Main

Neurodegenerative diseases are an increasing health concern in the aging population, but despite massive research two fundamental questions remain: (1) what are the mechanisms of cell death governing neurodegenerative diseases? The seminal work of Kerr et al.1 and the introduction of the terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) method2 rapidly pinpointed apoptosis as the causative cell death pathway, although the relevance of alternative degeneration mechanisms is becoming increasingly evident.3 (2) How long is the actual cell death process? Although sounding simple, this question has never been answered satisfactorily,4 primarily because it is difficult to test experimentally.5 The questions are obviously connected, not the least since different cell death pathways run on different timescales. For instance, necrosis is seen as a rapid, chaotic, and unordered destruction of the cell taking between a few minutes to 1–2 h to complete,3 whereas apoptosis refers to a comparatively slow, program driven, and orderly cellular disintegration that may take 6–18 h to complete.6, 7 Knowledge on the time course of cell death will define the window-of-opportunity and may thus strongly influence future therapeutic strategies.

To follow cell death, from the first symptoms to the disappearance of a cell, requires sophisticated long-term, live-tissue imaging technology.5 Yet, previous in vivo imaging experiments8 could not determine the precise time frame for cell death, mainly because markers for the beginning of cellular deterioration were lacking, and most knowledge on cell death duration hence comes from dissociated cell cultures.9 The use of intact neuronal tissues for ex vivo analyses presents an alternative and such studies have focused on the late phases of cell death, identified by pyknosis or DNA fragmentation (DAPI or TUNEL staining, respectively) to resolve the time a dying cell takes to completely disappear. This ‘clearance time’ was suggested to range from 1 to 5 h in different models for neurodegeneration.7, 10 However, as pathological alterations in DNA and nuclear structure are detectable only toward the end of the cell death process, the clearance time does not indicate how much time any affected cell has spent going from the initiation to the very end.

We set out to study the duration of neuronal cell death, using the rd1 mouse, a homologous animal model for retinitis pigmentosa (inherited retinal degeneration, RD) with an early, rapid loss of photoreceptors, the light-sensitive neurons of the retina. The rd1 mutation leads to loss-of-activity in rod photoreceptor cyclic guanosine-mono-phosphate (cGMP) phosphodiesterase-6 (PDE6)11 and an accumulation of cGMP, triggering cell death.12, 13 The mechanisms behind hereditary photoreceptor neurodegeneration as such are unsettled and have been suggested to involve apoptosis,14 necrosis,15 as well as non-apoptotic cell death.16 Neuronal degeneration models – including the rd1 mouse – often exhibit a constant rate of cell death, resembling the exponential decay of radioactive elements.17, 18 We built on this knowledge and used markers characteristic for different cell death stages to create a mathematical model, which for the first time allowed estimating the temporal duration of photoreceptor neurodegeneration in vivo. The model predictions were validated using organotypic retinal in vitro culture, demonstrating that the photoreceptor cell death mechanism was considerably slower than both necrosis and apoptosis.

Results

Accumulation of cGMP and photoreceptor cell death in the rd1 retina

cGMP accumulation found in rd1 photoreceptors is seen as the first sign of impending cellular degeneration.13 Cell death is easily detected using the TUNEL method, which detects both necrotic and apoptotic cells.2, 19 A variety of different TUNEL-positive phenotypes were observed: some cells stained only in perinuclear areas, in others the entire nucleus was strongly positive, and yet others showed a very condensed, pyknotic, TUNEL-positive nucleus, all probably relating to different phases of cell death (Figure 1a, Supplementary Figure 1, 2). Interestingly, although high cGMP triggers TUNEL-positive rd1 cell death,12 cGMP did not co-label with TUNEL in photoreceptor cells (Figure 1a). Hence, cGMP and TUNEL labeled two distinct degeneration stages, separated in time by a transition period. Seen from a mechanistic point of view, PDE6 dysfunction caused a temporary rise in cGMP, followed by (yet unidentified) intermediate processes in a transition stage, before the cells turned TUNEL positive to be finally cleared away (Figure 1b). Our methodology thus provided an opportunity to study three different and temporally unique events during an individual photoreceptor cell’s death.

