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Dynamique physiologique dans les maladies démyélinisantes : démêler les relations complexes grâce à la modélisation informatique

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Title Dynamique physiologique dans les maladies démyélinisantes : démêler les relations complexes grâce à la modélisation informatique
Authors Jay S. Coggan · Stefan Bittner · Klaus M. Stiefel · Sven G. Meuth · Steven A. Prescott
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Date 2021
Journal Int J Mol Sci.
DOI 10.3390/ijms160921215
PUBMED https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4613250/#!po=53.5714
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Dynamique physiologique dans les maladies démyélinisantes : démêler les relations complexes grâce à la modélisation informatique

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Free resource by Jay S. Coggan  · Stefan Bittner · Klaus M. Stiefel  · Sven G. Meuth · Steven A. Prescott



Physiological Dynamics in Demyelinating Diseases: Unraveling Complex Relationships through Computer Modeling

Jay S. Coggan, Stefan Bittner, [...], and Steven A. Prescott

Additional article information

Abstrait

Malgré des recherches intenses, peu de traitements sont disponibles pour la plupart des troubles neurologiques. Les maladies démyélinisantes ne font pas exception. Ce n'est peut-être pas surprenant compte tenu de la nature multifactorielle de ces maladies, qui impliquent des interactions complexes entre les cellules du système immunitaire, la glie et les neurones. Dans le cas de la sclérose en plaques, par exemple, il n'y a pas d'unanimité parmi les chercheurs sur la cause ou même sur le système ou le type de cellule qui pourrait être le point zéro. Cette situation empêche le développement et l'application stratégique de thérapies basées sur les mécanismes. Nous discuterons de la manière dont la modélisation computationnelle appliquée à des questions à différents niveaux biologiques peut aider à relier des observations disparates et à déchiffrer des mécanismes complexes dont les solutions ne se prêtent pas au simple réductionnisme. En faisant des prédictions vérifiables et en révélant des lacunes critiques dans les connaissances existantes, ces modèles peuvent aider à orienter la recherche et fourniront un cadre rigoureux dans lequel intégrer de nouvelles données au fur et à mesure de leur collecte. De nos jours, les données ne manquent pas ; le défi est de donner un sens à tout cela. À cet égard, la modélisation informatique est un outil inestimable qui pourrait, à terme, transformer la façon dont nous comprenons, diagnostiquons et traitons les maladies démyélinisantes.

Mots-clés : myéline, démyélinisation, sclérose en plaques, maladie neurodégénérative, modèle informatique, découverte de médicaments



Introduction

Les systèmes nerveux des vertébrés sont souvent divisés en matière grise et blanche en fonction de leur apparence et des rôles fonctionnels correspondants. Alors que la matière grise se compose en grande partie de corps cellulaires et de dendrites, la matière blanche contient principalement des axones et tire son nom des feuilles de membrane lipidique appelées myéline qui sont étroitement enroulées autour de ces axones..[1] La myéline provient de différentes classes de cellules gliales appelées oligodendrocytes dans le système nerveux central (SNC) et cellules de Schwann dans le système nerveux périphérique (SNP).

L'isolation électrique fournie par les feuilles de myéline améliore la fonction axonale en augmentant à la fois l'efficacité énergétique et la vitesse de conduction des potentiels d'action (PA). Ces deux fonctions peuvent avoir changé d'importance relative au cours de l'évolution.[2] La myéline est apparue pour la première fois à l'Ordovicien (485 à 443 ma, soit des millions d'années avant le présent) après la scission des ancêtres de la lamproie et de la myxine du reste des lignées de vertébrés.[3] Avec quelques exceptions intéressantes,[4][5]la myéline ou des structures analogues se trouvent chez tous les vertébrés et sont essentielles au bon fonctionnement de leur système nerveux. Le temps approximatif de l'évolution de la myéline peut être déduit du temps connu de divergence entre les accords sans (agnatha) et avec (tous les autres vertébrés) myéline.

L'enveloppe de myéline est interrompue par des tronçons non myélinisés régulièrement espacés connus sous le nom de nœuds de Ranvier. La myéline accélère la conduction en limitant le flux de charge transmembranaire à travers les canaux ioniques situés dans les nœuds. Dans les soi-disant entre-nœuds, le courant circule le long de l'axone avec peu de passage à travers la membrane cellulaire isolée. Le PA est régénéré à chaque nœud où la densité des canaux sodiques et potassiques voltage-dépendants est très élevée. Ce processus est appelé "conduction saltatoire" car le point d'accès semble sauter d'un nœud à l'autre. Les perturbations de ce système de communication rapide peuvent être associées à un éventail de dysfonctionnements du système nerveux.[6]

À plusieurs égards, les axones semblent fonctionner à des limites physiques. Un exemple intéressant est que la taille des axones semble être contrainte par le bruit thermique intrinsèque aux protéines des canaux ioniques ; tout axone plus fin que 0,1 μm serait inutile pour le transfert d'informations en raison de ses niveaux de bruit élevés.[7] Curieusement, 0,1 μm est également à peu près le plus petit diamètre d'axone observé dans les systèmes nerveux [7]. Ceci et des découvertes similaires suggèrent que les axones et leurs sous-structures sont des dispositifs biologiques finement réglés, mais que le réglage peut évidemment être perturbé dans des conditions pathologiques..[8]

La démyélinisation met en mouvement des changements fonctionnels qui sont importants pour les caractéristiques cliniques mais qui ne sont pas facilement expliqués par des changements immunologiques ou radiologiques. L'emplacement d'une plaque prédit quel système sera affecté (moteur vs sensoriel, visuel vs tactile) mais pas comment il sera affecté. Cela met en évidence l'importance d'évaluer la fonction (en plus de la structure) et comment elle change après la démyélinisation. Après avoir présenté les maladies démyélinisantes, nous discuterons de la manière dont les manifestations cliniques de ces maladies reflètent divers changements pathologiques dans la fonction des axones. Nous soutiendrons que comprendre ces changements et tirer pleinement parti de cette compréhension à des fins diagnostiques et thérapeutiques peut bénéficier énormément de la modélisation informatique.

