M isfolding and aggregation of peptides and proteins into fibrils are the hallmarks of around 40 human

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1 OPEN SUBJECT AREAS: KINETICS PROTEINS COMPUTATIONAL BIOPHYSICS CONFOCAL MICROSCOPY Received 20 Octobe 204 Accepted 9 Januay 205 Published Mach 205 A monome-time model suppots intemittent glucagon fibil gowth Andej Košmlj, Pia Codsen 2, Andes Kysting 2 *, Daniel E. Otzen 2,3, Lene B. Oddeshede 2 & Mogens H. Jensen 2 Havad Univesity, Depatment of Physics, 7 Oxfod Steet, Cambidge, MA 0238, USA, 2 Copenhagen Univesity, Niels Boh Institute, CMOL, Blegdamsvej 7, DK-200 Copenhagen, Denmak, 3 Intedisciplinay Nanoscience Cente (inano), Depatment of Molecula Biology and Genetics, Aahus Univesity, Gustav Wieds Vej 4, DK-8000 Aahus C, Denmak. We investigate in vito fibillation kinetics of the homone peptide glucagon at vaious concentations using confocal micoscopy and detemine the glucagon fibil pesistence length 60mm. At all concentations we obseve that peiods of individual fibil gowth ae inteupted by peiods of stasis. The gowth pobability is lage at high and low concentations and is educed fo intemediate glucagon concentations. To explain this behavio we popose a simple model, whee fibils come in two foms, one built entiely fom glucagon monomes and one entiely fom glucagon times. The opposite building blocks act as fibil gowth blockes, and this geneic model epoduces expeimental behavio well. Coespondence and equests fo mateials should be addessed to A.K. (andej@physics. havad.edu); L.B.O. (oddeshede@nbi.dk) o M.H.J. (mhjensen@ nbi.dk) * Cuent addess: Univesity of Cambidge, Depatment of Chemical Engineeing and Biotechnology, Cambidge CB2 3RA, UK. M isfolding and aggegation of peptides and poteins into fibils ae the hallmaks of aound 40 human diseases,2. Undestanding the fibillation pocess of one potein may povide a geneic mechanistic insight useful fo undestanding fibillation of a class of poteins. In this pape we focus on the potein glucagon, which is a 29 amino acid esidue homone peptide, that upegulates blood suga levels. It is an impotant phamaceutical molecule, which is used to teat diabetic patients in situations of acute hypoglycemia 3,4. As obesity and the numbe of diabetic patients is inceasing, this dug becomes moe and moe elevant. The active state of glucagon is the monome, but duing phamaceutical poduction the peptide has a high tendency to misfold and aggegate into fibils devoid of biological function 5. When glucagon is solubilized, it can be found in two states, which poduce glucagon fibils of diffeent mophologies. Below a concentation of mg/ml, glucagon is pedominantly found in an unstuctued monomeic state, while above mg/ml glucagon fom associated states such as times and othe oligomes 6 0. The monome and oligome pecuso states lead to twisted and non-twisted fibils, espectively 3. Expeiments suggest that at high glucagon concentations, the monomeic species ae not incopoated into fibils 0 and the gowth of twisted fibils is inhibited 2. Fibillation of poteins and peptides is typically followed in bulk using the fibil-binding fluoescent dye Thioflavin T (ThT). While ThT-based fibillation kinetics can povide highly valuable infomation on the mechanisms of fibillation 4, studies of the gowth of individual fibils can also yield impotant insights. This infomation is povided by techniques such as Total Intenal Reflection Fluoescence Micoscopy (TIRFM) and Confocal Micoscopy (CM). In TIRFM the obsevation depth is, 50 nm while with CM it is, 500 nm. Anothe elegant way to esolve fibes is by popelling a nanopaticle along the fibe 5. Peviously, we have studied gowth of individual glucagon fibils in eal-time using TIRFM 6 at one fixed glucagon concentation. In that study, fibil gowth was found to be inteupted by peiods of stasis, and the statistics of gowth and stasis duations wee well descibed by a Poissonian pocess. This dynamic behaviou was denoted stop-go kinetics. Switching ates between the gowing and aested states suggested the pobability of being in the gowing state to be, /4. To explain this value, a Makovian fou-state model of fibil gowth