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Journal of Neuroscience Methods 167 (2008) 376–383

The linkage of neural progenitor cell cycle profiles between embryonicand adult stroke models: Analytical approach II

Mei Lu a,b,∗, Rui Lan Zhang b, Zheng Gang Zhang b, Michael Chopp b,c

a Department of Biostatistics and Research Epidemiology, Henry Ford Hospital, One Ford Place, Ste. 3E, Detroit, MI 48202, USAb Department of Neurology, Henry Ford Hospital, Detroit, MI 48202, USAc Department of Physics, Oakland University, Rochester, MI 48309, USA

Received 18 May 2007; received in revised form 15 August 2007; accepted 16 August 2007

bstract

Cell kinetics employed for embryonic models was modified and used to study the neuronogenesis in the subventricular zone (SVZ) in adult ratsubjected to stroke. Enhanced analytical approaches were introduced and used to compare the cell cycle length (TC) and length in G1 phase, TG1,t various times after stroke to study the correlation between TG1 and TC and to compare cell cycle evolution and proliferation profiles between thetroke and embryonic models. Our data indicate that cell cycle kinetics for the embryonic model can be applied to stroke in the adult. Significanteduction of TG1 early after stroke (p < 0.05) corresponds to an increase of neural progenitor cells remaining in the cycle at early times and cellsxiting at later times. TG1 correlates with TC (r = 0.99, p < 0.05). In conclusion, the analytical approaches proposed can be used to study the cell

roliferation profiles in adult rats subjected to stroke with and without stroke therapy. The cell kinetics the cell proliferation profile differs betweenhe stroke and embryonic models. TC evolution is three-fold slower in the cells and leave the cycle earlier and more frequently in the stroke model,ompared to the embryonic model. TC is a surrogate measure of TG1. 2007 Elsevier B.V. All rights reserved.

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eywords: Neural progenitor cells; Cycle length evolution; Cell proliferation p

. Introduction

In the adult brain, neural progenitor cells are present inhe subventricular zone (SVZ) of the lateral ventricle and theubgranular zone of the dentate gyrus (Luskin et al., 1997;arez-Buylla et al., 2000). Proliferation of neural progenitorells is tightly controlled by cell cycle kinetics (Takahashi et al.,993; Caviness et al., 2003). Using cumulative and single pulseromodeoxyuridine (BrdU) labeling methods, Nowakowski etl. (1989) have determined the length of the cell cycle andstablished the cell cycle interval of mice during neocorticalormation, the embryonic model. By adapting this approach, weound that stroke significantly increases the proliferating popula-

ion of SVZ neural progenitor cells in rats subjected to 7 days ofmbolic middle cerebral artery occlusion (S7), which is associ-ted with the reduction of the cell cycle length (TC), especially

∗ Corresponding author at: Department of Biostatistics and Research Epidemi-logy, Henry Ford Hospital, One Ford Place, 3E, Detroit, MI 48202, USA.el.: +1 313 874 6413; fax: +1 313 874 6730.

E-mail address: mlu1@hfhs.org (M. Lu).

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165-0270/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.jneumeth.2007.08.015

s; Rats; Stroke

he length in G1 phase (TG1) (Zhang et al., 2006). Using thenhanced analytic approach which permits the precision for cellycle kinetic parameters, we further demonstrate that migrationf neural progenitor cells out of the SVZ can be ignored in thestimation of the cell cycle parameters (Lu et al., 2007).

The cell cycle length is associated with neural progenitor cellrogression from proliferation to neurogenic divisions duringortical neurogenesis (Caviness et al., 1995, 2003). The pro-ortion of neural progenitors that remain in (P fraction) and exitrom (Q fraction) the cell cycle in the pseudostratified ventricularpithelium determines the degree of cortical neurogenesis duringmbryonic development 11–17 days after (E11–17, Takahashit al., 1996a,b). However, it remains to be determined whetherhe reduction of the cell cycle length of adult neural progenitorells after stroke is related to P and Q fractions.

