Circadian rhythm of cell population structure of Rauwolfia serpentina Benth under different culture conditions in vitro

In tro duc tion. Plant tis sue cul tures are char ac ter ized by high level of cytogenetic vari abil ity [1, 2]. Pre vi ously we have re ported sev eral stud ies of quan ti ta tive cell subpopulation dy nam ics with dif fer ent rel a tive con tent of DNA (rcDNA) in nu cleus de pend ing on nu cle o lus area as well as dy nam ics of spe cific rate of pro duc tiv ity ac cu mu la tion in dexes dur ing the pas sage for dif fer ent cul ti va tion vari ants of a high pro duc tive K-27 strain of Rau wol fia serpentina Benth a me dic i nal plant used as a source of indoline al ka loids. In those stud ies we have used the math e mat i cal model spe cif i cally de vel oped for con ju gated pro cesses in phys i cal, chem i cal and bi o log i cal sys tems, which was called the ther mo dy namic ap proach. This model con tains a sys tem of equa tions vir tu ally char ac ter iz ing a network of cross interactions or conjugated processes. The math e mat i cal model (ther mo dy namic of ir re vers ible pro cess) pub lished in [3, 4], which was ini tially de vel oped for de scrib ing of higher or gan ism’s tis sue growth and dif fer en ti a tion, can be un doubt edly ap plied for study ing of higher plant’s tis sue cul ture. The only prob lem is to se lect ap pro pri ately the fluxes, forces and phenomenological co ef fi cients and to as cribe them the bi o log i cal sig nif i cance. Dur ing cul tures pass ing we have con ducted some ex per i ments that al lowed us to chose and to as cribe the bi o log i cal sig nif i cance for the fluxes, forces and phenomenological co ef fi cients as well as to de ter mine the di men sion co ef fi cients that have been de scribed in de tail in [5]. The con tri bu tion of dy nam ics of the quan ti ta tive con tent of

In tro duc tion.Plant tis sue cul tures are char ac ter ized by high level of cytogenetic vari abil ity [1,2].Pre viously we have re ported sev eral stud ies of quan ti ta tive cell subpopulation dy nam ics with dif fer ent rel a tive con tent of DNA (rcDNA) in nu cleus de pend ing on nucle o lus area as well as dy nam ics of spe cific rate of produc tiv ity ac cu mu la tion in dexes dur ing the pas sage for dif fer ent cul ti va tion vari ants of a high pro duc tive K-27 strain of Rau wol fia serpentina Benth -a me dic i nal plant used as a source of indoline al ka loids.In those stud ies we have used the math e mat i cal model spe cif ically de vel oped for con ju gated pro cesses in phys i cal, chem i cal and bi o log i cal sys tems, which was called the ther mo dy namic ap proach.This model con tains a sys -tem of equa tions vir tu ally char ac ter iz ing a network of cross interactions or conjugated processes.
The math e mat i cal model (ther mo dy namic of ir revers ible pro cess) pub lished in [3,4], which was initially de vel oped for de scrib ing of higher or gan ism's tis sue growth and dif fer en ti a tion, can be un doubt edly ap plied for study ing of higher plant's tis sue cul ture.The only prob lem is to se lect ap pro pri ately the fluxes, forces and phenomenological co ef fi cients and to ascribe them the bi o log i cal sig nif i cance.Dur ing cul tures pass ing we have con ducted some ex per i ments that allowed us to chose and to as cribe the bi o log i cal sig nif icance for the fluxes, forces and phenomenological coef fi cients as well as to de ter mine the di men sion co ef ficients that have been de scribed in de tail in [5].The con tri bu tion of dy nam ics of the quan ti ta tive con tent of cor re spond ing subpopulations (as bi o log i cal forces) to dy nam ics of bi o log i cal fluxes i.e. spe cific rates of produc tiv ity ac cu mu la tion in dex has been stud ied and an alyzed [3][4][5][6].At the low est hi er ar chy level, i.e. a cir cadian, the al ter ation dy nam ics of the quan ti ta tive content of dif fer ent cell subpopulations with rcDNA in nu cleus have been con sid ered to be fluxes and cir cadian dy nam ics of quan ti ta tive con tent of pro lif er at ing cells -to be forces, since the physiological phenomena in tissue cultures, in particular the proliferation activity, had circadian rhythm [2,7].
