Inactivation of nitric oxide by rat cerebellar slices

Abstract

Nitric oxide (NO) functions as an intercellular messenger throughout the brain. For this role to be performed efficiently, there must be a mechanism for neutralizing NO, but whether an active biological process exists, or whether NO is lost mainly through diffusion is unclear. To investigate this issue, rat cerebellar slices were exposed to constant levels of NO and the cGMP generated within the slice used as an indicator of NO concentrations therein. NO was about 1000-fold less potent in slices (EC₅₀, 1 μm) than in separated cells from the same tissue (EC₅₀, 1.6 nm), consistent with access of NO to the slice interior being greatly hindered by inactivation. Supporting this interpretation, immunohistochemical analysis indicated a marked concentration gradient of cGMP across the thickness of slices exposed to subsaturating NO concentrations, signifying a marked NO gradient. Several known NO-degrading processes, including reaction with lipid peroxyl radicals, erythrocytes and superoxide ions, were eliminated as contributing factors, indicating a novel mechanism. A diffusion–inactivation model was used to estimate the kinetics of NO consumption by the slices. The best fits to experimental data indicated a Michaelis-Menten-type reaction having a V_max of 1–2 μm s⁻¹ and a K_m of around 10 nm. The rates predict that inactivation would impose a very short half-life (<10 ms) on NO in physiological concentrations (up to 10 nm) and that it would play an important role in shaping the NO concentration profiles when it is synthesized by multiple nearby sites.

In the brain, synthesis of the intercellular signalling molecule nitric oxide (NO) is stimulated by increased intracellular calcium levels, for example following activation of NMDA receptors (Garthwaite et al. 1988). Being small and non-polar, NO can readily cross cell membranes to reach neighbouring cells. By binding to a haem moiety on its receptor, the NO-activated guanylyl cyclase (NO_GC), NO causes synthesis of the second messenger cGMP, which has a number of physiological targets, including cGMP-dependent protein kinase, cyclic nucleotide-gated channels and phosphodiesterases (Francis et al. 2005). The NO–cGMP pathway has several neurophysiological roles; for example, in synaptic plasticity, neuronal development and the modulation of membrane excitability (Hall & Garthwaite, 2005). At high concentrations, NO causes cellular damage by inhibiting mitochondrial respiration and generating reactive free radicals (Keynes & Garthwaite, 2004).

Protection against NO-induced toxicity and control over the spatial and temporal spread of NO under physiological conditions necessitates regulation of the NO concentration, which is dictated by the rates of synthesis and loss. The synthesis pathway, through nitric oxide synthase (NOS) is relatively well characterized at the enzyme level (Alderton et al. 2001), but how the NO signal is terminated remains unclear. Reaction with oxyhaemoglobin in erythrocytes in nearby blood vessels is likely to play a role (Lancaster, 1994; Liu et al. 1998a) and diffusion away from the site of synthesis has also been considered to be important (Wood & Garthwaite, 1994; Lancaster, 1994). The reaction of NO with oxygen in aqueous solution, termed autoxidation, is too slow to be of physiological importance but partitioning of the reactants into lipid membranes may accelerate the process sufficiently to contribute to tissue NO breakdown (Liu et al. 1998b). The reaction of NO with superoxide (O₂⁻) is almost diffusion limited (Kissner et al. 1997) but is limited physiologically by high concentrations of superoxide dismutase (SOD) which scavenges O₂⁻ (Beckman & Koppenol, 1996; Wink & Mitchell, 1998), such that this reaction is likely to be of greater significance in pathophysiological situations when O₂⁻ production is enhanced, for example during leakage of electrons from the respiratory chain during reperfusion following ischaemia, or from NADPH oxidase in activated microglia (Sankarapandi et al. 1998). NO also reacts at an almost diffusion-limited rate with lipid peroxyl radicals (O'Donnell et al. 1997), which are generated at increased rates during pathological conditions (Moosmann & Behl, 2002) and which account for a component of NO consumption by acutely prepared brain cell suspensions and brain homogenates (Keynes et al. 2005a). Enzymatic NO consumption by lipoxygenases and prostaglandin H synthase (PGHS) in reticulocytes and platelets (O'Donnell et al. 1999, 2000) and unidentified flavohaemoprotein(s) in mammalian cell lines (Gardner et al. 2001; Hallstrom et al. 2004), endothelial cells (Schmidt & Mayer, 2004) and cultured cerebellar glia (Keynes et al. 2005b) have also been reported.

All the above studies of NO inactivation have relied on dispersed tissue preparations and the relevance of any of the processes to intact brain has not been examined. Brain slices, which retain the balance of cell types and connectivity of the intact brain, provide a better model of intact brain than do isolated cells. Indirect evidence supports the existence of NO consumption processes in intact brain tissue, as organotypic hippocampal slice cultures are resistant to levels of NO that are toxic to dispersed cells (Keynes et al. 2004), but no direct evidence for slice NO consumption has yet been reported. Here, we report that cerebellar slices rapidly inactivate NO by a mechanism that is independent of lipid peroxidation and other known mechanisms of NO consumption. The apparent kinetics of NO inactivation predict that this inactivation process will be influential in shaping physiological NO signals when several sources are active.

Methods

All compounds were purchased from Sigma (Poole, UK) unless stated.

Cerebellar slice preparation

Experiments used brain tissue from 8-day-old Sprague-Dawley rats. The animals were killed by decapitation as approved by the British Home Office and the local ethics committee. Sagittal slices of cerebellum (400 μm thick) were prepared using a McIlwain tissue chopper. Slices were incubated in shaking, gassed (95% CO₂–5% O₂) artificial cerebrospinal fluid (aCSF) at 37°C containing (mm): NaCl 120, KCl 2, NaHCO₃ 26, MgSO₄.7H₂O 1.19, KH₂PO₄ 1.18, glucose 11, CaCl₂ 2, l-nitroarginine 0.1 and kynurenic acid 1. After 1 h recovery, slices were transferred to kynurenic acid-free aCSF. All slice experiments were carried out in gassed aCSF at pH 7.45 at 37°C. In the relevant experiments, slices were preincubated for 30 min with the lipid peroxidation inhibitors Trolox and diethylenetiaminepentaacetic acid (DTPA) or for 15 min with sodium cyanide (NaCN) and diphenyleneiodium chloride (DPI).

NO measurement

For NO measurements, samples (1 ml) were incubated in a stirred vessel (at 37°C) equipped with an NO electrode (ISO-NOP, World Precision Instruments, Stevenage, UK). The chamber was open and samples were continuously gassed over their surface with 95% CO₂–5% O₂. NO was delivered using the NONOate donors spermine NONOate (Sper/NO), 2-(N,N-diethylamino)-diazenolate-2-oxide, diethylammonium salt (DEA/NO) and (Z)-1-[2-(2-aminoethyl)-N-(2-ammonioethyl)amino]diazen-1-ium-1,2-diolate (DETA/NO; all Alexis Biochemicals, Nottingham, UK). Stock solutions at 100 times the desired final concentration were prepared in 10 mm NaOH and were kept on ice prior to use. Experiments on tissue blocks and homogenates were carried out in the presence of 1000 U ml⁻¹ superoxide dismutase, 100 μm DTPA and 100 μm Trolox.

