Budding yeast colony growth study based on circular granular cell

Transcription

1 Jounal of Physcs: Confeence Sees PAPER OPEN ACCESS Buddng yeast colony gowth study based on ccula ganula cell To cte ths atcle: Dev Apant et al 2016 J. Phys.: Conf. Se Vew the atcle onlne fo updates and enhancements. Ths content was downloaded fom IP addess on 17/09/2018 at 21:59

2 Buddng yeast colony gowth study based on ccula ganula cell Dev Apant 1, S N Khotmah 2, S Vd 2 1 Computatonal Scence Depatment, Faculty of Mathematcs and Natual Scences, Insttut Teknolog Bandung, Jl. Ganesha 10, Bandung 40132, Indonesa 2 Nuclea and Bophyscs Reseach Dvson, Physcs Depatment, Faculty of Mathematcs and Natual Scences, Insttut Teknolog Bandung, Jl. Ganesha 10, Bandung 40132, Indonesa E-mal: apantdev@gmal.com Abstact. Yeast colony gowth can be modelled by usng ccula ganula cells, whch can gow and poduce buds. The bud gowth angle can be set to egulate cell buddng patten. Coheson foce, contact foce and Stokes foce wee adopted to accommodate the behavou and nteactons among cells. Smulaton steps ae dvded nto two steps, the explct step s due to cell gowng and mplct step fo the cell eaangement. Only n explct step that tme change was pefomed. In ths study, we examne the nfluence of cell damete gowth tme and epoducton tme combnaton towad the gowth of cell numbe and colony fomaton. We fnd a commutatve elaton between the cell damete gowth tme and epoducton tme to the specfc gowth ate. The geate value of the multplcaton of the paametes, the smalle specfc gowth ate s obtaned. It also shows a lnea coelaton between the specfc gowth ate and colony damete gowth ate. 1. Intoducton A multcellula behavou that exhbted by buddng yeast cells s boflm fomaton. In pathogenc yeast such as Candda sp, boflm stuctue s assocated wth fungal nfecton n the human body [1]. Othe speces of buddng yeast, Sacchaomycess ceevsae, s well known as non-pathogenc buddng yeast that has smla chaactestc n fomng colony stuctue wth Candda sp. Thus, boflm fomaton n Sacchaomycess ceevsae becomes a model fo fungal boflm fomaton [2]. Ths complex stuctue stats wth colony fomaton n gowth meda. Obsevaton of eal colony fomaton was caed out though a vdeo [3]. In ths wok, smulaton s pefomed to mmc the colony fomaton. The ntal confguaton of the colony n smulaton s set smla to the ntal confguaton of the colony fom vdeo (fgue 1). Colony gowth s assumed to be seen above. Theoetcal obsevaton was also done to ensue that smulaton esults as t should be n bologcal system. 2. Buddng Yeast Colony Gowth Sacchaaomycess ceevsae cell s n ellpsodal shape wth the damete between 5 and 10 mcometes. Ths speces epoduces asexually by fomng bud on the suface of pecuso cell. The epoducton s occung asymmetcally. Nucleus dvson has happened when daughte cell sze s smalle than ts mothe cell. Afte the dvson s completed, daughte cell sze keeps nceasng untl t eaches ts maxmum sze and eady to epoduce. Content fom ths wok may be used unde the tems of the Ceatve Commons Attbuton 3.0 lcence. Any futhe dstbuton of ths wok must mantan attbuton to the autho(s) and the ttle of the wok, jounal ctaton and DOI. Publshed unde lcence by Ltd 1