In deed, the quan tity gra di ent of "cells with cer tain DNA con tent in nu cleus" ver sus "bi o log i cal de vel opment time" un der tran si tion to the low est hi er ar chy level has been con sid ered to be the rate of ac cu mu la tion of cells with the same char ac ter is tic, i.e. bi o log i cal flux.If the prin ci ples of lin ear ity for the de pend ence of bi o log i cal fluxes on pre sumed bi o log i cal forces, accord ing to Cu rie and Onsager, are ful filled, one may con clude about suc cess ful choice of se lected fluxes and forces [8].On the other hand, de scend ing one step in relax ation time hi er ar chy to the level, where the slow est mo lec u lar os cil la tors act, au thors of [9][10][11] have shown on yeast cul ture that the ex pres sion group con sist ing of five genes, which con trol three states of cell dif fer en tia tion in cul ture, form a net work of post-transcriptional reg u la tion, where the spec i fic ity of one gene in the group is de ter mined by a higher num ber of con nec tions [10].How ever, dur ing study ing the mul ti ple cells in terac tions at this hi er ar chy level [9][10][11], the cell quan tity in pop u la tion, si mul ta neously syn the siz ing the same tran scripts, has been es ti mated by in di rect meth ods.When es ti mat ing the quan tity of cell subpopulations, cor re spond ing to dif fer ent phys i o log i cal states, we used the sta tis ti cal ap proach, which was sim i lar to the method de scribed in [10].But, in con trast, we tried to present our results (that also represent a network of interactions at the level of cell population) by the system of differential equations.
In the cur rent work we make an ef fort to de scribe the con tri bu tion of bi o log i cal forces, i.e. the al ter ation dy nam ics of pro lif er at ing (by mitoses or amitoses) cell por tion into bi o log i cal fluxes, i.e. the al ter ation dy namics of por tion of cell subpopulations with dif fer ent rel ative DNA con tent (rcDNA) in nu cleus, un der dif fer ent cul ti va tion con di tions of R. serpentina K-27 strain.
Ma te ri als and Meth ods.Ob ject of in ves ti ga tion.Ge net i cally sta ble (dur ing last 15 years) K-27 strain of tis sue cul ture of R. serpentina (150 pas sages) was studied un der stan dard cul ti va tion con di tions in 10 S medium, con tain ing 10% su crose (vari ant K-27(10 S), that was de scribed in [2,12]).Cul ti va tion of K-27 strain was also stud ied by the man ner of a sub merged cul ture in liq uid nu tri ent me dium Rzh (K-27(Rzh) vari ant).Rzh me dium dif fers from 10 S me dium by four fold lower con cen tra tion of su crose (2.5%) and by the reduced con tent of macro-and mi cro-salts as well [13,14].Be sides, this me dium was rec om mended for indus trial cul ti va tion of R. serpentina tis sues [15].It's im por tant to point out that K-27(Rzh) vari ant of cells is very sen si tive to some mod i fi ca tions of cul ti va tion method, for ex am ple, tran si tion from agar to shak ing in liq uid me dium and sig nif i cant vari a tions of su crose and salts con cen tra tions in nu tri ent me dium.All these changes of cul ti va tion con di tions may re sult in phys i olog i cal stress for K-27(Rzh).All cul tural vari ants were grown in dark ness in this study due to the reason that original tissue culture was grown in darkness for 44 years since the moment of its creation.
For both an a lyzed vari ants of cell strains, sam ples were taken out ev ery two hours of growth to study passage dy nam ics.Ad di tion ally, to con duct cir ca dian inves ti ga tion the sam ples were taken out at the same time points ev ery two hours but only when the pro duc tion of indoline al ka loids had max i mal lev els, namely 12-15 th days of growth for K-27(10 S) and 9-11 th days -for K-27(Rzh) vari ant.More de tails of cul tur ing con ditions and pro duc tiv ity were pub lished else where [12, 14, and 15].Pieces of cal lus (1g in av er age) were withdrawn ev ery two hours from two flasks, start ing at 10 a.m. of the first in ves ti ga tion day, and end ing at 8 a.m. of the last in ves ti ga tion day.Taken ma te rial was im medi ately placed into the mix ture of gla cial ace tic acid and 96% eth a nol (1:3) and af ter 24 hours transferred to 70% ethanol, where it was kept until staining.