Maladies démyélinisantes

Figure 1 : Affections démyélinisantes du système nerveux périphérique (SNP). (A) Polyneuropathies démyélinisantes primaires et (B) Polyneuropathies avec lésions axonales. Abréviations : CMT 1, 2 et 4 : maladie de Charcot-Marie-Tooth ; CMTX : maladie de Charcot-Marie-Tooth liée à l'X ; HNPP : neuropathie héréditaire avec risque de paralysie de pression ; AIDP : polyneuropathie démyélinisante inflammatoire aiguë ; SGB : syndrome de Guillain-Barré. PIDC : polyneuropathie démyélinisante inflammatoire chronique ; MGUS : gammapathie monoclonale de signification indéterminée ; POEMS : polyneuropathie, organomégalie, endocrinopathie ou œdème de la protéine M et anomalies cutanées ; HSAN I–IV : neuropathie sensorielle et autonome héréditaire.

Il existe un grand nombre de maladies démyélinisantes affectant à la fois le SNP (Figure 1) et le SNC (Figure 2). Les étiologies sont hétérogènes, allant des troubles génétiques aux mécanismes métaboliques, infectieux ou auto-immuns. La sclérose en plaques (SEP) est la plus répandue de ces maladies, avec environ 3 millions de patients dans le monde. Sa cause sous-jacente est incertaine, mais on pense qu'elle implique une prédisposition génétique aux agents environnementaux[9][10]et peut impliquer des composants immunologiques, de réactivité aux traumatismes, biophysiques, génétiques et/ou métaboliques.[10] Les symptômes et les lésions doivent être multiples dans le temps et dans l'espace. Autrement dit, il doit y avoir plusieurs épisodes dans le temps, impliquant des parties déconnectées du système nerveux central. Il n'est pas clair si la démyélinisation inflammatoire est un événement primaire ou secondaire dans le processus de la maladie.[9][11][12]La plupart des traitements ciblent le système immunitaire ou la barrière hémato-encéphalique, mais la gestion des symptômes neurologiques par la modulation de l'excitabilité axonale joue également un rôle important (voir ci-dessous).

Figure 2 : Troubles démyélinisants du système nerveux central (SNC). Abréviations : SEP : sclérose en plaques ; ADEM : encéphalomyélite aiguë disséminée ; VIH : virus de l'immunodéficience humaine ; LMP : leucoencéphalopathie multifocale progressive ; HTLV-1 : virus T-lymphotrope humain 1 ; PRES : syndrome d'encéphalopathie postérieure réversible.

Évaluation clinique de la sclérose en plaques

Les symptômes sont divers et peuvent survenir dans toutes les combinaisons au sein d'un même patient. Le diagnostic exige qu'il y ait plusieurs lésions et épisodes symptomatiques au fil du temps, impliquant des parties déconnectées du SNC. De plus, les symptômes ont tendance à être peu corrélés aux mesures radiologiques. Dans la grande majorité des cas, les caractéristiques cliniques individuelles ne sont pas bien corrélées avec les résultats de l'IRM, en particulier pour les lésions cérébrales.[13][14][15]Cette dissociation clinico-radiologique demande une meilleure compréhension théorique des symptômes de démyélinisation et des changements biophysiques sous-jacents qui les accompagnent, ce qui soulève bien sûr la question de ce qu'il advient exactement des axones affectés.

Les symptômes sont souvent intermittents et peuvent inclure à la fois une perte de fonction (symptômes négatifs tels qu'engourdissement, faiblesse musculaire, picotements, cécité, incontinence, perte de la fonction sexuelle, perte d'équilibre, troubles de l'élocution, constipation, fatigue invalidante, dépression, dysfonctionnement cognitif , incapacité à avaler, perturbation de la marche et perte de contrôle de la respiration) et gain de fonction (symptômes positifs tels que spasmes, spasticité, crampes, douleur, vision floue ou double, urgence ou hésitation urinaire, nausées, entre autres).[16]Les critères diagnostiques différentiels précoces incluent le signe de Lhermitte (sensations liées à la flexion du cou) et le phénomène d'Uhthoff (aggravation des symptômes liée à la température). Le diagnostic différentiel de la SEP suit de près les critères de McDonald.[17]

Dans les études diagnostiques humaines des potentiels évoqués visuels, sensoriels ou moteurs (VEP, SEP, MEP), seule la latence ou la vitesse de conduction peut être mesurée avec précision (avec des variations d'environ 30 % à 40 % entre les différents laboratoires). Mais ces mesures donnent peu d'indices sur les mécanismes sous-jacents qui impliquent un ralentissement ou un blocage de la conduction, ou des facteurs morphologiques ou fonctionnels tels que la ramification, la démyélinisation, la remyélinisation, l'effilement axonal (diminution de la section transversale), l'atténuation ou la repousse, les changements de conduction liés à la température. , ou malpolarisation (hyper ou hypo). Néanmoins, le type de lésion démyélinisante peut fournir des indices sur l'étiologie et donc orienter le traitement ; par exemple, les facteurs génétiques semblent être plus fortement corrélés aux processus pathologiques internodaux et les dysfonctionnements immunologiques provoquent des anomalies paranodales.[18]

