Cannabinoid receptors and their ligands

There are at least two types of cannabinoid receptors, CB(1) and CB(2), both coupled to G proteins. CB(1) receptors exist primarily on central and peripheral neurons, one of their functions being to modulate neurotransmitter release. CB(2) receptors are present mainly on immune cells. Their roles are proving more difficult to establish but seem to include the modulation of cytokine release. Endogenous agonists for cannabinoid receptors (endocannabinoids) have also been discovered, the most important being arachidonoyl ethanolamide (anandamide), 2-arachidonoyl glycerol and 2-arachidonyl glyceryl ether. Other endocannabinoids and cannabinoid receptor types may also exist. Although anandamide can act through CB(1) and CB(2) receptors, it is also a vanilloid receptor agonist and some of its metabolites may possess yet other important modes of action. The discovery of the system of cannabinoid receptors and endocannabinoids that constitutes the "endocannabinoid system" has prompted the development of CB(1)- and CB(2)-selective agonists and antagonists/inverse agonists. CB(1)/CB(2) agonists are already used clinically, as anti-emetics or to stimulate appetite. Potential therapeutic uses of cannabinoid receptor agonists include the management of multiple sclerosis/spinal cord injury, pain, inflammatory disorders, glaucoma, bronchial asthma, vasodilation that accompanies advanced cirrhosis, and cancer. Following their release onto cannabinoid receptors, endocannabinoids are removed from the extracellular space by membrane transport and then degraded by intracellular enzymic hydrolysis. Inhibitors of both these processes have been developed. Such inhibitors have therapeutic potential as animal data suggest that released endocannabinoids mediate reductions both in inflammatory pain and in the spasticity and tremor of multiple sclerosis. So too have CB(1) receptor antagonists, for example for the suppression of appetite and the management of cognitive dysfunction or schizophrenia.     

Blocking the cannabinoid receptors: drug candidates and therapeutic promises

The CB1 and CB2 cannabinoid receptors have been described as two prime sites of action for endocannabinoids. Both the localization and pharmacology of these two G-protein-coupled receptors are well-described, and numerous selective ligands have been characterized. The physiological effects of Cannabis sativa (cannabis) and a throughout study of the endocannabinoid system allowed for the identification of several pathophysiological conditions--including obesity, dyslipidemia, addictions, inflammation, and allergies--in which blocking the cannabinoid receptors might be beneficial. Many CB1 receptor antagonists are now in clinical trials, and the results of several studies involving the CB1 antagonist lead compound rimonabant (SR141716A) are now available. This review describes the pharmacological tools that are currently available and the animal studies supporting the therapeutic use of cannabinoid receptor antagonists and inverse agonists. The data available from the clinical trials are also discussed.     

A neutral CB1 receptor antagonist reduces weight gain in rat

Cannabinoid (CB)1 receptor inverse agonists inhibit food intake in animals and humans but also potentiate emesis. It is not clear whether these effects result from inverse agonist properties or from the blockade of endogenous cannabinoid signaling. Here, we examine the effect of a neutral CB1 antagonist, AM4113, on food intake, weight gain, and emesis. Neutral antagonist and binding properties were confirmed in HEK-293 cells transfected with human CB1 or CB2 receptors. AM4113 had no effect on forskolin-stimulated cAMP production at concentrations up to 630 nM. The Ki value of AM4113 (0.80 +/- 0.44 nM) in competitive binding assays with the CB1/2 agonist [3H]CP55,940 was 100-fold more selective for CB1 over CB2 receptors. We determined that AM4113 antagonized CB1 receptors in brain by blocking hypothermia induced by CP55,940. AM4113 (0-20 mg/kg) significantly reduced food intake and weight gain in rat. Compared with AM251, higher doses of AM4113 were needed to produce similar effects on food intake and body weight. Unlike AM251 (5 mg/kg), a highly anorectic dose of AM4113 (10 mg/kg) did not significantly potentiate vomiting induced by the emetic morphine-6-glucoronide. We show that a centrally active neutral CB1 receptor antagonist shares the appetite suppressant and weight loss effects of inverse agonists. If these compounds display similar properties in humans, they could be developed into a new class of antiobesity agents.     