Figure 1
figure 1

cGMP and photoreceptor degeneration: co-stainings in P13 rd1 retina showed no colocalization between cGMP and TUNEL (a). These markers hence labeled two different stages in PDE6 dysfunction induced cell death, separated in time by a transition phase (b). The final clearance of cells characterizes an additional stage in cell death. Images shown are representative for at least five different wt and rd1 animals

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Cellular photoreceptor cGMP accumulation (Figure 2a) was an extremely rare event in wild-type (wt) retina, with only few positive cells observed per retinal cross-section, in particular at early post-natal (P) days. In contrast, the number of cGMP-positive photoreceptors was significantly elevated in the outer nuclear layer (ONL) of the rd1 retina already from P8.

Figure 2
figure 2

Progression of rd1 photoreceptor neurodegeneration: the analysis of cellular cGMP accumulation over time (green curve in a) showed significant rd1 over wt increases from P8 onward. The rate of cell death (red curve) rose significantly from P11 onward. Based on the in vivo data, a model was constructed (b) to simulate the temporal progression of cell death. The model accounted for six different stages (healthy, transition-1, cGMP⊕, transition-2, TUNEL⊕, and dead) each represented by a differential equation. The resulting curves are shown in (b) and allowed estimating the average time an individual cell needed to complete these cell death stages. Note that, since healthy cells and cells in Tr1 are morphologically indistinguishable, the respective data sets were summed up. Increased cell death was reflected in a strong decline of surviving rd1 photoreceptor rows (dark red curve in c) after P13. Wt retina (dark green curve) showed only a minor decrease in ONL rows because of developmental processes. In a second, independent approach, a Gauss curve was fitted to the in vivo cGMP⊕ data and compared with the derived in vivo photoreceptor survival data (d). The 30-h distance between the two peaks was interpreted as the average time a dying cell needs to progress from the cGMP⊕ stage to complete disappearance. Values in (a and c) represent means from n=3–6 independent observations for each genotype and time point; error bars indicate S.E.M.; dotted lines in (a) indicate wt situation; DPN, days post-natal, NS, nonsignificant

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The early post-natal mouse retina displays a measurable amount of developmental photoreceptor cell death,20 seen also here by the TUNEL assay in wt specimens (Supplementary Figure 1A). Although rd1 photoreceptor cell death was numerically higher at P9 when compared with wt, statistically significant differences were found only from P11 onward (Figure 2a).

The cGMP-dependent cell death under study was negative for caspase activity (Supplementary Figure 2) – indicating a non-apoptotic cell death mechanism – and topologically independent (i.e., no clumping of dying cells), suggesting cell-autonomous, non-necrotic processes. The delay between the significant rise of cGMP at P8, and TUNEL at P11, indicated that photoreceptor death execution could take as long as 2 to 3 days.

The percentage of cGMP-positive ONL cells in the rd1 retina peaked at P13, coinciding with the peak of cell death (Figure 2a), after which both cGMP and TUNEL-positive cells declined, but cells with high cGMP remained more numerous than TUNEL-positive cells. As the cellular life-time of a marker determines its detection probability, these results proposed that cGMP positivity lasted longer than TUNEL positivity.

The amount of surviving photoreceptor rows showed a minor decrease in wt retina (because of developmental processes), whereas in rd1 retina photoreceptor numbers strongly declined from P13 onward (Figure 2b). These data served as an index of the clearance of cells.

