Clock/Sleep-Dependent Learning and Memory in Male 3xTg-AD Mice at Advanced Disease Stages and Extrinsic Effects of Huprine X and the Novel Multitarget Agent AVCRI104P3.

A new hypothesis highlights sleep-dependent learning/memory consolidation and regards the sleep-wake cycle as a modulator of ß-amyloid and tau Alzheimer's disease (AD) pathologies. Sundowning behavior is a common neuropsychiatric symptom (NPS) associated with dementia. Sleep fragmentation resulting from disturbances in sleep and circadian rhythms in AD may have important consequences on memory processes and exacerbate the other AD-NPS. The present work studied the effect of training time schedules on 12-month-old male 3xTg-AD mice modeling advanced disease stages. Their performance in two paradigms of the Morris water maze for spatial-reference and visual-perceptual learning and memory were found impaired at midday, after 4 h of non-active phase. In contrast, early-morning trained littermates, slowing down from their active phase, exhibited better performance and used goal-directed strategies and non-search navigation described for normal aging. The novel multitarget anticholinesterasic compound AVCRI104P3 (0.6 µmol·kg-1, 21 days i.p.) exerted stronger cognitive benefits than its in vitro equipotent dose of AChEI huprine X (0.12 µmol·kg-1, 21 days i.p.). Both compounds showed streamlined drug effectiveness, independently of the schedule. Their effects on anxiety-like behaviors were moderate. The results open a question of how time schedules modulate the capacity to respond to task demands and to assess/elucidate new drug effectiveness.

Neuroprotective Effects of the Multitarget Agent AVCRI104P3 in Brain of Middle-Aged Mice.

Molecular factors involved in neuroprotection are key in the design of novel multitarget drugs in aging and neurodegeneration. AVCRI104P3 is a huprine derivative that exhibits potent inhibitory effects on human AChE, BuChE, and BACE-1 activities, as well as on AChE-induced and self-induced Aß aggregation. More recently, cognitive protection and anxiolytic-like effects have also been reported in mice treated with this compound. Now, we have assessed the ability of AVCRI104P3 (0.43 mg/kg, 21 days) to modulate the levels of some proteins involved in the anti-apoptotic/apoptotic processes (pAkt1, Bcl2, pGSK3ß, p25/p35), inflammation (GFAP and Iba1) and neurogenesis in C57BL/6 mice. The effects of AVCRI104P3 on AChE-R/AChE-S isoforms have been also determined. We have observed that chronic treatment of C57BL/6 male mice with AVCRI104P3 results in neuroprotective effects, increasing significantly the levels of pAkt1 and pGSK3ß in the hippocampus and Bcl2 in both hippocampus and cortex, but slightly decreasing synaptophysin levels. Astrogliosis and neurogenic markers GFAP and DCX remained unchanged after AVCRI104P3 treatment, whereas microgliosis was found to be significantly decreased pointing out the involvement of this compound in inflammatory processes. These results suggest that the neuroprotective mechanisms that are behind the cognitive and anxiolytic effects of AVCRI104P3 could be partly related to the potentiation of some anti-apoptotic and anti-inflammatory proteins and support the potential of AVCRI104P3 for the treatment of brain dysfunction associated with aging and/or dementia.

Huprine X Attenuates The Neurotoxicity Induced by Kainic Acid, Especially Brain Inflammation.

Huprine X (HX) is a synthetic anticholinesterasic compound that exerts a potent inhibitory action on acetylcholinesterase (AChE) activity, an agonist effect on cholinergic receptors, neuroprotective activity in different neurotoxicity models in vivo and in vitro and cognition enhancing effects in non-transgenic (C57BL/6) and transgenic (3xTg-AD, APPswe) mice. In this study, we assessed the ability of HX (0.8 mg/kg, 21 days) to prevent the damage induced by kainic acid (KA; 28 mg/kg) regarding apoptosis, glia reactivity and neurogenesis in mouse brain. KA administration significantly modified the levels of pAkt1, Bcl2, pGSK3ß, p25/p35, increased the glial cell markers and reduced the neurogenesis process. We also observed that pre-treatment with HX significantly reduced the p25/p35 ratio and increased synaptophysin levels, which suggests a protective effect against apoptosis and an improvement of neuroplasticity. The increase in GFAP (88%) and Iba-1 (72%) induced by KA was totally prevented by HX pre-treatment, underlying a relevant anti-inflammatory action of the anticholinesterasic drug. Our findings highlight the potential of HX, in particular, and of AChEIs, in general, to treat a number of diseases that course with both cognitive deficits and chronic inflammatory processes.