Effects of cannabinoids on endogenous K+ and Ca2+ currents in HEK293 cells

Effects of cannabinoids on endogenous potassium and calcium currents in HEK293 cells were studied using the whole-cell variant of the patch-clamp technique. The cannabinoid agonists WIN 55,212-2, methanandamide, and anandamide (1 microM) decreased the calcium current by 53.1 +/- 2.6, 47.5 +/- 1.2, and 38.8 +/- 3.1%, respectively, after transfection of human CB1 cannabinoid receptor (hCB1) cDNA into HEK293 cells. The delayed rectifier-like current was not changed after application of these agonists, but the inward rectifier was increased by 94.0 +/- 3.6, 83.7 +/- 5.1, and 63.0 +/- 2.5% after application of WIN 55,212-2, methanandamide, and anandamide, respectively. The effects of the cannabinoid antagonists (AM251, AM281, and AM630) on the inward rectifier and calcium currents were the opposite of those seen with cannabinoid agonists; thus, these compounds act as inverse agonists in this preparation. These results suggest that endogenous inward rectifier and calcium currents are modulated by cannabinoids in HEK293 cells, and that some expressed receptors may be constitutively active.     

Controlled downregulation of the cannabinoid CB1 receptor provides a promising approach for the treatment of obesity and obesity-derived type 2 diabetes

Increased activity of the endocannabinoid system has emerged as a pathogenic factor in visceral obesity, which is a risk factor for type 2 diabetes mellitus (T2DM). The endocannabinoid system is composed of at least two G-protein-coupled receptors (GPCRs), the cannabinoid receptor type 1 (CB1), and the cannabinoid receptor type 2 (CB2). Downregulation of CB1 activity in rodents and humans has proven efficacious to reduce food intake, abdominal adiposity, fasting glucose levels, and cardiometabolic risk factors. Unfortunately, downregulation of CB1 activity by universally active CB1 inverse agonists has been found to elicit psychiatric side effects, which led to the termination of using globally active CB1 inverse agonists to treat diet-induced obesity. Interestingly, preclinical studies have shown that downregulation of CB1 activity by CB1 neutral antagonists or peripherally restricted CB1 inverse agonists provided similar anorectic effects and metabolic benefits without psychiatric side effects seen in globally active CB1 inverse agonists. Furthermore, downregulation of CB1 activity may ease endoplasmic reticulum and mitochondrial stress which are contributors to obesity-induced insulin resistance and type 2 diabetes. This suggests new approaches for cannabinoid-based therapy in the management of obesity and obesity-related metabolic disorders including type 2 diabetes.     

The inhibitory action of exo- and endocannabinoids on [³H]GABA release are mediated by both CB₁and CB₂receptors in the mouse hippocampus

Exogenous and endogenous cannabinoids play an important role in modulating the release of neurotransmitters in hippocampal excitatory and inhibitory networks, thus having profound effect on higher cognitive and emotional functions such as learning and memory. In this study we have studied the effect of cannabinoid agonists on the potassium depolarization-evoked [(3)H]GABA release from hippocampal synaptosomes in the wild-type (WT) and cannabinoid 1 receptor (CB(1)R)-null mutant mice. All tested cannabinoid agonists (WIN55,212-2, CP55,940, HU-210, 2-arachidonoyl-glycerol, 2-AG; delta-9-tetra-hydrocannabinol, THC) inhibited [(3)H]GABA release in WT mice with the following rank order of agonist potency: HU-210>CP55,490>WIN55,212-2>2-AG>THC. By contrast, 2-AG and THC displayed the greatest efficacy eliciting almost complete inhibition of evoked [(3)H]GABA efflux, whereas the maximal inhibition obtained by HU-210, CP55,490, and WIN55,212-2 were less, eliciting not more than 40% inhibition. The inhibitory effect of WIN55,212-2, THC and 2-AG on evoked [(3)H]GABA efflux was antagonized by the CB(1) receptor inverse agonist AM251 (0.5 μM) in the WT mice. In the CB(1)R knockout mice the inhibitory effects of all three agonists were attenuated. In these mice, AM251 did not antagonize, but further reduced the [(3)H]GABA release in the presence of the synthetic agonist WIN55,212-2. By contrast, the concentration-dependent inhibitory effects of THC and 2-AG were partially antagonized by AM251 in the absence of CB(1) receptors. Finally, the inhibition of evoked [(3)H]GABA efflux by THC and 2-AG was also partially attenuated by AM630 (1 μM), the CB(2) receptor-selective antagonist, both in WT and CB(1) knockout mice. Our data prove the involvement of CB(1) receptors in the effect of exo- and endocannabinoids on GABA efflux from hippocampal nerve terminals. In addition, in the effect of the exocannabinoid THC and the endocannabinoid 2-AG, non-CB(1), probably CB(2)-like receptors are also involved.     

