Difference between revisions of "Dinámica fisiológica en enfermedades desmielinizantes: desentrañar relaciones complejas a través del modelado por computadora"

=== 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.<ref>Soltesz I., Staley K.  Computational Neuroscience in Epilepsy. 1st ed. Elsevier; London, UK: 2008.  [Google Scholar]</ref> 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,<ref>Hodgkin A.L., Huxley A.F. The components of membrane conductance in the giant axon of ''Loligo''. J. Physiol. 1952;116:473–496. doi: 10.1113/jphysiol.1952.sp004718. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Hodgkin A.L., Huxley A.F. Currents carried by sodium and potassium ions through the membrane of the giant axon of ''Loligo''. J. Physiol. 1952;116:449–472. doi: 10.1113/jphysiol.1952.sp004717. [PMC free article] [PubMed] </ref> 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.<ref>Fitzhugh R. Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber. Biophys. J. 1962;2:11–21. doi: 10.1016/S0006-3495(62)86837-4. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> Goldman & Albus<ref>Goldman L., Albus J.S. Computation of impulse conduction in myelinated fibers; theoretical basis of the velocity-diameter relation. Biophys. J. 1968;8:596–607. doi: 10.1016/S0006-3495(68)86510-5. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref>Frankenhaeuser B., Huxley A.F. The action potential in the myelinated nerve fiber of ''Xenopus'' ''laevis'' as computed on the basis of voltage clamp data. J. Physiol. 1964;171:302–315. doi: 10.1113/jphysiol.1964.sp007378.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> Subsequent studies have used the same basic form for the model with some variations for the representation of the axolemma.<ref name=":2" /><ref>Smith R.S., Koles Z.J. Myelinated nerve fibers: Computed effect of myelin thickness on conduction velocity. Am. J. Physiol. 1970;219:1256–1258.[PubMed] [Google Scholar]</ref><ref>Hutchinson N.A., Koles Z.J., Smith R.S. Conduction velocity in myelinated nerve fibres of ''Xenopus'' ''laevis''. J. Physiol. 1970;208:279–289. doi: 10.1113/jphysiol.1970.sp009119. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Koles Z.J., Rasminsky M. A computer simulation of conduction in demyelinated nerve fibres. J. Physiol. 1972;227:351–364. doi: 10.1113/jphysiol.1972.sp010036. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Hardy W.L. Propagation speed in myelinated nerve. II. Theoretical dependence on external Na and on temperature. Biophys. J. 1973;13:1071–1089. doi: 10.1016/S0006-3495(73)86046-1. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Schauf C.L., Davis F.A. Impulse conduction in multiple sclerosis: A theoretical basis for modification by temperature and pharmacological agents. J. Neurol. Neurosurg. Psychiatry. 1974;37:152–161. doi: 10.1136/jnnp.37.2.152.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Brill M.H., Waxman S.G., Moore J.W., Joyner R.W. Conduction velocity and spike configuration in myelinated fibres: Computed dependence on internode distance. J. Neurol. Neurosurg. Psychiatry. 1977;40:769–774. doi: 10.1136/jnnp.40.8.769. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Waxman S.G., Brill M.H. Conduction through demyelinated plaques in multiple sclerosis: Computer simulations of facilitation by short internodes. J. Neurol. Neurosurg. Psychiatry. 1978;41:408–416. doi: 10.1136/jnnp.41.5.408.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Wood S.L., Waxman S.G., Kocsis J.D. Conduction of trans of impulses in uniform myelinated fibers: Computed dependence on stimulus frequency. Neuroscience. 1982;7:423–430. doi: 10.1016/0306-4522(82)90276-7. [PubMed] [CrossRef] [Google Scholar]</ref><ref>Goldfinger M.D. Computation of high safety factor impulse propagation at axonal branch points. Neuroreport. 2000;11:449–456. doi: 10.1097/00001756-200002280-00005. [PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref name=":14">Blight A.R. Computer simulation of action potentials and afterpotentials in mammalian myelinated axons: The case for a lower resistance myelin sheath. Neuroscience. 