1
|
Fernández Santoro EM, Karim A, Warnaar P, De Zeeuw CI, Badura A, Negrello M. Purkinje cell models: past, present and future. Front Comput Neurosci 2024; 18:1426653. [PMID: 39049990 PMCID: PMC11266113 DOI: 10.3389/fncom.2024.1426653] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2024] [Accepted: 06/24/2024] [Indexed: 07/27/2024] Open
Abstract
The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.
Collapse
Affiliation(s)
| | - Arun Karim
- Department of Neuroscience, Erasmus MC, Rotterdam, Netherlands
| | - Pascal Warnaar
- Department of Neuroscience, Erasmus MC, Rotterdam, Netherlands
- Netherlands Institute for Neuroscience, Royal Academy of Arts and Sciences, Amsterdam, Netherlands
| | - Chris I. De Zeeuw
- Department of Neuroscience, Erasmus MC, Rotterdam, Netherlands
- Netherlands Institute for Neuroscience, Royal Academy of Arts and Sciences, Amsterdam, Netherlands
| | | | - Mario Negrello
- Department of Neuroscience, Erasmus MC, Rotterdam, Netherlands
| |
Collapse
|
2
|
Hepburn I, Lallouette J, Chen W, Gallimore AR, Nagasawa-Soeda SY, De Schutter E. Vesicle and reaction-diffusion hybrid modeling with STEPS. Commun Biol 2024; 7:573. [PMID: 38750123 PMCID: PMC11096338 DOI: 10.1038/s42003-024-06276-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2023] [Accepted: 05/01/2024] [Indexed: 05/18/2024] Open
Abstract
Vesicles carry out many essential functions within cells through the processes of endocytosis, exocytosis, and passive and active transport. This includes transporting and delivering molecules between different parts of the cell, and storing and releasing neurotransmitters in neurons. To date, computational simulation of these key biological players has been rather limited and has not advanced at the same pace as other aspects of cell modeling, restricting the realism of computational models. We describe a general vesicle modeling tool that has been designed for wide application to a variety of cell models, implemented within our software STochastic Engine for Pathway Simulation (STEPS), a stochastic reaction-diffusion simulator that supports realistic reconstructions of cell tissue in tetrahedral meshes. The implementation is validated in an extensive test suite, parallel performance is demonstrated in a realistic synaptic bouton model, and example models are visualized in a Blender extension module.
Collapse
Affiliation(s)
- Iain Hepburn
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan
| | - Jules Lallouette
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan
| | - Weiliang Chen
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan
| | - Andrew R Gallimore
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan
| | - Sarah Y Nagasawa-Soeda
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan
| | - Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-son, Okinawa, Japan.
| |
Collapse
|
3
|
Lee DS, Kim TH, Park H, Kim JE. PDI augments kainic acid-induced seizure activity and neuronal death by inhibiting PP2A-GluA2-PICK1-mediated AMPA receptor internalization in the mouse hippocampus. Sci Rep 2023; 13:13927. [PMID: 37626185 PMCID: PMC10457386 DOI: 10.1038/s41598-023-41014-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2023] [Accepted: 08/20/2023] [Indexed: 08/27/2023] Open
Abstract
Protein disulfide isomerase (PDI) is a redox-active enzyme and also serves as a nitric oxide donor causing S-nitrosylation of cysteine residues in various proteins. Although PDI knockdown reduces α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptor (AMPAR)-mediated neuronal activity, the underlying mechanisms are largely unknown. In the present study, we found that under physiological condition PDI knockdown increased CaMKII activity (phosphorylation) in the mouse hippocampus. However, PDI siRNA inhibited protein phosphatase (PP) 2A-mediated GluA2 S880 dephosphorylation by increasing PP2A oxidation, independent of S-nitrosylation. PDI siRNA also enhanced glutamate ionotropic receptor AMPA type subunit 1 (GluA1) S831 and GluA2 S880, but not GluA1 S845 and GluA2 Y869/Y873/Y876 phosphorylations, concomitant with the enhanced protein interacting with C kinase 1 (PICK1)-mediated AMPAR internalization. Furthermore, PDI knockdown attenuated seizure activity and neuronal damage in response to kainic acid (a non-desensitizing agonist of AMPAR). Therefore, these findings suggest that PDI may regulate surface AMPAR expression through PP2A-GluA2-PICK1 signaling pathway, and that PDI may be one of the therapeutic targets for epilepsy via AMPAR internalization without altering basal neurotransmission.
Collapse
Affiliation(s)
- Duk-Shin Lee
- Department of Anatomy and Neurobiology, College of Medicine, Hallym University, Chuncheon, Kangwon-do, 24252, South Korea
- Institute of Epilepsy Research, College of Medicine, Hallym University, Chuncheon, 24252, South Korea
| | - Tae-Hyun Kim
- Department of Anatomy and Neurobiology, College of Medicine, Hallym University, Chuncheon, Kangwon-do, 24252, South Korea
- Institute of Epilepsy Research, College of Medicine, Hallym University, Chuncheon, 24252, South Korea
| | - Hana Park
- Department of Anatomy and Neurobiology, College of Medicine, Hallym University, Chuncheon, Kangwon-do, 24252, South Korea
- Institute of Epilepsy Research, College of Medicine, Hallym University, Chuncheon, 24252, South Korea
| | - Ji-Eun Kim
- Department of Anatomy and Neurobiology, College of Medicine, Hallym University, Chuncheon, Kangwon-do, 24252, South Korea.
- Institute of Epilepsy Research, College of Medicine, Hallym University, Chuncheon, 24252, South Korea.
| |
Collapse
|
4
|
Rodrigues YE, Tigaret CM, Marie H, O'Donnell C, Veltz R. A stochastic model of hippocampal synaptic plasticity with geometrical readout of enzyme dynamics. eLife 2023; 12:e80152. [PMID: 37589251 PMCID: PMC10435238 DOI: 10.7554/elife.80152] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Accepted: 03/22/2023] [Indexed: 08/18/2023] Open
Abstract
Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either (1) top-down and interpretable, but not flexible enough to account for experimental data, or (2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit to data. To avoid the shortcomings of these approaches, we present a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to predict plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model also predicts that in vivo-like spike timing irregularity strongly shapes plasticity outcome. This geometrical readout modelling approach can be readily applied to other excitatory or inhibitory synapses to discover their synaptic plasticity rules.
Collapse
Affiliation(s)
- Yuri Elias Rodrigues
- Université Côte d’AzurNiceFrance
- Institut de Pharmacologie Moléculaire et Cellulaire (IPMC), CNRSValbonneFrance
- Inria Center of University Côte d’Azur (Inria)Sophia AntipolisFrance
| | - Cezar M Tigaret
- Neuroscience and Mental Health Research Innovation Institute, Division of Psychological Medicine and Clinical Neurosciences,School of Medicine, Cardiff UniversityCardiffUnited Kingdom
| | - Hélène Marie
- Université Côte d’AzurNiceFrance
- Institut de Pharmacologie Moléculaire et Cellulaire (IPMC), CNRSValbonneFrance
| | - Cian O'Donnell
- School of Computing, Engineering, and Intelligent Systems, Magee Campus, Ulster UniversityLondonderryUnited Kingdom
- School of Computer Science, Electrical and Electronic Engineering, and Engineering Mathematics, University of BristolBristolUnited Kingdom
| | - Romain Veltz
- Inria Center of University Côte d’Azur (Inria)Sophia AntipolisFrance
| |
Collapse
|
5
|
Sumi T, Harada K. Muscarinic acetylcholine receptor-dependent and NMDA receptor-dependent LTP and LTD share the common AMPAR trafficking pathway. iScience 2023; 26:106133. [PMID: 36866246 PMCID: PMC9972575 DOI: 10.1016/j.isci.2023.106133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2022] [Revised: 10/30/2022] [Accepted: 01/31/2023] [Indexed: 02/05/2023] Open
Abstract
The forebrain cholinergic system promotes higher brain function in part by signaling through the M1 muscarinic acetylcholine receptor (mAChR). Long-term potentiation (LTP) and long-term depression (LTD) of excitatory synaptic transmission in the hippocampus are also induced by mAChR. An AMPA receptor (AMPAR) trafficking model for hippocampal neurons has been proposed to simulate N-methyl-D-aspartate receptor (NMDAR)-dependent synaptic plasticity in the early phase. In this study, we demonstrated the validity of the hypothesis that the mAChR-dependent LTP/LTD shares a common AMPAR trafficking pathway associated with NMDAR-dependent LTP/LTD. However, unlike NMDAR, Ca2+ influx into the spine cytosol occurs owing to the Ca2+ stored inside the ER and is induced via the activation of inositol 1,4,5-trisphosphate (IP3) receptors during M1 mAChR activation. Moreover, the AMPAR trafficking model implies that alterations in LTP and LTD observed in Alzheimer's disease could be attributed to age-dependent reductions in AMPAR expression levels.