Cannabinoid pharmacology in the cardiovascular system: potential protective mechanisms through lipid signalling

Cannabinoids include not only plant-derived compounds (of which delta9-tetrahydrocannabinol is the primary psychoactive ingredient of cannabis), but also synthetic agents and endogenous substances termed endocannabinoids which include anandamide (2-arachidonoylethanolamide) and 2-arachidonoylglycerol. Cannabinoids act on specific, G-protein-coupled, receptors which are currently divided into two types, CB1 and CB2. Relatively selective agonists and antagonists for these receptors have been developed, although one agent (SR141716A) widely used as an antagonist at CB1 receptors has non-cannabinoid receptor-mediated effects at concentrations which are often used to define the presence of the CB1 receptor. Both cannabinoid receptors are primarily coupled to Gi/o proteins and act to inhibit adenylyl cyclase. Stimulation of CB1 receptors also modulates the activity of K+ and Ca2+ channels and of protein kinase pathways including protein kinase B (Akt) which might mediate effects on apoptosis. CB, receptors may activate the extracellular signal-regulated kinase cascade through ceramide signalling. Cannabinoid actions on the cardiovascular system have been widely interpreted as being mediated by CB1 receptors although there are a growing number of observations, particularly in isolated heart and blood vessel preparations, that suggest that other cannabinoid receptors may exist. Interestingly, the currently identified cannabinoid receptors appear to be related to a wider family of lipid receptor, those for the lysophospholipids, which are also linked to Gi/o protein signalling. Anandamide also activates vanilloid VR1 receptors on sensory nerves and releases the vasoactive peptide, calcitonin gene-related peptide (CGRP), which brings about vasodilatation through its action on CGRP receptors. Current evidence suggests that endocannabinoids have important protective roles in pathophysiological conditions such as shock and myocardial infarction. Therefore, their cardiovascular effects and the receptors mediating them are the subject of increasing investigative interest.     

Cannabinoid receptor antagonists and fatty acids alter endocannabinoid system gene expression and COX activity

Cyclooxygenase (COX) possesses substrate affinity for the endocannabinoids (EC) anandamide (AEA) and 2-arachidonylglycerol (2-AG). We hypothesized that selective antagonism/activation of the cannabinoid receptors will increase COX activity and the availability of EC as substrates will lead to higher COX activity. Since the relationship between EC signaling of the endocannabinoid system (ECS) and the COX pathway in muscle has not been investigated, we examined agonist, antagonists and polyunsaturated fatty acid effects on ECS genes in myoblasts. At 50% confluency, C2C12 myoblasts were pretreated with 5 μM of the cannabinoid receptor (CB)2 inverse agonist AM630 for 2 h and one with both AM630 and 1 μM of the CB1 antagonist NESS0327. Cell cultures pretreated with AM630 were then administered with 25 μM of either arachidonic acid (20:4n6), eicosapentaenoate (EPA) (20:5n3), docosahexaenoate (DHA) (22:6n3), AEA or bovine serum albumin (vehicle control) for 24 h. Quantitative polymerase chain reaction analyses were performed looking at ECS and prostaglandin genes. Total COX activity and COX-1 protein were greater in the AM630+AEA-treated cells compared to all other cell cultures. The mRNA for the AEA synthesis enzyme N-acyl phosphatidylethanolamine phospholipase D and the 2-AG synthesis enzymes diacylglycerol lipase (DAGL)α and DAGLβ were higher in AM630+EPA-treated cells compared to the other groups. The mRNA levels of CB1 and CB2 were both highest in the AM630+EPA group. The mRNA for interleukin-6 and tumor necrosis factor-α was higher with AEA but lower with DHA and docosahexaenoyl ethanolamide (DHEA), supporting previous findings that the EC AEA supports activation of the COX system. These findings suggest that COX activity and protein levels are influenced by the ECS, specifically by the ligand AEA for CB1 and by inverse agonism of CB2.     

