forthcoming article published online at www.m-hikari.comInternational audienceWe expose first a biological model of memory based on one hand of the mechanical oscillations of axons during action potential and on the other hand on the changes in the extra cellular matrix composition when a mechanical strain is applied on it. Due to these changes, the stiffness of the extra cellular matrix along the most excited neurons will increase close to these neurons due to the growth of astrocytes around them and to the elastoplastic behavior of collagen. This will create preferential paths linked to a memory effect. In a second part, we expose a physical model based on random walk of the action potential on the array composed of dendrites and axons. This last model shows that repetition of the same event leads to long time memory of this event and that paradoxical sleep leads to the linking of different events put into memory

Kanani, Sandra

Olivi-Tran, Nathalie

Robbins, Ian

arXiv

HAL-UNILIM

The role of the extra cellular matrix on memoryNathalie Olivi-Tran, Sandra Kanani, Ian RobbinsTo cite this version:Nathalie Olivi-Tran, Sandra Kanani, Ian Robbins. The role of the extra cellular matrix onmemory. Advanced Studies in Biology, 2009, 1 (1), pp.9-14. <hal-00134775v4>HAL Id: hal-00134775https://hal.archives-ouvertes.fr/hal-00134775v4Submitted on 18 Sep 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.The role of the extra cellular matrix on memoryN.Olivi-Tran(1),Sandra Kanani (2), Ian Robbins (3)(1)S.P.C.T.S., UMR-CNRS 6638,Universite de Limoges,E.N.S.C.I., 47 avenue Albert Thomas 87065 Limoges cedex, France(2) IGF, 141 rue de la Cardonille,34094 Montpellier cedex 05, France(3) IGMM, UMR-CNRS 5535, 1919 route de Mende, 34293 Montpellier cedex 5, France(Dated: March 26, 2008)AbstractWe expose first a biological model of memory based on one hand of the mechanical oscillationsof axons during action potential and on the other hand on the changes in the extra cellular matrixcomposition when a mechanical strain is applied on it. Due to these changes, the stiffness of theextra cellular matrix along the most excited neurons will increase close to these neurons due to thegrowth of astrocytes around them and to the elastoplastic behavior of collagen. This will createpreferential paths linked to a memory effect. In a second part, we expose a physical model basedon random walk of the action potential on the array composed of dendrites and axons. This lastmodel shows that repetition of the same event leads to long time memory of this event and thatparadoxical sleep leads to the linking of different events put into memory.PACS numbers:1I. INTRODUCTIONMemory is one of the mystery in biology and especially in neurosciences. Up to now nomodel has been able to model correctly the memory process. We present here two modelswhich are in relation to explain some features of memory. One model is based on biology ofthe central nervous system and the other on physics and random walk on an array.II. BIOLOGICAL MODEL FOR MEMORYIwasa et al [1] detected small lateral movement of nerve fibres during the propagationof an action potential. This lateral movement is due to swelling of the nerve fibre duringexcitation and has an amplitude of a few tens of angstroms. This was an in vivo study.Moreover several in vitro studies [2–5] showed the same swelling and shrinking on a squidgiant axon due to intracellular pressure during the action potential.This leads to a mechanical action on the extra cellular matrix in the nervous centralsystem. The lateral movement due to the mechanical oscillations of the nerves or of theaxons will create a strain on the surrounding extra cellular matrix.Let us make the hypothesis that the mechanical actions of axons (swelling and shrinking)is also present in the whole neuron during excitation but to small to be detected.One of the major component of the brain extra cellular matrix are glial cells. We shallfocus here on a particular type of glial cells: astrocytes. Astrocytes can feel mechanicalstrains which induces several different results [6] (Ca2+ intracellular increase,endothelinproduction...). Moreover, Wenzel et al. showed that high frequency stimulations of neuronscaused astrocytes to wrap around the potentiated synapses [7]. This is the biological pointof view of our model.On the physical point of view, let us recall that another component of the extra cellularmatrix is collagen type I in the central nervous system, This collagen is a biological polymerwhich has an elasto plastic response to stress: when a mechanical stress is applied on it andovercomes a given threshold, collagen becomes plastic and does not recover its former shape[8]. This leads to a lower concentration in collagen around the most excited neurons.This changes in the extra cellular matrix composition along one axon or dendrite due tomechanical strain creates a preferential path. Explicitly, the difference in the extra cellular2matrix composition along one neuron which is more excited compared to another will createa preferential path along the first neuron cited.During neuronal excitations, several neurons connected one to each other via synapseswill apply mechanical strains on the extra cellular matrix and therefore create a preferentialpath where the stiffness of the surrounding extra cellular matrix is larger due to the presenceof astrocytes and the plastic behavior of collagen.Now that preferential paths have been created in our model , let us also model thememory effect Ganguly-Fitzgerald et al [9] showed that for Drosophila, exposure to enrichedenvironments (i.e. exposure to rich sensorial environments) affects the number of synapsesand the size of regions involved in information processing. In our model, the preferentialpaths in the extra cellular matrix are regions where this last has a larger stiffness.Therefore it will be easier for two neurons to connect along