Haemoglobin–agarose preparation

Haemoglobin (Hb)-coated beaded agarose (Hb–agarose) was used to scavenge bath NO. A 50% v/v suspension was prepared by washing by fltration (0.4 μm pore) with 20 volumes of Tris-HCl (pH 7.4) and resuspension in this same buffer. The Hb was reduced using 10 mm sodium dithionite, which was removed by filtration and washing with more than 50 volumes of aCSF. Finally, the Hb–agarose was resuspended in aCSF to make a 50% v/v suspension and kept on ice until use. Hb reduction was confirmed spectrophotometrically, by observation of the shift in the Soret peak at 412–415 nm (Feelisch et al. 1996). Immediately before the beads were used, the aCSF was aspirated and replaced with freshly gassed aCSF at 37°C.

cGMP measurement and visualization

Slices were inactivated by immersion in boiling buffer (50 mm Tris-HCl and 4 mm EDTA, pH 7.4) and then sonicated. A sample was taken for protein determination and the remainder was centrifuged at 10 000 g for 5 min at 4°C. cGMP in the supernatant was measured by radioimmunoassay. Protein concentrations were measured by the bicinchoninic acid method (BCA Protein Assay Kit, Pierce, IL, USA). cGMP levels were normalized to the response to 100 μm DEA/NO, which generates a maximum cGMP response in a cerebellar slice (data not shown).

Visualization of cGMP was accomplished by immunocytochemistry (de Vente et al. 1998). Slices were fixed for 2 h in 4% paraformaldehyde in 0.1 m phosphate buffer (pH 7.4) at room temperature (21-24°C). Cryoprotection was achieved by overnight incubation in 20% sucrose solution in the phosphate buffer at 4°C. The tissue was then frozen in Tissue-Tek OCT (Raymond Lamb, Eastbourne, UK). Frozen sections (10 μm thick) were cut perpendicular to the plane of the slice and collected on chrome alum/gelatin-coated microscope slides. Slides were rinsed in Tris-buffered saline (TBS) with 0.1% Triton X-100 (pH 7.6) and incubated first with normal donkey serum for 30 min, then with the primary sheep anti-cGMP antibody overnight at 4°C (1: 8000, a gift from J. de Vente, University of Maastricht, the Netherlands). After rinsing, the sections were incubated with donkey anti-sheep biotinylated secondary antibody for 1 h at room temperature (1: 200). Slides were washed and incubated with Vectastain elite ABC complex for 45 min, stained for 4 min with 0.05% 3,3′-diaminobenzidine then counterstained with Mayers haemalum for 15 s. Finally, slides were air-dried and mounted in DPX mounting medium.

Lipid peroxidation assay

Each cerebellar slice was inactivated by addition to 400 μl ice-cold trichloroacetic acid (10% w/v). After homogenization by sonication and then centrifugation at 2000 g for 10 min, thiobarbituric acid reactive species (TBARS) were detected according to a published protocol (Esterbauer & Cheeseman, 1990). Briefly, 300 μl supernatant, 10 μl butylated hydroxytoluene (BHT, 10% w/v) and 300 μl thiobarbituric acid were mixed and heated to 90°C for 20 min, cooled to room temperature and 200 μl transferred to a 96-well plate. Absorbance at 532 and 600 nm was measured spectrophotometrically. The ratio of the difference of the absorbances at 532 and 600 nm to that at 600 nm was compared to that generated from malonaldehyde standards.

Modelling

All partial differential equations were solved using the pdepe function in MATLAB 6.5 (The Mathworks Inc., Natick, MA, USA). All other modelling used Mathcad 2001i (Mathsoft, Bagshot, UK).

NO profile across the slice

Diffusion of NO into the slice from the bathing medium approximates to one-dimensional diffusion from two infinite planar sources of NO, as the vast majority of NO entering the slice will be from the slice surfaces rather than the edges. As such, it can be described by Fick's second law of diffusion. The overall change in concentration over time at a certain position in the slice (x) is given by the net of diffusion and inactivation by the slice. Were the inactivation process first order with respect to NO, this would be described by eqn (1), if it were Michaelis-Menten in nature, eqn (2) would apply.

(1)

(2)

D is the diffusion constant for NO (3.3 × 10⁻⁵ cm² s⁻¹; Malinski et al. 1993), [NO] is the NO concentration and k, the first order rate constant, and the Michaelis-Menten parameters V_max and K_m are the inactivation parameters to be determined. Numerically solving this equation to steady state, with NO at the edge of the slice fixed as the bath NO concentration, generates predicted profiles of NO concentration across the slice.

cGMP profile across the slice and predicted NO concetration–cGMP response curves

The cGMP concentration at each position in the slice can be calculated from the NO concentration from the Hill equation for NO_GC (eqn (3)). Normalizing cGMP levels to the maximum that can be produced (cGMP_max = 1), the concentration at which it is half-maximum (K_GC) is 1.6 nm and the slope (n) is 2 (parameters were found by fitting the NO–cGMP data in Fig. 1C with eqn (3)). Normalization means that cGMP becomes a dimensionless variable, representing the fraction of the maximum cGMP concentration that is produced.

Figure 1. Quantification of cGMP generation in cerebellar slices.

A, NO concentration on addition of Sper/NO (concentrations as labelled) to aCSF. B, cGMP levels in cerebellar slices exposed to constant levels of NO generated by pre-equilibrated Sper/NO (concentrations as labelled). C, cGMP produced in dispersed cells and slices in response to applied NO. Data represent means ±s.e.m., n= 4–21.

(3)

The fraction of the maximal cGMP response produced in the whole slice can be calculated by expressing the area under each cGMP profile as a proportion of the total area (for a 400 μm slice, 400 μm × 1 = 400 μm²). Calculation of this value for a range of bath NO concentrations allows the generation of a predicted NO concentration–cGMP response curve for cerebellar slices. A family of such curves was generated using a number of different values for the V_max for NO decay. Quantification of inactivation can be achieved by comparison of the experimental data with the predicted curves, based on the diffusional model above.

Accounting for release of NO from Sper/NO within the slice

A complication of the method using steady-state NO delivery is that Sper/NO may enter the slice and release NO within the tissue, increasing cGMP production above that predicted here. The measured cGMP (cGMP_total), expressed as a fraction of the maximum, is therefore given by eqn (4), where cGMP_bathNO is that predicted from eqns (2 and 3) to be produced by diffusion of NO into the slice from the bathing solution and cGMP_donorNO is that produced from NO released from the donor within the slice.