DNA con tent in nu clei of interphase cells was de termined.Felgen's method was used for cells stain ing, as de scribed in [16,17].Im ages of 100 stained cell nu clei pre pared from four dif fer ent tis sue parts were taken using op tic sys tem, con sist ing of a green light fil ter of NU-2E mi cro scope (Carl Zeiss, Aus tria), red light filter of CCD Sac-410 PA dig i tal cam era, and Asus V 3000 video driver.The sig nal of stained interphase nucleus was quan ti fied using Scion Im age soft ware.Rel ative DNA con tent (des ig nated as C) was cal cu lated as a ra tio of peak area of stained nu cleus to the peak area of stained anaphase nu cleus.Tak ing into ac count that anaphase nu cleus has 4C DNA, the abovementioned ra tio was mul ti plied by fac tor 4 to ob tain the ac tual num ber of C in the mea sured sample.
De ter mi na tion of pro lif er a tion in dexes.Squashed cells sam ples stained with aceto-orcein were pre pared as de scribed in [17].Mi totic and amitotic in dexes (MI and AMI, re spec tively) were cal cu lated af ter anal y sis of 5 thou sand cells pre pared from dif fer ent parts of callus tis sue (four dif fer ent prep a ra tions).The data obtained were used to build cir ca dian dy nam ics of re spective pro lif er a tion in dex.Dy nam ics' of mitoses and amitoses quo tas (MI*0.01 or AMI*0.01) were used as biological forces.
Sta tis tic anal y sis. 100 cells from ev ery sam ple was taken and ac cord ing to the rcDNA in nu cleus dis tributed into sep a rate morphometrical classes (Ta ble 1), thus, the dy nam ics of cell dis tri bu tions ac cord ing to rcDNA was ob tained.An ax ial sec tion along the tempo ral axis was made for ev ery class.The por tion of cells at each mo ment was mul ti plied by the por tion of cells of this class in the gen eral data se lec tion (Ta ble 1), thus, the dy nam ics' of cell por tions with dif fer ent rcDNA in nu cleus for sev eral morphometrical classes, pre sented in Ta ble 1, were ob tained (Fig. 1).These curves as well as the dy nam ics' of mitoses and amitoses quo tas (cal cu lated for 5000 cells us ing standard method) were smoothed by two points mov ing aver age method.Af ter that, the dy nam ics' of cell por tions with dif fer ent rcDNA in nu cleus were com pared with the dy nam ics' of pro lif er a tion in dexes us ing the method of paired lin ear re gres sion ac cord ing to [18].Cor re la tion co ef fi cients and cor re spond ing value of cri te rion sta tis tics were cal cu lated ac cord ing to the formula, in di cated in the leg end for Ta ble 2. If the cor re lation was in sig nif i cant, cor re spond ing co ef fi cients were con sid ered to be equal to zero.
Un der the prin ci ple of ther mo dy namic ap proach, we will con sider the al ter ation dy nam ics of the cell portion, ac cord ing to the value of rcDNA in the nu cleus, for cell subpopulations, se lected at the each pas sage, as bi o log i cal fluxes on cir ca dian hierarchy level [6].
Lin ear dependences be tween dy nam ics of cell portions of cor re spond ing subpopulations and dy nam ics of mitoses and amitoses quo tas, which may be con sid ered as bi o log i cal forces, were de ter mined by paired lin ear re gres sion method ac cord ing to [18].Fur ther cal cu lation pro ce dure was de scribed in de tails in [5].To es timate the ad e quacy of com puted curves to ex per i men tal ones we used the nor mal dis tri bu tion eval u a tion method with zero math e mat i cal ex pec ta tion of the deviations squares between compared curves [18].
Re sults and Dis cus sion.Dur ing tis sue cul ture of R. serpentina K-27(10 S) and K-27(Rzh) strains passaging two main subpopulation of cells were used.Each of them con tained dif fer ent rcDNA in nu cleus, namely 1.0-2.9Cand 3.0-6.9Cfor K-27(10 S) and 1.0-2.9Cand 3.0-8.9Cfor K-27(Rzh).The cir ca dian dy nam ics' of al ter ation of abovementioned cell portions at 12-15 th days of growth for K-27(10 S) and 9-11 th days for K-27(Rzh) are shown on Fig. 1.The shares of spe cific morphometrical classes for cir ca dian dy nam ics, fur ther com bined into subpopulations, are pre sented in Ta ble 1. Dur ing in di cated time in ter val two dom i nat ing subpopulations were found, namely the subpopulation of K-27(10 S) with 3.0-6.9C of rcDNA in nu cleus was 70.6% (0.71) and subpopulation of K-27(Rzh) with 3.0-8.9C of rcDNA -82% (0.82).Thus, on cir ca dian level dur ing three days of passaging, there was no change of dom i nat ing cell subpopulation, according to rcDNA in nucleus.