Behavioural effects of novel multitarget anticholinesterasic derivatives in Alzheimer's disease.

The current pharmacological approach to Alzheimer's disease (AD) treatment, mostly based on acetylcholinesterase inhibitors (AChEIs), is being revisited, especially in terms of the temporal frames and the potential benefits of their noncanonic actions, raising the question of whether inhibitors of AChE might also act in a disease-modifying manner. Besides, in the last decades, the pharmacophoric moieties of known AChEIs have been covalently linked to other pharmacophores in the pursuit of multitarget hybrid molecules that are expected to induce long-lasting amelioration of impaired neurotransmission and clinical symptoms but also to exert disease-modifying effects. Our research consortium has synthesized and defined the pharmacological profile of new AChEIs derivatives of potential interest for the treatment of AD. Among these, huprines and derivatives have been characterized successfully. Huprine X, a reversible AChE inhibitor, designed by molecular hybridization of tacrine and huperzine A, has been shown to affect the amyloidogenic process in vitro, and the AD-related neuropathology in vivo in mice models of the disease. More recently, we have shown that a group of donepezil-huprine heterodimers exerts a highly potent and selective inhibitory action on AChE both in vitro and ex vivo, simultaneously interacting with both peripheral and catalytic binding sites, and inhibiting the ß-amyloid aggregation, whereas some levetiracetam-huprine hybrids have been shown to reduce epileptiform activity, neuroinflammation and amyloid burden in an animal model of AD. Here, we summarize the behavioural correlates of these noncanonic actions as assessed in three distinct biological scenarios: middle-age, cognitive deficits associated with ageing and AD-like phenotype in mice. Besides the improvement in the hallmark cognitive symptomatology without inducing side effects, these drugs have shown to be able to modulate emotional and anxiety-like behaviours or to reduce spontaneous seizures, all of them related to the so-called 'behavioural and psychological symptoms of dementia'. Overall, the studies show that these novel multitarget anticholinesterasics exert noncanonic actions providing symptomatic and disease-modifying benefits of potential interest for the management of AD.

Undifferentiated and differentiated PC12 cells protected by huprines against injury induced by hydrogen peroxide.

Oxidative stress is implicated in the pathogenesis of neurodegenerative disorders and hydrogen peroxide (H2O2) plays a central role in the stress. Huprines, a group of potent acetylcholinesterase inhibitors (AChEIs), have shown a broad cholinergic pharmacological profile. Recently, it has been observed that huprine X (HX) improves cognition in non transgenic middle aged mice and shows a neuroprotective activity (increased synaptophysin expression) in 3xTg-AD mice. Consequently, in the present experiments the potential neuroprotective effect of huprines (HX, HY, HZ) has been analyzed in two different in vitro conditions: undifferentiated and NGF-differentiated PC12 cells. Cells were subjected to oxidative insult (H2O2, 200 µM) and the protective effects of HX, HY and HZ (0.01 µM-1 µM) were analyzed after a pre-incubation period of 24 and 48 hours. All huprines showed protective effects in both undifferentiated and NGF-differentiated cells, however only in differentiated cells the effect was dependent on cholinergic receptors as atropine (muscarinic antagonist, 0.1 µM) and mecamylamine (nicotinic antagonist, 100 µM) reverted the neuroprotection action of huprines. The decrease in SOD activity observed after oxidative insult was overcome in the presence of huprines and this effect was not mediated by muscarinic or nicotinic receptors. In conclusion, huprines displayed neuroprotective properties as previously observed in in vivo studies. In addition, these effects were mediated by cholinergic receptors only in differentiated cells. However, a non-cholinergic mechanism, probably through an increase in SOD activity, seems to be also involved in the neuroprotective effects of huprines.