these preferential paths by asimple steric effect [10]. Indeed, if we suppose that the direction of growth of neurons (den-drites or axons) is simply leaded by the stiffness of the extra cellular matrix, the connectionof two neurons via one synapse will be more frequent on preferential paths.To conclude, for young mammals, the water concentration of brain is larger and thereforethe concentration of the extra cellular matrix is lower. This will lead to vanishing preferentialpaths and vanishing memory.III. PHYSICAL MODEL FOR MEMORYLet us make the hypothesis that the preferential paths modelled in section II exist. Wemodel the assembly of neurons by a packing of overlapping dendrites and axons at firstapproximation. This random array without excluding volume may be modelled by a simplerandom walk or Brownian motion. We make also the hypothesis that the random arrayobtained by the random walk and the random array formed by the neurons is the same.Let us consider the Brownian motion of a particle and let us try to find it at location Rat time t, knowing that it is at the origin at time t = 0. The central limit theorem allowsone to obtain the distribution RN when N tends towards infinity. This central limit theoremmay be written :P (R, t)→1(4piDt)d/4exp−R24Dt(1)with t = Nτ and the diffusion constant D =< r2 > /2τ Let us now examine the scalar3Brownian motion. If g is the gain at time t knowing that it was zero at time t = 0, theprobability to have a gain g > 0 or a loss g < 0 after a time t (the time between two eventsis then equivalent to the unit interval) is:P (g, t) =1(2pit)3/4exp−g22t(2)After one neuronal excitation, this last equation may be related to the length of the neuronalpath by replacing the gain g by the end to end length of this path. Note that their may becrossings of the path which model the synapses. The probability to have exactly the samepath with the same gain g but in the inverse direction is then exactly the same as equation(2). If the path is long i.e. t is large the probability will tend to zero. This is a model forimmediate memory. But for long time memory, when exactly the same neuronal excitationis repeated n times independently, the probability becomes:nP (g, t) = n1(2pit)3/4exp−g22t(3)with a maximum equal to one; and the inverse path (long time memory) has the sameprobability.All this first part of our model is valid if the paths have an underlying random arrayfor the random walk. This underlying array is simply the neurons with their dendrites andaxons. Once a random walker (or neuronal excitation) jumps from one axon (or dendrite) toanother axon (or dendrite) it creates a synapse which remains due to the action of astrocytes(see section II). Moreover, the extracellular matrix which is compressed in the neighbouringof the excited neuron will create a void path in the collagen leading to less mechanicalresistance and leading to preferential growth of another dendrite or axon on the same path:the random walker may return on the same path that he visited before.Let us known analyze the action of paradoxical sleep. We model the paradoxical sleep asa random walker which will visit all the underlying lattice, i.e. all the existing paths. Forthat we need to take a gain g equal to zero in order to model the return to the origin. Thereturn to the origin (null gain) follows the law:P (0, t) =1(2pit)3/4(4)Following the duration of paradoxical sleep, one has to calculate:N0 =∫ tOP (0, t′)dt′ =∫ t0dt′(2pit′)3/4=23pit1/4 (5)4Therefore, the probability to link to different long memory paths is equal to 23pit1/4. Thismay explain that after paradoxical sleep, two different events which are memorized may belinked.IV. CONCLUSIONWe made two models of memory, one biological based on bibliographic data, the otherbased on random walks on the dendrites and axons formed array. The biological modelshows that the action of the extracellular matrix is essential for memory. The physicalmodel shows that the probability to memorize an event is dependent on the number of timesthis event has excited the corresponding neurons.[1] K.Iwasa,I.Tasaki R.C.Gibbons, Swelling of nerve fibers associated with action potentials Sci-ence, 210 (1980) 338[2] D.K.Hill, The effect of stimulation on the opacity of a crustacean nerve trunk and its relationto fibre diameter J. of Physiology, 111 (1950) 283[3] B.C.Hill,E.D.Schubert, M.A.Nokes, R.P.Michelson, Laser interferometer measurement ofchanges in crayfish axon diameter concurrent with action potential Science, 196 (1977) 426[4] K.Iwasa and I.Tasaki, Mechanical changes in squid giant axons associated with production ofaction potentials Biochem. And Biophys. Res. Comm. 95 (1980) 1328[5] I.Tasaki and K.Iwasa, Rapid pressure changes and surface displacements in the squid giantaxon associated with production of action potentials Jap. J. of Physiology 32 (1982) 69[6] L.W.Ostrow and F.Sachs, Mechanosensation and endothelin in astrocytes–hypothetical rolesin CNS pathophysiology Brain Res. Reviews 48 (2005) 488[7] J.Wenzel,G.Lammert, U.Meyer,M.Krug, The influence of long-term potentiation on the spa-tial relationship between astrocyte processes and potentiated synapses in the dentate gyrusneuropil of rat brain Brain Res. 560 (1991) 122[8] Z.Feng, M.Yamato,T.Akutsu,T.Nakamura,T.Okano,M.Umezu, Investigation on the mechani-cal properties of contracted collagen gels as a scaffold for tissue engineering Artif. Orga. 27(2003) 845[9] I.Ganguly-Fitzgerald, J.Donlea, P.J.Shaw, Waking experience affects sleep need in DrosophilaScience, 313 (2006) 177[10] J.M.Corey and E.L.Feldman, Substrate patterning: an emerging technology for the study ofneuronal behavior Experimental Neurology, 184 (2003) S896

The role of the extra cellular matrix on memory

Hal-Diderot

https://hal.archives-ouvertes.fr/hal-00134775

The role of the extra cellular matrix on memory

Abstract

Similar works

Full text

Available Versions

HAL-UNILIM

Hal-Diderot