For both cell vari ants (K-27 (10 S) and K-27(Rzh)) two mech a nisms of pro lif er a tion were de fined, namely, mi totic and amitotic pro lif er a tion.Their cir ca dian dynam ics' are shown on Fig. 2.
Both cell vari ants showed sim i lar cir ca dian rhythms of mitoses dur ing three days of ob ser va tion.Six main peaks were ob served in both cases; there were two peaks of mi totic ac tiv ity daily, po si tions of which var ied from day to day (Fig. 2, a, b).Chang ing of the cul ti va tion con di tions in flu enced nei ther av er age nor max i mal MI val ues, which re mained for both cell cultures at the level of 0.14 and 0.4% respectively.
The dy nam ics of AMI for both cul ture vari ants showed also six main peaks; how ever, the curve shape was some what dif fer ent (Fig. 2, c, d).For K-27(10 S) the av er age AMI was about 1.1%, ex ceed ing MI (0.14%) al most ten fold, while the av er age AMI for K-27(Rzh) vari ant was 0.52% that was about three times higher than MI (0.14%).Max i mal AMI val ues were higher for K-27(10 S) vari ant, i.e. 2.5% com paring to 1.2% for K-27(Rzh).
The o ret i cal ba sis that al lows in ter pre ta tion of exper i men tal data by phenomenological sys tem of equations was pub lished in ar ti cles of Zotina and Zotin [3,4], where the main prin ci ples of ther mo dy namic approach for cell and tis sue cul tures were stated.In partic u lar, in the ref er ence [5], the bi o log i cal sig nif i cance was given to fluxes and forces for study ing tis sue culture of R. serpentina at the pas sage level and ev i dences were pro duced prov ing the pos si bil ity of ap pli ca tion of the de vel oped ther mo dy namic model with corresponding values of fluxes and forces.
In our pre vi ous work [6], we have re ported the results for three cul ture vari ants, for which the val ues of phenomenological co ef fi cients have been es tab lished.In the same work [6] the no tion of ad ap ta tion co ef ficient has been in tro duced to char ac ter ize the change of the value of "con duc tiv ity" co ef fi cient of an ap pro priate char ac ter is tic (the gra di ent of which is the dy nam ics of the cell por tion with this char ac ter is tic un der sys tem re lax ation af ter the cell trans fer -that is a force by itself) in com par i son to the ad ap ta tion co ef fi cient of the bio mass ac cu mu la tion prop erty (al ways equal to 1) in the "con duc tor".The "con duc tor" is a tis sue cul ture, which is placed into the me dium with cer tain con tent of nu tri ent sub stances, cre ates a spe cific con cen tra tions gra di ent of these sub stances dur ing growth and dif feren ti a tion of cells by dif fer ent ways re sult ing in the change of cell por tion of re spec tive spe cial iza tion during pas sage.
Trying to pro ceed to cir ca dian level of study ing, we used the data, pre vi ously ob tained by Kunakh et alt.[2], as well as ex per i ments and mod els of yeast cul ture un der con di tions of con tin u ous cul ti va tion, op po site to con di tions of pe ri odic cul ti va tion, used by us [19].From the last work we have also taken the idea to consider the "age" of cells and ap plied it for gen er a tion of a cor re spond ing sys tem of phenomenological equa tions.Our in ves ti gated sys tem was ergodic, we did not synchro nize cell di vi sions by any method, in clud ing special light treat ment, and thus, it was a sys tem with "a clock switched off" [9].
It is known that it's al most im pos si ble to dis tin guish the length of mi totic cy cle and cy cles of epigenetic processes us ing spe cific times of re lax ation [20].There fore, we prob a bly ob serve on the curves of cir ca dian dy namics the spec trum of os cil la tions of met a bolic pro cesses, For the convenience of thermodynamic equations calculation, instead of proliferation indexes (%) we used the mitoses or amitoses quotas where 1 is assumed to be not re lated to light clock, that is why the os cil la tion period changes dur ing pe ri odic cul ti va tion (along with deple tion of nu tri ent sub stances, pro vided af ter the cul ture trans fer) [2].This con sid er ation has also given us the rea son to ap ply the ther mo dy namic ap proach.