1-Pentyl-3-phenylacetylindoles, a new class of cannabimimetic indoles

A new class of cannabimimetic indoles, with 3-phenylacetyl or substituted 3-phenylacetyl substituents, has been prepared and their affinities for the cannabinoid CB1 and CB2 receptors have been determined. In general those compounds with a 2-substituted phenylacetyl group have good affinity for both receptors. The 4-substituted analogs have little affinity for either receptor, while the 3-substituted compounds are intermediate in their affinities. Two of these compounds, 1-pentyl-3-(2-methylphenylacetyl)indole (JWH-251) and 1-pentyl-3-(3-methoxyphenylacetyl)indole (JWH-302), have 5-fold selectivity for the CB1 receptor with modest affinity for the CB2 receptor. GTPgammaS determinations indicate that both compounds are highly efficacious agonists at the CB1 receptor and partial agonists at the CB2 receptor.     

Early Endogenous Activation of CB1 and CB2 Receptors after Spinal Cord Injury Is a Protective Response Involved in Spontaneous Recovery

Spinal cord injury (SCI) induces a cascade of processes that may further expand the damage (secondary injury) or, alternatively, may be part of a safeguard response. Here we show that after a moderate-severe contusive SCI in rats there is a significant and very early increase in the spinal cord content of the endocannabinoids 2-arachidonoylglycerol (2-AG) and arachidonoyl ethanolamide (anandamide, AEA). Since 2-AG and AEA act through CB1 and CB2 cannabinoid receptors, we administered at 20 minutes after lesion a single injection of their respective antagonists AM281 and AM630 alone or in combination to block the effects of this early endocannabinoid accumulation. We observed that AM281, AM630 or AM281 plus AM630 administration impairs the spontaneous motor recovery of rats according to the Basso-Beattie-Bresnahan (BBB) locomotor scale. However, blockade of CB1, CB2 or both receptors produced different effects at the histopathological level. Thus, AM630 administration results at 90 days after lesion in increased MHC-II expression by spinal cord microglia/monocytes and reduced number of serotoninergic fibres in lumbar spinal cord (below the lesion). AM281 exerted the same effects but also increased oedema volume estimated by MRI. Co-administration of AM281 and AM630 produced the effects observed with the administration of either AM281 or AM630 and also reduced white matter and myelin preservation and enhanced microgliosis in the epicentre. Overall, our results suggest that the endocannabinoids acting through CB1 and CB2 receptors are part of an early neuroprotective response triggered after SCI that is involved in the spontaneous recovery after an incomplete lesion.     

BML-190 and AM251 act as inverse agonists at the human cannabinoid CB2 receptor: signalling via cAMP and inositol phosphates

The aminoalkylindole BML-190 and diarylpyrazole AM251 ligands have previously been shown to bind to cannabinoid CB(2) and CB(1) receptors, respectively. In HEK-293 cells stably expressing the human CB(2) receptor, BML-190 and AM251 potentiated the forskolin-stimulated accumulation of cAMP. Moreover, the CB(2) receptor can interact productively with 16z44, a promiscuous G alpha(16/z) chimera. BML-190 and AM251 reduce the basal levels of inositol phosphate production in cells expressing the CB(2) receptor and 16z44. These results demonstrate that BML-190 and AM251 act as inverse agonists at the human CB(2) receptor acting via G alpha(i/o) and G alpha(q) family-coupled pathways.     

Constitutive activity of the cannabinoid CB1 receptor regulates the function of co-expressed Mu opioid receptors

