Difference between revisions of "Physiological Dynamics in Demyelinating Diseases: Unraveling Complex Relationships through Computer Modeling"

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Despite intense research, few treatments are available for most neurological disorders. Demyelinating diseases are no exception. This is perhaps not surprising considering the multifactorial nature of these diseases, which involve complex interactions between immune system cells, glia and neurons. In the case of multiple sclerosis, for example, there is no unanimity among researchers about the cause or even which system or cell type could be ground zero. This situation precludes the development and strategic application of mechanism-based therapies. We will discuss how computational modeling applied to questions at different biological levels can help link together disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism. By making testable predictions and revealing critical gaps in existing knowledge, such models can help direct research and will provide a rigorous framework in which to integrate new data as they are collected. Nowadays, there is no shortage of data; the challenge is to make sense of it all. In that respect, computational modeling is an invaluable tool that could, ultimately, transform how we understand, diagnose, and treat demyelinating diseases.

Keywords: myelin, demyelination, multiple sclerosis, neurodegenerative disease, computational model, drug discovery

The nervous systems of vertebrates are often divided into grey and white matter based on their appearance and corresponding functional roles. While the grey matter consists largely of cell bodies and dendrites, white matter contains mostly axons and gets its name from the lipid membrane sheets called myelin that are wound tightly around those axons [1]. Myelin originates from different classes of glial cells referred to as oligodendrocytes in the central nervous system (CNS) and Schwann cells in the peripheral nervous system (PNS).

Demyelination sets in motion functional changes that are important for clinical features but which are not readily explained by immunological or radiological changes. Location of a plaque predicts what system will be affected (motor vs. sensory, visual vs. tactile) but not how it will be affected. This highlights the importance of assessing function (in addition to structure) and how it changes following demyelination. After introducing demyelinating diseases, we will discuss how the clinical manifestations of those diseases reflect diverse pathological changes in axon function. We will argue that understanding those changes and fully capitalizing on that understanding for diagnostic and therapeutic purposes can benefit enormously from computational modeling.

There are a large number of demyelinating diseases affecting both the PNS (Figure 1) and CNS (Figure 2). The etiologies are heterogeneous, ranging from genetic disorders to metabolic, infectious or autoimmune mechanisms. Multiple sclerosis (MS) is the most prevalent of these disorders, with an estimated 3 million patients worldwide. Its underlying cause is uncertain but is thought to involve genetic predisposition to environmental agents [9,10] and can involve immunological, responsiveness to trauma, biophysical, genetic and/or metabolic components [10]. The symptoms and lesions must be multiple in both time and space. That is, there must be multiple episodes in time, involving disconnected parts of the central nervous system. It is not clear whether inflammatory demyelination is a primary or secondary event within the disease process [9,11,12]. Most treatments target the immune system or the blood-brain barrier, but managing neurological symptoms through modulation of axonal excitability also plays an important role (see below).

Figure 2

Figure 2

Symptoms are diverse and can occur in all combinations within an individual patient. Diagnosis requires that there must be multiple lesions and symptomatic episodes over time, involving disconnected parts of the CNS. Furthermore, symptoms tend to be poorly correlated with radiological measures. In the great majority of cases, individual clinical characteristics do not correlate well with MRI findings, especially for cerebral lesions [13,14,15]. This clinico-radiologic dissociation begs for better theoretical understanding of demyelination symptoms and the underlying biophysical changes that accompany them, which of course raises the question of what exactly happens to the affected axons.

A number of tests are routinely used to assess the neural function. In electroneurography, a brief electrical stimulus is applied to a peripheral nerve at an anatomically predefined position in order to measure the latency and amplitude of the compound action potential at another location along the nerve. Results need to be interpreted in combination with clinical findings and tests (e.g., electromyography) but, importantly, different diseases exhibit different patterns of electroneurographic changes. This is important not only for diagnostic purposes but can also point to specific pathological changes in axon function which could, in turn, help guide the choice of therapy (if the axon pathobiology were understood; see below). Using threshold tracking, excitability has been measured in humans for the several peripheral demyelinating diseases including Charcot-Marie-Tooth Disease Type 1A (CMT1A), chronic inflammatory demyelinating polyneuropathy (CIDP), Guillain-Barré syndrome (GBS) and multifocal motor neuropathy (MMN) [19,20,21,22,23,24,25]. The challenge lies in interpreting those observations. To this end, the group of Stephanova has simulated progressively greater degrees of systematic and focal demyelination of motor fibers to try to explain the observed physiological changes [26,27,28,29,30,31] (see Modeling section below).

Progression from relapsing-remitting MS (RRMS) to the secondary progressive MS (SPMS) is associated with greater involvement of grey matter pathology, although axonal/grey matter involvement can be observed already in early disease stages [32,33,34,35]. Damage to the grey matter is regarded as the underlying mechanism of disease progression and permanent disability in MS patients, and is measured by loss of brain parenchymal fraction or brain volume by MRI or clinically by progression on the expanded disability status scale (EDSS) [36]. Transition from RRMS to SPMS is foreboding for the lack of therapeutics to combat the exacerbated physical and cognitive deterioration that most SPMS patients face [9,37].

The main interventions for MS involve modulation of the immune response with, for example, methly-prednisolone, interferon betas, glatiramer acetate or fingolimod, or by preventing inflammatory cells from crossing the BBB (monoclonal antibodies e.g., Tysabri (anti α4-integrin, Natalizumab)). Very recently the first two oral agents (fumarate and teriflunomide) as well as the anti-CD52 directed antibody Natalizumab where approved for treatment of RRMS, which can be successfully treated by first-line therapies like interferons, glatiramer acetate, or fingolimod, or by second-line therapies, but progressive forms (PPMS, SPMS) still represent an unmet biomedical need [38]. Anti-neoplastics are used in extremely advanced or difficult cases [39].

The above discussion raises the important point that although much ado has been made about immune mechanisms, their connection with clinical changes is largely correlational. One must consider the intermediary effects on axonal function, namely the primary and secondary (compensatory) changes in axon excitability, in order to appreciate how neurological function is altered. Those changes are not simple and direct consequences of demyelination but, instead, suggest that axonal physiology itself changes in response to demyelination. Some of those changes are adaptive whereas others are maladaptive, or perhaps adaptive changes can become maladaptive as the situation (myelination status) evolves. If changes in axonal physiology dictate the manifestation of various symptoms, then symptom management will largely fall on treatments that aim to manipulate axon physiology. Strategically developing such treatments require a deep, mechanistic understanding of axonal excitability and its regulation.

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].

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).

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.

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.

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.

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.

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]).

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.

Table 1

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

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.

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].

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.

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.

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]. 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.

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.

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.

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

The authors declare no conflict of interest.

Int J Mol Sci. 2015 Sep; 16(9): 21215–21236.

Published online 2015 Sep 7. doi: 10.3390/ijms160921215

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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