methods we successfully reconstruct the stack morphology within the theory of bending elasticity. We demonstrate that energy-wise the stack prefers an overall bent shape and show strong evidence that the adhesion strength determines the equilibrium number of cisternae per stack. We explore the morphological role of fenestrations and discuss their impact on the overall stack structure. We also comment on the effects of the asymmetry in the composition of membrane leaflets on the shape of the cisternae and thus offer a broad steady-state study of the stack morphology and present a method that can be used also for other membrane-bound organelles.
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Affiliation(s)
- U Jelerčič
- Department of Theoretical Physics, Jožef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia. Current affiliation: Department of Chemical Engineering and Ilse Kats Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva, Israel
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7
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Mayorga LS, Cebrian I, Verma M, Hoops S, Bassaganya-Riera J. Reconstruction of endosomal organization and function by a combination of ODE and agent-based modeling strategies. Biol Direct 2018; 13:25. [PMID: 30621747 PMCID: PMC6883406 DOI: 10.1186/s13062-018-0227-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2018] [Accepted: 10/16/2018] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Reproducing cell processes using an in silico system is an essential tool for understanding the underlying mechanisms and emergent properties of this extraordinary complex biological machine. However, computational models are seldom applied in the field of intracellular trafficking. In a cell, numerous molecular interactions occur on the surface or in the interior of membrane-bound compartments that continually change position and undergo dynamic processes of fusion and fission. At present, the available simulation tools are not suitable to develop models that incorporate the dynamic evolution of the cell organelles. RESULTS We developed a modeling platform combining Repast (Agent-Based Modeling, ABM) and COPASI (Differential Equations, ODE) that can be used to reproduce complex networks of molecular interactions. These interactions occur in dynamic cell organelles that change position and composition over the course of time. These two modeling strategies are fundamentally different and comprise of complementary capabilities. The ODEs can easily model the networks of molecular interactions, signaling cascades, and complex metabolic reactions. On the other hand, ABM software is especially suited to simulate the movement, interaction, fusion, and fission of dynamic organelles. We used the combined ABM-ODE platform to simulate the transport of soluble and membrane-associated cargoes that move along an endocytic route composed of early, sorting, recycling and late endosomes. We showed that complex processes that strongly depend on transport can be modeled. As an example, the hydrolysis of a GM2-like glycolipid was programmed by adding a trans-Golgi network compartment, lysosomal enzyme trafficking, endosomal acidification, and cholesterol processing to the simulation model. CONCLUSIONS The model captures the highly dynamic nature of cell compartments that fuse and divide, creating different conditions for each organelle. We expect that this modeling strategy will be useful to understand the logic underlying the organization and function of the endomembrane system. REVIEWERS This article was reviewed by Drs. Rafael Fernández-Chacón, James Faeder, and Thomas Simmen.
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Affiliation(s)
- Luis S Mayorga
- Facultad de Ciencias Médicas, Facultad de Ciencias Exactas y Naturales, IHEM (Universidad Nacional de Cuyo, CONICET), Casilla de Correo 56, 5500, Mendoza, Argentina.
| | - Ignacio Cebrian
- Facultad de Ciencias Médicas, Facultad de Ciencias Exactas y Naturales, IHEM (Universidad Nacional de Cuyo, CONICET), Casilla de Correo 56, 5500, Mendoza, Argentina
| | - Meghna Verma
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA.,Graduate Program in Translational Biology, Medicine and Health, Virginia Tech, Blacksburg, VA, USA
| | - Stefan Hoops
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA.,Biocomplexity Institute and Initiative University of Virginia, 995 Research Park Boulevard, Charlottesville, VA, 22911, USA
| | - Josep Bassaganya-Riera
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA
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Mayorga LS, Verma M, Hontecillas R, Hoops S, Bassaganya-Riera J. Agents and networks to model the dynamic interactions of intracellular transport. CELLULAR LOGISTICS 2017; 7:e1392401. [PMID: 29296512 DOI: 10.1080/21592799.2017.1392401] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Revised: 10/03/2017] [Accepted: 10/10/2017] [Indexed: 01/28/2023]
Abstract
Cell biology is increasingly evolving to become a more formal and quantitative science. The field of intracellular transport is no exception. However, it is extremely challenging to formulate mathematical and computational models for processes that involve dynamic structures that continuously change their shape, position and composition, leading to information transfer and functional outcomes. The two major strategies employed to represent intracellular trafficking are based on "ordinary differential equations" and "agent-" based modeling. Both approaches have advantages and drawbacks. Combinations of both modeling strategies have promising characteristics to generate meaningful simulations for intracellular transport and allow the formulation of new hypotheses and provide new insights. In the near future, cell biologists will encounter and hopefully overcome the challenge of translating descriptive cartoon representations of biological systems into mathematical network models.
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Affiliation(s)
- Luis S Mayorga
- IHEM (Universidad Nacional de Cuyo, CONICET), Facultad de Ciencias Médicas, Facultad de Ciencias Exactas y Naturales, Mendoza, Argentina
| | - Meghna Verma
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA
| | - Raquel Hontecillas
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA
| | - Stefan Hoops
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA
| | - Josep Bassaganya-Riera
- Nutritional Immunology and Molecular Medicine Laboratory, Biocomplexity Institute, Virginia Tech, Blacksburg, VA, USA
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