Modeling photoreceptor cell death kinetics

Based on the in vivo data on cGMP accumulation, TUNEL positivity, and survival of photoreceptors, we constructed a mathematical model for the temporal progression of neurodegeneration in the rd1 retina (Figure 2b). We reasoned that in addition to three phases defined by cGMP, TUNEL, and clearance of cells, at least two additional transition states must exist: (1) a first one relating to unknown molecular events that, while cGMP negative, eventually cause unphysiologically high cGMP. (2) A second one in between cGMP and TUNEL positivity, because there was no apparent colocalization between these two markers (Figure 1a). The model also included an initial stage in which the cells were healthy. Thus, in total six different stages were considered, going from healthy (H) to transition-1 (Tr1) to high cGMP (cGMP⊕) to transition-2 (Tr2) to TUNEL-positive (TU⊕) to dead (D). These stages were represented by a set of differential equations (1, 2, 3, 4, 5, 6), to allow calculating the average life-times for each stage as the inverse of the respective decay constant k. The values for these equation constants representing the five cell death stages are given in Table 1, together with approximate average life-times and parameter errors. The decay constant k3 of cGMP⊕ was considerably larger than the decay of the upstream stage Tr1 (k2), hence the average life time of cGMP⊕ was governed by k2, rather than k3. The model reproduces the progression of cell death as evidenced by cGMP accumulation (sum squared error (SQE)=0.82), TUNEL assay (SQE=0.79), and loss of photoreceptor rows (SQE=0.98). Altogether, the average time for an individual cell to die was predicted to take 83.8±9.4 h (Table 1).

Table 1 Constants and times for the different stages of cell death
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As the loss of photoreceptor cells (Figure 2c) did not follow a strictly exponential decay, we tested an alternative mathematical approach in which k1 was defined by an asymmetric, generalized logistic function rather than a step function. This may reflect photoreceptor biology in the sense that toward the end of differentiation, the risk for a photoreceptor to die increases dramatically, to then remain constant once full differentiation is reached. Indeed, this approach allowed for a better model fit to cell loss in the initial stage of the degeneration, but in later stages the model fit was not significantly improved (Supplementary Figure 3).

Another, independent estimate of how long the cell death process took, was obtained by plotting data on cGMP accumulation (Figure 2a) together with the derived photoreceptor survival data (Figure 2c) and fitting Gauss curves to these data sets (Figure 2d, see Table 2 for parameters). The distance between the peaks of the two curves was approximately 30.2±4.9 h and this was interpreted as the average duration of a cell’s transit from displaying high levels of cGMP until complete disappearance.

Table 2 Constants of fitted Gauss curves
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Progression of zaprinast–cGMP-induced cell death

To test and validate the model predictions, we used organotypic retinal explant cultures derived from wt animals, exposed to the selective PDE6 inhibitor zaprinast.20 Zaprinast raises intracellular cGMP levels and induces wt photoreceptor degeneration similar to what is seen in rd1 retina.12, 21 The effects of zaprinast on cGMP levels and TUNEL positivity were investigated at time points ranging from 8 h to 10 d. A significant rise in cGMP-positive cells was detected after 36 h of zaprinast treatment and at all later time points assessed (Figure 3a). Retinal explantation is a traumatic event and the cultures therefore displayed elevated rates of cell death (TUNEL assay) even under control conditions (Figure 3a). This can be regarded as basal level of cell death. Zaprinast caused a significant rise in cell death, but only after 72 h of treatment.

Figure 3
figure 3

cGMP and photoreceptor degeneration in vitro: retinal explant cultures derived from wt animals were exposed to the selective PDE6 inhibitor zaprinast (Zap) or control (Ctrl) conditions (a). Zap treatment caused an accumulation of cGMP (green curve) only after 36 h, suggesting feedback processes keeping cGMP levels under control initially. The numbers of TUNEL positive, degenerating photoreceptors (red curve) initially remained similar. The number of cGMP-positive cells rose sharply after 36 h of Zap treatment and remained high thereafter. After another 36 h, at P13, the rate of cell death (red curve) increased significantly, a finding that was also reflected in the decreased number of photoreceptor rows (b) in Zap-treated (dark red curve) versus -untreated specimens. n=3–5 retinae from different wt animals; error bars indicate S.E.M.; dotted lines in (a) indicate wt situation

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As a result of the culture situation, the number of photoreceptor rows in the ONL in vitro is decreasing more strongly than it would in vivo, in healthy wt retina (Figure 3b). Yet, zaprinast significantly exacerbated this cell loss from 6 d of treatment onward. The delay of almost 36 h between the zaprinast induced rise of cGMP and the rise of cell death another 36 h later corresponded to both the in vivo findings and the results of mathematical modeling (Figure 4).