Collapse
Affiliation(s)
- Tomonari Sumi
- Research Institute for Interdisciplinary Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan
- Department of Chemistry, Faculty of Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama 700-8530, Japan
- Corresponding author
| | - Kouji Harada
- Department of Computer Science and Engineering, Toyohashi University of Technology, Tempaku-cho, Toyohashi 441-8580, Japan
- Center for IT-Based Education, Toyohashi University of Technology, Tempaku-cho, Toyohashi, 441-8580, Japan
| |
Collapse
|
6
|
Chen W, Carel T, Awile O, Cantarutti N, Castiglioni G, Cattabiani A, Del Marmol B, Hepburn I, King JG, Kotsalos C, Kumbhar P, Lallouette J, Melchior S, Schürmann F, De Schutter E. STEPS 4.0: Fast and memory-efficient molecular simulations of neurons at the nanoscale. Front Neuroinform 2022; 16:883742. [DOI: 10.3389/fninf.2022.883742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2022] [Accepted: 09/30/2022] [Indexed: 11/13/2022] Open
Abstract
Recent advances in computational neuroscience have demonstrated the usefulness and importance of stochastic, spatial reaction-diffusion simulations. However, ever increasing model complexity renders traditional serial solvers, as well as naive parallel implementations, inadequate. This paper introduces a new generation of the STochastic Engine for Pathway Simulation (STEPS) project (http://steps.sourceforge.net/), denominated STEPS 4.0, and its core components which have been designed for improved scalability, performance, and memory efficiency. STEPS 4.0 aims to enable novel scientific studies of macroscopic systems such as whole cells while capturing their nanoscale details. This class of models is out of reach for serial solvers due to the vast quantity of computation in such detailed models, and also out of reach for naive parallel solvers due to the large memory footprint. Based on a distributed mesh solution, we introduce a new parallel stochastic reaction-diffusion solver and a deterministic membrane potential solver in STEPS 4.0. The distributed mesh, together with improved data layout and algorithm designs, significantly reduces the memory footprint of parallel simulations in STEPS 4.0. This enables massively parallel simulations on modern HPC clusters and overcomes the limitations of the previous parallel STEPS implementation. Current and future improvements to the solver are not sustainable without following proper software engineering principles. For this reason, we also give an overview of how the STEPS codebase and the development environment have been updated to follow modern software development practices. We benchmark performance improvement and memory footprint on three published models with different complexities, from a simple spatial stochastic reaction-diffusion model, to a more complex one that is coupled to a deterministic membrane potential solver to simulate the calcium burst activity of a Purkinje neuron. Simulation results of these models suggest that the new solution dramatically reduces the per-core memory consumption by more than a factor of 30, while maintaining similar or better performance and scalability.
Collapse
|
7
|
Autoregulation of switching behavior by cellular compartment size. Proc Natl Acad Sci U S A 2022; 119:e2116054119. [PMID: 35349334 PMCID: PMC9169097 DOI: 10.1073/pnas.2116054119] [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] [Indexed: 11/30/2022] Open
Abstract
Biochemical reactions often occur in small volumes within a cell, restricting the number of molecules to the hundreds or even tens. At this scale, reactions are discrete and stochastic, making reliable signaling difficult. This paper shows that the transition between discrete, stochastic reactions and macroscopic reactions can be exploited to make a self-regulating switch. This constitutes a previously unidentified kind of reaction network that may be present in small structures, such as synapses. Many kinds of cellular compartments comprise decision-making mechanisms that control growth and shrinkage of the compartment in response to external signals. Key examples include synaptic plasticity mechanisms that regulate the size and strength of synapses in the nervous system. However, when synaptic compartments and postsynaptic densities are small, such mechanisms operate in a regime where chemical reactions are discrete and stochastic due to low copy numbers of the species involved. In this regime, fluctuations are large relative to mean concentrations, and inherent discreteness leads to breakdown of mass-action kinetics. Understanding how synapses and other small compartments achieve reliable switching in the low–copy number limit thus remains a key open problem. We propose a self-regulating signaling motif that exploits the breakdown of mass-action kinetics to generate a reliable size-regulated switch. We demonstrate this in simple two- and three-species chemical reaction systems and uncover a key role for inhibitory loops among species in generating switching behavior. This provides an elementary motif that could allow size-dependent regulation in more complex reaction pathways and may explain discrepant experimental results on well-studied biochemical pathways.
Collapse
|
8
|
Sumi T, Harada K. Mechanism underlying hippocampal long-term potentiation and depression based on competition between endocytosis and exocytosis of AMPA receptors. Sci Rep 2020; 10:14711. [PMID: 32895399 PMCID: PMC7477194 DOI: 10.1038/s41598-020-71528-3] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2020] [Accepted: 08/17/2020] [Indexed: 02/08/2023] Open
Abstract
N-methyl-D-aspartate (NMDA) receptor-dependent long-term potentiation (LTP) and long-term depression (LTD) of signal transmission form neural circuits and thus are thought to underlie learning and memory. These mechanisms are mediated by AMPA receptor (AMPAR) trafficking in postsynaptic neurons. However, the regulatory mechanism of bidirectional plasticity at excitatory synapses remains unclear. We present a network model of AMPAR trafficking for adult hippocampal pyramidal neurons, which reproduces both LTP and LTD. We show that the induction of both LTP and LTD is regulated by the competition between exocytosis and endocytosis of AMPARs, which are mediated by the calcium-sensors synaptotagmin 1/7 (Syt1/7) and protein interacting with C-kinase 1 (PICK1), respectively. Our result indicates that recycling endosomes containing AMPAR are always ready for Syt1/7-dependent exocytosis of AMPAR at peri-synaptic/synaptic membranes. This is because molecular motor myosin Vb constitutively transports the recycling endosome toward the membrane in a Ca2+-independent manner.
Collapse
Affiliation(s)
- Tomonari Sumi
- Research Institute for Interdisciplinary Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama, 700-8530, Japan. .,Department of Chemistry, Faculty of Science, Okayama University, 3-1-1 Tsushima-Naka, Kita-ku, Okayama, 700-8530, Japan.
| | - Kouji Harada
- Department of Computer Science and Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi, 441-8580, Japan
| |
Collapse
|
9
|
Pinto TM, Schilstra MJ, Roque AC, Steuber V. Binding of Filamentous Actin to CaMKII as Potential Regulation Mechanism of Bidirectional Synaptic Plasticity by β CaMKII in Cerebellar Purkinje Cells. Sci Rep 2020; 10:9019. [PMID: 32488204 PMCID: PMC7265541 DOI: 10.1038/s41598-020-65870-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Accepted: 05/01/2020] [Indexed: 11/10/2022] Open
Abstract
Calcium-calmodulin dependent protein kinase II (CaMKII) regulates many forms of synaptic plasticity, but little is known about its functional role during plasticity induction in the cerebellum. Experiments have indicated that the β isoform of CaMKII controls the bidirectional inversion of plasticity at parallel fibre (PF)-Purkinje cell (PC) synapses in cerebellar cortex. Because the cellular events that underlie these experimental findings are still poorly understood, we developed a simple computational model to investigate how β CaMKII regulates the direction of plasticity in cerebellar PCs. We present the first model of AMPA receptor phosphorylation that simulates the induction of long-term depression (LTD) and potentiation (LTP) at the PF-PC synapse. Our simulation results suggest that the balance of CaMKII-mediated phosphorylation and protein phosphatase 2B (PP2B)-mediated dephosphorylation of AMPA receptors can determine whether LTD or LTP occurs in cerebellar PCs. The model replicates experimental observations that indicate that β CaMKII controls the direction of plasticity at PF-PC synapses, and demonstrates that the binding of filamentous actin to CaMKII can enable the β isoform of the kinase to regulate bidirectional plasticity at these synapses.