In the present study, we seek to establish the temporal profilef stroke neural progenitor cells by studying the cell kinetics and

he cell behaviors over a period of 2–14 days after stroke. Withnalytical extension of Takahashi et al. (1994, 1997) previousork for the embryonic model, we tested the hypothesis that

dult neural progenitor cells after stroke recapture embryonic

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M. Lu et al. / Journal of Neurosc

ell kinetics. Mathematical modeling is used to study the cellength, TC or TG1, evolution over time, the correlation betweenC andTG1, and the likelihood of the cells in the SVZ remained inr exited from the cycle. Given that stroke induces neurogenesis,e expect that after the stroke, more cells exit the cycle and the

ell proliferation profile differs from the embryonic model.

. Methods

Experimental procedures were approved by the Institutionalnimal Care and Use Committee of Henry Ford Hospital.

.1. Animal model of stroke

Male Wistar rats (age 3–4 months) were employed. The mid-le cerebral artery (MCA) was occluded by placement of anmbolus at the origin of the MCA (Zhang et al., 1997). Exper-ments were initiated in rats at 2, 4, 7 and 14 days after stroke,orresponding to the maximum period of stroke induced neuro-enesis (Zhang et al., 2001, 2004a,b, 2006).

.2. Cumulative and single labeling experiments for cellycle kinetics

BrdU labeling of stroke rats was performed by repeatedntraperitoneal (i.p.) injection (2–3 h intervals; 50 mg/kg, Sigma)ver a total period of 18.5 h, beginning at 08:00 a.m. Selectedats from 2, 4, 7 and 14 days after stroke were killed 30 minfter each of the BrdU injections. Three to four animals per timeoint were sacrificed with a total of 10 time points. All neuralrogenitor cells passing through the S phase were labeled withrdU until the cell proliferation reaches to the maximum. Theumber of BrdU labeled cells at S phase were counted in fourections per subject at each sacrifice time. The cumulative label-ng experiment was used to estimate the total cycle length andhe length in S phase.

Animals were injected with a single dose BrdU, 50 mg/kg,nd were sacrificed from 30 min (the minimum) until the timehen 100% of the labeled cells were mitotic in the S phase. Theercent of labeled cells in S phase was zero when cells were in2 phase, linearly increasing when cells entered in M phase,

nd were completely labeled when the first labeled mitotic cellppeared in S phase. Based on this experiment, the duration ofG2 and TG2+M was determined. This experiment was completed

n rats with 2, 4, 7 and 14 day after stroke for estimation of .theycle lengths in phases M and G2, respectively, therefore, toalculate the cycle length in G2 phase (Lu et al., 2007).

.3. Determining cell proliferation and postmitoticehaviors in the SVZ

Two separate tracers, 5-chloro-2′-deoxyuridine (CldU,0 mg/kg, Sigma) and 5-iodo-2′-deoxyuridine (IdU, 50 mg/kg,

igma) (Zink et al., 1998; Maslov et al., 2004) were used in twoeparate labeling protocols and were injected into two subsets ofnimals to distinguish the primary cohort of proliferating SVZells that exit the cycle (Q cells) from those which remain in the

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Methods 167 (2008) 376–383 377

ycle (P cells) in a 2 h interval (Takahashi et al., 1994, 1995a).Q+P is determined from Protocol 1 for one subset of animalsnd NQ (the number of Q cells) is determined from Protocol 2or the second subset of animals. The Q fraction was calculateds the ratio of NQ to NQ+P, and the P fraction is equal to 1 − Qraction.

.4. Histology evaluation

At the end of the experiments, animals were transcardiallyerfused with heparinized saline followed by 4% paraformalde-yde. Brains were removed and fixed in 4% paraformaldehyde.o analyze BrdU labeling, every 40th BrdU immunostainedoronal brain section at the level of AP + 10.6 mm andP + 9.2 mm (Paxinos and Watson, 1986) was digitized using

omputer imaging (Olympus BX40) via the MCID computermaging analysis system (Imaging Research, St. Catharines,anada). BrdU labeled and unlabeled cells or mitosis in eachVZ coronal section were presented as the number of theells/section. Density for the four sections per subject was aver-ged to obtain a mean density value for each brain, according toublished methods (Kuhn et al., 1996; Zhang et al., 2001).