was poposed. The model pedicted that the gowth pobability is independent of the glucagon concentation. This is in contast to ou findings since hee we demonstate that the fibil gowth pobability does depend on the glucagon concentation. Hee we significantly expand ou pevious wok 6 by monitoing fibil kinetics ove a wide ange of glucagon concentations and by poposing a new model that captues the undelying molecula mechanisms of the pocess. This allows us to sample conditions spanning diffeent pecuso states of glucagon, i.e. monomes o times, leading to twisted o non-twisted fibils, espectively. Fibils wee labeled with the fluoescent dye ThT and monitoed using a confocal micoscope with an Agon lase. On feshly plasmated glass plates we obseved a volume of, mm 3. Fo each of the five diffeent initial glucagon concentations (.5, 3, 6, 0 and SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep09005

2 Figue 2 Distibutions of stop (a) and gowth (b) duations fo fibils gown at vaious glucagon concentations. Staight lines indicate linea fits to the cumulative data. Thee extemely long pauses wee emoved fom the 3 mg/ml sample. 5 mg/ml), a minimum of two expeiments wee conducted in aqueous buffe (50 mm glycine HCl, ph 2.5). The time inteval between captued fames was 3.3 mins and the total obsevation time of each expeiment was about thee days. When fibils gew along the suface we tacked thei length as a function of time. Sample images of eal time gowth of an individual fibil ae shown in Fig. (a c). The obseved gowing fibils ae elatively staight and thei pesistence length, p can be extacted by compaing the geometic distance between fibil ends R ee to the fibil length L. Fo semi-flexible fibils the aveage end-to-end distance is expected to be 7 R 2 ee h i ~2 p L{2 2 p {e{l= p, Þ Figue (a c): Confocal micoscopy images of glucagon fibils with initial concentation 3 mg/ml in aqueous buffe (50 mm glycine HCl, ph 2.5) at thee consecutive times: 64, 87 and 26 mins afte the onset of fibillation. Scale ba shows 5 mm. Each cicle epesents a data point and the ed line epesents the cumulated tacked positions of the gowing fibil end. (d) Gowth of 20 fibils at the glucagon concentation of 3 mg/ml. Plateaus coespond to aested states while fibils elongate outside the plateaus. (e) The aveage end-to-end-distance squaed ( R 2 ee )asa function of fibil length. The solid geen line is obtained by fitting Eq. () to combined expeimental data (ed points) fom all glucagon concentations. The pesistence length of fibils is etuned by the fit as mm. which agees extemely well with expeimental data (Fig. e). The fitting of equation above to expeimental data povides a pesistence length, p mm. Note that this is of the same ode as the pesistence length of actin filaments (, 20 mm) 8, while much smalle than the pesistence length of micotubules (, 5, 000 mm) 8, and lage than the pesistence lengths of DNA (, 50 nm) 9 and amyloid fibils (0. 4 mm) 20. By inspecting the time couses of fibil lengths (Fig. d), we find that at all glucagon concentations the fibil gowth is chaacteized by peiods of gowth (go state) inteupted by peiods of stasis (stop state). The stop states ae seen as plateaus, whee the fibil does not elongate. As seen in ou pevious wok 6, the distibutions of the stop and go event duations (displayed in Fig. 2) follow exponential distibutions and ae fitted to the fom f(x) 5 a? exp(2k? t). A fibil leaves the stop state at ate k srg given by stop duations (Fig. 2a) and go state at ate k grs given by gowth duations (Fig. 2b). Both switching ates depend on the glucagon concentation and esults ae summaized in Table. SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep

3 Table Values of switching ates between gowth and stop states obtained by fitting expeimental data in Fig. 2 and the coesponding pobability of gowth as defined in Eq. (6) [G tot ] (mg/ml) k srg (min 2 ) k grs (min 2 ) p G The access to kinetic data at diffeent glucagon concentations allows us to develop a model fo glucagon s fibillation. The analytical models fo the kinetics of fibil gowth wee initiated with the Oosawa model 2 and futhe elaboated to include hydolysis and beakage of fibils 22,23. Ou model is an extension of the Oosawa model, which includes both monomes and times as basic building blocks fo fibils. To explain the intemittent fibil gowth behavio we popose a model sketched in Fig. 3. In the bulk solution glucagon monomes ae in equilibium with glucagon times and these two components give ise to twisted and non-twisted fibils, espectively. Successive binding of glucagon monomes to the twisted fibil end coesponds to the gowing state, while binding of times to the twisted fibil end pevents futhe gowth until the time is detached. Duing this time the twisted fibil appeas to be in the aested state. The opposite is tue fo non-twisted fibils, which ae fomed fom glucagon times, while glucagon monomes inhibit thei gowth. In the mean field appoximation, the fibil gowth pobability can be expessed in tems of the model ate constants, which ae defined in Fig. 3, and compaed to the expeimentally obseved gowth pobabilities. Below we use simple physical tems to guide the deivation of main equations and to intepet esults at vaious levels of glucagon concentations. We tied to be systematic in naming ate constants (see Fig. 3): supescipts (M) and (T) ae used to descibe monome and time fibils, espectively; subscipts b, u and ae used to descibe binding, unbinding and eaangement events, espectively; and subscipts and 3 ae used to descibe binding and unbinding of glucagon monome and times, espectively. The gowth pobability pedicted by the model is calculated by consideing the aveage time spent in the gowing o aested state as outlined below. In a bulk solution glucagon is in equilibium between monomes (M) of concentation [G] and times (T) of concentation [G 3 ] with the equilibium constant K0 2 ~ ½GŠ3 ½G 3 Š ~ k 3 2Þ k 3 and the total glucagon concentation [G tot ] 5 [G] 3[G 3 ]. As mentioned befoe at low (high) glucagon concentations, i.e., ½G tot Š=K 0 ½G tot Š?K 0 Þ, glucagon is pedominantly in the monome (time) state. Fo the fee gowing twisted fibil end it takes on aveage the time { ½GŠz ½G 3 Š befoe the glucagon monome o time binds to the tip. This occus with pobabilities o 3 espectively, whee ~ ½GŠ ½GŠz ½ G 3 ~{ 3 : 3Þ Š If a glucagon monome is bound to the gowing twisted fibil end, it takes on aveage the time { zk fo the glucagon monome to unbind with pobability u o to undego confomational eaangement and fom a longe fibil with pobability, whee u ~ k M Þ ~{ zk M g : 4Þ Þ g Figue 3 Schematic oveview of the glucagon gowth model showing (uppe pat) monome-time equilibium and (lowe pat) fibillation pocess. Glucagon monomes ae in equilibium with glucagon times. Elongation of a fibil is a two-step pocess, which can be inteupted by binding of the othe oligome. Fibils consist of eithe monomes o times but neve a combination of the two. A glucagon time (monome) can bind to a gowing fibil end and then dissociate o elongate the fibil afte confomational eaangement. Filled tiangles (cicles) symbolize times (monomes) bound ievesibly to a fibil, while hollow tiangles (cicles) mean unbound times (monomes). A glucagon monome (time) can also bind to a gowing fibil end, but in this aested state it pevents futhe attachment of glucagon times (monomes). SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep

4 The aveage time t fo a monome to bind and subsequently eithe unbind o undego confomational eaangement to elongate the twisted fibil is t ~ ½GŠz ½ G 3 z, 5Þ Š z while the aveage time t 3 fo the binding and unbinding of a glucagon time is t 3 ~ z ½GŠz ½ Š k M G 3 k u3 : 6Þ We define the gowth pobability G as the expected aveage faction of time the twisted fibil spends in the gowing state: G ~ p M Þ g t t z 3 t 3 : 7Þ Similaly, we can analyze the dynamics of the gowing non-twisted fibils, which ae fomed fom glucagon times. The gowth pobability fo non-twisted fibils is then p 3 p 3g t 3 p t zp 3 t 3 G ~ p T, 8Þ whee all quantities ae defined in analogous way as above fo the twisted fibils. Howeve, in this case the ole of glucagon monomes and times is evesed, i.e., in Eqns. (3 6) above one should eplace (M) with(t) and make the «3 substitutions to obtain the elevant quantities. Since the