Collapse
Affiliation(s)
- Thiago M Pinto
- Instituto Federal de Educação, Ciência e Tecnologia do Rio de Janeiro, Nilópolis, RJ, 26530-060, Brazil.,Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP, 14040-901, Brazil
| | - Maria J Schilstra
- Centre for Computer Science and Informatics Research, University of Hertfordshire, Hatfield, Herts, AL10 9AB, UK
| | - Antonio C Roque
- Departamento de Física, FFCLRP, Universidade de São Paulo, Ribeirão Preto, SP, 14040-901, Brazil.
| | - Volker Steuber
- Centre for Computer Science and Informatics Research, University of Hertfordshire, Hatfield, Herts, AL10 9AB, UK
| |
Collapse
|
10
|
Miningou N, Blackwell KT. The road to ERK activation: Do neurons take alternate routes? Cell Signal 2020; 68:109541. [PMID: 31945453 PMCID: PMC7127974 DOI: 10.1016/j.cellsig.2020.109541] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2019] [Revised: 01/11/2020] [Accepted: 01/12/2020] [Indexed: 01/29/2023]
Abstract
The ERK cascade is a central signaling pathway that regulates a wide variety of cellular processes including proliferation, differentiation, learning and memory, development, and synaptic plasticity. A wide range of inputs travel from the membrane through different signaling pathway routes to reach activation of one set of output kinases, ERK1&2. The classical ERK activation pathway beings with growth factor activation of receptor tyrosine kinases. Numerous G-protein coupled receptors and ionotropic receptors also lead to ERK through increases in the second messengers calcium and cAMP. Though both types of pathways are present in diverse cell types, a key difference is that most stimuli to neurons, e.g. synaptic inputs, are transient, on the order of milliseconds to seconds, whereas many stimuli acting on non-neural tissue, e.g. growth factors, are longer duration. The ability to consolidate these inputs to regulate the activation of ERK in response to diverse signals raises the question of which factors influence the difference in ERK activation pathways. This review presents both experimental studies and computational models aimed at understanding the control of ERK activation and whether there are fundamental differences between neurons and other cells. Our main conclusion is that differences between cell types are quite subtle, often related to differences in expression pattern and quantity of some molecules such as Raf isoforms. In addition, the spatial location of ERK is critical, with regulation by scaffolding proteins producing differences due to colocalization of upstream molecules that may differ between neurons and other cells.
Collapse
Affiliation(s)
- Nadiatou Miningou
- Department of Chemistry and Biochemistry, George Mason University, Fairfax, VA 22030, United States of America
| | - Kim T Blackwell
- Interdisciplinary Program in Neuroscience and Bioengineering Department, George Mason University, Fairfax, VA 22030, United States of America.
| |
Collapse
|
11
|
Karbowski J. Metabolic constraints on synaptic learning and memory. J Neurophysiol 2019; 122:1473-1490. [PMID: 31365284 DOI: 10.1152/jn.00092.2019] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Dendritic spines, the carriers of long-term memory, occupy a small fraction of cortical space, and yet they are the major consumers of brain metabolic energy. What fraction of this energy goes for synaptic plasticity, correlated with learning and memory? It is estimated here based on neurophysiological and proteomic data for rat brain that, depending on the level of protein phosphorylation, the energy cost of synaptic plasticity constitutes a small fraction of the energy used for fast excitatory synaptic transmission, typically 4.0-11.2%. Next, this study analyzes a metabolic cost of new learning and its memory trace in relation to the cost of prior memories, using a class of cascade models of synaptic plasticity. It is argued that these models must contain bidirectional cyclic motifs, related to protein phosphorylation, to be compatible with basic thermodynamic principles. For most investigated parameters longer memories generally require proportionally more energy to store. The exceptions are the parameters controlling the speed of molecular transitions (e.g., ATP-driven phosphorylation rate), for which memory lifetime per invested energy can increase progressively for longer memories. Furthermore, in general, a memory trace decouples dynamically from a corresponding synaptic metabolic rate such that the energy expended on new learning and its memory trace constitutes in most cases only a small fraction of the baseline energy associated with prior memories. Taken together, these empirical and theoretical results suggest a metabolic efficiency of synaptically stored information.NEW & NOTEWORTHY Learning and memory involve a sequence of molecular events in dendritic spines called synaptic plasticity. These events are physical in nature and require energy, which has to be supplied by ATP molecules. However, our knowledge of the energetics of these processes is very poor. This study estimates the empirical energy cost of synaptic plasticity and considers theoretically a metabolic rate of learning and its memory trace in a class of cascade models of synaptic plasticity.
Collapse
Affiliation(s)
- Jan Karbowski
- Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland.,Nalecz Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, Warsaw, Poland
| |
Collapse
|
12
|
Gallimore AR, Kim T, Tanaka-Yamamoto K, De Schutter E. Switching On Depression and Potentiation in the Cerebellum. Cell Rep 2019; 22:722-733. [PMID: 29346769 DOI: 10.1016/j.celrep.2017.12.084] [Citation(s) in RCA: 33] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2017] [Revised: 11/10/2017] [Accepted: 12/22/2017] [Indexed: 12/30/2022] Open
Abstract
Long-term depression (LTD) and long-term potentiation (LTP) in the cerebellum are important for motor learning. However, the signaling mechanisms controlling whether LTD or LTP is induced in response to synaptic stimulation remain obscure. Using a unified model of LTD and LTP at the cerebellar parallel fiber-Purkinje cell (PF-PC) synapse, we delineate the coordinated pre- and postsynaptic signaling that determines the direction of plasticity. We show that LTP is the default response to PF stimulation above a well-defined frequency threshold. However, if the calcium signal surpasses the threshold for CaMKII activation, then an ultrasensitive "on switch" activates an extracellular signal-regulated kinase (ERK)-based positive feedback loop that triggers LTD instead. This postsynaptic feedback loop is sustained by another, trans-synaptic, feedback loop that maintains nitric oxide production throughout LTD induction. When full depression is achieved, an automatic "off switch" inactivates the feedback loops, returning the network to its basal state and demarcating the end of the early phase of LTD.
Collapse
Affiliation(s)
- Andrew R Gallimore
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan.
| | - Taegon Kim
- Center for Functional Connectomics, Korea Institute of Science and Technology (KIST), Seoul 136-791, Republic of Korea
| | - Keiko Tanaka-Yamamoto
- Center for Functional Connectomics, Korea Institute of Science and Technology (KIST), Seoul 136-791, Republic of Korea
| | - Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan.
| |
Collapse
|
13
|
Mahajan G, Nadkarni S. Intracellular calcium stores mediate metaplasticity at hippocampal dendritic spines. J Physiol 2019; 597:3473-3502. [PMID: 31099020 PMCID: PMC6636706 DOI: 10.1113/jp277726] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2019] [Accepted: 05/16/2019] [Indexed: 12/21/2022] Open
Abstract
Key points Calcium (Ca2+) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca2+ stores. The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca2+ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression. A physiologically detailed computational model of Ca2+ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols. ER Ca2+ release via IP3 receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines. Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.
Abstract Long‐term plasticity mediated by NMDA receptors supports input‐specific, Hebbian forms of learning at excitatory CA3–CA1 connections in the hippocampus. There exists an additional layer of stabilizing mechanisms that act globally as well as locally over multiple time scales to ensure that plasticity occurs in a constrained manner. Here, we investigated the role of calcium (Ca2+) stores associated with the endoplasmic reticulum (ER) in the local regulation of plasticity at individual CA1 synapses. Our study was spurred by (1) the curious observation that ER is sparsely distributed in dendritic spines, but over‐represented in larger spines that are likely to have undergone activity‐dependent strengthening, and (2) evidence suggesting that ER motility at synapses can be rapid, and accompany activity‐regulated spine remodelling. We constructed a physiologically realistic computational model of an ER‐bearing CA1 spine, and examined how IP3‐sensitive Ca2+ stores affect spine Ca2+ dynamics during activity patterns mimicking the induction of long‐term potentiation and long‐term depression (LTD). Our results suggest that the presence of ER modulates NMDA receptor‐dependent plasticity in a graded manner that selectively enhances LTD induction. We propose that ER may locally tune Ca2+‐based plasticity, providing a braking mechanism to mitigate runaway strengthening at potentiated synapses. Our study provides a biophysically accurate description of postsynaptic Ca2+ regulation, and suggests that ER in the spine may promote the re‐use of hippocampal synapses with saturated strengths. Calcium (Ca2+) entry mediated by NMDA receptors is considered central to the induction of activity‐dependent synaptic plasticity in hippocampal area CA1; this description does not, however, take into account the potential contribution of endoplasmic reticulum (ER) Ca2+ stores. The ER has a heterogeneous distribution in CA1 dendritic spines, and may introduce localized functional differences in Ca2+ signalling between synapses, as suggested by experiments on metabotropic receptor‐dependent long‐term depression. A physiologically detailed computational model of Ca2+ dynamics at a CA3–CA1 excitatory synapse characterizes the contribution of spine ER via metabotropic signalling during plasticity induction protocols. ER Ca2+ release via IP3 receptors modulates NMDA receptor‐dependent plasticity in a graded manner, to selectively promote synaptic depression with relatively diminished effect on LTP induction; this may temper further strengthening at the stronger synapses which are preferentially associated with ER‐containing spines. Acquisition of spine ER may thus represent a local, biophysically plausible ‘metaplastic switch’ at potentiated CA1 synapses, contributing to the plasticity–stability balance in neural circuits.