.5. Cell kinetic parameters and their interpretation

.5.1. The total cell cycle length TC, the length in S phaseTS) and growth fraction (GF)

The number of BrdU labeled cells under the cumulative label-ng experiment were measured at each time point per subject inats with stroke at day 2, 4, 7 and day 14 after symptom onsetnd in rats without stroke. Concurrent linear regressions weresed to fit the data through nonlinear interaction processes atach time point, with estimation of total cycle length, TC, theength in S phase (TS) and growth fraction (GF). Z-test statisticas used to compare the cycle parameter differences betweenifferent stroke models (e.g., 2-day stroke versus 4-day stroke)Lu et al., 2007).

.5.2. The length in G2, M or G1 phaseThe labeled cells in the S phase under the single pulse labeling

xperiment were fitted into different concurrent linear regres-ions with the estimation of length both G2 and M phasesTG2+M). The length of G1, TG1 and its standard error (S.E.)an be estimated based on the estimation of TC−S and TG2+Mrom both the cumulative labeling and single pulse labelingxperiments. Z-test statistic was used to compare cycle lengthifferences between different stroke models (Lu et al., 2007).

.5.3. TC as a function of time after stroke onsetIn the embryonic study of the embryonic models at day 11

E11) to day 16 (E16), TC values ranged from 8.1 to 18.4 hTakahashi et al., 1995b) and were studied for TC evolution overime. For the present study, we adapted Takahashi’s approach

sing the regression analysis and also assessed the model fit,hich are described in the following.Assume ti for i = 1, 2, . . ., M for some M > 2 are the time

oints after an event (e.g., days after stroke or embryonic), TC(t)

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78 M. Lu et al. / Journal of Neuro

an be fitted with either a linear regression model as

C(t) = α + βt, (1a)

here α (intercept) and β (slope) are the unknown parameters,r otherwise a sigmoid regression model as

C(t) = α + 1 + m e(−t/τ)

1 + n e(−t/τ) , (1b)

here α, m, n and τ are the unknown parameters.Using Proc REG or Proc NLIN in SAS, the commercially

vailable statistical computational package (SAS Institution,999), we estimated unknown parameters described either in Eq.1a) or in Eq. (1b), respectively, based on estimated TC(ti), for= 1, 2, . . ., M. The selection of the regression model depends onhe model indentifiability and the model goodness-of-fit. Sincenly four onset time points (day 2, 4, 7 and day 14) were con-ucted for stroke models, the linear model would be fitted firstnto Eq. (1a) because of the simplicity. Fitting Eq. (1b) for thetroke model may be problematic for the model indentifiability.

.5.4. Cycle length TG1 evolution and correlation of TG1

ith TC

A similar mathematical discussion for TC(t) can be appliedo the study of TG1 evolution as a function of time after strokenset. In addition, the relationship between TC and TG1 can beeasured by calculating the correlation coefficient, r. The cor-

elation coefficient (r) between two variables (e.g., variables Ynd X), has a range of −1 to 1, where |r| = 1 means a perfectorrelation and 0 means no correlation. A positive correlationoefficient indicates that an increase in Y is correlated withn increase in X; a negative correlation coefficient, in contrast,ndicates an increase in Y correlated with a decrease in X. Theorrelation coefficient can be tested against no correlation at all.he G1 phase has been identified as the key regulation phaseuring neurogenesis in the developing brain (Takahashi et al.,995b; Caviness et al., 1999; Siegenthaler and Miller, 2005).he reduction of total cycle length led to the reduction in G1

ength (Takahashi et al., 1995b; Zhang et al., 2006), however,he report of the TC and TG1 relationship was rather descriptive.n this study, the correlation coefficient was calculated for bothhe stroke model and the embryonic model (Takahashi et al.,995b). Later, we show that TC could be the surrogate of TG1.

