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The '''Soliton model''' in [[neuroscience]] is a recently developed [[biological neuron models|model]] that attempts to explain how signals are conducted within [[neuron]]s. It proposes that the signals travel along the cell's [[cell membrane|membrane]] in the form of certain kinds of [[sound]] (or [[density]]) pulses known as [[soliton]]s. As such the model presents a direct challenge to the widely accepted [[Hodgkin–Huxley model]] which proposes that signals travel as [[action potential]]s: [[voltage-gated ion channel]]s in the membrane open and allow [[ion]]s to rush into the cell, thereby leading to the opening of other nearby ion channels and thus propagating the signal in an essentially electrical manner.

==History==
The Soliton model was developed beginning in 2005 by Thomas Heimburg and Andrew D. Jackson,<ref>{{cite journal |author=Heimburg, T., Jackson, A.D. |title=On soliton propagation in biomembranes and nerves |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=102 |issue=2 |pages=9790 |date=12 July 2005 |url=http://www.pnas.org/cgi/content/full/102/28/9790 |doi=10.1073/pnas.0503823102 |bibcode=2005PNAS..102.9790H}}</ref><ref>{{cite journal |doi=10.1142/S179304800700043X |author=Heimburg, T., Jackson, A.D. |title=On the action potential as a propagating density pulse and the role of anesthetics |journal=Biophys. Rev. Lett. |volume=2 |pages=57–78 |year=2007 |arxiv=physics/0610117 |bibcode=2006physics..10117H}}</ref><ref>{{cite journal |doi=10.1016/j.pneurobio.2009.03.002 |author=Andersen, S.S.L., Jackson, A.D., Heimburg, T. |title=Towards a thermodynamic theory of nerve pulse propagation |journal=Progr. Neurobiol. |volume=88 |issue=2 |pages=104–113 |year=2009 |url=http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T0R-4VTVR43-2&_user=641710&_coverDate=06%2F30%2F2009&_alid=1453303237&_rdoc=1&_fmt=high&_orig=search&_origin=search&_zone=rslt_list_item&_cdi=4869&_sort=r&_st=13&_docanchor=&view=c&_ct=1&_acct=C000034378&_version=1&_urlVersion=0&_userid=641710&md5=a5e46d6a5aad16abb0d54f6970434ba4&searchtype=a}}</ref> both at the [[Niels Bohr Institute]] of the [[University of Copenhagen]]. Heimburg heads the institute's Membrane Biophysics Group and as of early 2007 all published articles on the model come from this group.

==Justification==
The model starts with the observation that cell membranes always have a [[melting point|freezing point]] (the temperature below which the consistency changes from fluid to gel-like) only slightly below the organism's body temperature, and this allows for the propagation of solitons. It has been known for several decades that an action potential traveling along a neuron results in a slight increase in temperature followed by a decrease in temperature.<ref>{{cite journal |doi=10.1098/rspb.1958.0012 |author=Abbott, B.C., Hill, A.V., Howarth, J.V. |title=The positive and negative heat associated with a nerve impulse |journal=[[Proceedings of the Royal Society B]] |volume=148 |issue=931 |pages=149–187 |year=1958 |url=http://rspb.royalsocietypublishing.org/content/148/931/149.abstract?sid=55350fa9-13b9-4280-90f3-99a1fc01b2c5|bibcode = 1958RSPSB.148..149A }}</ref> No net heat is released during the overall pulse. The decrease during the second phase of the action potential is not explained by the Hodgkin–Huxley model (electrical charges traveling through a [[resistor]] always ''produce'' heat), but traveling solitons do not lose energy in this way and the observed temperature profile is consistent with the Soliton model. Further, it has been observed that a signal traveling along a neuron results in a slight local thickening of the membrane and a force acting outwards;<ref>{{cite journal |author=Iwasa, K., Tasaki I., Gibbons, R. |title=Swelling of nerve fibres associated with action potentials |journal=Science |volume=210 |issue=4467 |pages=338–9 |year=1980 |url=http://www.sciencemag.org/cgi/content/abstract/sci;210/4467/338?maxtoshow=&hits=10&RESULTFORMAT=&author1=Iwasa%2C+K&andorexacttitle=or&andorexacttitleabs=or&andorexactfulltext=or&searchid=1&FIRSTINDEX=0&sortspec=relevance&fdate=1/1/1980&tdate=12/31/1980&resourcetype=HWCIT,HWELTR |pmid=7423196 |doi=10.1126/science.7423196 |bibcode=1980Sci...210..338I}}</ref> this effect is not explained by the Hodgkin–Huxley model but is clearly consistent with the Soliton model. 

It is undeniable that an electrical signal can be observed when an action potential propagates along a neuron. The Soliton model explains this as follows: the traveling soliton locally changes density and thickness of the membrane, and since the membrane contains many charged and [[chemical polarity|polar]] substances, this will result in an electrical effect, akin to [[piezoelectricity]].