Un certain nombre de tests sont couramment utilisés pour évaluer la fonction neurale. En électroneurographie, un bref stimulus électrique est appliqué à un nerf périphérique à une position anatomiquement prédéfinie afin de mesurer la latence et l'amplitude du potentiel d'action composé à un autre endroit le long du nerf. Les résultats doivent être interprétés en combinaison avec les résultats cliniques et les tests (par exemple, l'électromyographie) mais, ce qui est important, différentes maladies présentent différents modèles de changements électroneurographiques. Ceci est important non seulement à des fins de diagnostic, mais peut également indiquer des changements pathologiques spécifiques dans la fonction axonale qui pourraient, à leur tour, aider à guider le choix de la thérapie (si la pathobiologie axonale était comprise ; voir ci-dessous). À l'aide d'un suivi de seuil, l'excitabilité a été mesurée chez l'homme pour plusieurs maladies démyélinisantes périphériques, notamment la maladie de Charcot-Marie-Tooth de type 1A (CMT1A), la polyneuropathie démyélinisante inflammatoire chronique (PDIC), le syndrome de Guillain-Barré (SGB) et la neuropathie motrice multifocale (MMN). ).[19][20][21][22][23][24][25] The Le défi réside dans l'interprétation de ces observations. À cette fin, le groupe de Stephanova a simulé des degrés progressivement plus élevés de démyélinisation systématique et focale des fibres motrices pour tenter d'expliquer les changements physiologiques observés.[26][27][28][29][30][31] (voir la section Modélisation ci-dessous).

Implication des corps cellulaires

La progression de la SEP récurrente-rémittente (RRMS) à la SEP progressive secondaire (SPMS) est associée à une plus grande implication de la pathologie de la matière grise, bien que l'implication axonale/de la matière grise puisse déjà être observée dans les premiers stades de la maladie.[32][33][34][35] Les dommages à la matière grise sont considérés comme le mécanisme sous-jacent de la progression de la maladie et de l'invalidité permanente chez les patients atteints de SEP, et sont mesurés par la perte de la fraction parenchymateuse cérébrale ou du volume cérébral par IRM ou cliniquement par la progression sur l'échelle élargie d'état d'invalidité (EDSS).[36]La transition de RRMS à SPMS est inquiétante en raison du manque de traitements pour lutter contre la détérioration physique et cognitive exacerbée à laquelle la plupart des patients SPMS sont confrontés.[9][37]

Traitement

Les principales interventions dans la SEP consistent à moduler la réponse immunitaire avec, par exemple, la méthy-prednisolone, l'interféron bêta, l'acétate de glatiramère ou le fingolimod, ou en empêchant les cellules inflammatoires de traverser la BHE (anticorps monoclonaux, par exemple Tysabri (anti α4-intégrine, Natalizumab )). Très récemment, les deux premiers agents oraux (fumarate et tériflunomide) ainsi que l'anticorps anti-CD52 Natalizumab ont été approuvés pour le traitement de la SEP-RR, qui peuvent être traités avec succès par des thérapies de première ligne comme les interférons, l'acétate de glatiramère ou le fingolimod, ou par thérapeutiques de seconde intention, mais les formes progressives (PPMS, SPMS) représentent encore un besoin biomédical non satisfait.[38]Les antinéoplasiques sont utilisés dans les cas extrêmement avancés ou difficiles.[39]

Les médicaments modificateurs de la maladie sont essentiels pour arrêter ou au moins atténuer le processus de démyélinisation, mais il est également essentiel de gérer les symptômes résultant de la démyélinisation qui s'est déjà produite. La modulation des canaux ioniques est de plus en plus prometteuse avec l'avènement de nouveaux bloqueurs de canaux ioniques comme l'Ampyra (blocage des canaux K).[40][41] Le blocage des canaux potassiques vise à améliorer l'excitabilité des axones. Le problème est que de telles interventions, bien qu'efficaces pour traiter les symptômes négatifs et restaurer la fonction, ont tendance à exacerber les symptômes positifs..[42]À l'inverse, le traitement des symptômes positifs tels que les spasmes avec des antiépileptiques comme la carbamazépine, par exemple, peut exacerber les symptômes négatifs.[43] En fait, le blocage des canaux Na+ réduit non seulement les symptômes positifs, mais peut également être neuroprotecteur (car l'accumulation de Na+ provoque des mécanismes d'échange Na+/Ca2+ pour charger les neurones avec Ca2+, qui est excitotoxique)[44] (Figure 3) mais ces avantages se font au détriment des symptômes négatifs. Par conséquent, et en particulier chez un patient présentant un mélange de symptômes positifs et négatifs, les options de traitement sont limitées.