Figure 4
figure 4

Major phases during neurodegeneration of an individual photoreceptor cell: genetic or pharmacological inactivation of photoreceptor PDE6 initiated cell death. The first transition stage (Tr1), from the healthy stage to the rise of intracellular cGMP, appeared devoid of specific markers. Yet, it may be associated with decreased outer segment length, as evidenced by staining for cyclic nucleotide channel b1 (Cngb1) in P11 wt and rd1 retina. Both in vitro data and modeling suggested that this stage could last around 36 h in total. Tr1 was followed by the transitory appearance of very high cGMP concentrations (cGMP⊕), a stage that may have lasted another 36 h, and possibly marked the beginning of cell death execution. High cGMP was followed by a second transition stage (Tr2), which took about 5–6 h and was negative for both cGMP and the TUNEL assay. The ensuing DNA fragmentation then caused the cell to turn TUNEL positive (TU⊕), first in the nuclear periphery, then in the entire nucleus, which finally became very small, pyknotic, before it disappeared. This final stage – the clearance phase – from the beginning of a positive reaction in the TUNEL assay to the complete clearance of the cell, lasted another 6–7 h. Together, in vivo and in vitro data, as well as modeling, proposed ≈80 h for the total duration of an individual cell’s death, a time frame that is remarkably long and axiomatically incompatible with execution of either necrosis or apoptosis

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Preservation of cone photoreceptors

In inherited RD in humans, primary rod degeneration is often followed by a secondary, mutation-independent loss of cone photoreceptors. The rd1 mouse also suffers from such a secondary loss of cones. Zaprinast inhibits both rod and cone PDE6 with similar specificity.22 To test how zaprinast treatment affected rod and cone photoreceptors, we performed immunostaining for the cone marker glycogen phosphorylase (GP)23 on retinal cultures after 10 d of zaprinast treatment (i.e., P20). Owing to a somewhat slower retinal development, P20 in vitro corresponds to P18 in vivo. At P18 in wt retina in vivo, approximately 5% of ONL cells stained positively for GP. In relative terms cone numbers were far higher in rd1 retina because of rod loss at this time point in vivo (Supplementary Figure 4A, B; quantified in E).

Higher numbers of cones were also found in zaprinast-treated versus -untreated in vitro retina (Supplementary Figure 4C, D; quantified in E). Even if the relative effect was much smaller than in vivo, this suggested that zaprinast-induced degeneration of ONL cells affected mostly rods, particularly when absolute numbers of cones at P18 were considered (Supplementary Figure 4F).

Discussion

Here, we show for the first time that inherited neuronal cell death in the retina – despite a rapid progression of overall tissue degeneration – is a surprisingly slow process at the level of the individual cell. This affords interesting insights into the underlying mechanism, since a total duration of cell death of approximately 80 h is incompatible with the execution of conventionally assumed necrotic or apoptotic cell death.

cGMP in photoreceptor cell death

High levels of cGMP are known to cause photoreceptor degeneration.13 In the rd1 retina accumulation of cGMP is caused by PDE6 dysfunction,11 and this situation can be replicated by pharmacological inhibition of PDE6.13, 21 The rd1 mouse seems particularly well suited for studies into the temporal characteristics of cell death, because cGMP accumulation provides a clear label for cell death induction, an event otherwise difficult to assess. cGMP has two prototypic targets: cGMP-dependent protein kinase G (PKG)12 and cyclic nucleotide gated (CNG) channels.24 In photoreceptors, cGMP levels are controlled by a physiologic feedback mechanism via activation of CNG channels, resulting in Ca2+ influx, which in turn inhibits guanylyl cyclase (GC) and cGMP production.25, 26 Why this control mechanism fails to keep cGMP in check after prolonged elevation of cGMP is unknown, but may be linked to cGMP-dependent activation of PKG12 and its effects on gene regulation.27 Indeed, extensive gene expression changes were seen in rd1 retina already at P11.28 At the same time, excessively high cGMP-levels may precipitate rd1 cell death via over-activation of CNG channels and subsequent influx of Ca2+ ions.29, 30