(4)

To investigate how much cGMP is produced by donor release during the 2 min time course used previously, Hb–agarose was used to scavenge external NO, isolating the effect of NO release from donor within the tissue. The beads were of a diameter of 45–85 μm (mean, 60.2 ± 3.5 μm, n = 11) and so could not penetrate the tissue. A 40% v/v bead suspension was able to scavenge all external NO in the presence of up to 1 mm Sper/NO for the period of the experiment (not shown). cGMP was measured following 2 min exposure to Sper/NO (0–1 mm), in the presence of 40% v/v Hb–agarose. The cGMP levels were then normalized and plotted against both Sper/NO concentration and the NO produced from each Sper/NO concentration with no Hb–agarose present. These data were fitted with a logistic function, constrained to a minimum cGMP of 0 and a maximum of 1 (eqn (5)). A best fit was achieved with NO₀ = 2.94 and p = 8.6. cGMP_beads denotes the cGMP produced in the presence of Hb–agarose. This function was used to predict the relative effect of donor release within the slice at all bathing concentrations of NO simulated.

(5)

The rapid diffusion of bath NO results in steady-state cGMP levels within 1 min (Fig. 1B), while NO release from donor alone takes 10 min to generate stable cGMP levels (not shown). As NO penetrates the slice much faster than does the donor, it is possible to first calculate the cGMP produced from NO diffusion and inactivation (cGMP_bathNO; from eqns (2 and 3)) and then to increase this according to eqn (5), to account for release from the donor. As NO accesses the slice first, in certain regions of the tissue, NO_GC will already be producing cGMP at its maximal rate, such that there can be no additional effect of NO release from the donor within the slice. In regions where the NO_GC is not already going at its maximal rate, however, donor release can have an additional effect.

If the simplifying assumptions are made, that (i) a given part of the slice is either empty or full of cGMP and (ii) the donor is equally distributed throughout the slice, then the fraction of the tissue that has no cGMP is given by 1 (the normalized maximum cGMP produced in the slice) minus the cGMP produced by diffusion of NO from the bath (cGMP_bathNO). The cGMP produced by release of NO from the donor is therefore given by eqn (6).

(6)

A failure to meet the above assumptions will simply reduce the effect of donor release within the slice beneath that predicted here, such that this model represents the maximum possible contribution of internal NO release. Combining eqns (4 and 6) gives eqn (7).

(7)

All the variables on the right hand side of eqn (7) can be now calculated from the bath NO concentration and the cGMP_bathNO predicted from eqns (2 and 3). Adjusting the predicted concentration–response curves in this way steepens the slopes considerably, such that high values of V_max produce curves that converge close to the experimental data.

Quantifying NO consumption by tissue blocks

When DETA/NO is added to a suspension of tissue blocks, a number of processes are at play: NO is being released into the suspension at a given constant rate, which is given by eqn (8), where x is the stoichiometry of NO release from DETA/NO (1.6; Griffiths & Garthwaite, 2001) and k_DETA/NO is the rate constant of release from DETA/NO, and is given by eqn (9). The half-life (t_1/2) for DETA/NO at 37°C is 20.5 h.

(8)

(9)

At steady state the NO level is not changing, so the overall rate of breakdown must equal the rate of release. One pathway by which NO is broken down in the solution is via autoxidation, which is given by eqn (10), where k_autox = 13.6 × 10⁶m⁻² s⁻¹ (Schmidt et al. 1997).

(10)

The biological rate of NO breakdown is therefore given by the overall rate of breakdown minus that due to autoxidation (eqn (11)).

(11)

As predicted above, biological NO consumption is also given by eqn (2), but as diffusion and inactivation by the tissue set up a concentration gradient throughout the tissue, it is not simple to calculate the rate of inactivation of a given block. Equations commonly used in biochemical engineering for the analysis of immobilized enzyme systems (Shuler & Kargi, 1992) do, however, allow us to test whether the V_max and K_m derived from the cGMP data are consistent with the NO plateau present in the bathing solution of tissue blocks. In order to do this, we determine the ratio between the overall rate of biological inactivation in the solution (given by eqn (12)) and that which would arise, were there no diffusion limitations (e.g. if the inactivation process was uniformly distributed throughout the solution, rather than being encapsulated in blocks). The ratio between these two rates is termed the effectiveness factor (η).

(12)

V′_max is related to V_max but will change depending on the protein concentration (Prot) in mg ml⁻¹.

(13)

The dimensionless variable β (eqn (14)), the Thiele modulus (φ; eqn (15)), is calculated from the K_m and V_max for NO consumption, the diffusion coefficient, the ‘radius’ of a block (R; 200 μm) and the external NO concentration ([NO]_o).

(14)

(15)

The calculated values of β and Ф can be used to find η by reading from published graphs. V′_max can be calculated from eqn (12) and the protein concentration which would give this level of inactivation can be calculated from eqn (13). Plots can therefore be constructed of NO plateau versus protein concentration, as for the experimental data.

Modelling autoxidation

If inactivation of NO by the slice is due to autoxidation, its concentration throughout the slice will be given by eqn (16).

(16)

O₂ was assumed to be the same concentration throughout the slice as found in gassed aCSF (1 mm; Vanderkooi et al. 1991). As the slice consumes O₂, this overestimates the rate of autoxidation and therefore any contribution of autoxidation to observed inactivation. The rate constant for autoxidation (k_autox) in buffer is 13.6 × 10⁶m⁻² s⁻¹ (Schmidt et al. 1997), but the apparent rate of autoxidation is accelerated 13-fold by the presence of hydrophobic compartments (Liu et al. 1998b), so this faster rate was also simulated.

Modelling physiological NO profiles

Step-wise activation of neuronal NOS (100 ms)

The following derivations of the Michaelis-Menten equation describe the generation of the NO signal at various rates of NO synthesis (eqn. 17) and the decline once NO production is halted (eqn. 18).

(17)

Here v1 is the rate of NO production (nm s⁻¹) and [NO] is the NO concentration (nm). The decline of NO concentration following cessation of synthesis was derived by the following equation where [NO] at t = 0 is the steady-state NO concentration (nm) at cessation of NO synthesis:

(18)

The equations were solved for a range of NO production rates (0.5–2 μm s⁻¹), which are similar to the maximum rate of neuronal NOS in cerebellum (50 nmol min⁻¹ g⁻¹ tissue or 0.8 μm s⁻¹; Salter et al. 1995) and were chosen to generate NO signals in the physiological range (0.5–20 nm; Bellamy et al. 2002). 100 ms or longer bursts of NO synthesis were simulated.

Dynamic activation of NOS

Sabatini et al. (2002) used measurements of Ca²⁺ concentrations to simulate Ca²⁺–calmodulin binding in dendritic spines following synaptic stimulation of NMDA receptors. Assuming that neuronal NOS activation matches that of Ca²⁺–calmodulin binding during such a Ca²⁺ transient, neuronal NOS activity was modelled using eqn (19).