Mécanismes de la neurodégénérescence liée à la démyélinisation. La démyélinisation peut entraîner progressivement des déséquilibres ioniques, une crise énergétique, un blocage de la conduction et éventuellement une neurodégénérescence. (A) un nœud normal de Ranvier avec des régions juxtaparanodales, paranodales et nodales intactes, représentant ions circulant à travers leurs canaux respectifs avec des mitochondries fournissant l'ATP pour l'énergie dépendante ases qui rétablissent les gradients ioniques appauvris par le flux ionique à travers les canaux. De nombreux canaux ioniques différents sont présents dans l'axone, mais seul un petit sous-ensemble est représenté ici ; (B) la démyélinisation partielle entraîne la dispersion des canaux ioniques nodaux, une insuffisance énergétique et des déséquilibres des gradients ioniques ; (C) une démyélinisation complète peut entraîner un blocage de la conduction et une dégénérescence axonale en raison de l'accumulation de qui résulte de la crise énergétique et de la perturbation des équilibres ioniques. Abbreviations :: canal potassique de type 1 et : : canaux sodiques types 1.6 et 1.2 ; Echangeur : pompe d'échange ; ase : dépendant de l'ATP (énergie) pompe d'échange ; CASPR1 : protéine 1 associée à la contactine (molécule d'interaction entre cellule myélinisante et axone) ;; : neurofascine 155 (molécule d'interaction prédominante entre la myéline et l'axone au niveau de la jonction axo-gliale paranodale)..


La discussion ci-dessus soulève le point important que bien que beaucoup de bruit ait été fait sur les mécanismes immunitaires, leur lien avec les changements cliniques est largement corrélationnel. Il faut considérer les effets intermédiaires sur la fonction axonale, à savoir les modifications primaires et secondaires (compensatoires) de l'excitabilité axonale, afin d'apprécier comment la fonction neurologique est altérée. Ces changements ne sont pas des conséquences simples et directes de la démyélinisation, mais suggèrent plutôt que la physiologie axonale elle-même change en réponse à la démyélinisation. Certains de ces changements sont adaptatifs tandis que d'autres sont inadaptés, ou peut-être que les changements adaptatifs peuvent devenir inadaptés à mesure que la situation (état de la myélinisation) évolue. Si des changements dans la physiologie axonale dictent la manifestation de divers symptômes, la gestion des symptômes reposera en grande partie sur des traitements visant à manipuler la physiologie axonale. Le développement stratégique de tels traitements nécessite une compréhension approfondie et mécaniste de l'excitabilité axonale et de sa régulation.

Axon Pathobiology

Structural and Molecular Changes

Axons are profoundly affected by demyelination. Axon morphology becomes irregular or swollen, often with a beaded appearance. Focal accumulation of proteins (by fast axonal transport) is also observed. In chronic active plaques, axonal loss of 20%–80% is apparent within peri-plaque white matter and normal distant white matter.[45] In early active and chronic active plaques, damage is thought to be caused by inflammatory and immune factors released during acute inflammatory demyelination. Proposed mediators include proteases, cytokines, excitotoxins and free radicals. Neuronal antigens are targets of immune reaction leading to CNS inflammation. Other factors causing axonal dysfunction or death include a lack of trophic support from myelin and oligodendrocytes, damage from soluble or cellular immune factors still present in the inactive plaque, and chronic mitochondrial failure in the setting of increased energy demands.[46] A critical role for oligodendrocytes and Schwann cells in axon survival has also been attributed to peroxisomes, lipid metabolism and reactive oxygen species (ROS) detoxification.[47]

Remyelination is often observed as shadow plaques formed by the recruitment of undifferentiated oligodendrocyte precursors that migrate to and surround the lesions enabling thin layers of remyelination.[48] This process occurs mostly in acute active plaques, but also in chronic phases. This observation triggered the development of a new monoclonal anitbody directed against LINGO-1 (Anti-LINGO-1). Binding of LINGO-1 to Nogo receptors prevents remyelinating processes in the CNS; inhibition of this interaction thus enables significant remyelination in animals with experimental autoimmune encephalomyelitis.[49]

During the disease process, autoreactive lymphocytes and macrophages can cross the blood brain barrier and accumulate in the brain and spinal cord.[50] Regulatory lymphocytes (Tregs) fail to suppress effector cells-mostly cytotoxic CD8+ cells.[51] Release of pro-inflammatory cytokines recruits naive microglia, which make contact with an oligodendrocyte-myelin unit by interactions with Fc and complement receptors. A cytotoxic death-triggering signal is then transmitted through surface bound tumor necrosis factor α (TNFα).[52] This occurs in concert with extensive axonal damage.[10]

Lucchinetti el al.[46] proposed four distinct immunopatterns of plaque formation found in patients at different stages of the disease. Type I and II plaques are dominated by T-lymphocyte and macrophage inflammation and are thought to mimic T-cell or T-cell plus antibody autoimmune encephalomyelitis models, respectively. Myelin loss in type I plaques may be caused by toxic factors released by activated macrophages, whereas IgG and complement deposition suggest a role of antibodies in type II plaques. In contrast, patterns III and IV show large oligodendrocyte dystrophy. Pattern III is thought to be related to hypoxia-induced lesions which are driven by defects in mitochondrial function,[53] whereas pattern IV lesions are associated with profound non-apoptotic death of oligodendrocytes in periplaque white matter.

Barnett and Prineas[54] analyzed lesions from patients directly after the onset of a relapse, during which active plaque formation was ongoing. Their results suggest that oligodendrocyte apoptosis and glial activation occur during early active plaque formation in the absence of inflammatory lymphocytes or myelin phagocytes. They proposed that the vulnerability of oligodendrocytes, described in Lucchinetti’s type III pattern, is present in the early stages of all plaque formation and is the trigger for subsequent post apoptotic necrosis which initiates the phagocytosis of myelin by macrophages at later stages. In vitro analyses of this process have implicated complement cascades, tumor necrosis factors or gaseous second messengers.[55] Although identification of plaques and monitoring of their progress has important clinical value, there is only a modest correlation between the demyelinating lesion load as determined by conventional MRI and the clinical disability of patients with MS (see above).