Cell death mechanisms

A variety of different mechanisms have been connected with neuronal cell death,3, 14 but necrosis and apoptosis are possibly the best well known and often seen as conceptual counterparts. While necrosis usually is very rapid, taking no more than a few hours to complete,3 apoptosis is somewhat slower, requiring 6–18 h typically.6, 7 Characteristic features of necrosis not seen in apoptosis are activation of the immune system and an inflammation, as well as necrotic clumping of dying cells. Photoreceptor cell death during primary RD is topologically independent and generally there is no evidence for inflammation,16 although an upregulation of innate immunity31 and secondary infiltration of microglial cells into the ONL has been reported.32 Both rd1 and wt retina show small numbers of cells with activated caspase-3 – a key feature of apoptosis and likely related to early post-natal developmental cell death.20 However, rd1 mutation-induced cell death is caspase-independent and devoid of classical apoptotic features.16 It is tempting to speculate that instead of necrosis or apoptosis, we may be facing an alternative cell death mechanism,3 possibly involving metabolic activities of PKG,12 histone deacetylase (HDAC),33 poly-ADP-ribose polymerase (PARP),28 and calpains.34 Our data indicate that this form of cell death is considerably more time consuming than both necrosis and apoptosis. This is in line with findings in caspase-deficient neurons suggesting that caspase-independent cell death may be slower than caspase-mediated apoptosis.35 An alternative explanation for the exceptionally slow progression observed here, could be that – maybe in the initial phases – the execution of cell death is counteracted by endogenous survival mechanisms.36

The kinetics of photoreceptor death

Rod photoreceptors in the mouse are born over a 16-d period ranging from 7 d before to 9 d after birth,37 and one could hypothesize that the lifespan of rd1 photoreceptors might be constant and predetermined by their respective date of birth. On the other hand, rd1 photoreceptor degeneration at the tissue level is governed by a constant rate of cell death and first-order kinetics,17 with one cell’s death entirely independent from another cell’s death. This is very similar to what is observed in the exponential decay of radioactive elements and hence, the lifespan of an individual photoreceptor cell will be random and governed by probabilistic and stochastic effects.38 In this model, the average life-span of a cell population will be governed by the severity of the (genetic) insult.18

The kinetics of cell death presented here are generally compatible with the ‘one-hit-model’.17 We introduced several novel parameters to this model, including different cell death stages and a variable risk for the initial stage. Indeed, we found that an individual rd1 photoreceptor’s risk to die may increase during early post-natal differentiation and reach a constant value only once the fully differentiated state is reached. This would result in an apparent wave of cell death at the time of differentiation and may serve to explain the center to periphery progression of the rd1 degeneration, which follows the pattern of retinal development.

Zaprinast treatment: simulation of an inherited disease?

Studies of inherited RDs can be helped by disease simulation on different genetic backgrounds or in different species. Pioneering works by Lolley et al.13 used the general PDE inhibitor 3-isobutyl-1-methylxanthine to pharmacologically induce selective, cGMP-dependent photoreceptor degeneration in Xenopus embryos. In mammalian systems, zaprinast is a highly selective PDE6 inhibitor,22 which – as used here (100 μM) – causes cGMP accumulation and exclusive photoreceptor death.12, 21 Interestingly, and very similar to the in vivo characteristics of the rd1 retina, zaprinast affected sub-populations of photoreceptor cells at different times, which also in vitro might be connected to ongoing development of photoreceptors,37 superseded by stochastic effects.38