1985;15:13–31. doi: 10.1016/0306-4522(85)90119-8. [PubMed] [CrossRef] [Google Scholar]</ref> 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<ref name=":15">Halter J.A., Clark J.W., Jr. A distributed-parameter model of the myelinated nerve fiber. J. Theor. Biol. 1991;148:345–382. doi: 10.1016/S0022-5193(05)80242-5. [PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref name=":15" /><ref>Schwarz J.R., Eikhof G. Na currents and action potentials in rat myelinated nerve fibres at 20 and 37 °C. Pflugers Arch. 1987;409:569–577. doi: 10.1007/BF00584655. [PubMed] [CrossRef] [Google Scholar]</ref><ref name=":16">Stephanova D.I. Myelin as longitudinal conductor: A multi-layered model of the myelinated human motor nerve fibre. Biol. Cybern. 2001;84:301–308. doi: 10.1007/s004220000213. [PubMed] [CrossRef] [Google Scholar]</ref><ref name=":17">McIntyre C.C., Richardson A.G., Grill W.M. Modeling the excitability of mammalian nerve fibers: Influence of afterpotentials on the recovery cycle. J. Neurophysiol. 2002;87:995–1006. [PubMed] [Google Scholar]</ref><ref name=":18">Einziger P.D., Livshitz L.M., Mizrahi J. Generalized cable equation model for myelinated nerve fiber. IEEE Trans. Biomed. Eng. 2005;52:1632–1642. doi: 10.1109/TBME.2005.856031. [PubMed] [CrossRef] [Google Scholar]</ref> Anatomical representations of the paranodal area have allowed more detailed assessment of the effects of traumatic brain injury (TBI) on myelinated axons.<ref>Volman V., Ng L. Primary paranode demyelination modulates slowly developing axonal depolarization in a model of axonal injury. J. Neural Comput. 2014;37:439–457. [PubMed] [Google Scholar]</ref> 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.<ref name=":6" /><ref name=":16" />

Newer models have also considered the non-uniform distribution of ion channels throughout the axon [19,84,85,86,87,88,89,90].<ref name=":4" /><ref>Stephanova D.I., Bostock H. A Distributed-parameter model of the myelinated human motor nerve fibre: Temporal and spatial distributions of action potentials and ionic currents. Biol. Cybern. 1995;73:275–280. doi: 10.1007/BF00201429. [PubMed] [CrossRef] [Google Scholar]</ref><ref>Chiu S.Y., Ritchie J.M. On the physiological role of internodal potassium channels and the security of conduction in myelinated nerve fibres. Proc. R. Soc. Lond. B Biol. Sci. 1984;220:415–422. doi: 10.1098/rspb.1984.0010.[PubMed] [CrossRef] [Google Scholar]</ref><ref>Brismar T., Schwarz J.R. Potassium permeability in rat myelinated nerve fibres. Acta Physiol. Scand. 1985;124:141–148. doi: 10.1111/j.1748-1716.1985.tb07645.x. [PubMed] [CrossRef] [Google Scholar]</ref><ref>Chiu S.Y., Schwarz W. Sodium and potassium currents in acutely demyelinated internodes of rabbit sciatic nerves. J. Physiol. 1987;391:631–649. doi: 10.1113/jphysiol.1987.sp016760. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Baker M., Bostock H., Grafe P., Martius P. Function and distribution of three types of rectifying channel in rat spinal root myelinated axons. J. Physiol. 1987;383:45–67. [PMC free article] [PubMed] [Google Scholar</ref><ref>Röper J., Schwarz J.R. Heterogeneous distribution of fast and slow potassium channels in myelinated rat nerve fibres. J. Physiol. 1989;416:93–110. doi: 10.1113/jphysiol.1989.sp017751. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Bittner S., Meuth S.G. Targeting ion channels for the treatment of autoimmune neuroinflammation. Ther. Adv. Neurol. Disord. 2013;6:322–336. doi: 10.1177/1756285613487782. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> Beyond ion channels, energy-dependent pumps and other ion-transport mechanisms provide important therapeutic targets for a number of neurological disorders.<ref>Waxman S.G., Ritchie J.M. Molecular dissection of the myelinated axon. Ann. Neurol. 1993;33:121–136. doi: 10.1002/ana.410330202. [PubMed] [CrossRef] [Google Scholar]</ref><ref>Bittner S., Budde T., Wiendl H., Meuth S.G. From the background to the spotlight: TASK channels in pathological conditions. Brain Pathol. 