.5.5. Comparison of TC difference between embryonic andtroke models

Assuming the cycle length fits into the linear regression inq. (1a), the slope β represents the rate of cell cycle evolu-

ion. Therefore, differences in slope between the stroke andmbryonic models would indicate the cycle evolution differenceetween the two models. To test the slope difference, we use theingle regression model proposed by Kleinbaum et al. (1988)

C(t) = η + β1t + Z(γ + (β2 − β1)t) (2)

here β1 and β2 are the slopes for the embryonic model andhe stroke model, respectively, Z the indicator variable of thetroke model and η and γ are the nuisance parameters. The same

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e Methods 167 (2008) 376–383

nalysis approach can be used to test the difference in slopesetween TC and TG1 in the stroke model.

.5.6. The number cell cycles from time ta to time tb (CC)ta < tb)

From Eq. (1a) or Eq. (1b), we can see that TC is evolving ashe stroke onset time, t, increases, therefore, the number of cellycles in 24 h, in the early time period of event, e.g., E11–E12s an example, with TC in a range of 8.1–10.2 (Takahashi et al.,995b), would differ from the number of cell cycles in a laterime period (e.g., E15–E16 with TC in a range of 17.5–18.4).

The concept of number of cell cycles was introducedTakahashi et al., 1995a,b), and their approach for cell cyclentervals (cell cycles as CC) E11–E17 can be described in theollowing:

1) For each 24 h period of E11 (e.g., at 09:00 a.m. of E11 to09:00 a.m. of E12), a weighted TC is calculated as T w11–12

C =(1/24)

∫ 240 (8.315 + 0.0825t) dt, where

TC(t) = 8.315 + 0.0825t is the regression model fromEq. (1a) and (1b) based on estimated TC on day 11 to day16.

2) To calculate cell cycles in time period E11–E12 as CC11–12

= 24/T w11–12C .

3) To sum the CC11–12 to CC16–17 and obtain the CC11–16.

Using above methods, we could replicate the 11CC over11–E16 for embryonic models.

In addition, the above mentioned methods for CC calculationan be simplified using the following integral equation

Ctq−tb =∫ tb

ta

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TC(t)dt, (3)

here ta < tb. Eq. (3) is more accurate for CC estimation and cane used at any time period. Eq. (3) was used to estimate CCs foroth embryonic model and the stroke model.

.5.7. The cell leaving the cycle (Q fraction)The postmitotic behaviors of a 2 h cohort of cells in the SVZ

re monitored using two separate tracers based on two label-ng protocols with measurements of NQ and NP and Q fraction.his method was proposed by Takahashi et al. (1994) as thetudy of E14 model. Q behaviors had been studied extensivelyn the embryonic sequence E11–E17 (Takahashi et al., 1996b)nd in Q modeling (Lees et al., 2006) (Takahashi et al., 1997).mplification of neurogenesis would occur if the number of cell

ycles during Q fraction <0.5 increased (Caviness et al., 1995).ith each successive cycle there is an increase in the fraction of

ostmitotic cells that left the cycle (the Q fraction) and also anncrease in the length of the cell cycle due to an increase in theength of the G1 phase of the cycle (Caviness et al., 1999).

In addition, with respect to proliferative fate, cells could be

lassified as either “symmetric” when both daughter cells areither Q or P, or “asymmetric” when one daughter cell is Q andne is P (Rakic, 1988). Assuming the cells of Q or P obey ainomial distribution, the probability of the same fate daugh-

ience Methods 167 (2008) 376–383 379

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Fig. 1. Concurrent linear regressions were used to fit the data through nonlinearinteraction processes at each stroke time point (day 2, 4, 7 and day 14), respec-tively, with estimation of total cycle length, TC and the length in S phase. TG1,was be estimated based on the estimation of TC−S and TG2+M from both thecumulative labeling and single pulse labeling experiments at each time after thestd

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er cells will be P × P (P and P symmetric) or Q × Q (Q and Qymmetric); and the probability of asymmetric daughter cellsill be 2 × P × Q, given by Takahashi et al. (1996b). For this

tudy, the cells exiting and the proliferative fate of cells weretudied for a model of stroke. A one-way analysis of varianceANOVA) was used to compare P/Q fraction or the prolifera-ion fate difference among the stroke groups. Analysis wouldegin testing for the group effect, followed by pair-wise groupomparison if the group effect was detected at the level of 0.05.

polynomial regression model was used to model Q cells andhe cell proliferation fates as a function of time after the onset,espectively.