(19)

The rate of NO synthesis (v; nm s⁻¹) at time t (s), is given by the product of the maximum activity (v1; μm s⁻¹) and two exponential functions, the parameters for which (k1 and k2) are adjusted to match the kinetic profile of Ca²⁺–calmodulin binding (e.g. peak activity at ∼80 ms). Values for maximum synthesis from 0.5 to 2 μm s⁻¹ were used to generate NO profiles which were calculated by finding the net of synthesis and inactivation (eqn (20)).

(20)

Modelling NO signals in three dimensions

Spatially discrete NO signalling was investigated by modelling diffusion, synthesis and inactivation in three dimensions and constraining NO synthesis to 0.5 μm diameter ‘terminal boutons’ (dimensions in Palay & Chan-Palay, 1974). The density of parallel fibre synapses in rat cerebellum is just under 10⁹ synapses μm⁻³, or approximately 1 synapse μm⁻³ (Napper & Harvey, 1988). Assuming that neuronal NOS is distributed uniformly within but constrained to boutons, then half of the total tissue volume is capable of producing NO, such that the maximum rate of synthesis within a bouton will be 1.6 μm s⁻¹, rather than 0.8 μm s⁻¹. The relevant equation (eqn (21)) describes radial diffusion away from a central point, where NO synthesis (v1) is positive within boutons and zero outside them.

(21)

This equation was numerically solved using the pdepe function in MATLAB. We then investigated the impact of inactivation on a larger single source, a granule cell body of diameter 10 μm.

Results

There are currently no reliable methods for directly measuring low physiological NO concentrations in brain slices (Garthwaite, 2005). To circumvent this problem, cGMP levels can be used as a sensitive index of NO_GC receptor activity which, in turn, calibrates to the NO concentration (Bellamy et al. 2002; Griffiths et al. 2003). Thus, if slices are exposed to a fixed concentration of NO in the aCSF, NO will diffuse in and, in the absence of any NO inactivation, will equilibrate to give the same concentrations inside and outside the slice. If, however, the tissue consumes NO, a concentration gradient of NO will be established across the slice, in much the same way that tissue oxygen consumption generates an oxygen gradient (Hill, 1929). Where submaximal for NO_GC receptor activation, the NO gradient will translate into a cGMP gradient.

Cerebellar slices inactivate NO

Constant concentrations of NO were generated by adding the NO donor, Sper/NO to aCSF. The half-life of the donor (39 min at 37°C) is long compared with the duration of the experiment, so that NO was effectively released at a constant rate. Within 10 min, the NO concentration in the gassed aCSF reached a plateau (Fig. 1A) when the rate of NO breakdown by reaction with oxygen equals the rate of release. By adding slices to different concentrations of Sper/NO (after 10 min pre-equilibration), different constant concentrations of NO could be administered.

When slices were exposed to varying NO concentrations in this way, cGMP rose to form steady state levels after 1 min (Fig. 1B). The steady states, graded to the NO concentration, arise because of the combination of NO_GC receptor desensitization and a slow hydrolysis of cGMP by phosphodiesterases (Bellamy et al. 2000; Mo et al. 2004). Most subsequent experiments were carried out with cGMP at steady state (2 min incubations).

Immunohistochemical staining of the cross-section of a cerebellar slice for cGMP revealed that at intermediate bath NO concentrations (∼100 nm) the edges of the slice stained but the centre did not, signifying that NO failed to access this region in active concentrations (Fig. 2B). A concentration gradient therefore existed across the slice, as predicted for tissue NO inactivation. The thickness of the band of cGMP staining was roughly uniform, indicating that the mechanism by which NO is inactivated has a grossly similar distribution throughout the cerebellar layers. Incubation with higher concentrations allowed NO to penetrate the whole slice in concentrations sufficient to activate NO_GC receptors maximally, as indicated by robust and uniform cGMP staining throughout the slice thickness (Fig. 2C). No cGMP staining was apparent in the absence of NO application (Fig. 2A). Longer incubations (up to 8 min) had no effect on the patterns of staining at different NO concentrations (data not shown), consistent with cGMP being at steady state (Fig. 1B).

Figure 2. Inactivation limits penetration of external NO into cerebellar slices.

Sections (10 μm) of 400 μm cerebellar slices, labelled by peroxidase-linked immunocytochemistry for cGMP (dark staining); nuclei are stained with haemalum (pale staining). Slices were incubated for 2 min with 0 (A) 102 nm (B) and 4.22 μm NO (C), produced from 0, 5 μm and 2 mm Sper/NO, respectively. EGC, external granule cell layer; ML, molecular layer; PC, Purkinje cell layer; IGC, internal granule cell layer. Images are representative of n = 3–4 independent experiments.

Exposure of slices to several different external NO concentrations (20 nm–4 μm) allowed generation of an NO concentration–cGMP response curve (Fig. 1C). Comparison with the equivalent curve for dispersed cerebellar cells (Griffiths & Garthwaite, 2001) revealed the curve in slices to be markedly shifted rightwards to the extent that the EC₅₀ in slices was three orders of magnitude greater than in cells (∼1 μm compared to 1.6 nm), as expected for access of NO to the slice interior being substantially hindered by NO inactivation.

Role of lipid peroxidation

In cerebellar cell suspensions, NO consumption is predominantly the result of ascorbate and iron together initiating the formation of lipid peroxyl radicals, which avidly react with NO (O'Donnell et al. 1997; Keynes et al. 2005a). To determine whether this process accounts for NO consumption in cerebellar slices, we tested the transition metal chelator, DTPA and the vitamin E analogue, Trolox (Britt et al. 1992), both of which inhibit lipid peroxidation-dependent NO consumption in the cell suspensions (Keynes et al. 2005a). Slices were stimulated with both a sub-EC₅₀ concentration of NO (240 ± 30 nm NO, n = 10; generated from 10 μm Sper/NO), and a maximal concentration (100 μm DEA/NO). With a 30 min preincubation period, neither inhibitor significantly affected the resultant cGMP levels (Fig. 3A). Equally, there was no significant difference between control slices and those incubated with Trolox when endogenous NO synthesis was stimulated by exposure to 100 μm NMDA (Fig. 3B). Some slices were incubated with Trolox from the time of slice preparation, which caused a reduction in cGMP accumulation in response to the submaximal NO concentration (Fig. 3C). This is indicative of an increase, rather than a decrease in inactivation, suggesting oxidative stress reactions such as lipid peroxidation impair rather than cause slice NO consumption.

Figure 3. Inhibitors of lipid peroxidation do not influence inactivation of NO by cerebellar slices.