Functional Changes

The mechanisms of functional impairment during demyelination often include the disruption of transmembrane Na+, K+ and Ca2+ ions, the dispersal of their corresponding ion channels, a decrease in the efficiency of AP conduction and a resulting metabolic crisis (Figure 3). Demyelination can readily explain conduction failure within the affected axon. If conduction does not completely fail, conduction velocity can nonetheless be slowed and differential slowing across different axons can cause variable conduction delays that result in desynchronized spiking.

Demyelination also allows denuded axons to become closely apposed, thus setting the stage for ephaptic interactions and crosstalk.[10] Reflection can also occur because of impedance mismatch between myelinated and unmyelinated lengths of axon. On the other hand, hyperexcitability cannot be directly ascribed to demyelination; instead, secondary changes in intrinsic excitability need to be invoked to explain phenomena like ectopic spike generation and afterdischarge (AD). Alterations in excitability likely represent compensatory changes aimed at restoring function following the disruption caused directly by demyelination, consistent with a process referred to as homeostatic plasticity,[56] but that compensation can evidently be maladaptive. Each of the aforementioned outcomes, which are not mutually exclusive, contribute to producing different symptoms observed in demyelinating diseases.

Paroxysmal symptoms characterized by the sudden onset or intensification of symptoms such as spasm or shooting pain likely arise from AD or otherwise inappropriate burst-type spiking. Such spiking patterns suggest highly nonlinear interactions among the contributing ion currents[57][58] and could, in theory at least, involve interactions between different regions of the neuron.[59] As opposed to more generic forms of hyperexcitability (e.g., increased firing rate or reduced threshold), these specific patterns are limited in terms of the precise mechanisms through which they might arise. Therefore, identifying the ion channel changes underlying those specific forms of hyperexcitability can help constrain the search for ion channel changes responsible for associated, yet less distinctive, forms of hyperexcitability.

The disruption of energy balance in a neuron could also profoundly impact neuron well-being (Figure 3). Indeed, compensatory changes may manage to restore certain functions but, without reversing the primary problem, other problems may arise. For example, even if conduction block is prevented by an appropriate compensatory change in excitability (i.e., one that does not result in hyperexcitability), the system may be less energy efficient. Losing the energy savings afforded by saltatory conduction induces compensatory mitochondrial energy production that can result in oxidative damage and neurodegeneration.[53][60][61]

Keeping track of this long list of neurobiological changes, understanding the inter-relationships between those changes, and ultimately linking those changes with clinical manifestations and applying effective treatment is no easy task. To this end, computational modeling is an invaluable tool. Simulations not only serve to organize what information is already known, they also identify crucial gaps in knowledge. The judicious use of computational modeling can therefore enable more comprehensive understanding and facilitate the more effective application of that understanding, as discussed below.

Computational Modeling

Especially when paired with traditional experiments, computational modeling is indispensable for making sense of inconsistent data and complex mechanisms. These benefits are exemplified by the application of simulations in other fields, such as epilepsy.[62] Here we survey some of the history of computational modeling of axons, ion conductances, the physiology of myelin and demyelination, the immune system, mitochondria and other biological factors that are critical for understanding demyelinating diseases. Our review is not exhaustive but will provide a broad introduction to past, present, and future efforts in this area.

Modeling Axons

The computational modeling of axons has evolved taxonomically, from squid to mammalian tissues with a corresponding increase in sophistication. The Hodgkin and Huxley (HH) model, which provided the first thorough explanation of AP generation, was derived from experiments in unmyelinated giant axons of squid,[63][64] but this early model has proven to be an invaluable tool from which later, more sophisticated models of myelinated axons have evolved.

The spatial and biophysical heterogeneity conferred by the addition of myelin, and the consequent formation of nodes and internodal regions, represents a significant increase in axon complexity. The first computational model of a myelinated axon was a one-dimensional model that collapsed the myelin sheath into the underlying passive axolemma, used a uniform spatial step size to form the discrete approximation used in the numerical solution and employed a HH characterization of the nodal membrane.[65] Goldman & Albus[66] modified this model to include a description of the nodal membrane derived from experimental data on Xenopus laevis myelinated nerve fibers as determined by Frankenhaeuser & Huxley.[67] Subsequent studies have used the same basic form for the model with some variations for the representation of the axolemma.[15][68][69][70][71][72][73][74][75][76] The single cable model, describing the axon and all of its conductance and capacitance properties in one cable equation, has dominated the field until the present day despite the introduction of double cable models by Blight.[77] In double cable models, the internodal axolemma and the myelin sheath are independently represented. The double cable model has been expanded by Halter and Clark[78] to explore effects of the complex geometry of CNS oligodendrocytes (or Schwann cells in the case of the PNS).