Unexpectedly, the dramatic rise of photoreceptor cGMP levels was not an immediate effect of zaprinast treatment. Although zaprinast increases Ca2+-levels cGMP dependently in mouse photoreceptors within minutes of application,39 a catastrophic rise of cellular cGMP to levels detectable with immunostaining appeared only after 36 h and beyond. These non-linear kinetics of cGMP accumulation suggest that feedback control mechanisms, such as the CNG-Ca2+-GC loop,25 prevent the rise of cGMP for approximately 1.5 d, before a changing metabolism causes cGMP levels to go unchecked.

Contrary to what might be expected from its inhibitory capacity on both rod and cone PDE6 isoforms,20 zaprinast did not seem to affect cones. This may point at an increased resistance of cones to higher cGMP levels40 but could also be due to their later differentiation.41 Anyhow, within the time frame of our experiments, in vitro application of zaprinast on wt retina faithfully reproduced the selective rod photoreceptor loss seen in rd1 retina in vivo. This approach could prove very useful to study retinal neurodegenerative mechanisms, for instance on non-degenerating knock-out rodent models21 or on large, non-rodent animal models.

The slow death of photoreceptors: three phases in cell death

Our different experimental approaches delineate three major phases in the progression of cell death and give estimates on their duration (Figure 4).

  1. 1

    The initiation phase: this phase of cell death is inherently difficult to study because of our lack of understanding of relevant metabolic processes and suitable markers. Nevertheless, both in vivo and in vitro data suggested that after inhibition or genetic inactivation of PDE6, cGMP levels rise but are maintained within physiological limits by feedback control mechanisms.25 Possibly, the cell is not yet committed to die at this stage, although toward its end the feedback control is shut down and cGMP rises beyond physiological limits. PKG is involved in the degeneration12 and has a 100-fold higher sensitivity to cGMP compared with CNG channels.42 PKG could therefore have a preeminent role during this phase, which our data suggest takes about 36 h.

  2. 2

    The execution phase: once the cellular metabolism has switched to allow for a catastrophic rise of cGMP, the cell likely becomes committed to die and enters the death execution phase. This phase may be characterized by an over-activation of HDAC33 and subsequently PARP,28 resulting in chromatin changes and rearrangements. In addition, high cGMP likely acts on CNG channels,30 to cause excessive Ca2+ influx29 and calpain activation.34 The execution phase may last between 36 and 48 h. Similarly, chick embryo neuronal precursor cells became committed to die approximately 2 d before clear signs of impending cell death were observed.6

  3. 3

    The clearance phase: once the cell has reached the final stages of cell death, extensive DNA fragmentation sets in, as evidenced by the TUNEL assay. It is worth mentioning that the TUNEL assay generally labels dying cells, including in necrosis19 and apoptosis.2 Our model suggests that it may take about 4 h until a maximal degree of DNA fragmentation is reached, and from then on the nucleus becomes more and more condensed and pyknotic until the cellular debris is completely removed, a stage that may take another 3 h. This is in agreement with studies on clearance of TUNEL-positive cells in rat and mouse neocortex, estimated to last between 1 and 4 h,10 and clearance of pyknotic ganglion cells during retinal development within 1 h.43

Even with cautious extrapolation to the human situation, where RD caused by homologous mutations may take several decades to complete, the observed delays suggest a window-of-opportunity sufficiently large for therapeutic interventions in patients. They also confirm previous observations that photoreceptor metabolism may suffer significantly before evident cell loss leads to first clinical symptoms.44 With respect to potential neuroprotective treatments, targeting of metabolic processes36 during initiation or early execution phases may be particularly promising.