Collapse
Affiliation(s)
- Gaurang Mahajan
- Indian Institute of Science Education and Research, Pune, 411 008, India
| | - Suhita Nadkarni
- Indian Institute of Science Education and Research, Pune, 411 008, India
| |
Collapse
|
14
|
Kim T, Tanaka-Yamamoto K. Postsynaptic Stability and Variability Described by a Stochastic Model of Endosomal Trafficking. Front Cell Neurosci 2019; 13:72. [PMID: 30863286 PMCID: PMC6399135 DOI: 10.3389/fncel.2019.00072] [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: 10/12/2018] [Accepted: 02/13/2019] [Indexed: 12/04/2022] Open
Abstract
Neurons undergo dynamic processes of constitutive AMPA-type glutamate receptor (AMPAR) trafficking, such as the insertion and internalization of AMPARs by exocytosis and endocytosis, while stably maintaining synaptic efficacy. Studies using advanced imaging techniques have suggested that the frequency of these constitutive trafficking processes, as well as the number of AMPARs that are involved in a particular event highly fluctuate. In addition, mechanisms that trigger some forms of synaptic plasticity have been shown to include not only these processes but also additional fluctuating processes, such as the sorting of AMPARs to late endosomes (LEs). Thus, the regulation of postsynaptic AMPARs by the endosomal trafficking system appears to have superficially conflicting properties between the stability or organized control of plasticity and highly fluctuating or stochastic processes. However, it is not clear how the endosomal trafficking system reconciles and utilizes such conflicting properties. Although deterministic models have been effective to describe the stable maintenance of synaptic AMPAR numbers by constitutive recycling, as well as the involvement of endosomal trafficking in synaptic plasticity, they do not take stochasticity into account. In this study, we introduced the stochasticity into the model of each crucial machinery of the endosomal trafficking system. The specific questions we solved by our improved model are whether stability is accomplished even with a combination of fluctuating processes, and how overall variability occurs while controlling long-term synaptic depression (LTD). Our new stochastic model indeed demonstrated the stable regulation of postsynaptic AMPAR numbers at the basal state and during LTD maintenance, despite fast fluctuations in AMPAR numbers as well as high variability in the time course and amounts of LTD. In addition, our analysis suggested that the high variability arising from this stochasticity is beneficial for reproducing the relatively constant timing of LE sorting for LTD. We therefore propose that the coexistence of stability and stochasticity in the endosomal trafficking system is suitable for stable synaptic transmission and the reliable induction of synaptic plasticity, with variable properties that have been observed experimentally.
Collapse
Affiliation(s)
- Taegon Kim
- Center for Functional Connectomics, Korea Institute of Science and Technology (KIST), Seoul, South Korea
| | - Keiko Tanaka-Yamamoto
- Center for Functional Connectomics, Korea Institute of Science and Technology (KIST), Seoul, South Korea.,Division of Bio-Medical Science & Technology, KIST School, Korea University of Science and Technology, Seoul, South Korea
| |
Collapse
|
15
|
From membrane receptors to protein synthesis and actin cytoskeleton: Mechanisms underlying long lasting forms of synaptic plasticity. Semin Cell Dev Biol 2019; 95:120-129. [PMID: 30634048 DOI: 10.1016/j.semcdb.2019.01.006] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2018] [Revised: 01/07/2019] [Accepted: 01/08/2019] [Indexed: 12/13/2022]
Abstract
Synaptic plasticity, the activity dependent change in synaptic strength, forms the molecular foundation of learning and memory. Synaptic plasticity includes structural changes, with spines changing their size to accomodate insertion and removal of postynaptic receptors, which are correlated with functional changes. Of particular relevance for memory storage are the long lasting forms of synaptic plasticity which are protein synthesis dependent. Due to the importance of spine structural plasticity and protein synthesis, this review focuses on the signaling pathways that connect synaptic stimulation with regulation of protein synthesis and remodeling of the actin cytoskeleton. We also review computational models that implement novel aspects of molecular signaling in synaptic plasticity, such as the role of neuromodulators and spatial microdomains, as well as highlight the need for computational models that connect activation of memory kinases with spine actin dynamics.
Collapse
|
16
|
Zamora Chimal CG, De Schutter E. Ca 2+ Requirements for Long-Term Depression Are Frequency Sensitive in Purkinje Cells. Front Mol Neurosci 2018; 11:438. [PMID: 30564097 PMCID: PMC6288660 DOI: 10.3389/fnmol.2018.00438] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Accepted: 11/13/2018] [Indexed: 01/06/2023] Open
Abstract
Cerebellar long-term depression (LTD) is a form of synaptic plasticity dependent on postsynaptic Ca2+ changes. One fundamental question is how LTD is selectively induced by specific numbers of Ca2+ pulses and which are the frequency and duration of this train of pulses required for LTD induction. The molecular mechanism which leads the integration of postsynaptic Ca2+ pulses in the LTD signaling network has not been elucidated either. Recent publications have shown that Ca2+/calmodulin-dependent protein kinase II (CaMKII) is required for LTD induction. Additionally, protein kinase C (PKC), CaMKII, and MAPK play an important role to transduce the frequency of Ca2+ pulses into their enzymatic activity levels; however, it is still unknown which enzymes are involved in decoding Ca2+ pulses in LTD. We have extended a stochastic model of LTD by adding the molecular network regulating CaMKII activity and its activation. We solved this model with stochastic engine for pathway simulation to include the effect of biochemical noise in LTD. We systematically investigated the dependence of LTD induction on stimulus frequencies, and we found that LTD is selectively induced by a specific number of Ca2+ spikes at different frequencies. We observed that CaMKII is essential to induce LTD, and LTD is only weakly induced when its Thr286 phosphorylation site has been deleted. We found that CaMKII decodes the frequency of Ca2+ spikes into different amounts of kinase activity during LTD induction. In addition, PKC and ERK enzyme activity is highly sensitive to the frequency and the number of Ca2+ pulses and this sensitivity has an important effect on LTD activation. This research predicts the postsynaptic Ca2+ requirements to induce LTD using a typical synaptic activation sequence and explains how LTD is selectively induced by specific number of Ca2+ pulses at different frequencies.
Collapse
Affiliation(s)
- C G Zamora Chimal
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan
| | - Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan.,Department of Biomedical Sciences, University of Antwerp, Antwerp, Belgium
| |
Collapse
|
17
|
Molecular mechanisms of detection and discrimination of dynamic signals. Sci Rep 2018; 8:2480. [PMID: 29410522 PMCID: PMC5802782 DOI: 10.1038/s41598-018-20842-y] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Accepted: 01/24/2018] [Indexed: 12/25/2022] Open
Abstract
Many molecules decode not only the concentration of cellular signals, but also their temporal dynamics. However, little is known about the mechanisms that underlie the detection and discrimination of dynamic signals. We used computational modelling of the interaction of a ligand with multiple targets to investigate how kinetic and thermodynamic parameters regulate their capabilities to respond to dynamic signals. Our results demonstrated that the detection and discrimination of temporal features of signal inputs occur for reactions proceeding outside mass-action equilibrium. For these reactions, thermodynamic parameters such as affinity do not predict their outcomes. Additionally, we showed that, at non-equilibrium, the association rate constants determine the amount of product formed in reversible reactions. In contrast, the dissociation rate constants regulate the time interval required for reversible reactions to achieve equilibrium and, consequently, control their ability to detect and discriminate dynamic features of cellular signals.