There fore, the con tri bu tion of each al ter ation dynam ics of the por tion of pro lif er at ing cells into al teration dy nam ics of the por tion of cor re spond ing cell subpopulation, ac cord ing to rcDNA in nu cleus, can be de scribed in gen eral by the sys tem of phenomenological equations: where I 1 (t) -flow of the cell subpopulation with rcDNA 1.0-2.9C; I 2 (t) -flow of cell subpopulation with rcDNA 3.0-6.9C for K-27(10 S) or 3.0-8.9C for K-27(Rzh); I l (t), l = 1, 2); phenomenological co ef ficients (and forces as well) have more com pli cated compo si tion than L ls = R lsk A lsk (X lk (t), s = 1, 2) due to the con tri bu tions of pre vi ous force val ues into sub se quent val ues of the flow (see in ter pre ta tion of sym bols t, m, k).Spe cific value and sign of cor re la tion co ef fi cient (R lsk ) in di cate the con tri bu tion of par tic u lar al ter ation dy nam ics of pro lif er at ing cell por tion (mitoses or amitoses), i.e. the ther mo dy namic force: X 1 (t + k) or X 2 (t + k) -into a spe cific bi o log i cal flux I 1 (t) or I 2 (t) (ttime, m -ini tial value of t, when the first sam ple for circa dian dy nam ics study was taken out, k -num ber of points, which re flects the shift of force value dy nam ics rel a tive to fluxes value dy nam ics, to con sider the con -  Ex per i men tal val ues of the dy nam ics of fluxes and their val ues, cal cu lated from equa tions are pre sented on Fig. 4. To eval u ate ad e quacy of com puted curves we used the method of es ti mat ing dis tri bu tion nor mal ity with zero math e mat i cal ex pec ta tion of the de vi a tions squares be tween com pared curves.This ap proach demon strates the sim i lar ity of com puted curves at least for the last two days from three days pe riod of ob ser va tion (first day de vi a tions may be the con se quence of not taking into ac count the con tri bu tions of forces from the pre vi ous day).

Com par i son of con tri bu tion of mitoses and amitoses dy nam ics into dy nam ics of cell por tion with dif fer ent rcDNA in nu cleus.
Af ter chang ing of cul ti vation con di tions, we ob served the dif fer ences in cor re lation be tween some cell subpopulations dy nam ics, accord ing to their rcDNA, and por tion of pro lif er at ing cells.Pos i tive con tri bu tion of MI and AMI into the change of cell por tion with 3.0-6.9C of rcDNA and neg a tive con tri bu tion into the change of cell por tion with 1.0-2.9C of rcDNA were ob served for K-27(10 S) vari ant with out any tem po ral shift and with 2-12 hours shift of dy nam ics of pro lif er at ing cell por tion rel a tively to dy nam ics of the portion of cell subpopulation with different rcDNA.
Pos i tive con tri bu tion of MI and AMI into the change of cell por tion with 1.0-2.9C of rcDNA and neg a tive con tri bu tion of AMI (with out cor re la tion to MI) into the change of por tion of cell subpopulation with 3.0-6.9C (Ta ble 2) were ob served for K-27(Rzh) vari ant with out any tem po ral shift and with the 2-16 hours shift along t-axis to the right.Thus, dur ing in vesti gated in ter val of time, the pro lif er a tion ac tiv ity of both cul ti va tion vari ants that goes for ward the ap pearance of cer tain cell subpopulation on the above-mentioned shift, prob a bly de ter mines the com ing out of pre cur sor cells of the same subpopulation, which are different for investigated cultivation variants.
The con tri bu tions of MI and AMI into the change of the cell por tion of both subpopulations for K-27(10 S) vari ant, with more than 16 hours-shift of dy nam ics of pro lif er a tion in dexes along t-axis to the right side, rel a tive to the dy nam ics of the cell por tion of cor respond ing subpopulation with dif fer ent rcDNA, were ob served to change con trarily: they be come pos i tive for subpopulation 1.0-2.9C, and neg a tive -for 3.0-6.9C. The dy nam ics of MI and AMI for K-27(Rzh) vari ant with the shift along t-axis to the right side rel a tive to dy nam ics of cor re spond ing subpopulations ac cord ing to their rcDNA make both pos i tive and neg a tive con tribu tions into the change of cells por tion of both subpopulations with different rcDNA (Table 2).