The comparison between stroke and embryonic models wasonsidered as a magnitude study for illustration of the mathe-atic modeling and approaches. We are aware of the possible

iological differences between embryonic mice and embryonicats; however, from the cell cycle kinetic point of view, theyre compatible. TC were 11 and 19 h for embryonic rat E12 and18 (von and Jaensch, 1972), and 10.2 and 18.4 h for embryonicice E12 and E16 (Takahashi et al., 1996b), respectively.

. Results

.1. Cell kinetics for stroke models S2, S4, S7 and S14

Based on the above experiments, we estimated the cell cyclearameters at different time points of the stroke and the resultsre presented in Table 1 and Fig. 1. 18.98 (±1.22) h of TC and2.63 (±0.49) of TG1 were previously reported in the non-strokeodel (Lu et al., 2007). The total cell cycle lengths, TC, in

he stroke model, except 14-day stroke, significantly decreased,ompared to the non-stroke (p < 0.05). In the stroke model, TCere significantly increased in the when the time of stroke onsetas increased (p < 0.01), except the time between day 2 and day

of the stroke onsets (p = 0.26). Similar to the total cell cycle

ength, TG1 significantly increased in the stroke model when theime of stroke onset was increased (p < 0.05), except the timeetween day 4 and day 7 after stroke (p = 0.96).

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able 1VZ cell cycle parameter estimation (S.E.) in stroke rats

arameters 2-day stroke 4-da

umulated labeling (N) 22 40F 23.55 (0.39) 30.1

Ca 11.49 (0.66) 12.5

S 2.25 (0.41) 2.40

C−S 9.24 (0.36) 10.1odel-fit: SSR/MSE 29/1.52 75/2

ingle pulse labeling (N) 27 24

G2 0.57 (0.02) 0.54

M 1.22 (0.05) 1.26

G2+M 1.79 (0.04) 1.80odel-fit: SSR/MSE 438/17.5 239

G1b 7.45 (0.24) 8.32

a TC difference (p < 0.01) between any two stroke onsets, except stroke onset 2 dayb G1 length difference (p < 0.05) between any two stroke onsets, except stroke onse

troke onset, respectively. TG1 significantly increased in the stroke model whenhe time of stroke onset was increased (p < 0.05), except time between day 4 anday 7 after stroke (p = 0.96).

.2. Stroke TC and TG1 evolution and correlation

The TC estimations for S2, S4, S7 and S14 were fitted in Eq.2) with a regression line of TC(t) = 11.428 + 0.029(t − 48) andhe goodness-of-fit R2 = 0.994 (Fig. 2). TG1 progressed over times TG1(t) = 7.351 + 0.020(t − 48) with R2 = 0.997 (Fig. 2). TG1as strongly correlated with TC (correlation coefficient r = 0.99

nd p < 0.01 for testing no correlation) and no slope differenceas detected between TC and TG1 regressions (p = 0.85), indi-

ating that TC is the surrogate of TG1. The same correlationattern was observed for the embryonic model between TC andG1 using the data collected in Table 1 (Takahashi et al., 1995b)ith r = 0.99, p < 0.01 for testing no correlation.

.3. Comparison of TC between the embryonic model and

he stroke model

Fitting the estimated TC values in Fig. 1 (Takahashi etl., 1995b) of the embryonic model E11–E16, one obtains

y stroke 7-day stroke 14-day stroke

50 347 (0.29) 31.05 (0.32) 24.14 (0.69)1 (0.62) 15.28 (0.59) 19.74 (0.99)(0.36) 3.94 (0.37) 4.78 (0.60)2 (0.34) 11.34 (0.30) 14.96 (0.65).03 94/ 2.00 58/1.88

27 27(0.02) 0.53 (0.02) 0.55 (0.02)(0.04) 1.24 (0.05) 1.24 (0.05)(0.03) 1.78 (0.03) 1.79 (0.03)

/10.8 368/14.7 348/13.9

(0.27) 9.56 (0.24) 13.17 (0.49)

s vs. 4 days (p = 0.26).t 4 days versus 7 days (p = 0.95).