Collapse
|
18
|
Timely regulated sorting from early to late endosomes is required to maintain cerebellar long-term depression. Nat Commun 2017; 8:401. [PMID: 28864821 PMCID: PMC5581341 DOI: 10.1038/s41467-017-00518-3] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2016] [Accepted: 07/05/2017] [Indexed: 11/16/2022] Open
Abstract
An important feature of long-term synaptic plasticity is the prolonged maintenance of plastic changes in synaptic transmission. The trafficking of AMPA-type glutamate receptors (AMPARs) is involved in the expression of many forms of synaptic plasticity, yet the subsequent events accomplishing the maintenance of plastic changes in synaptic AMPAR numbers are not fully understood. Here, we find that maintenance of cerebellar long-term depression results from a reduction in the number of AMPARs residing within endocytic recycling pathways. We then develop a genetically encoded, photosensitive inhibitor of late endosome sorting and use this to discover that initial maintenance of long-term depression relies on timely regulated late endosome sorting, which exhibits a threshold as well as switch-like behavior. Thus, our results indicate that recycling AMPAR numbers are reduced by a switching machinery of transient late endosome sorting, and that this process enables the transition from basal synaptic transmission to long-term depression maintenance. Long term depression (LTD) of the cerebellum is known to be mediated by postsynaptic trafficking of glutamate receptor AMPAR. Here, Kim and colleagues show that early- to late-endosomal sorting of AMPAR represents the switch from expression to maintenance phase of cerebellar LTD.
Collapse
|
19
|
Jȩdrzejewska-Szmek J, Luczak V, Abel T, Blackwell KT. β-adrenergic signaling broadly contributes to LTP induction. PLoS Comput Biol 2017; 13:e1005657. [PMID: 28742159 PMCID: PMC5546712 DOI: 10.1371/journal.pcbi.1005657] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2016] [Revised: 08/07/2017] [Accepted: 06/27/2017] [Indexed: 12/18/2022] Open
Abstract
Long-lasting forms of long-term potentiation (LTP) represent one of the major cellular mechanisms underlying learning and memory. One of the fundamental questions in the field of LTP is why different molecules are critical for long-lasting forms of LTP induced by diverse experimental protocols. Further complexity stems from spatial aspects of signaling networks, such that some molecules function in the dendrite and some are critical in the spine. We investigated whether the diverse experimental evidence can be unified by creating a spatial, mechanistic model of multiple signaling pathways in hippocampal CA1 neurons. Our results show that the combination of activity of several key kinases can predict the occurrence of long-lasting forms of LTP for multiple experimental protocols. Specifically Ca2+/calmodulin activated kinase II, protein kinase A and exchange protein activated by cAMP (Epac) together predict the occurrence of LTP in response to strong stimulation (multiple trains of 100 Hz) or weak stimulation augmented by isoproterenol. Furthermore, our analysis suggests that activation of the β-adrenergic receptor either via canonical (Gs-coupled) or non-canonical (Gi-coupled) pathways underpins most forms of long-lasting LTP. Simulations make the experimentally testable prediction that a complete antagonist of the β-adrenergic receptor will likely block long-lasting LTP in response to strong stimulation. Collectively these results suggest that converging molecular mechanisms allow CA1 neurons to flexibly utilize signaling mechanisms best tuned to temporal pattern of synaptic input to achieve long-lasting LTP and memory storage. Long-term potentiation of the strength of synaptic connections is a mechanism of learning and memory storage. One of the most confusing aspects of hippocampal synaptic potentiation is that numerous experiments have revealed the requirement for a plethora of signaling molecules. Furthermore the degree to which molecules activated by the stress response modify hippocampal synaptic potentiation and memory is still unclear. We used a computational model to demonstrate that this molecular diversity can be explained by considering a combination of several key molecules. We also show that activation of β-adrenergic receptors by the stress response appears to be involved in most forms of synaptic potentiation, though in some cases unconventional mechanisms are utilized. This suggests that novel treatments for stress-related disorders may have more success if they target unconventional mechanisms activated by β-adrenergic receptors.
Collapse
Affiliation(s)
- Joanna Jȩdrzejewska-Szmek
- The Krasnow Institute for Advanced Studies, George Mason University, Fairfax, Virginia, United States of America
| | - Vincent Luczak
- Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Ted Abel
- Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America
| | - Kim T Blackwell
- The Krasnow Institute for Advanced Studies, George Mason University, Fairfax, Virginia, United States of America
- * E-mail:
| |
Collapse
|
20
|
Fujii M, Ohashi K, Karasawa Y, Hikichi M, Kuroda S. Small-Volume Effect Enables Robust, Sensitive, and Efficient Information Transfer in the Spine. Biophys J 2017; 112:813-826. [PMID: 28256240 DOI: 10.1016/j.bpj.2016.12.043] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2016] [Revised: 12/27/2016] [Accepted: 12/29/2016] [Indexed: 10/20/2022] Open
Abstract
Why is the spine of a neuron so small that it can contain only small numbers of molecules and reactions inevitably become stochastic? We previously showed that, despite such noisy conditions, the spine exhibits robust, sensitive, and efficient features of information transfer using the probability of Ca2+ increase; however, the mechanisms are unknown. In this study, we show that the small volume effect enables robust, sensitive, and efficient information transfer in the spine volume, but not in the cell volume. In the spine volume, the intrinsic noise in reactions becomes larger than the extrinsic noise of input, resulting in robust information transfer despite input fluctuation. In the spine volume, stochasticity makes the Ca2+ increase occur with a lower intensity of input, causing higher sensitivity to lower intensity of input. The volume-dependency of information transfer increases its efficiency in the spine volume. Thus, we propose that the small-volume effect is the functional reason why the spine has to be so small.
Collapse
Affiliation(s)
- Masashi Fujii
- Department of Biological Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan; Molecular Genetics Research Laboratory, Graduate School of Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan
| | - Kaoru Ohashi
- Department of Biological Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan
| | - Yasuaki Karasawa
- Department of Neurosurgery, Graduate School of Medicine, University of Tokyo, Bukyo-ku, Tokyo, Japan
| | - Minori Hikichi
- Department of Biological Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan
| | - Shinya Kuroda
- Department of Biological Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan; Molecular Genetics Research Laboratory, Graduate School of Sciences, University of Tokyo, Bukyo-ku, Tokyo, Japan; CREST, Japan Science and Technology Agency, Bunkyo-ku, Tokyo, Japan.
| |
Collapse
|
21
|
Hepburn I, Jain A, Gangal H, Yamamoto Y, Tanaka-Yamamoto K, De Schutter E. A Model of Induction of Cerebellar Long-Term Depression Including RKIP Inactivation of Raf and MEK. Front Mol Neurosci 2017; 10:19. [PMID: 28220061 PMCID: PMC5292618 DOI: 10.3389/fnmol.2017.00019] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2016] [Accepted: 01/16/2017] [Indexed: 01/27/2023] Open
Abstract
We report an updated stochastic model of cerebellar Long Term Depression (LTD) with improved realism. Firstly, we verify experimentally that dissociation of Raf kinase inhibitor protein (RKIP) from Mitogen-activated protein kinase kinase (MEK) is required for cerebellar LTD and add this interaction to an earlier published model, along with the known requirement of dissociation of RKIP from Raf kinase. We update Ca2+ dynamics as a constant-rate influx, which captures experimental input profiles accurately. We improve α-amino-3-hydroxy-5-methyl-4 isoxazolepropionic acid (AMPA) receptor interactions by adding phosphorylation and dephosphorylation of AMPA receptors when bound to glutamate receptor interacting protein (GRIP). The updated model is tuned to reproduce experimental Ca2+ peak vs. LTD amplitude curves at four different Ca2+ pulse durations as closely as possible. We find that the updated model is generally more robust with these changes, yet we still observe some sensitivity of LTD induction to copy number of the key signaling molecule Protein kinase C (PKC). We predict natural variability in this number by stochastic diffusion may influence the probabilistic LTD response to Ca2+ input in Purkinje cell spines and propose this as an extra source of stochasticity that may be important also in other signaling systems.
Collapse
Affiliation(s)
- Iain Hepburn
- Computational Neuroscience Unit, Okinawa Institute of Science and TechnologyOkinawa, Japan; Theoretical Neurobiology, University of AntwerpAntwerp, Belgium
| | - Anant Jain
- Computational Neuroscience Unit, Okinawa Institute of Science and TechnologyOkinawa, Japan; Department of Neurobiology, Northwestern UniversityEvanston, IL, USA
| | - Himanshu Gangal
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Okinawa, Japan
| | - Yukio Yamamoto
- Center for Functional Connectomics, Korea Institute of Science and Technology Seoul, South Korea
| | - Keiko Tanaka-Yamamoto
- Center for Functional Connectomics, Korea Institute of Science and Technology Seoul, South Korea
| | - Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and TechnologyOkinawa, Japan; Theoretical Neurobiology, University of AntwerpAntwerp, Belgium
| |
Collapse
|
22
|
Stochastic Induction of Long-Term Potentiation and Long-Term Depression. Sci Rep 2016; 6:30899. [PMID: 27485552 PMCID: PMC4971485 DOI: 10.1038/srep30899] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Accepted: 07/10/2016] [Indexed: 01/23/2023] Open
Abstract
Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca2+]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A2, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca2+ induced both processes stochastically. The magnitudes of the Ca2+ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca2+ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.