numbe of twisted and non-twisted fibils is popotional to the numbe of glucagon monomes and times, espectively, the pobability p G that the andomly chosen fibil is found in the gowing state is p G ~ G ½GŠzp G ½ G 3Š : 9Þ ½GŠz½G 3 Š It is possible to deive the exact expession fo the gowth pobability above in tems of the ate constants and the total glucagon concentation, but fo simplicity we pesent only the asymptotic egimes at low and high glucagon concentation. At low glucagon concentation, ½G tot Š=K 0, the majoity of glucagon is in the monomeic state. The slow time scales coespond to binding of glucagon monomes o times to the fibil ends and the gowing pobability fo twisted fibils is " G < k M Þ { # ½G tot Š 2 : 0Þ z K 0 Thee ae only a small numbe of non-twisted fibils, whose gowth is futhe suppessed by binding of glucagon monomes p G < k T Þ k ½ G totš 2 : Þ u3 zk The fibil gowth pobability is thus appoximately p low K 0 G < p M Þ G ½GŠ ½GŠz½G 3 ŠÞ, 2Þ Figue 4 Expeimentally measued fibil gowth pobabilities (black bas) calculated fom Eq.(6). The eo bas in expeimentally obseved gowth pobabilities ae calculated fom uncetainties in the switching ates between the stop and go states fom fitting in Figs. 2(a b). The black line shows a fit of the model in Eq. (9) to the expeimental data. whee ½GŠ= ½GŠz½G 3 ŠÞ<{ ½G tot Š 2 K0 2 : At high glucagon concentations, ½G tot Š?K 0, most of the glucagon is in the timeic state. The binding events ae fast because of the lage concentation of glucagon times and the slow time steps ae the unbinding and confomational econfiguation. The gowth pobability of non-twisted fibils is appoximately G < k T p u3 zk { k 3K 2=3 0 : 3Þ ½ Š G tot Thee ae only a small numbe of twisted fibils, whose gowth is futhe suppessed by binding of glucagon times G < k M Þ k u3 3K 2=3 0 z 2 : 4Þ ½G tot Š The fibil gowth pobability is thus appoximately p high G < p T Þ G ½ G 3Š ½GŠz½G 3 ŠÞ, 5Þ whee [G 3 ]/([G] [G 3 ]) < 2 (3K 0 /[G tot ]) 2/3. Table 2 Values of unknown ate constants obtained by fitting expeimental p data in Fig. 4. The value of equilibium constant K 0 ~ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 3 =k 3 < mg/ml is known expeimentally 2. The ate constants whose fitted atios ae given in this Table ae defined in Figue 3 u3 K 0 K 0 k K K 0 u3 K 0 Þ K k T k T 0.59 k T SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep

5 Figue 5 Gowth speed distibutions of glucagon fibils at vaious glucagon concentations (displayed in top-ight cones) ae pesented as histogams (boxes of width 0 nm/min). At intemediate glucagon concentations, [G tot ], K 0, thee is a mix of twisted and non-twisted fibils whose gowth is suppessed due to binding of the opposite glucagon components. The pobability that at any moment a given fibil is in the gowing state can be detemined fom the expeimental switching ates between the stop and go states as k s?g p G ~ : 6Þ k s?g zk g?s Assuming that the eo estimates s srg and s grs fo expeimental switching ates k srg and k grs, which ae obtained by linea fits in Fig. 2, ae uncoelated, we can estimate the eo s G fo the gowth pobability as s 2 G ~ Lp 2 G s 2 Lk g?s g?s z Lp 2 G s 2 s?g Lk ~ k2 s?g s2 g?s zk2 g?s s2 s?g 4 :7Þ s?g k s?g zk g?s The measued fibil gowth pobabilities at diffeent glucagon concentations, given by equation (6) above, ae displayed in Fig. 4 as black bas (see also Table ). We notice that fibil gowth pobabilities ae lage at high and low glucagon concentations, while they ae smalle at intemediate glucagon concentations (, 3 mg/ml), which appoximately coespond to the equilibium constant K 0 of glucagon monomes and times 2. In ode to see how ou model compaes to the expeimental data, we need to detemine 2 ate constants (see Fig. 3). Howeve, if we ae only inteested in the gowth pobability of fibils thee ae 9 independent constants, because the gowth pobability does not depend on the absolute values of time scales fo gowing fibils and the time scale fo switching between monomes and times. In pactice we fixed values of k 3, and. Since the value of equilibium constant K 0 < mg/ml is known expeimentally 2, we fit the atios of the othe 8 ate constants