3 Colony fomaton s found n semsold meda such as aga. If nutent s suffcent, the gowth of cell numbe s descbed by followng equaton [4] Integaton of the equaton gves dn dt = λ t. (1) ln N =λ t+ ln N, (2) whee N s the numbe of cells that pesent at tme t, N 0 s the numbe of cells at t = 0 and λ s cell numbe gowth ate o specfc gowth ate. In nuttous gowth meda, colony can be found n ccula shape [5]. At the ntal stage of gowth, when the colony damete s less than 0.2 mm o about 20 cells n cell damete unt by assumng a cell damete s 10 mcometes, colony damete s obseved ncease exponentally [4]. 0 Fgue 1.Intal gowth of buddng yeast colony unde fluoescent mcoscope fom vdeo expement [3]. 3. Cell Gowth Modellng Cell gowth s ncluded cell damete gowth and cell dvson (epoducton). The cell s modelled by usng ganula cell n ccula shape wth damete [7]. Cells damete gowth s defned as follows d ( t) = d ( t t) 0, t< t0, δ + v δt, t t t, (3) d max wth t 0, v D, d max and t G stand fo cell bth tme, damete gowth ate, maxmum damete, and damete gowth tme, espectvely. Damete gowth tme t G s the tme fo cell to gow fom bud ntaton untl eachng a maxmum cell damete. All cells have the same maxmum cell damete value. At patcula tme t, a cell s located at ( t) coespond to the cente of mass of the cell. daughte cell emeges at a poston n mothe cell ccumfeence wth decton o bud angle θ (fgue 2(a)). Evey mothe cell can epoduce only one daughte cell n a epoducton tme. The peod between two daughte cell ntaton at a mothe cell s temed as t B. Cell gowth tme s llustated n fgue 2(b). Movement of cells s govened by thee foces, namely coheson foce, contact foce, and Stokes foce. The fst two foces ae to accommodate the nteacton of cells. Coheson foce s adapted fom gavtaton foce to mmc the attactve nteacton between cells, whle contact foce s epulsve D 0 t G < t, G 2

4 foce that s happenng because of ovelap between two cells. The thd foce, Stoke foces, epesents the fcton between cell and gowth meda. (a) (b) 1 FIGURE 2. (a) Daughte cell (bud) emeges n θ j = π at mothe cell. (b) Cell gowth tmes ae 4 govened by damete gowth tme t G and epoducton tme t B. Coheson foce between two cells s defned as follows F coh j mm = G 2 j j eˆ, (4) j whee j s the dstance between two cells, and G epesents the stength of coheson between cells. Contact foce s affected by the ovelap between two cells ξ j, whch s defned as j ( 0 R + R ) ξ = max,, (5) wth R and R j epesent adus of cell and. The contact o collson foce s defned as follows col F = k ξ k v eˆ. (6) j j j ( j v j ) j The tem of k and k v s spng coeffcent and dampng coeffcent, espectvely. Stokes foce fo sphecal object that movng though flud n low speed s adapted to epesent cell movement n gowth meda, defned as flu F = 6πηR v, (7) whch η s temed as fcton coeffcent that epesent the vscosty of gowth meda. Fom (4), (6), and (7), the total foce that suffeed by -th cell F s obtaned. Usng Newton s second law, acceleaton of evey cell s calculated evey tme t. Then, fom the acqued acceleaton, velocty and poston of evey cell s detemned by Eule ntegaton method. 4. Smulaton Smulaton steps ae dvded nto two step, explct step and mplct step. The explct step s due to cell gowng and mplct step fo the cell eaangement. Only n explct step that tme change was pefomed. Smulaton s estcted by cell maxmum numbe N max. Intal confguaton of colony conssts of thee cells whch ae ntally at 1 = (0, 0), 2 = (-1.0, -1.0), and 3 = (0.1, 0.6) to mmc the ntal confguaton of cells colony n vdeo. Othe paametes that ae used n ths smulaton ae pesented n table 1. 3

5 TABLE 1 Smulaton paametes. Paametes Value N max 50 d max 1.0 k 10 4 k v 1.0 G 5.0 η 15.0 t 10-5 m 1.0 Implct teaton 5 t B 3, 3.2, 3.5, and 3.8 t G 3, 3.2, 3.5, and 3.8 All smulaton paametes ae chosen delbeately. The value of damete gowth tme t G and epoducton tme t B ae combned. A combnaton of t B and t G value s used fo one smulaton. Thee ae 16 combnatons of damete gowth tme and epoducton tme that used n smulaton. The bud 1 ntal angle that s used n the smulaton s = π whee n s an ntege numbe that chosen andomly between 0, 1, 2 and 3. θ 4 5. Result and Dscusson The nfluence of a combnaton of damete gowth tme and epoducton tme s shown by the gowth of cell numbe n the colony and ts damete gowth. Both of them ae obseved fom t = 0 untl t = 12. Smulaton esults ae compaed to the eal colony gowth fom vdeo. 5.1 Gowth of cell numbe Fgue 3 shows smulaton esults fo combnaton value t B = 3 and t G = 3 and colony gowth fom vdeo at t = 12. To obtan cell numbe gowth ate, cell numbe fo evey tme t both of smulatons and eal colony ae calculated. Then, the data ae ftted by smple lnea functon as follows y = ax+ b. (8) The tem a n (8) efes to the cell numbe gowth ate o specfc gowth ate λ n (2), whle b efes to natual logathm of ntal cell numbe N 0. Cell numbe gowth ate λ fo some smulaton s pesented n fgue 4. The specfc gowth ate value of all smulatons s pesented n table 2. It shows that the geate multplcaton value of t B and t G, the smalle specfc gowth ate λ s obtaned. Fo longe damete gowth tme and epoducton tme, the smalle numbe of cells n colony s acheved. Hence, thee s commutatve elaton between the cell damete gowth tme and epoducton tme to the specfc gowth ate. The same multplcaton esult of damete gowth tme t G and epoducton tme t B gves same specfc gowth ate value. Specfc gowth ate values λ of smulaton wth followng t B and t G combnaton value s smalle fom the specfc gowth ate of eal colony gowth. 5.2 Gowth of colony damete Colony damete D measuement s detemned by the mnmum aea of a ccle that can cove all cells n the colony [6]. The measuement s caed out by mnmzng the empty space that coveed by the ccle. The colony damete s measued n cell damete unt. Colony damete gowth ates that 4