Thus, un der the chang ing of cul ti va tion con ditions, the pro lif er a tion is switched to the pro duc tion of op po site subpopulation of cells (in our case -to cells with higher val ues of rcDNA, i.e. polyploidy cells).Note: *Flux I 1 -dynamics of portion of cell subpopulation with 1.0-2.9C of rcDNA in nucleus; flux I 2 -dynamics of portion of cels subpopulation with 3.0-6.9C of rc DNA in nucleus for K-27 (10 S), and 3.0-8.9C for K-27 (Rzh); ** force X lk -dynamics of cell portion, proliferating by mitoses (l = 1) or amitoses (l = 2).Paired linear regression method was used to compare the dynamics.Criterion statistics was calculated by the formula F 1,N-2 = (N-2)R 2 /(1-R 2 ), for non-zero correlation coefficients the criterion statistic value was higher than 5% of treshhold limit for F-distribution, namely, F   (the value of flux of cell subpopulation with 3.0-8.9C of rcDNA at the start ing point of sam ple with draw ing).As can be seen, the ad ap ta tion co ef fi cients of both bi olog i cal forces rel a tive to the flux of cell subpopulation with 1.0-2.9C of rcDNA for K-27(10 S) vari ant were equal.In the case of cell subpopulation 3.0-6.9C, the ad ap ta tion co ef fi cient of bi o log i cal force -dy nam ics of change of mitoses quota was 1.67-fold higher than that of the other bi o log i cal force -dy nam ics of change of amitoses quota.For the bi o log i cal flux of cell subpopulation with 1.0-2.9C of rcDNA for K-27(Rzh) cul ti va tion vari ant, the ad ap ta tion co ef fi cient of bi olog i cal force -dy nam ics of change of mitoses quota was 5-fold higher than the value of the same pa ram e ter for amitoses.In the case of sec ond flux-dy nam ics of cell subpopulation with 3.0-8.9C of rcDNA, the adaptation coefficient of biological force-dynamics of the change of mitoses quota was 60-fold higher than the value of the same parameter for amitoses.
Com par a tive anal y sis ev i denced that un der the change of cul ti va tion con di tions the ad ap ta tion co ef ficient of dy nam ics of change of mitoses quota in creased 12-fold and the same pa ram e ter of amitoses quota decreased 3-fold to wards the pro duc tion of cells with high val ues of rcDNA, re lated to dif fer en ti a tion, due to ac cu mu la tion of indoline al ka loids or cre ation of tracheids, as it was shown for the passage hierarchical level.
Con clu sions.Math e mat i cal model, de signed to describe phys i cal, chem i cal, and bi o log i cal sys tems with con ju gated pro cesses, was mod i fied to con sider the "age" of cells.It al lows de ter min ing the cor re la tion between al ter ation dy nam ics of cell por tion with dif fer ent rcDNA in nu cleus (as bi o log i cal fluxes) and dy nam ics of por tion of mi totic and amitotic pro lif er at ing cells (as bi o log i cal forces) at circadian hierarchical level in tissue culture.
The anal y sis of cor re la tion co ef fi cients be tween forces and fluxes showed that the change of cul ti va tion con di tions leads to the change of the cell dy nam ics with dif fer ent rel a tive DNA con tent in nu cleus.This dy namics is pos i tively con trib uted, with some tem po ral shift, by bi o log i cal forces -the dy nam ics of mitoses and amitoses quotas.

Fig. 1
Fig.1 Alteration dynamics of cell portion (where 1 is assumed to be 100%) with different relative DNA content in nucleus under standard cultivation conditions in 10S medium (K-27(10 S) variant) (a, b) and under conditions of submerged cultivation in liquid medium Rzh (K-27(Rzh) variant) (c, d) during 12-15 th and 9-12 th days of cultivation.Arrows indicate the beginning of the corresponding day of growth.