A, cGMP accumulation in aCSF controls and in response to intermediate or maximal NO stimulation (10 μm Sper/NO and 100 μm DEA/NO, respectively), in the absence (open bars) and presence of the lipid peroxidation inhibitors Trolox (100 μm, hatched bars) and DTPA (100 μm, filled bars). Univariate ANOVA, p = 0.278. Data represent mean ±s.e.m., n = 4–9. B, cGMP accumulation following treatment with NMDA or DEA/NO (100 μm) in control (open bars) and Trolox-treated (100 μm, hatched bars) slices. Univariate ANOVA, p = 0.874. Data represents mean ±s.e.m.,n = 4–5. C, cGMP accumulation after treatment with 100 μm Trolox (hatched bars), or its vehicle, 0.1% v/v DMSO (filled bars), from the start of slice preparation. cGMP is decreased after exposure to 10 μm Sper/NO in the presence of Trolox (one-way ANOVA on Sper/NO-treated slices: P < 0.001, with Tukey's post hoc tests. There is no significant effect of treatment in control or DEA/NO-stimulated slices). Data represents mean ±s.e.m., n = 3–8. D, accumulation of TBARS in control cerebellar slices (open bars) and those preincubated with 100 μm Trolox (hatched bars) and 100 μm DTPA (filled bars), following 60 min incubation with 10 μm each of Fe₂SO₄ and ascorbate (Fe/Asc). There is no significant ongoing lipid peroxidation (univariate ANOVA on TBARS at 0 and 60 min; p = 0.086), though Trolox decreases basal TBARS levels (Tukey's post hoc test, p = 0.009). Trolox and DTPA both abolish lipid peroxidation stimulated with iron and ascorbate (control, significant increase in TBARS on incubation with Fe/Asc; Student's t test, p = 0.003; Trolox, no increase in TBARS with Fe/Asc, p = 0.695; DTPA, no increase in TBARS with Fe/Asc, p = 0.348). Data represents mean ±s.e.m., n = 10–14.

Finally, attempts were made to determine whether there was any lipid peroxidation taking place in the incubated slices. From measurement of the stable products of lipid peroxidation (TBARS), no ongoing lipid peroxidation could be detected (Fig. 3D), unlike with dispersed cerebellar cells (Keynes et al. 2005a). However, preincubation with 100 μm Trolox (but not DTPA) for 30 min reduced the basal levels of TBARS. As a positive control, lipid peroxidation was induced in the slices using a mixture of 10 μm Fe₂SO₄ and 10 μm ascorbate. Both 100 μm Trolox and 100 μm DTPA abolished the increase in TBARS stimulated in this way. The lack of effect of the inhibitors on cGMP levels, together with a lack of measurable ongoing lipid peroxidation, suggests that this process is not responsible for the NO consumption in cerebellar slices.

Role of superoxide ions or red blood cells

As slices do not inactivate NO by the same mechanism that predominates in dispersed cells, we investigated other known mechanisms for NO breakdown. A contribution of the reaction of NO with superoxide ions (forming peroxynitrite) was tested by incubating slices with 1000 U ml⁻¹ SOD or 200 μm of the cell-permeable SOD analogue, Mn(III)tetrakis(4–benzoic acid)porphyrin (MnTBAP).

Only MnTBAP significantly increased the accumulation of cGMP (Fig. 4A). The NO concentration generated (by 10 μm Sper/NO) in the presence of 200 μm MnTBAP, however, was increased more than 2-fold compared to control (Fig. 4B). This increase occurred even in the presence of SOD, and SOD alone did not affect the NO profile generated by 10 μm Sper/NO (not shown). This indicated that the increased NO production in the presence of MnTBAP was not due to scavenging of superoxide, but instead suggested that MnTBAP increased the rate of release of NO from the donor. In support of this hypothesis, the initial rate of release of NO was greater in the presence of MnTBAP (0.57 μm min⁻¹) than in aCSF alone (0.10 μm min⁻¹). The cGMP generated in the presence of MnTBAP was entirely as predicted from the resulting increased NO concentration (Fig. 4C). This, together with the lack of effect of SOD, suggested that superoxide does not contribute significantly to NO inactivation.

Figure 4. Inactivation of NO by slices is not due to red blood cells or superoxide.

A, cGMP accumulation in response to 10 μm Sper/NO or 100 μm DEA/NO in control (hatched bars) and following incubation with 200 μm MnTBAP (open bars), 1000 U ml⁻¹ SOD (cross-hatched bars) or following intracardial perfusion of rats prior to slice preparation (black bars). Only MnTBAP affects cGMP levels (univariate ANOVA with Tukey's post hoc tests, p = 0.018). Data represent mean ±s.e.m, n = 3–8. B, NO generated from 10 μm Sper/NO in the presence of 200 μm MnTBAP and in control conditions (as labelled). Data represent mean ±s.d., n = 2. C, cGMP accumulation in the presence of 200 μm MnTBAP (data from A) plotted against the NO concentration present. D, cGMP produced in response to 10 μm Sper/NO or 100 μm DEA/NO is not significantly affected by the presence (hatched bars) or absence (open bars) of 20 μm indomethacin (univariate ANOVA, p = 0.336). Data represent mean ±s.e.m., n = 6.

The contribution of reaction with oxyhaemoglobin in residual red blood cells was tested by reducing their number by intracardial perfusion of the rats with saline before decapitation. Cell counts of dispersed preparations of cerebellar cells indicate that this decreases the red blood cell count to one-fifth of that present in control preparations (not shown). No effect was observed (Fig. 4A).

Role of known NO-consuming enzymes

The involvement of PGHS was addressed by preincubating slices with 20 μm indomethacin, which inhibits PGHS-mediated NO consumption by activated platelets (O'Donnell et al. 2000; Fig. 4D). There was no significant effect on NO-evoked cGMP accumulation in the slices. Lipoxgenases have also been implicated in NO breakdown (O'Donnell et al. 1999; Coffey et al. 2001) but the effect of inhibition of these enzymes with the usual inhibitor, 5,8,11,14-eicosatetraynoic acid (ETYA; O'Donnell et al. 1999; Coffey et al. 2001), could not be tested as ETYA quenched NO release from 10 μm Sper/NO. This quench was relieved by addition of 1000 U ml⁻¹ SOD, indicating that ETYA caused generation of superoxide ions, which reacted with NO (data not shown). Generation of superoxide in the slices would cause artefactually high NO consumption, confounding interpretation of any inhibitory effect on biological NO consumption. In any case, lipoxygenases are also inhibited by Trolox (Panganamala et al. 1977), presumably by reaction with the enzyme-bound lipid peroxyl radical that consumes NO (O'Donnell et al. 1999). As Trolox does not effect NO inactivation (Fig. 3A), lipoxygenases are unlikely to underlie slice NO consumption.