Collapse
|
23
|
Jedlicka P, Deller T. Understanding the role of synaptopodin and the spine apparatus in Hebbian synaptic plasticity - New perspectives and the need for computational modeling. Neurobiol Learn Mem 2016; 138:21-30. [PMID: 27470091 DOI: 10.1016/j.nlm.2016.07.023] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2016] [Revised: 07/15/2016] [Accepted: 07/23/2016] [Indexed: 12/17/2022]
Abstract
Synaptopodin (SP) is a proline-rich actin-associated protein essential for the formation of a spine apparatus (SA) in dendritic spines. The SA consists of stacks of smooth endoplasmic reticulum (sER) contiguous with the meshwork of somatodendritic ER. Spines of SP-deficient mice contain sER but no SA, demonstrating that SP is necessary for the assembly of ER cisterns into the more complex SA organelle. Although the SA was described decades ago, its function was difficult to investigate and remained elusive, in part because reliable markers for the SA were missing. After SP was identified as an essential component and a reliable marker of the SA, a role of SP/SA in hippocampal synaptic plasticity could be firmly established using loss-of-function approaches. Further studies revealed that SP/SA participate in the regulation of Ca2+-dependent spine-specific Hebbian plasticity and in activity-dependent changes in the spine actin cytoskeleton. In this review we are summarizing recent progress made on SP/SA in Hebbian plasticity and discuss open questions such as causality, spatiotemporal dynamics and complementarity of SP/SA-dependent mechanisms. We are proposing that computational modeling of spine Ca2+-signaling and actin remodeling pathways could address some of these issues and could indicate future research directions. Moreover, reaction-diffusion simulations could help to identify key feedforward and feedback regulatory motifs regulating the switch between an LTP and an LTD signaling module in SP/SA-containing spines, thus helping to find a unified view of SP/SA action in Hebbian plasticity.
Collapse
Affiliation(s)
- Peter Jedlicka
- Institute of Clinical Neuroanatomy, Neuroscience Center, Goethe University Frankfurt, D-60590 Frankfurt/Main, Germany.
| | - Thomas Deller
- Institute of Clinical Neuroanatomy, Neuroscience Center, Goethe University Frankfurt, D-60590 Frankfurt/Main, Germany.
| |
Collapse
|
24
|
A Computational Model for the AMPA Receptor Phosphorylation Master Switch Regulating Cerebellar Long-Term Depression. PLoS Comput Biol 2016; 12:e1004664. [PMID: 26807999 PMCID: PMC4726815 DOI: 10.1371/journal.pcbi.1004664] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2015] [Accepted: 11/12/2015] [Indexed: 02/08/2023] Open
Abstract
The expression of long-term depression (LTD) in cerebellar Purkinje cells results from the internalisation of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptors (AMPARs) from the postsynaptic membrane. This process is regulated by a complex signalling pathway involving sustained protein kinase C (PKC) activation, inhibition of serine/threonine phosphatase, and an active protein tyrosine phosphatase, PTPMEG. In addition, two AMPAR-interacting proteins-glutamate receptor-interacting protein (GRIP) and protein interacting with C kinase 1 (PICK1)-regulate the availability of AMPARs for trafficking between the postsynaptic membrane and the endosome. Here we present a new computational model of these overlapping signalling pathways. The model reveals how PTPMEG cooperates with PKC to drive LTD expression by facilitating the effect of PKC on the dissociation of AMPARs from GRIP and thus their availability for trafficking. Model simulations show that LTD expression is increased by serine/threonine phosphatase inhibition, and negatively regulated by Src-family tyrosine kinase activity, which restricts the dissociation of AMPARs from GRIP under basal conditions. We use the model to expose the dynamic balance between AMPAR internalisation and reinsertion, and the phosphorylation switch responsible for the perturbation of this balance and for the rapid plasticity initiation and regulation. Our model advances the understanding of PF-PC LTD regulation and induction, and provides a validated extensible platform for more detailed studies of this fundamental synaptic process.
Collapse
|
25
|
Bower JM. The 40-year history of modeling active dendrites in cerebellar Purkinje cells: emergence of the first single cell "community model". Front Comput Neurosci 2015; 9:129. [PMID: 26539104 PMCID: PMC4611061 DOI: 10.3389/fncom.2015.00129] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2014] [Accepted: 10/02/2015] [Indexed: 11/13/2022] Open
Abstract
The subject of the effects of the active properties of the Purkinje cell dendrite on neuronal function has been an active subject of study for more than 40 years. Somewhat unusually, some of these investigations, from the outset have involved an interacting combination of experimental and model-based techniques. This article recounts that 40-year history, and the view of the functional significance of the active properties of the Purkinje cell dendrite that has emerged. It specifically considers the emergence from these efforts of what is arguably the first single cell "community" model in neuroscience. The article also considers the implications of the development of this model for future studies of the complex properties of neuronal dendrites.
Collapse
|
26
|
Mosconi MW, Wang Z, Schmitt LM, Tsai P, Sweeney JA. The role of cerebellar circuitry alterations in the pathophysiology of autism spectrum disorders. Front Neurosci 2015; 9:296. [PMID: 26388713 PMCID: PMC4555040 DOI: 10.3389/fnins.2015.00296] [Citation(s) in RCA: 66] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2015] [Accepted: 08/06/2015] [Indexed: 01/23/2023] Open
Abstract
The cerebellum has been repeatedly implicated in gene expression, rodent model and post-mortem studies of autism spectrum disorder (ASD). How cellular and molecular anomalies of the cerebellum relate to clinical manifestations of ASD remains unclear. Separate circuits of the cerebellum control different sensorimotor behaviors, such as maintaining balance, walking, making eye movements, reaching, and grasping. Each of these behaviors has been found to be impaired in ASD, suggesting that multiple distinct circuits of the cerebellum may be involved in the pathogenesis of patients' sensorimotor impairments. We will review evidence that the development of these circuits is disrupted in individuals with ASD and that their study may help elucidate the pathophysiology of sensorimotor deficits and core symptoms of the disorder. Preclinical studies of monogenetic conditions associated with ASD also have identified selective defects of the cerebellum and documented behavioral rescues when the cerebellum is targeted. Based on these findings, we propose that cerebellar circuits may prove to be promising targets for therapeutic development aimed at rescuing sensorimotor and other clinical symptoms of different forms of ASD.
Collapse
Affiliation(s)
- Matthew W Mosconi
- Clinical Child Psychology Program and Schiefelbusch Institute for Life Span Studies, University of Kansas Lawrence, KS, USA ; Center for Autism and Developmental Disabilities, University of Texas Southwestern Dallas, TX, USA ; Department of Psychiatry, University of Texas Southwestern Dallas, TX, USA ; Department of Pediatrics, University of Texas Southwestern Dallas, TX, USA
| | - Zheng Wang
- Center for Autism and Developmental Disabilities, University of Texas Southwestern Dallas, TX, USA ; Department of Psychiatry, University of Texas Southwestern Dallas, TX, USA
| | - Lauren M Schmitt
- Center for Autism and Developmental Disabilities, University of Texas Southwestern Dallas, TX, USA ; Department of Psychiatry, University of Texas Southwestern Dallas, TX, USA
| | - Peter Tsai
- Center for Autism and Developmental Disabilities, University of Texas Southwestern Dallas, TX, USA ; Department of Psychiatry, University of Texas Southwestern Dallas, TX, USA ; Department of Pediatrics, University of Texas Southwestern Dallas, TX, USA ; Department of Neurology and Neurotherapeutics, University of Texas Southwestern Dallas, TX, USA ; Department of Neuroscience, University of Texas Southwestern Dallas, TX, USA
| | - John A Sweeney
- Center for Autism and Developmental Disabilities, University of Texas Southwestern Dallas, TX, USA ; Department of Psychiatry, University of Texas Southwestern Dallas, TX, USA ; Department of Pediatrics, University of Texas Southwestern Dallas, TX, USA
| |
Collapse
|
27
|
Anwar H, Roome CJ, Nedelescu H, Chen W, Kuhn B, De Schutter E. Dendritic diameters affect the spatial variability of intracellular calcium dynamics in computer models. Front Cell Neurosci 2014; 8:168. [PMID: 25100945 PMCID: PMC4107854 DOI: 10.3389/fncel.2014.00168] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2014] [Accepted: 06/02/2014] [Indexed: 11/13/2022] Open
Abstract
There is growing interest in understanding calcium dynamics in dendrites, both experimentally and computationally. Many processes influence these dynamics, but in dendrites there is a strong contribution of morphology because the peak calcium levels are strongly determined by the surface to volume ratio (SVR) of each branch, which is inversely related to branch diameter. In this study we explore the predicted variance of dendritic calcium concentrations due to local changes in dendrite diameter and how this is affected by the modeling approach used. We investigate this in a model of dendritic calcium spiking in different reconstructions of cerebellar Purkinje cells and in morphological analysis of neocortical and hippocampal pyramidal neurons. We report that many published models neglect diameter-dependent effects on calcium concentration and show how to implement this correctly in the NEURON simulator, both for phenomenological pool based models and for implementations using radial 1D diffusion. More detailed modeling requires simulation of 3D diffusion and we demonstrate that this does not dissipate the local concentration variance due to changes of dendritic diameter. In many cases 1D diffusion of models of calcium buffering give a good approximation provided an increased morphological resolution is implemented.