==Formalism==
The soliton representing the action potential of nerves is the solution of the [[partial differential equation]]

<math> \frac{\partial^2 \Delta \rho}{\partial t^2} = \frac{\partial}{\partial x} \left[\left(c_0^2 + p\Delta \rho + q\Delta \rho^2\right)\frac{\partial \Delta \rho}{\partial x}\right] - h\frac{\partial^4 \Delta\rho}{\partial x^4}, </math>

where {{math|''t''}} is time and {{math|''x''}} is the position along the nerve axon. {{math|Δ''ρ''}} is the change in membrane density under the influence of the action potential,  {{math|''c''<sub>0</sub>}} is the sound velocity of the nerve membrane, {{math|''p''}} and {{math|''q''}} describe the nature of the phase transition and thereby the nonlinearity of the elastic constants of the nerve membrane. The parameters {{math|''c''<sub>0</sub>}}, {{math|''p''}} and {{math|''q''}} are dictated by the thermodynamic properties of the nerve membrane and cannot be adjusted freely. They have to be determined experimentally. The parameter {{math|''h''}} describes the frequency dependence of the sound velocity of the membrane ([[dispersion relation]]). The above equation does not contain any fit parameters. It is formally related to the [[Boussinesq approximation (water waves)]] for solitons in water canals. The solutions of the above equation possess a limiting maximum amplitude and a minimum propagation velocity that is similar to the pulse velocity in myelinated nerves. There also exist periodic solutions that display hyperpolarization and refractory periods.<ref>{{cite journal |author=Villagran Vargas, E., Ludu, A., Hustert, R., Gumrich, P., Jackson, A.D., Heimburg, T. |title=Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve |year=2010 |pmid=21177017 |doi=10.1016/j.bpc.2010.11.001 |volume=153 |issue=2–3 |pages=159–167 |journal=Biophysical Chemistry |arxiv=1006.3281 }}</ref>

==Role of ion channels==
The Soliton model explains several aspects of the action potential, which are not explained by Hodgkin–Huxley. Since it is of thermodynamic nature it does not address the properties of single macromolecules like [[ion channel]] proteins on a molecular scale. It is rather assumed that their properties are implicitly contained in the macroscopic thermodynamic properties of the nerve membranes. The model is therefore neither in conflict with the action of membrane proteins nor with pharmacology. The soliton model predicts membrane current fluctuations during the action potential. These currents are of similar appearance as those reported for ion channel proteins.<ref>{{cite journal |doi=10.1016/j.bpc.2010.02.018 |author=Heimburg, T. |title=Lipid Ion Channels |journal=Biophys. Chem. |volume=150 |issue=1–3 |pages=2–22 |year=2010 |arxiv=1001.2524 |pmid=20385440}}</ref> They are thought to be caused by lipid membrane pores spontaneously generated by the thermal fluctuations, which are at the core of the soliton model.

==Application to anesthesia==
The authors claim that their model explains the previously obscure mode of action of numerous [[anesthetic]]s. The [[anesthesia|Meyer-Overton observation]] holds that the strength of a wide variety of chemically diverse anesthetics is proportional to their [[lipid]] solubility, suggesting that they do not act by binding to specific [[protein]]s such as ion channels but instead by dissolving in and changing the properties of the lipid membrane. Dissolving substances in the membrane lowers the membrane's freezing point, and the resulting larger difference between body temperature and freezing point inhibits the propagation of solitons.<ref>{{cite journal |author=Heimburg, T., Jackson, A.D. |title=The thermodynamics of general anesthesia |journal=Biophys. J. |volume=92 |issue=9 |pages=3159–65 |url=http://www.cell.com/biophysj/abstract/S0006-3495(07)71124-4 |year=2007 |pmid=17293400 |pmc=1852341 |doi=10.1529/biophysj.106.099754 |bibcode=2007BpJ....92.3159H|arxiv = physics/0610147 }}</ref> By increasing pressure, lowering [[pH]] or lowering temperature, this difference can be restored back to normal, which should cancel the action of anesthetics: this is indeed observed. The amount of pressure needed to cancel the action of an anesthetic of a given lipid solubility can be computed from the soliton model and agrees reasonably well with experimental observations.

==See also==
*[[Biological neuron models]]
*[[Hodgkin–Huxley model]]
*[[Vector soliton]]

==Sources==
*[http://www.eurekalert.org/pub_releases/2007-03/uoc-ot030607.php On the (sound) track of anesthetics], Eurekalert, according to a press release University of Copenhagen, 6 March 2007
*[http://www.scienceline.eu/health/on-the-sound-track-of-anesthetics/ On the (sound) track of anesthetics], ScienceLine
*{{cite journal |author=Kaare Græsbøll |title=Function of Nerves — Action of Anesthetics |journal=Gamma |volume=143 |year=2006 |url=http://www.gamma.nbi.dk/Galleri/gamma143/nerves.pdf |format=PDF}} An elementary introduction.
*{{cite journal |author=Pradip Das, W.H. Schwarz |title=Solitons in cell membrane |journal=Physical Review E |volume=51 |issue=4 |pages=3588 |date=4 November 1994 |url=http://link.aps.org/abstract/PRE/v51/p3588 |doi=10.1103/PhysRevE.51.3588 |bibcode=1995PhRvE..51.3588D}}

==References==
{{Reflist}}

{{DEFAULTSORT:Soliton Model}}
[[Category:Cellular neuroscience]]
[[Category:Computational neuroscience]]
[[Category:Biophysics]]