Effect of cyanide

NO consumption by intact and homogenized colorectal cancer (CaCo-2) cells, endothelial cells, cerebellar glia and forebrain synaptosomes has been found to be at least partially inhibited by the haem poison cyanide (NaCN) and the flavoprotein inhibitor DPI (Gardner et al. 2001; Schmidt & Mayer, 2004; Keynes et al. 2005b). Incubation with these compounds at concentrations that have maximal effects in dispersed preparations (100 μm NaCN and 50 μm DPI) had no effect on cGMP accumulation in response to 10 μm Sper/NO or 100 μm DEA/NO (Fig. 5A). It has previously been shown that 100 μm NaCN reduces brain slice ATP levels to 69% of control levels (Banay-Schwartz et al. 1974). A concentration of 50 μm DPI is sufficient to inhibit NO and cGMP production in response to 100 μm NMDA (vehicle-treated slices, 243 ± 19 pmol cGMP (mg protein)⁻¹; 50 μm DPI-treated slices, 12 ± 12 pmol cGMP (mg protein)⁻¹; n = 8). The lack of an inhibitory effect is therefore not due to a lack of slice permeability of these compounds. The lack of cyanide sensitivity was not due to the indirect method of gauging NO levels. Chopping sagittal cerebellar slices additionally in the coronal plane produces tissue blocks that retain good histological preservation (Garthwaite et al. 1980) and an intact NMDA receptor–cGMP pathway (Garthwaite, 1985) but their reduced dimensions mean that they can be held in suspension by fast stirring, allowing direct measurement of NO levels using an electrochemical probe. Different numbers of blocks were added to the probe chamber and NO accumulation in response to the slow NO releaser, DETA/NO (100 μm) and then NaCN (100 μm) recorded (Fig. 5B). As the concentration of blocks was increased, the plateau NO concentrations generated in the presence of DETA/NO became progressively lower (Fig. 5B) because of tissue NO consumption. Addition of 100 μm NaCN once the plateau had been achieved had no effect. When the blocks were homogenized, however, NO consumption was increased by addition of NADPH and this increase was inhibited by NaCN (Fig. 5C), as previously observed in homogenates of whole brain, synaptosomes and cultured glial cells (Keynes et al. 2005b). Intact brain preparations therefore consume NO in a qualitatively different manner from homogenates of the same tissue.

Figure 5. Inactivation of NO by homogenized, but not intact, cerebellar slices is sensitive to NaCN and DPI.

A, cGMP accumulation in response to 10 μm Sper/NO or 100 μm DEA/NO is not significantly affected by incubation with 100 μm NaCN (hatched panels) or 50 μm DPI (cross-hatched panels). Open bars represent control slices, filled bars represent vehicle treatment with 0.2% v/v DMSO. Univariate ANOVA; p = 0.421. Data represent means ±s.e.m., n = 4–8. B, plateau levels of NO following addition of 100 μm DETA/NO was not significantly affected by addition of 100 μm NaCN to different concentrations of blocks of cerebellum (univariate ANOVA: effect of protein concentration, P < 0.001; effect of NaCN treatment, p = 0.760). Data represent means ±s.e.m., n = 3–15. C, plateau levels of NO following addition of 100 μm DETA/NO (open bars) followed by 100 μm NADPH (hatched bars) then 100 μm NaCN (black bars) to homogenates of cerebellar slice blocks (at 2 mg ml⁻¹ protein). Data represents mean ±s.e.m., n = 4.

Estimation of the kinetics of NO inactivation

The extent to which the NO consumption described here contributes to physiological and pathological effects of NO depends on the kinetics. By using diffusional modelling it is possible to derive values for the inactivation rates that would account for the experimental data. The model was a simple one, in which slices are treated as homogenous slabs into which NO diffuses in a Fickian manner, and which consume NO by a process that is describable either by a first-order decay (corresponding to a fixed half-life) or by saturable (Michaelis-Menten) kinetics (for details of modelling see Methods).

The rate of NO consumption determines the steepness of the NO concentration gradient existing across the slice thickness at steady state (Fig. 6A). At each point, the NO concentration can be translated into a cGMP level (Fig. 6B) by reference to the NO concentration–cGMP response curve obtained at steady state (see eqn (3) in Methods). Then, the total slice cGMP can be calculated as a fraction of the maximum attainable, giving predicted concentration–response curves at different rates of tissue NO inactivation (Fig. 6C and D). When first-order decay was considered the curves were much shallower than the experimental data (Fig. 6C). A better fit was obtained by assuming saturable inactivation kinetics with the Michaelis-Menten parameters being V_max ∼2 μm s⁻¹ and K_m ∼100 nm but the predicted NO concentration–cGMP response curve was still shallower than that found experimentally (Fig. 6D). In reality, the slice is exposed not only to NO diffusing from the bath, but also from NO released within the tissue itself, from donor that has diffused into the slice (Fig. 7). Both corrected and uncorrected curves overlay at low NO concentrations, but at higher NO concentrations, the corrected curves are steeper than the uncorrected curves, giving an improved fit to the experimental data (Fig. 6D, dashed lines). NO_GC desensitizes and any effect of this was assessed by incorporating an exponential time-dependence (τ = 6.9 s) into the maximal NO_GC activity, such that it followed the desensitization kinetics previously described (Bellamy et al. 2000). This had no impact on the NO concentration–cGMP response curves, indicating that desensitization does not occur before the steady-state NO levels are established. Varying the K_m while fixing the V_max (2 μm s⁻¹), generated a family of curves that converged at around 1 nm (Fig. 8A), with the experimental data fitting a K_m of between 1 and 10 nm. Fixing the K_m at 1 nm, the data are again best fitted by an inactivation process with a V_max of 1–2 μm s⁻¹ (Fig. 8B). In short, the experimental data are consistent with a saturable tissue consumption process having a V_max of 1–2 μm s⁻¹ and a K_m of 1–10 nm.

Figure 6. Inactivation of NO is predicted to limit penetration of external NO into brain tissue.

A, steady-state NO profiles across a 400 μm slice modelled following exposure to constant bath NO, when bath NO is 0.05–5 μm, with Michaelis-Menten inactivation of NO (eqn (2); V_max= 1 μm s⁻¹ and K_m= 100 nm). B, NO profiles in A were converted into predicted cGMP profiles across the slice, using calculated kinetic parameters for NO_GC (eqn (3)).The area under each cGMP profile is plotted against the bath NO concentration to generate predicted NO concentration–cGMP response curves when inactivation is first order (C, with varying k, as labelled) or Michaelis-Menten (D, with varying V_max as labelled). In D the effect of NO release within the slice on cGMP levels is shown by the dashed lines (eqns (4–7)).

Figure 7. Quantification of cGMP produced from NO release within the slice.

A, cartoon illustrating how NO within a slice is a mixture of NO diffusing in from the bathing medium and NO released from the donor within the tissue (upper diagram). Addition of Hb–agarose scavenges external NO but is too large to penetrate the slice, leaving the donor in the tissue as the sole source (lower diagram). B, cGMP produced in the presence of 40% Hb–agarose (data points) is plotted against applied Sper/NO concentration (bottom axis). Also shown is the equivalent NO concentration that would be produced produced by these concentrations of Sper/NO in the absence of Hb–agarose (top axis). The experimental data, expressed in terms of this NO concentration, are fitted with a logarithmic function (solid line; eqn (5)). The contribution of NO release within the slice can now be predicted at any bath NO concentration.

Figure 8. Predicted NO concentration–cGMP response curves, following incubation of cerebellar slices with constant concentrations of bathing NO.