The human mu opioid receptor was expressed stably in Flp-In T-REx HEK293 cells. Occupancy by the agonist DAMGO (Tyr-d-Ala-Gly-N-methyl-Phe-Gly-ol) resulted in phosphorylation of the ERK1/2 MAP kinases, which was blocked by the opioid antagonist naloxone but not the cannabinoid CB1 receptor inverse agonist SR141716A. Expression of the human cannabinoid CB1 receptor in these cells from the inducible Flp-In T-REx locus did not alter expression levels of the mu opioid receptor. This allowed the cannabinoid CB1 agonist WIN55212-2 to stimulate ERK1/2 phosphorylation but resulted in a large reduction in the capacity of DAMGO to activate these kinases. Although lacking affinity for the mu opioid receptor, co-addition of SR141716A caused recovery of the effectiveness of DAMGO. In contrast co-addition of the CB1 receptor neutral antagonist O-2050 did not. Induction of the CB1 receptor also resulted in an increase of basal [(35)S]guanosine 5'-3-O-(thio)triphosphate (GTPgammaS) binding and thereby a greatly reduced capacity of DAMGO to further stimulate [(35)S]GTPgammaS binding. CB1 inverse agonists attenuated basal [(35)S]GTPgammaS binding and restored the capacity of DAMGO to stimulate. Flp-In T-REx HEK293 cells were generated, which express the human mu opioid receptor constitutively and harbor a modified D163N cannabinoid CB1 receptor that lacks constitutive activity. Induction of expression of the modified cannabinoid CB1 receptor did not limit DAMGO-mediated ERK1/2 MAP kinase phosphorylation and did not allow SR141716A to enhance the function of DAMGO. These data indicate that it is the constitutive activity inherent in the cannabinoid CB1 receptor that reduces the capacity of co-expressed mu opioid receptor to function.     

Cannabinoid receptors CB1 and CB2 form functional heteromers in brain

Exploring the role of cannabinoid CB(2) receptors in the brain, we present evidence of CB(2) receptor molecular and functional interaction with cannabinoid CB(1) receptors. Using biophysical and biochemical approaches, we discovered that CB(2) receptors can form heteromers with CB(1) receptors in transfected neuronal cells and in rat brain pineal gland, nucleus accumbens, and globus pallidus. Within CB(1)-CB(2) receptor heteromers expressed in a neuronal cell model, agonist co-activation of CB(1) and CB(2) receptors resulted in a negative cross-talk in Akt phosphorylation and neurite outgrowth. Moreover, one specific characteristic of CB(1)-CB(2) receptor heteromers consists of both the ability of CB(1) receptor antagonists to block the effect of CB(2) receptor agonists and, conversely, the ability of CB(2) receptor antagonists to block the effect of CB(1) receptor agonists, showing a bidirectional cross-antagonism phenomenon. Taken together, these data illuminate the mechanism by which CB(2) receptors can negatively modulate CB(1) receptor function.     

Cannabinoid modulation of electrically evoked pH and oxygen transients in the nucleus accumbens of awake rats

Cannabinoid receptors have been implicated in the regulation of blood flow in the cerebral vasculature. Because the nucleus accumbens (NAc) shows high levels of central cannabinoid receptor 1 (CB1) expression we examined the effects of cannabinoids on the local transient alkaline shifts and increases in extracellular oxygen induced by electrical stimulation of the medial forebrain bundle (MFB) in conscious animals. These changes result from increases in cerebral blood flow (CBF) and metabolism in the NAc that are evoked by the stimulation. Oxygen and pH changes were monitored using fast-scan cyclic voltammetry at carbon-fiber microelectrodes in the NAc of freely moving rats. Administration of the cannabinoid receptor agonist WIN55,212-2 potently inhibited extracellular oxygen and pH changes, an effect that was reversed and prevented by pre-treatment with the CB1 receptor antagonists SR141716A and AM251. The effects on pH following WIN55,212-2 were similar to those following nimodipine, a recognized vasodilator. When AM251 was injected alone, the amplitude of electrically evoked pH shifts was unaffected. Administration of AM404 and VDM11, endocannabinoid transport inhibitors, partially inhibited pH transients in a CB1 receptor-dependent manner. The present findings suggest that CB1 receptor activation modulates changes in two well-established indices of local blood flow and metabolism resulting from electrically evoked activation of ascending fibers. Although endogenous cannabinoid tone alone is not sufficient to modify these responses, uptake blockade demonstrates that the system has the potential to exert CB1-specific effects similar to those of full agonists.     

Regulation of bone mass, bone loss and osteoclast activity by cannabinoid receptors

Accelerated osteoclastic bone resorption has a central role in the pathogenesis of osteoporosis and other bone diseases. Identifying the molecular pathways that regulate osteoclast activity provides a key to understanding the causes of these diseases and to the development of new treatments. Here we show that mice with inactivation of cannabinoid type 1 (CB1) receptors have increased bone mass and are protected from ovariectomy-induced bone loss. Pharmacological antagonists of CB1 and CB2 receptors prevented ovariectomy-induced bone loss in vivo and caused osteoclast inhibition in vitro by promoting osteoclast apoptosis and inhibiting production of several osteoclast survival factors. These studies show that the CB1 receptor has a role in the regulation of bone mass and ovariectomy-induced bone loss and that CB1- and CB2-selective cannabinoid receptor antagonists are a new class of osteoclast inhibitors that may be of value in the treatment of osteoporosis and other bone diseases.     