Conclusion

Our study for the first time provides consistent estimates on the duration of neuronal cell death in a hereditary neurodegenerative disease. With a period of about 80 h – from initiation, to cGMP accumulation, to TUNEL-positive reaction, to clearance – the time an individual cell needs to die is remarkably long and points toward execution of non-necrotic, non-apoptotic, and relatively slow cell death mechanisms. This has clear relevance for the development of potential therapies, for instance in acute neurodegenerative disorders such as stroke or spinal-cord injury, where the time frame for cell death will directly determine the window-of-opportunity and potential therapeutic options. Similarly, for chronic and inherited forms of neurodegeneration, knowledge on the temporal progression of cell death will provide insights into the underlying degenerative mechanisms and again define possible treatment approaches.

The mathematical model presented here may be extended to also include other processes causally involved in cell death, such as enzymatic activities of PKG, HDAC, PARP, and calpain. Combined with the use of transgenic biosensors for cGMP and Ca2+,39 this could allow precise delineation of the temporal progression and interdependence of different metabolic processes causing cell death. Furthermore, the current experimental approach and type of mathematical modeling may be used to study cell death in general, provided at least two temporally distinct degeneration markers can be identified.

Materials and Methods

Animals

C3H rd1/rd1 (rd1) and control C3H wt mice were housed under standard white cyclic lighting, had free access to food and water, and were used irrespective of gender. All procedures were performed in accordance with the local ethics committee at Tübingen University (§4 registration from 23 January 2008), and the ARVO statement for the use of animals in ophthalmic and visual research. All efforts were made to minimize the number of animals used and their suffering. Day of birth was considered as post-natal day (P) 0.

Organotypic retinal explant culture

Retinae from P5 rd1 and wt animals were used to generate retinal explants as described before.21, 33 Explanted retinae were cultured on Millicell HA culture dish filter inserts (Millipore, Carrigtwohill, Cork, Ireland; PIHA03050) with the retinal pigment epithelium facing the membrane. Inserts were put into six-well culture plates and incubated in R16 nutrient medium with supplements at 37 °C. Every second day the full volume of nutrient medium, 1.5 ml per well, was replaced with fresh medium. After 5 d in vitro (i.e., P10), the two retinal explants obtained from one animal were split into two groups, one was exposed to 100 μM zaprinast in DMSO (treatment group), one was exposed to DMSO only (control group; 0.3% DMSO). The culture period was ended by immediate fixation in 4% paraformaldehyde in PBS at post-treatment time points ranging from 8 h to 10 d.

Immunostaining and TUNEL assay

Retinal cryosections obtained either from in vivo animals or following in vitro explant culture, were dried for 30–60 min at 37 °C. Subsequently, the tissue was rehydrated in PBS, and pre-incubated for 1 h at room temperature in blocking solution, containing 10% normal serum, and 0.1% or 0.3% Triton in PBS (PBST). Immunostaining was performed overnight at 4 °C, using primary antibodies against cGMP (provided by Harry Steinbusch, Maastricht University, The Netherlands), Cngb1 (provided by Stylianos Michalakis, Ludwig Maximilian University of Munich, Germany), and GP (provided by Brigitte Pfeiffer-Gugliemi, University of Tübingen, Germany) diluted 1 : 500 in blocking solution. The tissue was rinsed with PBST, and incubated for 1 h with a corresponding, Alexafluor-488 conjugated, secondary antibody (1 : 200–1 : 750, Life technologies, Darmstadt, Germany), diluted in PBST. Sections were rinsed in PBS, and mounted in Vectashield with DAPI for nuclear counterstaining (Vector Laboratories Inc., Burlingame, CA, USA). The TUNEL assay was performed on using an in situ cell death detection kit conjugated with tetra-methyl-rhodamine or fluorescein isothiocyanate (Roche Diagnostics, Mannheim, Germany). For controls terminal deoxynucleotidyl transferase enzyme was either omitted from the labeling solution (negative control), or sections were pre-treated for 30 min with DNAse I (Roche, 3 U/ml) in 50 mM Tris-HCl, pH 7.5, 1 mg/ml BSA to induce DNA strand breaks (positive control). Although negative control gave no staining, positive control stained all nuclei in all layers of the retina.28