Fig. 2
Fig.2 Dynamics of change of mitoses (a) and amitoses (b) quotas under standard cultivation conditions in 10S medium (K-27(10 S) variant), as well as of mitoses (c) and amitoses (d) quotas under conditions of submerged cultivation in liquid medium Rzh (K-27(Rzh) variant) during 12-15 th and 9-12 th days of cultivation, respectively.Arrows indicate the day of growth beginning.For the convenience of thermodynamic equations calculation, instead of proliferation indexes (%) we used the mitoses or amitoses quotas where 1 is assumed to be

Fig. 3
Fig.3 Circadian dynamics of change of cell portion with 1.0-2.9C of rcDNA (curve 1) and mitoses quota (curve 2) during 12-15 th days of growth of K-27(10 S) cells of R. serpentina under cultivation on 10 S agar medium: without any shift (a) and with 12 hours-shift of the mitotic index curve relative to the curve of cell portion with 1.0-2.9C of rcDNA (b).The equations of fitted regression lines, obtained by the least-squares method, are shown on the plot.Criterion statistic values for R 2 showed on plot c is F 1,34 = 3.13 (does not exceed the upper 5% threshold of F-distribution for N = 36 (F 1,34 = 4.17)), and showed on plot d is F 1,28 = 7.84 (exceed the upper 5% threshold of F-distribution for N = 30 (F 1,28 = 4.20)).This means the absence of linear dependence in the first case and the presence of linear dependence in the second one.

2
Correlation coefficients R lsk of dynamics of fluxes* and forces ** with successive shifts in k points every two hours (k = 1? 33) of quantitative proliferation dynamics relative to quantitative dynamics of corresponding cell subpopulation, according to rcDNA in tri bu tions of pre ced ing val ues of bi o log i cal forces into the mo ments of time t + m to bi o log i cal fluxes in the mo ments of time t + m + k) (Fig.3, Ta ble 2); A ls -ad apta tion coefficients, i.e. particular values for every investigated system are presented below.
More over, when com par ing the cul ti va tion vari ants, we can see the change of cell subpopulations ac cording to their rcDNA in nu cleus.The dy nam ics of this change, with some tem po ral shift, is pos i tively contrib uted by the dy nam ics of bi o log i cal forcesmitoses and amitoses.Anal y sis of ad ap ta tion co ef fi cients of bi o log i cal forces and fluxes A ls un der the change of cul ti va tion con di tions.It was found that the change of cul ti va tion con di tions in flu enced the value of ad ap ta tion co ef ficient A ls (com puted ac cord ing to the above-men tioned sys tem of equa tions) of the dy nam ics of some pro lif era tion in dexes -bi o log i cal forces to a spe cific flux.The ad ap ta tion co ef fi cients for K-27(10 S) vari ant were de -scribed by a ma trix: for the sys tem of equa tions with ini tial val ues of m = 144 (time-point of sam ple withdraw ing, cor re spond ing to 10.00 o'clock of the 12 th day); I 1m = 0.12 (the value of flux of cell subpopulation with 3.0-6.9C of rcDNA at the start ing point of sam ple with draw ing); I 2m = 0.3 (the value of flux of cell subpopulation with 3.0-6.9C of rcDNA at the start ing point of sam ple with draw ing).Ad ap ta tion co ef fi cients for K-27(Rzh) vari ant were de scribed by a ma trix: for the sys tem of equa tions with ini tial value of m = 108 (time-point of sam ple with draw ing, cor re spond ing to 10.00 o'clock of the 9 th day); I 1m = 0.013 (the value of flux of cell subpopulation with 1.0-2.9C of rcDNA at the start ing point of sam ple with draw ing); I 2m = 0.35

Fig. 4
Fig.4Alteration dynamics of portion of cell subpopulation with 1.0-2.9C (a) and 3.0-6.9C (b) of rcDNA in nucleus for K-27(10 S) variant during 12-15 th days of cultivation, and portion of cell subpopulation with 1.0-2.9C (c) and 3.0-8.9C (d) of rcDNA in nucleus for K-27(Rzh) variant during 9-12 th days of cultivation.For all plots (a-d), curve 1 is the flux I l (t), determined from the experiment; curve 2 -flux I l (t), determined from the equation, l = 1, 2).All experimental data were smoothed by two points moving average method.Arrows indicate the beginning of corresponding day of growth.

Table 1
Share of cell classes with different relative DNA content in nucleolus in general cell population of different cultivation variants of the K-27 R. serpemtima strain.