to the 5 data points in Fig. 4 (see also Table 2). Model fits quite well to the expeimental data and esults suggest that once the coect component binds to the gowing fibil end, then the eaangement pocess leading to gowth is much moe likely than unbinding k? and k? u3. Fitting also suggests that once the wong component binds to the gowing fibil end, then it unbinds vey quickly k = u3 and k =. Pevious study of glucagon fibillation at a vey low concentation (0.25 mg/ml) found the gowth pobability to be, /4 6, which is smalle than the gowth pobabilities obseved in ou expeiments (Fig. 4). We speculate that in that study, fibil seeds gown at a highe glucagon concentation could bias the distibution of fibils towads timeic fibils and hence esult in a lowe gowth pobability than pedicted by ou equilibium model. The model pesented above with two competing fibil mophologies is futhe suppoted by the measuements of speeds at which the fibils ae gowing (Fig. 5). The speed distibutions seem to have two peaks, whose magnitudes depend on the glucagon concentation. At low glucagon concentation the dominant peak is at, nm/ min, which pobably coesponds to the gowing speed of twisted fibils composed of glucagon monomes. On the othe hand, at lage glucagon concentation the dominant peak is at, 00 nm/min, which pobably coesponds to the gowing speed of non-twisted fibils composed of glucagon times. In conclusion, we pesent a monome-time model fo glucagon fibillation and compaed it with ou expeimental data. The model pedicts a concentation dependent gowth pobability, which we test expeimentally at vaious glucagon concentations by analyzing the distibutions of gowth and stasis duation. Ou model captues the shot time behavio of gowth and pause duations and epoduce the expeimentally obseved gowth pobability well. The stopgo kinetics obseved equies two contasting pecuso states, one of which elongates while the othe one blocks. Thus, the model might geneically also explain, e.g., fibil gowth kinetics fo b-lactoglobulin which exists in a monome-dime equilibium, whee only the monome is capable of elongating fibils (via a patially unfolded state) 24. The model is an expansion of cuent models of amyloid fibil gowth, which only use a single pecuso species that feeds into the fibil, though this pecuso species may undego multiple confomational changes befoe it eaches a state that is activated fo incopoation into the fibilla stuctue 2,25. This type of selective uptake of pecusos fom a pool of diffeent species may also be elevant fo othe types of assembly, such as micotubule polymeization/depolymeization and actin filament gowth. Actin is known to access diffeent confomational states unde physiological conditions 26. This may allow the gowing filaments to select the most appopiate state fo incopoation as well as leading to stuctual plasticity in the polyme 27. On the othe hand, ou model is not likely to be elevant fo moe limited assemblies such as vial capsids, which consist of a finite numbe of capsid poteins and theefoe does not gow indefinitely; futhemoe the pecuso capsid poteins do not populate diffeent confomational states 28.. Selkoe, D. J. Folding poteins in fatal ways. Natue 426, (2003). 2. Chiti, F. & Dobson, C. M. Potein misfolding, functional amyloid, and human disease. Annu. Rev. Biochem. 75, (2006). 3. Ducke, D. J. Biologic actions and theapeutic potential of the poglucagondeived peptides. Nat. Clin. Pact. Endocinol. Metab., 22 3 (2005). 4. Jiang, G. & Zhang, B. B. Glucagon and egulation of glucose metabolism. Am. J. Physiol. Endocinol. Metab. 284, E67 E678 (2003). 5. Pedesen, J. S., Andesen, C. B. & Otzen, D. E. Amyloid stuctue one but not the same: the many levels of fibilla polymophism. FEBS J. 277, (200). 6. Gatze, W. B. & Beaven, G. H. Relation between confomation and association state. A study of the association equilibium of glucagon. J. Biol. Chem. 244, (969). 7. Fomisano, S., Johnson, M. L. & Edelhoch, H. Themodynamics of the selfassociation of glucagon. Poc. Natl. Acad. Sci. USA 74, (977). SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep

6 8. Johnson, M. L., Fomisano, S. & Edelhoch, H. Self-association of glucagon as measued by the optical popeties of hodamine 6G. J. Biol. Chem. 253, (978). 9. Wagman, M. E., Dobson, C. M. & Kaplus, M. Poton NMR studies of the association and folding of glucagon in solution. FEBS Lett. 9, (980). 0. Svane, A. S. P. et al. Ealy stages of amyloid fibil fomation studied by liquid-state NMR: the peptide homone glucagon. Biophys. J. 95, (2008).. Pedesen, J. S. et al. The changing face of glucagon fibillation: stuctual polymophism and confomational impinting. J. Mol. Biol. 355, (2006). 2. Andesen, C. B., Otzen, D., Chistiansen, G. & Rischel, C. Glucagon amyloid-like fibil mophology is selected via mophology-dependent gowth inhibition. Biochemisty 46, (2007). 3. Andesen, C. B. et al. Glucagon fibil polymophism eflects diffeences in potofilament backbone stuctue. J. Mol. Biol. 397, (200). 4. Cohen, S. I. A. et al. Polifeation of amyloid-b42 aggegates occus though a seconday nucleation mechanism. Poc. Natl. Acad. Sci. USA 0, (203). 5. Estada, L. C. & Gatton, E. 3D nanomete images of biological fibes by diected motion of gold nanopaticles. Nano Lett., (20). 6. Fekinghoff-Bog, J. et al. Stop-and-go kinetics in amyloid fibillation. Phys. Rev. E 82, 0090(R) (200). 7. Doi, M. & Edwads, S. F. The theoy of polyme dynamics. Oxfod Univesity Pess, Oxfod, Gittes, F., Mickey, B., Nettleton, J. & Howad, J. Flexual igidity of micotubules and actin filaments measued fom themal fluctuations in shape. J. Cell. Biol. 20, (993). 9. Hageman, P. J. Flexibility of DNA. Annu. Rev. Biophys. Biophys. Chem. 7, (988). 20. van den Akke, C. C., Engel, M. F. M., Velikov, K. P., Bonn, M. & Koendeink, G. H. Mophology and pesistence length of amyloid fibils ae coelated to peptide molecula stuctue. J. Am. Chem. Soc. 33, (20). 2. Oosawa, F. & Asakua, S. Themodynamics of the polymeization of potein. Academic Pess, Waltham, Knowles, T. P. J. et al. An analytical solution to the kinetics of beakable filament assembly. Science 326, (2009). 23. Aosio, P., Beeg, M., Nicoud, L. & Mobidelli, M. Time evolution of amyloid fibil length distibution descibed by a population balance model. Chem. Eng. Sci. 78, 2 32 (202). 24. Hamada, D. & Dobson, C. M. A kinetic study of b-lactoglobulin amyloid fibil fomation pomoted by uea. Potein Sci., (2002). 25. Cohen, S. I., Venduscolo, M., Dobson, C. M. & Knowles, T. J. [The Kinetics and Mechanisms of Amyloid Fomation] Amyloid Fibils and Pefibilla Aggegates: Molecula and Biological Popeties [Otzen, D. E. (ed.)] [83 209] (Wiley-VCH Velag GmbH & Co. KGaA, Weinheim, 203). 26. Olova, A., Pochniewicz, E. & Egelman, E. H. Stuctual dynamics of F-actin: II. Coopeativity in stuctual tansitions. J. Mol. Biol. 245, (995). 27. Kueh, H. Y. & Mitchison, T. J. Stuctual plasticity in actin and tubulin polyme dynamics. Science 325, (2009). 28. Zhdanov, V. P. Vial capsids: Kinetics of assembly unde tansient conditions and kinetics of disassembly. Phys. Rev. E 90, (204). Acknowledgments This wok was suppoted by the Lundbeck Foundation (BioNET2), the Danish National Reseach Foundation though the Cente fo Models of Life and the KU Cente of Excellence (MolPhysX). We ae gateful to Novo Nodisk A/S fo poviding glucagon samples. Autho contibutions M.H.J., L.B.O. and D.O.E. designed the poject and supevised the study. P.C. and A.Ky. collected expeimental data. P.C., A.Ky., M.H.J., D.E.O. and L.B.O. analyzed the data. A.Ko. fomulated the model. D.E.O. contibuted with eagents. All authos wote the manuscipt. Additional infomation Competing financial inteests: The authos declae no competing financial inteests. How to cite this aticle: Košmlj, A. et al. A monome-time model suppots intemittent glucagon fibil gowth. Sci. Rep. 5, 9005; DOI:0.038/sep09005 (205). This wok is licensed unde a Ceative Commons Attibution 4.0 Intenational License. The images o othe thid paty mateial in this aticle ae included in the aticle s Ceative Commons license, unless indicated othewise in the cedit line; if the mateial is not included unde the Ceative Commons license, uses will need to obtain pemissionfom the licenseholde in ode toepoduce the mateial. To view a copy of this license, visit SCIENTIFIC REPORTS 5 : 9005 DOI: 0.038/sep