A, V_max= 2 μm s⁻¹ and K_m= (left to right) 100, 10, 1 and 0.1 nm and B, K_m= 1 nm and V_max= (left to right) 1, 2, 4 and 8 μm s⁻¹. Dashed lines represent the curves predicted after adjusting for the effects of release from the donor within the slice. C, raw data (shown in summary in Fig. 5B) of NO plateaux achieved on addition of 100 μm DETA/NO to suspensions of tissue blocks, compared to the plateau heights predicted from eqns (8–15), were the K_m 10 nm and the V_max 1 μm s⁻¹, as predicted from the cGMP data fit, or with the V_max multiplied by 0.1, 0.05 and 0.01 (as labelled). D, the NO concentration–cGMP response curve observed in slices (•) compared to the predicted curve, if slice inactivation were due to autoxidation (solid line; eqn (16)). The NO-cGMP curve is the same whether or not, due to the presence of membranes autoxidation is accelerated 13-fold.

cGMP levels are an indirect measurement of NO levels within a slice. We also directly measured the NO level in a solution bathing a suspension of cerebellar blocks. Using methods from studies of immobilized enzyme kinetics, we tested whether the parameters for inactivation derived above would be expected to generate the experimentally determined bath NO concentration (see Methods; Shuler & Kargi, 1992; Fig. 8C). Inactivation appeared to be 10-fold slower than predicted from cGMP levels. It is well established, however, that unstirred layers surrounding red blood cells slow the apparent inactivation rate of NO and O₂ by haemoglobin by up to three orders of magnitude (Liu et al. 1998a, 2002). The contribution of a similar process in the larger tissue blocks used here is difficult to assess, as the magnitude of unstirred layers is very dependent on tissue geometry, but the 10-fold slowed rate observed here is well within the range expected due to unstirred layers. Direct measurements of NO therefore are unable to test the accuracy of the parameters derived above, but are consistent with their values and provide a further demonstration of inactivation of NO by rat cerebellum.

Influence of accelerated autoxidation

With the model, the potential significance of reaction of NO with oxygen (autoxidation) within the tissue can be discerned. In aqueous phases, this process is slow but it may be accelerated as much as 13-fold in lipid due to increased solubility of NO in this phase (Liu et al. 1998b). However, incorporating NO breakdown by autoxidation into the diffusional model above (see Methods) showed no observable difference between the curves using kinetics for normal autoxidation and for accelerated autoxidation (Fig. 8D), implying a negligible impact.

Discussion

Although it must be acknowledged that the data presented here are largely indirect measurements of NO levels present in brain, they nevertheless provide the first description of an active NO consumption process in intact brain tissue and a first approximation of the kinetics, allowing the possible implications of the mechanism on endogenous NO signals to be evaluated.

The identity of this process remains unclear, but it seems independent of several known pathways for NO breakdown, namely reaction with haemoglobin in red blood cells, superoxide, molecular oxygen and lipid peroxyl radicals or catalytic consumption by PGHS and lipoxygenase. Its insensitivity to NaCN and DPI also suggest it is different from the flavohaemoprotein(s) postulated to consume NO in several dispersed cell preparations (Gardner et al. 2001; Schmidt & Mayer, 2004; Keynes et al. 2005b).

The basic observation that exposure of cerebellar slices to NO results in a marked gradient of NO at steady state (as judged by the profile of cGMP immunostaining) is as predicted from a high rate of NO inactivation, a property confirmed by direct measurement of NO consumption by intact blocks of cerebellum kept in suspension. This being so, the steady-state NO concentration–cGMP response curve for NO in whole slices is dictated much more by the rate of NO consumption than by the kinetics of activation of NO_GC receptors. The situation with NO therefore becomes very similar to that applying to the neurotransmitter glutamate whose inward diffusion into brain slices is limited by the activity of transporters to the extent that very high external concentrations are needed to activate NMDA receptors throughout the tissue (Garthwaite, 1985). In both cases (glutamate and NO), the shift in apparent potency is about 1000-fold compared with their potencies measured using isolated cells, signifying that the rates of inactivation relative to their physiological concentrations are similar. This implies that the NO consumption mechanism may be of comparable importance in protecting the brain from high NO concentrations and for shaping physiological NO signals.

Without identifying it or having the means to alter its activity, the physiological significance of the NO inactivation mechanism is hard to address experimentally. The problem is compounded by the difficulties in reliably measuring endogenous NO signals in intact tissues (for discussion see Keynes & Garthwaite, 2004). Nevertheless, a number of predictions can be made from the apparent kinetics of the process derived by modelling, which suggested that NO consumption is saturable, with a V_max of 1–2 μm s⁻¹ and a K_m of 1–10 nm.

Most previous models of physiological NO signals assumed that micromolar concentrations were achieved (Wood & Garthwaite, 1994; Lancaster, 1994; Philippides et al. 2000) and that the biological half-life of NO in tissue was about 5 s, based on measurements of the rate of loss of NO as it was perfused over preparations of aorta (Palmer et al. 1987). One prediction was that NO from a single source could influence a very large number of synapses (2 million, Wood & Garthwaite, 1994) and that tissue inactivation of NO would only minimally affect NO profiles, unless multiple sources were active simultaneously. A recent paper by Garthwaite (2005) predicts physiological NO concentrations to be in the low nanomolar range, in keeping with more recent biochemical and electrophysiological estimates (see discussion by Hall & Garthwaite (2005) and Garthwaite (2005)), but does not address tissue consumption.

Because the basic features of a physiological NO signal (e.g. its amplitude and duration) are not known, we were guided by the experimentally measured maximum rates of NO synthesis in cerebellar tissue and considered three different scenarios: homogenous NO synthesis in a tissue volume activated in a step-wise fashion; transient NO synthesis in a tissue volume mirroring the time course of a synaptic NMDA receptor-mediated rise in cytosolic Ca²⁺; and, finally, spatially limited NO synthesis in dispersed boutons.

The cerebellum has one of the highest levels of NOS in the brain, the maximal rate of NO formation in homogenates amounting to 50 nmol min⁻¹ (g tissue)⁻¹ (Salter et al. 1995) or, assuming 1 ml (g tissue)⁻¹, 0.8 μm s⁻¹. In the first two scenarios, NOS rates of around this value were assumed to be occurring within a discrete tissue volume wherein multiple sources of NO are simultaneously active, a situation that may be analogous to the event-related activation of discrete brain regions in vivo (Buckner & Koutstaal, 1998; Shoham et al. 1999). It is further assumed that NO inactivation is homogeneous, consistent (at a gross level) with the results in cerebellar slices (Fig. 2B). If global NO synthesis is prolonged and occurs at a rate less than the V_max for inactivation (2 μm s⁻¹), it is predicted that the NO-consuming mechanism rapidly translates a given synthesis rate into a steady-state NO concentration (Fig. 9A) and thus a corresponding degree of activity of the NO_GC receptor. When the concentration on cessation of synthesis is within the presumed physiological range (<10 nm). NO disappears with a half-life of less than 10 ms.

Figure 9. Predicted temporal profiles of endogenous NO signals, when sources homogenously distributed throughout the tissue are synchronously activated and deactivated.