6 esulted n smulaton ae less than 20 cells n cell damete unt [7]. Theefoe the gowth of the colony should ncease exponentally n accodance wth the theoy [4]. (a) (b) FIGURE 3. Real colony fomaton at (left) and smulaton esult wth t B = 3, t G = 3 (ght). In smulaton esult, dake colo ndcates olde cell. FIGURE 4. The specfc gowth ate of eal colony s λ c = (left) and n smulaton usng paametes t B = 3 and t G = 3 s λ = (ght). FIGURE 5. Colony damete gowth ate of eal colony µ c = (left) and smulaton esult wth t B = 3.5 and t G = 3.2, µ = (ght). 5

7 TABLE 2. Specfc gowth ate and colony damete gowth ate value of all smulaton. t B t G λ λ λ c µ µ µ c The esult of colony damete measuement s ftted by usng the same lnea functon as n (8) Tem a and b n fgues 5(a) and 5(b) efe to colony damete gowth ate µ and the natual logathm of ntal colony damete, espectvely. All colony damete gowth ates µ ae also pesented n table 2. Colony damete gowth ate of eal colony s close to colony damete gowth ate n smulaton wth paametes t B = 3.5 and t G = 3.2. The commutatve elaton between damete gowth tme and epoducton tme s not exhbted n colony damete gowth ate. Ths s due to dffeent cell compacton pocess n colony fomaton. The coelaton between cell numbe gowth ate λ and colony damete gowth ate µ s pesented n followng fgue 6. FIGURE 6. Lnea coelaton s pesented between colony damete gowth ate µ and cell numbe gowth ate. 6

8 6. Concluson Buddng yeast colony gowth can be modeled by ccula ganula cell. Fo colony damete less than twenty cells n cell damete unt, the gowth of cell numbe and colony damete can exhbt exponental gowth. By choosng combnaton value of damete gowth tme t G and epoducton tme t B between 3,3.2,3.5 and 3.8, t was found that thee s a commutatve elaton between the combnaton of paamete value n specfc gowth ate but not n colony damete gowth due to the compacton pocess. The geate value of the multplcaton of damete gowth tme and epoducton tme, smalle specfc gowth ate s obtaned. It also shows a lnea coelaton between specfc gowth ate and colony damete gowth ate. Acknowledgment Rset Desentalsas 2015 wth contact numbe 310/I1.C01/PL/2015 suppots ths eseach so t can be pesented n Asan Physcs Symposum Refeences [1] Chanda J, Kuhn D M, Mukhejee P K, Hoye L L, McComck T, and Ghannoum M A 2001 J. Bacteol [2] Reynold T B and Fnk F R 2001 Scence [3] Buchle Lab, Tme lapse move of fluoescent yeast, (eteved 20/08/2014), eteve fom vdeo fle, 0:22 sec [4] Gay B F and Kwan N F 1974 Bophys. Chem [5] Ganek J A and Magwene P M 2010 PLos Genetcs 6 7 [6] Jonsson Hand and Levchencko A 2005 Multscale Model Smul [7] Apant D 2015 Stud petumbuhan sel-sel ag bedamete kolon kuang da dua puluh sel menggunakan model sel ganula bebentuk lngkaan Maste thess Insttut Teknolog Bandung pp