Newer models have also improved upon previous simplifications including the anatomical complexity of the node of Ranvier, the distribution of ionic channels in the axon beneath the myelin sheath, the different electrical properties of the myelin sheath and the axolemma, and accommodation of possible current flow within the periaxonal space.[78][79][80][81][82] Anatomical representations of the paranodal area have allowed more detailed assessment of the effects of traumatic brain injury (TBI) on myelinated axons.[83] One of the most anatomically sophisticated models includes representation of the complex aqueous sheath structure of myelin lamellae as a series of interconnecting parallel lamellae in a model of motor nerves.[30][80]

Newer models have also considered the non-uniform distribution of ion channels throughout the axon [19,84,85,86,87,88,89,90].[19][84][85][86][87][88][89][90] Beyond ion channels, energy-dependent pumps and other ion-transport mechanisms provide important therapeutic targets for a number of neurological disorders.[91][92][93] In that respect, regulating transmembrane ion gradients costs significant energy and itself becomes an important consideration (see below).[94] This is especially true since the small volume of axons renders them prone to ion concentration changes that can dramatically impact driving forces, and can become problematic in models that assume constant intracellular and extracellular concentrations. But recent models have also dealt with such issues (see below).

All of the aforementioned models focus on simulating the change in axon membrane potential but one does not necessarily have experimental access to that variable, which of course complicates efforts to compare simulation and experimental data. Indeed, since extracellular recordings are the primary source of electrophysiological data from human subjects, the mathematical description of the extracellular field potential is of great interest clinically. Mathematical evaluations based on Laplace equations and Fourier transforms are used for calculating these potentials (sometimes referred to as line-source modeling, e.g.,.[82][95]

Modeling Specific Mechanisms

Beyond modeling normal axonal function, models can be used to explore particular mechanisms of axonal dysfunction especially when combined with experimental results that might better pinpoint mechanisms.[96] For example, Barrett and Barrett[97] showed that the depolarizing afterpotential (DAP) is sensitive to changes in conductance densities and capacitative changes that might occur during demyelination. A model by Blight was designed for simulation of his experimental recording conditions[77][98] and represents a single internode with multiple discrete segments and adjacent nodes and internodes in single lumped-parameter segments. This model included K+ channels in the axolemma of the single multi-segmented internode and treats the remainder as purely passive.

Building on this work, with careful attention to anatomical and electrophysiological details, McIntyre et al.[81] addressed the role of the DAP and afterhyperpolarization (AHP) in the recovery cycle—the distinct pattern of threshold fluctuation following a single action potential exhibited by human nerves. The simulations suggested distinct roles for active and passive Na+ and K+ channels in both afterpotentials and proposed that differences in the AP shape, strength-duration relationship, and the recovery cycle of motor and sensory nerve fibers can be attributed to kinetic differences in nodal Na+ conductances. Richardson et al.[99] also found that alteration to the standard “perfect insulator” model is necessary to reproduce DAPs during high-frequency stimulation.

The temperature sensitivity of demyelination effects has also been investigated computationally. Zlochiver[100] modeled persistent resonant reflection across a single focal demyelination plaque and found that this effect was sensitive to temperature and axon diameter. All of these examples demonstrated the power of simulations to examine specific mechanisms to explain observed phenomena from the clinic and offer guidance for future research.

As mentioned above, distinct changes in axon function are likely to manifest certain gain- or loss-of-function symptoms. If one could reproduce those changes in a computational model, the necessary parameter changes needed to convert the model between normal and abnormal operation could be used to predict the underlying pathology. Ideally this can lead to specific experiments in which the suspect ion channel, for example, is directly manipulated to see if its acute alteration is sufficient to reproduce or reverse certain pathological changes. Recent studies from the Prescott lab illustrate this process.[101][102] This success of these studies depended on advanced techniques including the dynamic clamp technique, used to switch between normal and abnormal spiking patterns and optogenetic tools. The next step is to link changes in axon function with disease symptoms (or their behavioural correlates in animal models).

In auditory nerve experiments, Tagoe and colleagues[103] demonstrated that hearing loss related to morphological changes at paranodes and juxtaparanodes, including the elongation of the auditory nerve around nodes of Ranvier, can result from exposure to lound noise, Extending this work, Hamann and collegues built a computational model to examine possible mechanisms. Their model suggested that it is more likely that a decrease in the density of Na-channels, rather than a redistribution of Na or K channels in general, is responsible for the conduction inhibition associated with acoustic over-exposure.[104] This experiment-model tandem demonstrates the revelatory potential of pairing computational models with laboratory experiments.

With a myelinated axon multi-layered model Stephanova and colleagues have had on-going success identifying likely anatomical and physiological deficiencies underlying various symptoms and conditions related to demyelination by making comparisons to the threshold tracking measurements from patients including latencies, refractoriness (the increase in threshold current during the relative refractory period), refractory period, supernormality, and threshold electrotonus values including stimulus-response measures such as current-threshold relationships.[21] For example, they found that mild internodal systematic demyelination (ISD) is a specific indicator for CMT1A. Mild paranodal systematic demyelination (PSD) and paranodal systematic demyelination (PISD) are specific indicators for CIPD and its subtypes. Severe focal demyelinations, internodal and paranodal, paranodal-internodal (IFD and PFD, PIFD) are specific indicators for acquired demyelinating neuropathies such as GBS and MMN [18] (see Figure 1).

Mild systematic and severe focal demyelination correspond to hereditary (CMT1A) and acquired (CIDP, GBS and MMN) neuropathies (Table 1). It was also found that 70% systematic demyelination is insufficient to cause symptoms and 96% is required for conduction block at a single node [18]. Thus, there is a large safety factor for focal demyelination. With their temperature-dependent version of the model of the myelinated human motor nerve fiber, Stephanova and Daskalova[105] showed that the electrotonic potentials in patients with CIDP are in high risk for blocking during hypo- and even mild hyperthermia and suggest mechanisms involving increased magnitude of polarizing nodal and depolarizing internodal electrotonic potentials, inward rectifier K+ and leak K+ currents increase with temperature, and the accommodation to long-lasting hyperpolarization is greater than to depolarization.

