ABSTRACT For most neurodegenerative diseases the precise duration of an individual cell’s death is unknown, which is an obstacle when counteractive measures are being considered. To address

this, we used the _rd1_ mouse model for retinal neurodegeneration, characterized by phosphodiesterase-6 (PDE6) dysfunction and photoreceptor death triggered by high cyclic

guanosine-mono-phosphate (cGMP) levels. Using cellular data on cGMP accumulation, cell death, and survival, we created mathematical models to simulate the temporal development of the

degeneration. We validated model predictions using organotypic retinal explant cultures derived from wild-type animals and exposed to the selective PDE6 inhibitor zaprinast. Together,

for these neurons. SIMILAR CONTENT BEING VIEWED BY OTHERS THE TEMPORAL PROGRESSION OF RETINAL DEGENERATION AND EARLY-STAGE IDEBENONE TREATMENT IN THE PDE6BRD1/RD1 MOUSE MODEL OF RETINAL

DYSTROPHY Article Open access 23 January 2024 PATHOGENIC MECHANISMS CONTRIBUTING TO THE VULNERABILITY OF AGING HUMAN PHOTORECEPTOR CELLS Article 02 June 2021 HBEGF-TNF INDUCE A COMPLEX OUTER

RETINAL PATHOLOGY WITH PHOTORECEPTOR CELL EXTRUSION IN HUMAN ORGANOIDS Article Open access 19 October 2022 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. 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. 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 _k_3 of cGMP⊕ was considerably larger than the decay of the upstream stage Tr1 (_k_2), hence the average life time of

cGMP⊕ was governed by _k_2, rather than _k_3. 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). As the loss of photoreceptor cells (Figure 2c)

did not follow a strictly exponential decay, we tested an alternative mathematical approach in which _k_1 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. 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. 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). 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 _μ_M) – 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 _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 _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 _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 _μ_M 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: _k_1, _k_2, _k_3, _k_4, and _k_5

stand for the decay constants of the respective equation and cell death stage (see additional considerations in results). The average life-time _τ_x of a given cell death stage _x_ will be

the inverse of the respective decay constant _k_x. 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,

_y_p 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 _t_0 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 _t_0 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 _k_1 (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 Δ_t_ was assumed to be the time _t_2 (peak of cell death) minus the time _t_1 (peak of cGMP-positive

cells). To estimate the time point _t_1 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 _f_1 is a parameter for peak height and _σ_1 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. Δ_t_ 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. ABBREVIATIONS * cGMP: cyclic guanosine-mono-phosphate * d: days * DPN: days

post-natal * GP: glycogen phosphorylase * HDAC: histone deacetylase * ONL: outer nuclear layer * PDE6: phosphodiesterase-6 * PARP: poly-ADP-ribose-polymerase * PKG: protein kinase G * RD:

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process based on the analysis of the Fisher information matrix. _J Theor Biol_ 2006; 238: 111–123. Article  Google Scholar  Download references ACKNOWLEDGEMENTS We thank T Euler, B

Arango-Gonzalez and D Trifunović for helpful comments and discussions. This work was supported by grants from DFG (Pa1751/4-1, 1-1), and Open Access Publishing Fund of Tuebingen University,

EU (DRUGSFORD: HEALTH-F2-2012-304963), CIN (PP2009-20), and Kerstan Foundation. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Institute for Ophthalmic Research, University of Tübingen,

Tübingen, Germany A Sahaboglu, J Dietter, S Bernhard-Kurz, M Ueffing & F Paquet-Durand * Institute of Food Science and Biotechnology, University of Stuttgart Hohenheim, Stuttgart,

Germany O Paquet-Durand & B Hitzmann * Skin Clinic, University of Tübingen, Tübingen, Germany K Dengler * Department of Clinical Sciences, Lund, University of Lund, Lund, Sweden P AR

Ekström Authors * A Sahaboglu View author publications You can also search for this author inPubMed Google Scholar * O Paquet-Durand View author publications You can also search for this

author inPubMed Google Scholar * J Dietter View author publications You can also search for this author inPubMed Google Scholar * K Dengler View author publications You can also search for

this author inPubMed Google Scholar * S Bernhard-Kurz View author publications You can also search for this author inPubMed Google Scholar * P AR Ekström View author publications You can

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Correspondence to F Paquet-Durand. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no conflict of interest. ADDITIONAL INFORMATION Edited by A Verkhratsky Supplementary

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Sahaboglu, A., Paquet-Durand, O., Dietter, J. _et al._ Retinitis pigmentosa: rapid neurodegeneration is governed by slow cell death mechanisms. _Cell Death Dis_ 4, e488 (2013).

https://doi.org/10.1038/cddis.2013.12 Download citation * Received: 09 November 2012 * Revised: 21 December 2012 * Accepted: 03 January 2013 * Published: 07 February 2013 * Issue Date:

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retina * cGMP