380 M. Lu et al. / Journal of Neuroscience Methods 167 (2008) 376–383

Fig. 2. Based on TC estimation for S2, S4, S7 and S14, TC progresses asTC(t) = 11.428 + 0.029(t − 48) with the goodness-of-fit R2 = 0.994. TG1 obeysTG1(t) = 7.351 + 0.020(t − 48) and R2 = 0.997. TC or TG1 increased as the strokeoi(

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nset time increased, and TG1 was strongly correlated with TC (r = 0.99) Theres no slope difference between TC and TG1 regressions (p = 0.85) based on Eq.2).

he regression of TC(t) = 8.424 + 0.088(t − 246). Slight coeffi-ient differences were observed, compared to TC(t) = 8.315 +.0825(t − 246), reported by Takahashi et al. (1995b) and theifference is more likely be due to a rounding error.

TC progression is slower in the stroke model (slope = 0.029),ompared to 0.088 progression in the embryonic modelp = 0.025, in Fig. 3), indicating a different dynamic change inell cycle kinetics between the two models.

.4. Cell cycle numbers (CC) from S2 to S14

The integration function of CC (the cell cycles) for strokeodel is 34.483 × log(11.428 + 0.029 × time) using Eq. (3).

uring the 12 days of a stroke period from day 2 to day 14

S2–S14) a total of 19CC (actual 18.92) were completed (Fig. 4)nd the first 6 days of stroke period from day 2 was 11CC (actual0.73). 11CC (actual 10.76) were accomplished during the 6

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ig. 4. The number of cell cycles on a daily period. During the 12 days of a stroke perin the stroke model. 11CC (actual 10.76) were estimated in 6 days of the embryonic pell cycled 2.6 intervals in the embryonic model, compared 1.33CC in the stroke mod

s significantly slower in the stroke model (slope = 0.029), compared to 0.088rogressions in the embryonic model, indicating that cells in the stroke modelere less active than the cells in the embryonic model.

ays of the embryonic period from day 11 to day 17 (E11–E17),hile 8CC (actual 7.56) were calculated in 6 days of strokeeriod (S11–S17) based on the mathematical estimation.

.5. Cells leaving the cycle

Q cell progression, Q fraction = 0.094 + 0.131 × t − 0.013 ×2 + 0.001 × t3 (model-fit RRE = 0.06 and MSE = 0.004, whereis the day after the stroke onset) in Fig. 5, was flatter than

he progression in the embryonic model illustrated in Fig. 7 ofakahashi et al. (1996b), and the likelihood of the cell leaving

he cycle in the stroke was much higher than in the embryonicodel (e.g., 0.68 on S14 versus 0.34 on E14). Half of the cellsere leaving the cycle (50% of Q cells) at day 6 (actual 5.5) for

he stroke model (Fig. 5) and at day 15 (actual at day 14.5) forhe embryonic model.

The analysis shows that Q fractions were increased when timef stroke onset was increased (p < 0.05 for the pair-wise com-

od from day 2 to day 14, the cumulated cell cycles were 19CC (actual 18.92CC)eriod from day 11 to 17. At the same 1-day period of the onset, e.g., day 11–12,el.

M. Lu et al. / Journal of Neuroscience

Fig. 5. Q fraction regression, Q fraction = 0.094 + 0.131 × day −0.013 × day2 + 0.001 × day3 and its 95% confidence intervals over timeaws

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fter stroke onset with model-fit RRE = 0.06 and MSE = 0.004. Half of the cellsere leaving the cycle (50% of Q cells) at day 6 (actual at day 5.5) after the

troke onset.

arisons). 85% Q fraction in the non-stroke model was observednd was significantly higher than those in the stroke modelsp < 0.05).