Table 1

Correspondence between types of demyelination and diseases according to Stephanova and Dimitrov.[18]

Type of Demyelination Corresponding Disease (PNS)
Internodal systematic demyelination (ISD) Charcot-Marie-Tooth Disease Type 1A (CMT1A)
Paranodal systematic demyelination (PSD) Chronic inflammatory demyelinating polyneuropathy (CIDP)
Paranodal + internodal demyelination (PISD) Chronic inflammatory demyelinating polyneuropathy (CIPD) subtypes
Internodal focal demyelination (IFD) Guillain-Barré (GBS)
Paranodal focal demyelination (PFD) Multifocal Motor Neuropathy (MMN)
Paranodal + focal demyelination (PIFD) Multifocal Motor Neuropathy (MMN)

Simple Models and Nonlinear Dynamical Analysis

Given the temporal dissociation between the manifestation of symptoms and the rates of demyelination and remyelination, homeostatic processes undoubtedly occur within axons, which include the redistribution of ion channels in demyelinated plaques.[106][107] But given the diversity of ion channels expressed by different axons and only patchy knowledge of how expression levels change, building detailed models to investigate those homeostatic processes is problematic. Especially under those conditions, highly simplified models can help identify fundamental principles, as exemplified by joint use of modified HH and Morris-Lecar models [57,58]. The results of those studies suggested a simple explanation for the breadth of symptoms encountered during demyelination by revealing that the ratio of Na+ to leak K+ conductance, g(Na)/g(L), acted as a four-way switch controlling excitability patterns that included failure of AP propagation, normal AP propagation, AD, and spontaneous spiking.

Further studies with this model suggested the potential for competition or cooperation between different regions of the same neuron.[59] Cooperativity between remote sites of ectopic spiking allows AD to be initiated and maintained at different locations within a single axon, thus providing a compelling explanation for the temporal and spatial discontinuities of pain and other symptoms presented by MS patients. Remarkably, in a recent study of demyelinated axons in a cuprizone mouse model, experimental evidence was seen for a redistribution of ion channels from the node of Ranvier, enhanced ectopic excitability along with antidromically propagated APs from the demyelinated plaque, as well as a compensatory shift in the excitability of membranes proximal to the soma.[108] All of these observations concur or are consistent with the computational model predictions of Coggan and colleagues and imply the success of the computational approach to guiding laboratory studies.

Furthermore, these simplified models enabled application of mathematical tools to examine the nonlinear mechanisms by which AD is initiated and terminated.[57][58][59] Bifurcation analysis revealed the underlying bistability of axon excitability under pathological conditions, as well as the factors controlling the transition from one attractor state to another. AD, for example, requires a slow inward current that allows for two stable attractor states, one corresponding to quiescence and the other to repetitive spiking (a limit cycle). Termination of AD was explained by the attractor associated with repetitive spiking being destroyed. This occurred when ultra-slow negative feedback in the form of intracellular Na+ accumulation caused the destruction of the limit-cycle attractor state [58]. Other studies using bifurcation analysis suggest that ion concentration changes can introduce slow dynamics that may be important for understanding pathological outcomes [94,109].[94][109]

Modeling at Small Scales

Studies mentioned above highlight the importance of ion concentration changes but each of them only considered those changes at a relatively course scale. By comparison, the study by Lorpreore et al.[110] tackled the daunting problem of modeling three-dimensional electro-diffusion of ion fluxes in micro and nano-domains surrounding ion channels at the node of Ranvier. In this unique model, the fluxes of ions are calculated by Poisson-Nernst-Planck equations with finite volume techniques. The fluxes and electric potentials were evaluated within voxels formed by a Delaunay-Voronoi mesh of the axon interior and exterior close to the membrane. Importantly, the algorithm was validated and results agreed with cable model predictions. Divergence from cable model predictions at smaller cluster sizes revealed the importance of each channel’s own electric field.

The above example highlights the point that models can simulate more than ion channels and membrane potential. Indeed, models can and must dig deeper into biophysical mechanisms like electro-diffusion and into signaling pathways that ultimately serve to regulate ion channel function and expression. A promising method called Biochemical Systems Theory (BST) may be useful in the future for pre-screening the effects of drugs at the systemic level. Broome and Coleman[111] demonstrated the power of this technique by modeling several biochemical pathways in neurons associated with cell death during MS including reactive oxygen and nitrogen species formation, Ca2+ dynamics, death complex formation, apoptotic factor release, and inflammatory responses together with three different states: normal, MS disease and treatment. At the atomic-level, a computational model of myelin basic protein (MBP) structure was carried-out because post-translational modifications of MBP may contribute to demyelination in MS.[112] It is important to understand its 3D structure to predict interaction sites with other molecules but a crystal structure for this protein might never be measured directly. This type of modeling may, therefore, represent an effective way to predict the structure by combining knowledge of amino acid sequence with information from similar proteins. The challenge for and the true power of modeling lies in connecting mechanisms that operate at vastly different scales, from molecular structure to the nervous system as a whole, and beyond, to address how the nervous system interacts with the immune system.