Collapse
Affiliation(s)
- Haroon Anwar
- Theoretical Neurobiology and Neuroengineering, University of Antwerp Wilrijk, Belgium ; Computational Neuroscience Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| | - Christopher J Roome
- Optical Neuroimaging Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| | - Hermina Nedelescu
- Theoretical Neurobiology and Neuroengineering, University of Antwerp Wilrijk, Belgium ; Computational Neuroscience Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| | - Weiliang Chen
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| | - Bernd Kuhn
- Optical Neuroimaging Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| | - Erik De Schutter
- Theoretical Neurobiology and Neuroengineering, University of Antwerp Wilrijk, Belgium ; Computational Neuroscience Unit, Okinawa Institute of Science and Technology Onna-Son, Okinawa, Japan
| |
Collapse
|
28
|
Rasumov N, De Schutter E. ATP consumption in molecular reactions of neuronal signaling. BMC Neurosci 2014. [PMCID: PMC4126354 DOI: 10.1186/1471-2202-15-s1-p179] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
|
29
|
Koumura T, Urakubo H, Ohashi K, Fujii M, Kuroda S. Stochasticity in Ca2+ increase in spines enables robust and sensitive information coding. PLoS One 2014; 9:e99040. [PMID: 24932482 PMCID: PMC4059641 DOI: 10.1371/journal.pone.0099040] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2014] [Accepted: 04/18/2014] [Indexed: 11/19/2022] Open
Abstract
A dendritic spine is a very small structure (∼0.1 µm3) of a neuron that processes input timing information. Why are spines so small? Here, we provide functional reasons; the size of spines is optimal for information coding. Spines code input timing information by the probability of Ca2+ increases, which makes robust and sensitive information coding possible. We created a stochastic simulation model of input timing-dependent Ca2+ increases in a cerebellar Purkinje cell's spine. Spines used probability coding of Ca2+ increases rather than amplitude coding for input timing detection via stochastic facilitation by utilizing the small number of molecules in a spine volume, where information per volume appeared optimal. Probability coding of Ca2+ increases in a spine volume was more robust against input fluctuation and more sensitive to input numbers than amplitude coding of Ca2+ increases in a cell volume. Thus, stochasticity is a strategy by which neurons robustly and sensitively code information.
Collapse
Affiliation(s)
- Takuya Koumura
- Undergraduate Department of Bioinformatics and Systems Biology, University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Hidetoshi Urakubo
- Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Kaoru Ohashi
- Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Masashi Fujii
- Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan
| | - Shinya Kuroda
- Undergraduate Department of Bioinformatics and Systems Biology, University of Tokyo, Bunkyo-ku, Tokyo, Japan
- Department of Biophysics and Biochemistry, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo, Japan
- * E-mail:
| |
Collapse
|
30
|
Chen W, De Schutter E. Python-based geometry preparation and simulation visualization toolkits for STEPS. Front Neuroinform 2014; 8:37. [PMID: 24782754 PMCID: PMC3990042 DOI: 10.3389/fninf.2014.00037] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2013] [Accepted: 03/25/2014] [Indexed: 11/13/2022] Open
Abstract
STEPS is a stochastic reaction-diffusion simulation engine that implements a spatial extension of Gillespie's Stochastic Simulation Algorithm (SSA) in complex tetrahedral geometries. An extensive Python-based interface is provided to STEPS so that it can interact with the large number of scientific packages in Python. However, a gap existed between the interfaces of these packages and the STEPS user interface, where supporting toolkits could reduce the amount of scripting required for research projects. This paper introduces two new supporting toolkits that support geometry preparation and visualization for STEPS simulations.
Collapse
Affiliation(s)
- Weiliang Chen
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Okinawa, Japan
| | - Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology Okinawa, Japan
| |
Collapse
|
31
|
Bhalla US. Molecular computation in neurons: a modeling perspective. Curr Opin Neurobiol 2014; 25:31-7. [DOI: 10.1016/j.conb.2013.11.006] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2013] [Revised: 09/26/2013] [Accepted: 11/18/2013] [Indexed: 12/31/2022]
|
32
|
Sun GY, Chuang DY, Zong Y, Jiang J, Lee JCM, Gu Z, Simonyi A. Role of cytosolic phospholipase A2 in oxidative and inflammatory signaling pathways in different cell types in the central nervous system. Mol Neurobiol 2014; 50:6-14. [PMID: 24573693 DOI: 10.1007/s12035-014-8662-4] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2013] [Accepted: 02/11/2014] [Indexed: 12/30/2022]
Abstract
Phospholipases A(2) (PLA(2)s) are important enzymes for the metabolism of fatty acids in membrane phospholipids. Among the three major classes of PLA(2)s in the mammalian system, the group IV calcium-dependent cytosolic PLA(2) alpha (cPLA(2)α) has received the most attention because it is widely expressed in nearly all mammalian cells and its active participation in cell metabolism. Besides Ca(2+) binding to its C2 domain, this enzyme can undergo a number of cell-specific post-translational modifications, including phosphorylation by protein kinases, S-nitrosylation through interaction with nitric oxide (NO), as well as interaction with other proteins and lipid molecules. Hydrolysis of phospholipids by cPLA(2) yields two important lipid mediators, arachidonic acid (AA) and lysophospholipids. While AA is known to serve as a substrate for cyclooxygenases and lipoxygenases, which are enzymes for the synthesis of eicosanoids and leukotrienes, lysophospholipids are known to possess detergent-like properties capable of altering microdomains of cell membranes. An important feature of cPLA(2) is its link to cell surface receptors that stimulate signaling pathways associated with activation of protein kinases and production of reactive oxygen species (ROS). In the central nervous system (CNS), cPLA(2) activation has been implicated in neuronal excitation, synaptic secretion, apoptosis, cell-cell interaction, cognitive and behavioral function, oxidative-nitrosative stress, and inflammatory responses that underline the pathogenesis of a number of neurodegenerative diseases. However, the types of extracellular agonists that target intracellular signaling pathways leading to cPLA(2) activation among different cell types and under different physiological and pathological conditions have not been investigated in detail. In this review, special emphasis is given to metabolic events linking cPLA(2) to activation in neurons, astrocytes, microglial cells, and cerebrovascular cells. Understanding the molecular mechanism(s) for regulation of this enzyme is deemed important in the development of new therapeutic targets for the treatment and prevention of neurodegenerative diseases.