Microscopy, cell counting, and statistical analysis

Morphological observations and routine light microscopy were performed on a Zeiss Imager Z1 Apotome Microscope (Zeiss, Oberkochen, Germany), equipped with a Zeiss Axiocam digital camera. Images were captured using Zeiss Axiovision 4.8 software; image overlays and contrast enhancement were done using Adobe Photoshop CS5. Images shown in figures are representative for least three different animals for each genotype/treatment. Percentages of TUNEL-positive cells were assessed in a blinded fashion as reported previously.33, 34 The mean value for photoreceptor rows in the ONL was determined using DAPI staining on six different locations in close proximity to the optic nerve (in vivo) or in central areas of the retinal explant (in vitro). To generate the data set for dead cells and to account for early post-natal developmental cell death, the wt photoreceptor row count was subtracted from the respective rd1 values. Values are mean±S.E.M. Statistical significance was tested using one-way ANOVA with Bonferroni correction and GraphPad Prism 5 software (San Diego, CA, USA), significance levels were: *P<0.05, **P<0.01, and ***P<0.001.

Mathematical models

For modeling cell death progression and estimating its duration, irreversible first-order kinetics were assumed.17 The model consisted of six stages, termed ‘healthy’(H), ‘transition state-1’ (Tr1), ‘cGMP-positive’ (cGMP⊕), ‘transition state-2’ (Tr2), ‘TUNEL-positive’ (TU⊕) and ‘dead’ (D). The changes in the six stages are represented by an ordinary differential equation system:

k1, k2, k3, k4, and k5 stand for the decay constants of the respective equation and cell death stage (see additional considerations in results). The average life-time τx of a given cell death stage x will be the inverse of the respective decay constant kx. This model was implemented in Matlab 2010a (Mathworks, Natick, MA, USA). The system of differential equations was solved using ‘ode45’ algorithm (explicit Runge–Kutta based).

The SQE was calculated using equation (8) where y represents the measured values of healthy, cGMP-positive, TUNEL-positive and dead cells stages, yp represents predicted values of these variables, whereas n stands for the total number of observations. For the SQE calculation, we summed the predicted values for the healthy the Tr1 state, because these two states were indistinguishable experimentally.

To fit the parameters, we used the Nelder–Mead Simplex Algorithm (‘fminsearch’) to minimize SQE, and to match the model as closely as possible to the observed cell death processes. Initially, decay constants and starting time t0 of the system of differential equations were part of the optimization and subsequent bootstrapping. From the probability density function of possible start times, we choose the time with the highest probability below 10 d post-natal, which was 9.84 d. For biological reasons, solutions beyond 10 d were not considered. The final parameters were then optimized with a fixed starting time t0 of 9.84 d.

To model the continuous decay of the healthy stage, an extension of the above described model was tested, which used a generalized logistic function equation (9) instead of a constant k1 (Supplementary Figure 4). The simulation of this model and estimation of the generalized logistic functiońs parameters were performed using COPASI – software45 and the simulated annealing algorithm for parameter estimation. The decay constants k2–k5 were left unchanged.

An alternative, empirical approach is given in a second model, which provides an estimate of the ’life-time’ of the sick (S) state of a cell (i.e., the cell death execution phase). The ‘life-time’ of the sick cells Δt was assumed to be the time t2 (peak of cell death) minus the time t1 (peak of cGMP-positive cells). To estimate the time point t1 with the maximum number of cells that are in the sick state S(t), a Gauss function equation (10) was fitted to the normalized cGMP⊕ data peak, where f1 is a parameter for peak height and σ1 represents peak width. The maximal increase in dead cells was determined in the same way by fitting a Gauss function equation (11) to the derivative of the dead cell data. Δt equation (12) gives the average life-time of sick cells.

The second model was realized in Microsoft Excel 2010 (Microsoft, Unterschleissheim, Germany) using the ‘Solver’ functionality with genetic algorithms and SQE to fit the functions to the measured data.