Models of Immune Factors. While there are numerous computational models of the immune system,[113] those related to MS typically model genetic interaction networks, either represented as sets of ordinary differential equations (ODEs) or Boolean networks. One systems biology model of a possible cellular mechanism of RRMS found breakdown in homeostasis of effector (Teff) and regulatory T (Treg) cells.[114][115] By changing parameters in the Teff-Treg feedback loop, under continual stochastic external stimulus from antigens, the model reproduced spontaneous and apparently stochastic immune relapses. The irreversible damage from each episode accumulates over time. Novel predictions include the suggestion that the timing of Treg immunotherapy in the immune response cycle is critical in determining whether intervention is beneficial or deleterious.

Models of Mitochondrial Dysfunction. As mentioned above, myelin enables more energy efficient AP conduction along the axon. The increased energy demands placed on the demyelinated axon represents yet another challenge to the afflicted neuron. Beyond the loss of saltatory conduction, there is mounting evidence of a critical role for astrocytes and oligodendrocytes in supplying energy to neurons and this process has also been the subject of computational modeling.[116]

There are many ways mitochondrial function can go awry and the compensatory pathways are equally complicated.[53][60][61] For example, mitochondrial dysfunction can be rooted in perturbed Ca2+ signaling within mitochondria, disrupted proton gradients or electron chain, reduction-oxidation imbalance as well as the consequences of reduced ATP availability, locally and globally. Multi-scale models of heart, for example, have been used to link altered mitochrondrial Ca2+ signaling to arrhythmia [60]. Using mitochondrial network modeling, this study demonstrated how even slightly too much reactive oxygen species can trigger a cell-wide collapse of mitochondrial membrane potential. This is an excellent example of how a computational model can link processes occurring at different levels, and it is precisely these linkages that must be established in the field of demyelination diseases.

Missing Links and the Need for Integration

Within the field of demyelinating diseases, modeling efforts have traditionally focused on axon models aimed at explaining various aspects of excitability. But as outlined above, those models have undergone tremendous evolution in complexity. In the process, models at different biological scales have begun to coalesce. For instance, models have now begun to address the regulation of ion concentrations and the consequences thereof for slow excitability changes, energy consumption, and toxicity. A computational approach will be necessary for integrating parallel and multifactorial etiologies associated with cognitive decline such as immune system signaling, energy metabolism, grey and white matter interactions, and genetic networks [117].[117] These continued efforts are starting to uncover the vast and interconnected feedback loops that operate across a broad range of spatial and temporal scales. That said, such efforts are still in their infancy and wide gaps remain in the modeling of demyelinating diseases. It is easier to describe what has been modeled than what has not. A truly integrated model involving multiple cell types that addresses all the hypothesized etiological factors remains unrealized. Among the unexplored or under-explored but potentially useful targets for modeling are grey matter pathology, myelin sheath aqueous layers, energy metabolism, and perhaps most importantly, multi-scale or integrated modeling. One should recognize that the necessary tools exist in other fields of study and can, therefore, be readily applied to the study of demyelination diseases.

Conclusions

The normal physiological function of the CNS or PNS relies on a highly regulated interplay of neurons, glia, vasculature and immune cells. This process encompasses and integrates numerous cellular and signaling components that produce a dynamical, computational whole. When any part goes awry, the entire system is forced to compensate. Even when compensation manages to rescue the most obvious consequences of demyelination, certain processes may not return to a completely normal state, which can lead to problems on longer time scales. The resulting symptoms are a confusing mixture of direct and compensatory changes that continuously evolve. The overall complexity has proven to be intractable to efficient experimental dissection. The application of computational modeling techniques represents an invaluable approach to help break the impasse and engender a new era of understanding and discovery.

Acknowledgments

Support provided by the Canadian Institutes of Health Research New Investigator Award and the Ontario Early Researcher Award (SAP). We thank Heiki Blum for assistance with figure preparation.

Author Contributions

All authors contributed to the writing of this manuscript. Figures were provided by Sven G. Meuth.

Conflicts of Interest

The authors declare no conflict of interest.

Article information

Int J Mol Sci. 2015 Sep; 16(9): 21215–21236. Published online 2015 Sep 7. doi: 10.3390/ijms160921215 PMCID: PMC4613250 PMID: 26370960 Jay S. Coggan,1,* Stefan Bittner,2 Klaus M. Stiefel,1 Sven G. Meuth,2 and Steven A. Prescott3,4 Christoph Kleinschnitz, Academic Editor 1NeuroLinx Research Institute, La Jolla, CA 92039, USA; E-Mail: gro.xniloruen@sualk 2Department of Neurology, Institute of Physiology, Universitätsklinikum Münster, 48149 Münster, Germany; E-Mails: moc.kooltuo@renttib-nafets (S.B.); ed.retsneumku@htuem.nevs (S.G.M.) 3Neurosciences and Mental Health, the Hospital for Sick Children, Toronto, ON M5G 1X8, Canada; E-Mail: ac.sdikkcis@ttocserp.evets 4Department of Physiology and the Institute of Biomaterials and Biomedical Engineering, University of Toronto, Toronto, ON M5G 1X8, Canada

  • Author to whom correspondence should be addressed; E-Mail: gro.xniloruen@yaj; Tel.: +1-858-243-6720.

Received 2015 May 26; Accepted 2015 Aug 25. Copyright © 2015 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/4.0/). Articles from International Journal of Molecular Sciences are provided here courtesy of Multidisciplinary Digital Publishing Institute (MDPI)

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