A, profiles following a 100 ms pulse of NO synthesis at the rates labelled (in μms⁻¹). V_max for inactivation is 2 μm s⁻¹, K_m is 10 nm. Profiles generated from eqns (17 and 18). B, temporal profile of NO synthesis, produced by a typical NMDA receptor-mediated Ca²⁺ transient in a spine, where the maximum rate of NO synthesis is 0.5, 1, 1.5 and 2 μm s⁻¹, calculated according to eqn (19). C and D, predicted NO profiles generated by eqn (20), from the NO synthesis profiles in B, assuming inactivation is governed by a K_m of 10 nm and a V_max of either 2 μm s⁻¹ (B) or 0.2 μm s⁻¹ (C).

The rapid rise and fall of the NO concentration imposed by the NO sink under these global conditions of NO synthesis and inactivation implies that the local NO concentration should faithfully follow even very brief periods of NO formation. Taking as an extreme a pulse of NO synthesis matching the time course of Ca²⁺–calmodulin binding during an NMDA receptor-mediated calcium transient (Fig. 9B), the model predicts this to be so when the derived kinetics of NO inactivation are used, but not if the rate of inactivation is lowered by a factor of 10 (Fig. 9C and D).

Finally, we modelled NO synthesis from discrete boutons (0.5 μm diameter), chosen to resemble parallel fibre terminals, a major source of NO in the cerebellum (Shibuki & Kimura, 1997). This approach also allows assessment of the relative contributions of diffusion and NO consumption to spatial NO profiles.

In all cases, the derived peak NO concentration scaled with the rate of NO synthesis (not shown), as has been previously deduced (Philippides et al. 2005). With a single source active, inactivation was predicted to have a minimal influence on the NO profile, which was solely determined by diffusion (Fig. 10A). This seemed to be because with such a small source, diffusion was sufficiently fast for NO to reach a steady state before inactivation could impact upon the concentration. Slowing the diffusion rate constant increased the impact of inactivation (not shown). A single bouton produced only low picomolar levels of NO, even at presumed maximal rates of NO synthesis, suggesting that release from a single site would be insufficient to produce a biological effect. When a larger source was simulated (a whole granule cell; diameter, 10 μm), the kinetics of inactivation influenced the concentration and spatial extent of the NO profile (Fig. 10B), constraining the NO signal closer to the cell body than when inactivation was absent. However, the NO concentrations achieved were still in the low picomolar range, suggesting that more than one NO-producing cell would have to be active at a given time for a biologically relevant NO signal to be produced.

Figure 10. Predicted spatial NO profiles following endogenous NO synthesis at 1600 nM s⁻¹ constrained to a synaptic bouton of 0.5 μm diameter (A) or a granule cell of 10 μm diameter (B).

Profiles are shown for no inactivation (continous black line) and inactivation with a V_max of 2 μm s⁻¹ and a K_m of either 1 nm (dashed black line) or 10 nm (grey line) and were calculated by numerically solving eqn (21).

This theoretical analysis suggests that NO would be unable to function as a truly synapse-specific messenger and that prolonged activity producing temporal summation of NO produced from a single source, or spatial summation from several adjacent sources would be required to mediate NO-dependent functions, including synaptic plasticity. The extremely thin, cylindrical geometry and plexiform organization of NOS-positive fibres in the cerebral cortex have also led to suggestions that functional NO signals are likely to arise from the simultaneous activation of several sources, rather than from a single NO-producing fibre (Philippides et al. 2005). When applied to a cylindrical source, our model replicates these findings, which assumed a first-order inactivation mechanism only diverging at high synthesis rates when NO concentrations rise above the K_m (1 or 10 nm) and thus, inactivation in our model becomes saturated (not shown). In short, modelling of endogenous NO signals suggests co-operativity of NO sources and this is supported by much experimental evidence where activation of multiple NO sources leads to a biological effect. For example, stimulation of bundles of parallel fibres generate sufficient NO to produce long-term depression or potentiation in nearby unstimulated parallel fibre–Purkinje cell synapses (Reynolds & Hartell, 2000; Jacoby et al. 2001; Reynolds & Hartell, 2001).

These conclusions are not consistent, however, with reports of NO-dependent synaptic plasticity at a single parallel fibre–Purkinje cell synapse (Casado et al. 2002). Two possible explanations for this discrepancy are that, firstly, NO synthesis from adjacent boutons, or within the parallel fibre axon, can summate to generate physiologically significant NO concentrations, such that the parallel fibre represents a much bigger source than a single bouton. Secondly, it is possible that the NO synthesis rate used in the simulations is too low. The rates used here were based on experimental data from cerebellar homogenates (Salter et al. 1995), but variations in tissue NOS distribution, cofactor availability and oxygenation could result in endogenous synthesis rates that are higher or lower than those used here. In this respect it is notable that the maximum measured rate of purified neuronal NOS is only 3–4 molecules s⁻¹ at 10°C (Stuehr et al. 2004), a rate that, assuming it to be 4- to 8-fold higher at 37°C, corresponds to a maximum synthesis rate of about 12–32 molecules (NOS molecule) s⁻¹. A recent model (Garthwaite, 2005) used a maximal source strength of 20 000 molecule s⁻¹ as a point source (equivalent to 1000 synaptic NOS molecules each synthesizing 20 (molecules NO) s⁻¹ at a steady rate). The same steady-state source strength distributed evenly in a bouton equates to a synthesis rate of 500 μm s⁻¹ and generates a scaled-up profile of those in Fig. 10A (not shown). This will produce 3 nm NO at the surface of the bouton and 150 pm at 5 μm from the bouton centre, a profile that is again purely determined by diffusion, not inactivation. It may therefore be possible, depending on physiological conditions and the in vivo kinetics of NOS, to generate sufficient NO at a single site to produce a physiological effect. At more distant sites, however (e.g. neighbouring synapses), NO would be too low to be physiologically relevant, even with this high rate of synthesis, and summation of NO signals may be required. In these circumstances, the kinetics of inactivation will critically determine the sphere of influence of NO, constraining it closer to the active tissue.

In summary, cerebellar slices consume NO by an unidentified mechanism, with kinetics that predict that it will significantly impinge on endogenous NO signals that derive from multiple sites. Modulation of this process and its subcellular distribution may well affect the spatial and temporal patterns of NO signals and therefore influence the properties of physiological and pathophysiological NO profiles. Further characterization and identification of this mechanism is clearly of paramount importance to fully understand its impact. There is also a practical implication of the results in that avid NO inactivation by slices generates a sharp concentration gradient across the slice thickness when exogenous NO is administered. Even at applied NO concentrations that are clearly submaximal for cGMP synthesis therefore the responses generated by the slice will be very heterogeneous, being in the pathophysiological concentration range (0.1–1 μm) at the edge of the slice (e.g. producing inhibition of mitochondrial respiration and associated events), and physiological (or subphysiological) towards the centre of the tissue. This heterogeneity needs to be considered when designing and interpreting experiments using exogenous NO.