The symmetric Q + Q cells (both daughter cells leaving theycle) significantly increased to 20 ± 2% at day 4, compared to0 ± 1% at day 2 and increased consecutively at day 7 (30 ± 5%)nd at day 14 (48% ± 2%) with significant pair-wise group dif-erence on any consecutive time points (p < 0.03). The P and

in relation to proliferation fates from S2 to S18 were esti-ated based on Q regression and presented in Fig. 6. A similar

roliferation fate propensity was observed in the stroke model,ompared to the embryonic model, Fig. 11 of Takahashi et al.1996b). However, the proliferation fates in stroke were quiteifferent from the proliferation fate of the embryonic modelcalculated based on Table 3 in Takahashi et al., 1996b). At

he onset of day 14, as an example, the distributions of P + P and

+ Q symmetric and P/Q asymmetric were 11, 48 and 41%or stroke S14, 44, 13 and 43% for embryonic E14 and 65,

ig. 6. The P and Q in relation to proliferate fates from S2 to S17, estimated basedn Q regression, where the solid brown area is P + Q or Q + P asymmetric, theight brown area is Q + Q symmetric and the shaded line area is P + P symmetric.

ith the theoretical extension to S17, a similar proliferation fate propensityas observed in the stroke model, compared to embryonic model (Fig. 11 ofakahashi et al., 1996b). However, different proliferation fates were observed

n 6-day period of day 11 to day 17 after the onset between the two models.t the onset of day 14, as an example, the distributions of P + P and Q + Q

ymmetric and P/Q asymmetric were 11, 48 and 41% for stroke, 44, 13 and 43%or embryonic E14 and 65, 3 and 32% for embryonic E13 and 17, 35 and 48%or E15, respectively.

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Methods 167 (2008) 376–383 381

and 32% for embryonic E13 and 17, 35 and 48% for E15,espectively.

. Discussion

We extended analytical approaches for the cell cycle kinet-cs of the embryonic model to analyze neurogenesis in thedult stroke. This analytic algorithm is not only able to esti-ate the cell kinetic parameters of the interest with variation

e.g., S.E.) for stroke model, but also able to replicate the pub-ished results for embryonic models (Takahashi et al., 1995b,996b). The cell cycle kinetics of stroke models at day 2, 4nd day 14 seemed to fit into the cycle kinetics used for thembryonic models and the goodness-of-fit (SSR and MSE) aren same range as we have previously observed for the non-troke model and the 7-day stroke model (Lu et al., 2007).herefore, we concluded that the embryonic cell cycle kinet-

cs can be used for adult stroke. Although cell migration aftertroke is an important factor in neurogenesis after stroke, theigration factor can be omitted in the estimation of cell kinetic

arameters. Note that the cell death, as a part of neurogene-is process, has been omitted in analyzing the cell behaviorsnd cell cycles, but was previously discussed (Takahashi et al.,995b).

Mathematical models of cell proliferation attempt to mimiche process with restrictions to simplify the biological situa-ion. Therefore, the cell cycle parameter estimations should beiewed as reflecting principally the population proliferation pat-erns. Because of the heterogeneities in the proliferative cellopulation, these parameters are to be regarded as only anpproximation of the true values or the average of cell prolifer-tion from more than one proliferating cell type. This argumentas been consistent with the discussion on embryonic modelsTakahashi et al., 1993).

Proliferation of neural progenitor cells is tightly controlledy cell cycle kinetics (Takahashi et al., 1993; Caviness et al.,003). With proper mathematical modeling, we can analyzehe behaviors of neural progenitor cells beyond our observationexperiments). The extended mathematical algorithm, proposedn Section 2, provides a useful tool to predict time points of cellehavior change (e.g., the time for 50% of Q fraction) basedn the observed data. By extending the cell proliferation fatessymmetric and asymmetric cell divisions) for the stroke modelp to 18 days after the stroke onset (S2–S18), we are able toee a similar tendency of stroke proliferation fate profiles, butith different paces, compared to the embryonic proliferationsn E11–E17. However, the mathematical prediction needs to bealidated by a biological experiment. There could be possibleiological differences between embryonic mice and rats models.owever, 11–19 h of the total cell cycle lengths for embryonic

at E12 and E18 were reported by von and Jaensch (1972) and0.2–18.4 h were reported for embryonic mice E12 and E16 byakahashi et al. (1996b) suggesting that the two rodent mod-

ls were compatible. Nevertheless, given the different rodentssed in the stroke and in the embryonic models, cautious inter-retation of the stroke and embryonic model comparison isarranted.