Collapse
Affiliation(s)
- Grace Y Sun
- Biochemistry Department, University of Missouri, 117 Schweitzer Hall, Columbia, MO, 65211, USA,
| | | | | | | | | | | | | |
Collapse
|
33
|
Abstract
Bursts of dendritic calcium spikes play an important role in excitability and synaptic plasticity in many types of neurons. In single Purkinje cells, spontaneous and synaptically evoked dendritic calcium bursts come in a variety of shapes with a variable number of spikes. The mechanisms causing this variability have never been investigated thoroughly. In this study, a detailed computational model using novel simulation routines is applied to identify the roles that stochastic ion channels, spatial arrangements of ion channels, and stochastic intracellular calcium have toward producing calcium burst variability. Consistent with experimental recordings from rats, strong variability in the burst shape is observed in simulations. This variability persists in large model sizes in contrast to models containing only voltage-gated channels, where variability reduces quickly with increase of system size. Phase plane analysis of Hodgkin-Huxley spikes and of calcium bursts identifies fluctuation in phase space around probabilistic phase boundaries as the mechanism determining the dependence of variability on model size. Stochastic calcium dynamics are the main cause of calcium burst fluctuations, specifically the calcium activation of mslo/BK-type and SK2 channels. Local variability of calcium concentration has a significant effect at larger model sizes. Simulations of both spontaneous and synaptically evoked calcium bursts in a reconstructed dendrite show, in addition, strong spatial and temporal variability of voltage and calcium, depending on morphological properties of the dendrite. Our findings suggest that stochastic intracellular calcium mechanisms play a crucial role in dendritic calcium spike generation and are therefore an essential consideration in studies of neuronal excitability and plasticity.
Collapse
|
34
|
Blackwell KT. Approaches and tools for modeling signaling pathways and calcium dynamics in neurons. J Neurosci Methods 2013; 220:131-40. [PMID: 23743449 PMCID: PMC3830683 DOI: 10.1016/j.jneumeth.2013.05.008] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2013] [Revised: 05/15/2013] [Accepted: 05/16/2013] [Indexed: 01/25/2023]
Abstract
Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.
Collapse
Affiliation(s)
- K T Blackwell
- George Mason University, The Krasnow Institute for Advanced Studies, MS 2A1, Fairfax, VA 22030-444, USA.
| |
Collapse
|
35
|
Blackwell KT, Jedrzejewska-Szmek J. Molecular mechanisms underlying neuronal synaptic plasticity: systems biology meets computational neuroscience in the wilds of synaptic plasticity. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2013; 5:717-31. [PMID: 24019266 PMCID: PMC3947422 DOI: 10.1002/wsbm.1240] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Revised: 07/25/2013] [Accepted: 07/29/2013] [Indexed: 12/29/2022]
Abstract
Interactions among signaling pathways that are activated by transmembrane receptors produce complex networks and emergent dynamical behaviors that are implicated in synaptic plasticity. Temporal dynamics and spatial aspects are critical determinants of cell responses such as synaptic plasticity, although the mapping between spatiotemporal activity pattern and direction of synaptic plasticity is not completely understood. Computational modeling of neuronal signaling pathways has significantly contributed to understanding signaling pathways underlying synaptic plasticity. Spatial models of signaling pathways in hippocampal neurons have revealed mechanisms underlying the spatial distribution of extracellular signal-related kinase (ERK) activation in hippocampal neurons. Other spatial models have demonstrated that the major role of anchoring proteins in striatal and hippocampal synaptic plasticity is to place molecules near their activators. Simulations of yet other models have revealed that the spatial distribution of synaptic plasticity may differ for potentiation versus depression. In general, the most significant advances have been made by interactive modeling and experiments; thus, an interdisciplinary approach should be applied to investigate critical issues in neuronal signaling pathways. These issues include identifying which transmembrane receptors are key for activating ERK in neurons, and the crucial targets of kinases that produce long-lasting synaptic plasticity. Although the number of computer programs for computationally efficient simulation of large reaction-diffusion networks is increasing, parameter estimation and sensitivity analysis in these spatial models remain more difficult than in single compartment models. Advances in live cell imaging coupled with further software development will continue to accelerate the development of spatial models of synaptic plasticity.
Collapse
Affiliation(s)
- KT Blackwell
- Molecular Neuroscience Department, The Krasnow Institute for Advanced Studies George Mason University, Fairfax, VA 22030-444, USA
| | - J Jedrzejewska-Szmek
- Molecular Neuroscience Department, The Krasnow Institute for Advanced Studies George Mason University, Fairfax, VA 22030-444, USA
| |
Collapse
|
36
|
Lillacci G, Khammash M. The signal within the noise: efficient inference of stochastic gene regulation models using fluorescence histograms and stochastic simulations. ACTA ACUST UNITED AC 2013; 29:2311-9. [PMID: 23821649 DOI: 10.1093/bioinformatics/btt380] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
MOTIVATION In the noisy cellular environment, stochastic fluctuations at the molecular level manifest as cell-cell variability at the population level that is quantifiable using high-throughput single-cell measurements. Such variability is rich with information about the cell's underlying gene regulatory networks, their architecture and the parameters of the biochemical reactions at their core. RESULTS We report a novel method, called Inference for Networks of Stochastic Interactions among Genes using High-Throughput data (INSIGHT), for systematically combining high-throughput time-course flow cytometry measurements with computer-generated stochastic simulations of candidate gene network models to infer the network's stochastic model and all its parameters. By exploiting the mathematical relationships between experimental and simulated population histograms, INSIGHT achieves scalability, efficiency and accuracy while entirely avoiding approximate stochastic methods. We demonstrate our method on a synthetic gene network in bacteria and show that a detailed mechanistic model of this network can be estimated with high accuracy and high efficiency. Our method is completely general and can be used to infer models of signal-activated gene networks in any organism based solely on flow cytometry data and stochastic simulations. AVAILABILITY A free C source code implementing the INSIGHT algorithm, together with test data is available from the authors. CONTACT mustafa.khammash@bsse.ethz.ch SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
Collapse
Affiliation(s)
- Gabriele Lillacci
- ETH Zürich, Department of Biosystems Science and Engineering, Mattenstrasse 26, 4058, Basel, Switzerland
| | | |
Collapse
|
37
|
Jain A, Hepburn I, Chen W, De Schutter E. Initial state of single spines affects probability of induction of cerebellar long term depression in a stochastic model. BMC Neurosci 2013. [PMCID: PMC3704858 DOI: 10.1186/1471-2202-14-s1-p92] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022] Open
|
38
|
De Schutter E. The importance of stochastic signaling processes in the induction of long-term synaptic plasticity. Neural Netw 2012; 47:3-10. [PMID: 23267752 DOI: 10.1016/j.neunet.2012.11.015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2012] [Revised: 11/27/2012] [Accepted: 11/27/2012] [Indexed: 11/25/2022]
Abstract
A stochastic model of the signaling network responsible for the induction of long-term depression (LTD) at the parallel fiber to Purkinje cell synapse is described. The model includes a PKC-ERK-cPLA2 positive feedback loop and mechanisms of AMPA receptor trafficking. It was tuned to replicate calcium uncaging experiments that cause LTD. The ultrasensitive activation of ERK makes the signaling network activity bistable, causing either LTD or not. Therefore, in single synapses only two discrete stable states (LTD and non-LTD) can be expressed. The stochastic properties of the signaling network causes threshold dithering and probabilistic expression of LTD, which allows at the macroscopic level for many different and stable mean magnitudes of depression. When the volume of a single spine is simulated no thresholds for the calcium input signal are present. Such thresholds appear only when the volume of simulation is increased by a factor 100 or more and the model output is then bistable. Similarly, deterministic solutions of the same model show only bistable behavior. LTD induction requires activation of the PKC-ERK-cPLA2 positive feedback loop but this activity is not constant: the activities of ERK and of cPLA2 fluctuate strongly. This is much less the case for PKC which is more constantly activated and thereby promotes a stable output of the pathway.
Collapse
Affiliation(s)
- Erik De Schutter
- Computational Neuroscience Unit, Okinawa Institute of Science and Technology, 1919-1 Tancha, Onna-Son, Okinawa 904-0495, Japan.
| |
Collapse
|
39
|
Abstract
Cerebellar long-term depression (LTD) is induced by short-lasting synaptic activities, progressively expressed, and then maintained for hours or longer. Short-lasting events, such as calcium transients, are activated and required for the induction of LTD. Further, a positive-feedback kinase loop was shown to follow the transient events and to aid the transition between LTD induction and prolonged synaptic depression. Yet, it is not entirely clear as to how LTD is maintained and how the maintenance mechanisms are activated, mainly because of a lack of experimental studies regarding this topic, while an idea has been theoretically proposed. A new analysis of the experimental results suggests that early maintenance mechanisms display a threshold behavior and that they may be of stochastic nature. This suggestion is conceptually consistent with an idea from a computational study, which postulates that other bistable switch systems are required for LTD maintenance. We thus propose that cellular mechanisms showing a threshold behavior and a stochastic nature maintain LTD, and that future experimental studies in search of such mechanisms would be an important step toward fully understanding the time course of LTD.
Collapse
|