2010;20:999–1009. doi: 10.1111/j.1750-3639.2010.00407.x. [PMC free article][PubMed] [CrossRef] [Google Scholar]</ref><ref>Ehling P., Bittner S., Budde T., Wiendl H., Meuth S.G. Ion channels in autoimmune neurodegeneration. FEBS Lett. 2011;585:3836–3842. doi: 10.1016/j.febslet.2011.03.065. [PubMed] [CrossRef] [Google Scholar]</ref> In that respect, regulating transmembrane ion gradients costs significant energy and itself becomes an important consideration (see below).<ref name=":19">Hübel N., Dahlem M.A. Dynamics from seconds to hours in Hodgkin-Huxley model with time-dependent ion concentrations and buffer reservoirs. PLoS Comput. Biol. 2014;10:e1003941. doi: 10.1371/journal.pcbi.1003941.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> 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.,.<ref name=":18" /><ref>Ganapathy L., Clark J.W. Extracellular currents and potentials of the active myelinated nerve fibre. Biophys. J. 1987;52:749–761. doi: 10.1016/S0006-3495(87)83269-1. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref>

==== 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.<ref>Prescott S.A. Pathological changes in peripheral nerve excitability. In: Jaeger D., Jung R., editors. Encyclopedia of Computational Neurosci. 1st ed. Springer-Verlag; New York, NY, USA: 2015.  [Google Scholar]</ref> For example, Barrett and Barrett<ref>Barrett E.F., Barrett J.N. Intracellular recording from vertebrate myelinated axons: Mechanism of the depolarizing afterpotential. J. Physiol. 1982;323:117–144. doi: 10.1113/jphysiol.1982.sp014064. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> 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<ref name=":14" /><ref>Blight A.R., Someya S. Depolarizing afterpotentials in myelinated axons of mammalian spinal cord. Neuroscience. 1985;15:1–12. doi: 10.1016/0306-4522(85)90118-6. [PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref name=":17" /> 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.<ref>Richardson A.G., McIntyre C.C., Grill W.M. Modelling the effects of electric fields on nerve fibres: Influence of the myelin sheath. Med. Biol. Eng. Comput. 2000;38:438–446. doi: 10.1007/BF02345014. [PubMed] [CrossRef] [Google Scholar]</ref> 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<ref>Zlochiver S. Persistent reflection underlies ectopic activity in multiple sclerosis: A numerical study. Biol. Cybern. 2010;102:181–196. doi: 10.1007/s00422-009-0361-2. [PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref>Ratté S., Zhu Y., Lee K.Y., Prescott S.A. Criticality and degeneracy in injury-induced changes in primary afferent excitability and the implications for neuropathic pain. Elife. 2014;3:e02370. doi: 10.7554/eLife.02370.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref><ref>Zhu Y., Feng B., Schwartz E.S., Gebhart G.F., Prescott S.A. Novel method to assess axonal excitability using channelrhodopsin-based photoactivation. J. Neurophysiol. 2015;113:2242–2249. doi: 10.1152/jn.00982.2014.[PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> 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<ref>Tagoe T., Barker M., Jones A., Allcock N., Hamann M. Auditory nerve perinodal dysmyelination in noise-induced hearing loss. J. Neurosci. 2014;12:2684–2688. doi: 10.1523/JNEUROSCI.3977-13.2014.</ref> 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.<ref>Brown A.M., Hamann M. Computational modeling of the effects of auditory nerve dysmyelination. Front. Neuroanat. 2014;8doi: 10.3389/fnana.2014.00073. [PMC free article] [PubMed] [CrossRef] [Google Scholar]</ref> 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.<ref name=":5" /> 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<ref>Stephanova D.I., Daskalova M. Electrotonic potentials in simulated chronic inflammatory demyelinating polyneuropathy at 20 °C–42 °C. J. Integr. Neurosci. 2015;27:1–18. doi: 10.1142/S0219635215500119. [PubMed] [CrossRef] [Google Scholar]</ref> 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.