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Estimating the length of G1 requires the completion of bothumulative and single pulse labeling experiments, mathemati-al modeling and estimation of the cell cycle parameters andheir variance. Throughout this cell kinetics reference studyf the stroke model on the multiple onsets, we first demon-trated a superb correlation (r = 0.99) between TC and TG1.ince TC can be estimated only based on the cumulative label-

ng experiment alone, mathematically, TG1 can be quantifiedy TC as TG1(t) = − 0.31 + 0.67TC(t) for the stroke model andG1(t) = − 5.62 + 0.98TC(t) for the embryonic model, respec-

ively. Therefore, we conclude that TC can be used as theurrogate of TG1.

Stroke induces neural progenitor cell proliferation by short-ning the cell cycle length TC or G1 length in stroke up to 7ays after the stroke onset, compared to the non-stroke model.owever, TC evolution in stroke was three times slower (the pro-ortion in slopes between the two models) than its evolution inhe embryonic model (Fig. 2 and p = 0.025), suggesting possi-le different dynamic changes of P and Q fractions in the strokeodel, compared to the embryonic model.The mathematical model estimated that there were 11 and 8

ell cycles for the first and second 6 days, respectively, during–14 days after stroke, which is consistent with our previousndings that stroke augments neurogenesis by acutely expand-

ng the neural progenitor pool during 2–7 days after strokeZhang et al., 2001, 2006). Although the number of cell cycles isifferent between stroke-induced neurogenesis and embryonicortical neurogenesis, rapid expansion of a progenitor pool isbserved in the embryonic model, suggesting that the adult pro-enitor cells after stroke recaptures the cell cycle kinetics of thembryonic progenitors.

Fitting the observed Q fraction data on a mathematical poly-omial equation, illustrated in Fig. 5, we could identify 5.5 daysfter stroke (with estimated Q fraction 50% in Fig. 5) as the timeoint when more than 50% of neural progenitors start leavinghe cycle of the SVZ, which is about 10 days earlier than its inhe embryonic model in Fig. 7 of Takahashi et al. (1996b). Atay 14 of the onset, the Q fraction for the stroke model is dou-led, compared to the embryonic model, indicating that manyhe progenitor cells exit the cell cycle. In addition, extendingtroke model up to 18 days after the stroke onset, we are ableo see the similar propensity of the behaviors of cells remainingnd exiting the cycle between the stroke and embryonic models,owever, the differences between the two models are obviousFig. 6 for the stroke versus Fig. 11 of Takahashi et al., 1996b);persistent and high proportion of Q + Q symmetric cells are

bserved in the stroke model with a longer duration starting ear-ier than day 2 at 9%, remains steadily increasing, and becomes4% in between S13 and S14 while the Q + Q symmetric cellsn the embryonic is not formed until day 12 (E12) and becomes4% at E15. We conclude that cells leave the cycle earlier andore frequently after stroke compared to the embryonic model.From this study, we have, first, established the temporal pro-

le of the neural progenitor cell cycle kinetics and behaviors overperiod of time after stroke. The profile includes the parameters

or cell cycle evolution, cell cycle numbers at certain intervals,he time of the initial cell leaving and the cell leaving frequency.

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nformation provided from this present study may possibly besed to design the stroke therapeutic treatment. All the ana-ytic approaches proposed to compare the stroke model with thembryonic model, can be used to compare the stroke model withnd without a treatment therapy.

In conclusion, the cell cycle kinetics for the embryonic modelan be used for the stroke model with a goodness-of-fit. TC ishe surrogate measure of TG1. Different cell proliferation pro-les are observed between the stroke and embryonic models. TCvolution is three-fold slower but the cells leave the cycle earliernd more frequently in the stroke model, compared to those inhe embryonic model.

cknowledgements

This work was supported by NIH NINDS grants PO1S23393, PO1 NS42345, RO1NS38292 and RO1HL 64766.he authors thank Renee Williams for editing.

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