Modeling the geometry of the endoplasmic reticulum network

Conference ProceedingFirst International Conference, AlCoB 2014, held in July 2014 in Tarragona, Spain.We have studied the network geometry of the endoplasmic reticulum by means of graph theoretical and integer programming models. The purpose is to represent this structure as close as possible by a class of finite, undirected and connected graphs the nodes of which have to be either of degree three or at most of degree three. We determine plane graphs of minimal total edge length satisfying degree and angle constraints, and we show that the optimal graphs are close to the ER network geometry. Basically, two procedures are formulated to solve the optimization problem: a binary linear program, that iteratively constructs an optimal solution, and a linear program, that iteratively exploits additional cutting planes from different families to accelerate the solution process. All formulations have been implemented and tested on a series of real-life and randomly generated cases. The cutting plane approach turns out to be particularly efficient for the real-life testcases, since it outperforms the pure integer programming approach by a factor of at least 10. © 2014 Springer International Publishing

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium.

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines

Plant ER geometry and dynamics: biophysical and cytoskeletal control during growth and biotic response.

This is the author accepted manuscript. The final version is available from Springer via the DOI in this record.The endoplasmic reticulum (ER) is an intricate and dynamic network of membrane tubules and cisternae. In plant cells, the ER 'web' pervades the cortex and endoplasm and is continuous with adjacent cells as it passes through plasmodesmata. It is therefore the largest membranous organelle in plant cells. It performs essential functions including protein and lipid synthesis, and its morphology and movement are linked to cellular function. An emerging trend is that organelles can no longer be seen as discrete membrane-bound compartments, since they can physically interact and 'communicate' with one another. The ER may form a connecting central role in this process. This review tackles our current understanding and quantification of ER dynamics and how these change under a variety of biotic and developmental cues.IS, RW and CL are funded by a Leverhulme Trust grant (RPG-2015-106) and CP by a Sainsbury studentship. LG is funded by the Gordon and Betty Moore Foundation for the lattice light sheet microscopy and by the Biology Department, Texas A&M University. L. Griffing would like to thank John Heddleston and Teng-Leong Chew at the Advanced Imaging Center in Janelia-HHMI Research Campus, Ashburn VA, for images taken with the light sheet microscope

Defining the dance: Quantification and classification of ER dynamics

The availability of quantification methods for sub-cellular organelle dynamic analysis has increased rapidly over the last 20 years. The application of these techniques to contiguous sub-cellular structures that exhibit dynamic re-modelling over a range of scales and orientations is challenging as quantification of ‘movement’ rarely corresponds to traditional, qualitative classifications of types of organelle movement. The plant endoplasmic reticulum represents a particular challenge for dynamic quantification as it itself is an entirely contiguous organelle that is in a constant state of flux and gross remodelling, controlled by the actinomyosin cytoskeleton

Emergence of the mitochondrial reticulum from fission and fusion dynamics

Mitochondria form a dynamic tubular reticulum within eukaryotic cells. Currently, quantitative understanding of its morphological characteristics is largely absent, despite major progress in deciphering the molecular fission and fusion machineries shaping its structure. Here we address the principles of formation and the large-scale organization of the cell-wide network of mitochondria. On the basis of experimentally determined structural features we establish the tip-to-tip and tip-to-side fission and fusion events as dominant reactions in the motility of this organelle. Subsequently, we introduce a graph-based model of the chondriome able to encompass its inherent variability in a single framework. Using both mean-field deterministic and explicit stochastic mathematical methods we establish a relationship between the chondriome structural network characteristics and underlying kinetic rate parameters. The computational analysis indicates that mitochondrial networks exhibit a percolation threshold. Intrinsic morphological instability of the mitochondrial reticulum resulting from its vicinity to the percolation transition is proposed as a novel mechanism that can be utilized by cells for optimizing their functional competence via dynamic remodeling of the chondriome. The detailed size distribution of the network components predicted by the dynamic graph representation introduces a relationship between chondriome characteristics and cell function. It forms a basis for understanding the architecture of mitochondria as a cell-wide but inhomogeneous organelle. Analysis of the reticulum adaptive configuration offers a direct clarification for its impact on numerous physiological processes strongly dependent on mitochondrial dynamics and organization, such as efficiency of cellular metabolism, tissue differentiation and aging

1D-3D hybrid modeling—from multi-compartment models to full resolution models in space and time

Investigation of cellular and network dynamics in the brain by means of modeling & simulation has evolved into a highly interdisciplinary field, that uses sophisticated modeling & simulation approaches to understand distinct areas of brain function. Depending on the underlying complexity, these models vary in level of detail to cope with the attached computational cost. Hence for large network simulations, single neurons are typically reduced to time-dependent signal processors, dismissing spatial aspects of the cells. For single cell or small-world networks, general purpose simulators allow for space and time-dependent simulations of electrical signal processing, based on the cable equation theory. An emerging field in Computational Neuroscience encompasses a new level of detail by incorporating the 3D morphology of cells and organelles into 3D space and time-dependent simulations. Every approach has its advantages and limitations, such as computational cost, integrated and methods-spanning simulation approaches, depending on the network size could establish new ways to investigate the brain. We present a hybrid simulation approach, that makes use of reduced 1D-models using e.g. the NEURON which couples to fully resolved models for simulating cellular and sub-cellular dynamics, including the detailed 3D-morphology of neurons and organelles. To couple 1D- & 3D-simulations, we present a geometry and membrane potential mapping framework, with which graph-based morphologies, e.g. in swc-/hoc-format, are mapped to full surface and volume representations of the neuron; membrane potential data from 1D-simulations are used as boundary conditions for full 3D simulations. Thus, established models and data, based on general purpose 1D-simulators, can be directly coupled to the emerging field of fully resolved highly detailed 3D-modeling approaches. The new framework is applied to investigate electrically active neurons and their intracellular spatio-temporal Calcium Dynamics

Energetics Based Spike Generation of a Single Neuron: Simulation Results and Analysis

Existing current based models that capture spike activity, though useful in studying information processing capabilities of neurons, fail to throw light on their internal functioning. It is imperative to develop a model that captures the spike train of a neuron as a function of its intracellular parameters for non-invasive diagnosis of diseased neurons. This is the first ever article to present such an integrated model that quantifies the inter-dependency between spike activity and intracellular energetics. The generated spike trains from our integrated model will throw greater light on the intracellular energetics than existing current models. Now, an abnormality in the spike of a diseased neuron can be linked and hence effectively analyzed at the energetics level. The spectral analysis of the generated spike trains in a time–frequency domain will help identify abnormalities in the internals of a neuron. As a case study, the parameters of our model are tuned for Alzheimer’s disease and its resultant spike trains are studied and presented. This massive initiative ultimately aims to encompass the entire molecular signaling pathways of the neuronal bioenergetics linking it to the voltage spike initiation and propagation; due to the lack of experimental data quantifying the inter dependencies among the parameters, the model at this stage adopts a particular level of functionality and is shown as an approach to study and perform disease modeling at the spike train and the mitochondrial bioenergetics level