Cannabinoids reduce markers of inflammation and fibrosis in pancreatic stellate cells

Background

While cannabinoids have been shown to ameliorate liver fibrosis, their effects in chronic pancreatitis and on pancreatic stellate cells (PSC) are unknown.

Methodology/Principal Findings

The activity of the endocannabinoid system was evaluated in human chronic pancreatitis (CP) tissues. In vitro, effects of blockade and activation of cannabinoid receptors on pancreatic stellate cells were characterized. In CP, cannabinoid receptors were detected predominantly in areas with inflammatory changes, stellate cells and nerves. Levels of endocannabinoids were decreased compared with normal pancreas. Cannabinoid-receptor-1 antagonism effectuated a small PSC phenotype and a trend toward increased invasiveness. Activation of cannabinoid receptors, however, induced de-activation of PSC and dose-dependently inhibited growth and decreased IL-6 and MCP-1 secretion as well as fibronectin, collagen1 and alphaSMA levels. De-activation of PSC was partially reversible using a combination of cannabinoid-receptor-1 and -2 antagonists. Concomitantly, cannabinoid receptor activation specifically decreased invasiveness of PSC, MMP-2 secretion and led to changes in PSC phenotype accompanied by a reduction of intracellular stress fibres.

Conclusions/Significance

Augmentation of the endocannabinoid system via exogenously administered cannabinoid receptor agonists specifically induces a functionally and metabolically quiescent pancreatic stellate cell phenotype and may thus constitute an option to treat inflammation and fibrosis in chronic pancreatitis.     

Inhibition of pain responses by activation of CB(2) cannabinoid receptors

Cannabinoid receptor agonists diminish responses to painful stimuli. Extensive evidence demonstrates that CB(1) cannabinoid receptor activation inhibits pain responses. Recently, the synthesis of CB(2) cannabinoid receptor-selective agonists has allowed testing whether CB(2) receptor activation inhibits pain. CB(2) receptor activation is sufficient to inhibit acute nociception, inflammatory hyperalgesia, and the allodynia and hyperalgesia produced in a neuropathic pain model. Studies using site-specific administration of agonist and antagonist have suggested that CB(2) receptor agonists inhibit pain responses by acting at peripheral sites. CB(2) receptor activation also inhibits edema and plasma extravasation produced by inflammation. CB(2) receptor-selective agonists do not produce central nervous system (CNS) effects typical of cannabinoids retaining agonist activity at the CB(1) receptor. Peripheral antinociception without CNS effects is consistent with the peripheral distribution of CB(2) receptors. CB(2) receptor agonists may have promise for the treatment of pain and inflammation without CNS side effects.     

Constitutive endocytic cycle of the CB1 cannabinoid receptor

The CB1 cannabinoid receptor (CB1R) displays a significant level of ligand-independent (i.e. constitutive) activity, either when heterologously expressed in nonneuronal cells or in neurons where CB1Rs are endogenous. The present study investigates the consequences of constitutive activity on the intracellular trafficking of CB1R. When transfected in HEK-293 cells, CB1R is present at the plasma membrane, but a substantial proportion ( approximately 85%) of receptors is localized in intracellular vesicles. Detailed analysis of CB1-EGFP expressed in HEK-293 cells shows that the intracellular CB1R population is mostly of endocytic origin and that treatment with inverse agonist AM281 traps CB1R at the plasma membrane through a monensin-sensitive recycling pathway. Co-transfection with dominant positive or dominant negative mutants of the small GTPases Rab5 and Rab4, but not Rab11, profoundly modifies the steady-state and ligand-induced intracellular distribution of CB1R, indicating that constitutive endocytosis is Rab5-dependent, whereas constitutive recycling is mediated by Rab4. In conclusion, our results indicate that, due to its natural constitutive activity, CB1R permanently and constitutively cycles between plasma membrane and endosomes, leading to a predominantly intracellular localization at steady state.