Expanding the multipotent profile of huprine-tacrine heterodimers as disease-modifying anti-Alzheimer agents.

BACKGROUND: Multifactorial diseases such as Alzheimer's disease (AD) should be more efficiently tackled by drugs which hit multiple biological targets involved in their pathogenesis. We have recently developed a new family of huprine-tacrine heterodimers, rationally designed to hit multiple targets involved upstream and downstream in the neurotoxic cascade of AD, namely ß-amyloid aggregation and formation as well as acetylcholinesterase catalytic activity. OBJECTIVE: In this study, the aim was to expand the pharmacological profiling of huprine-tacrine heterodimers investigating their effect on muscarinic M(1) receptors as well as their neuroprotective effects against an oxidative insult. METHODS: Sprague-Dawley rat hippocampus homogenates were used to assess the specific binding of two selected compounds in competition with 1 nM [(3)H]pirenzepine (for M(1) receptors) or 0.8 nM [(3)H]quinuclidinyl benzilate (for M(2) receptors). For neuroprotection studies, SHSY5Y cell cultures were subjected to 250 µM hydrogen peroxide insult with or without preincubation with some huprine-tacrine heterodimers. RESULTS: A low nanomolar affinity and M(1)/M(2) selectivity has been found for the selected compounds. Huprine-tacrine heterodimers are not neurotoxic to SHSY5Y cells at a range of concentrations from 1 to 0.001 µM, and some of them can protect cells from the oxidative damage produced by hydrogen peroxide at concentrations as low as 0.001 µM. CONCLUSION: Even though it remains to be determined if these compounds act as agonists at M(1) receptors, as it is the case of the parent huprine Y, their low nanomolar M(1) affinity and neuroprotective effects expand their multitarget profile and increase their interest as disease-modifying anti-Alzheimer agents.

Huprine-tacrine heterodimers as anti-amyloidogenic compounds of potential interest against Alzheimer's and prion diseases.

A family of huprine-tacrine heterodimers has been developed to simultaneously block the active and peripheral sites of acetylcholinesterase (AChE). Their dual site binding for AChE, supported by kinetic and molecular modeling studies, results in a highly potent inhibition of the catalytic activity of human AChE and, more importantly, in the in vitro neutralization of the pathological chaperoning effect of AChE toward the aggregation of both the ß-amyloid peptide (Aß) and a prion peptide with a key role in the aggregation of the prion protein. Huprine-tacrine heterodimers take on added value in that they display a potent in vitro inhibitory activity toward human butyrylcholinesterase, self-induced Aß aggregation, and ß-secretase. Finally, they are able to cross the blood-brain barrier, as predicted in an artificial membrane model assay and demonstrated in ex vivo experiments with OF1 mice, reaching their multiple biological targets in the central nervous system. Overall, these compounds are promising lead compounds for the treatment of Alzheimer's and prion diseases.

Novel huprine derivatives with inhibitory activity toward ß-amyloid aggregation and formation as disease-modifying anti-Alzheimer drug candidates.

A new family of dual binding site acetylcholinesterase (AChE) inhibitors has been designed, synthesized, and tested for their ability to inhibit AChE, butyrylcholinesterase (BChE), AChE-induced and self-induced ß-amyloid (Aß) aggregation and ß-secretase (BACE-1), and to cross the blood-brain barrier. The new heterodimers consist of a unit of racemic or enantiopure huprine Y or X and a donepezil-related 5,6-dimethoxy-2-[(4-piperidinyl)methyl]indane moiety as the active site and peripheral site to mid-gorge-interacting moieties, respectively, connected through a short oligomethylene linker. Molecular dynamics simulations and kinetics studies support the dual site binding to AChE. The new heterodimers are potent inhibitors of human AChE and moderately potent inhibitors of human BChE, AChE-induced and self-induced Aß aggregation, and BACE-1, and are predicted to be able to enter the central nervous system (CNS), thus constituting promising multitarget anti-Alzheimer drug candidates with the potential to modify the natural course of this disease.

Effect of huprine X on ß-amyloid, synaptophysin and α7 neuronal nicotinic acetylcholine receptors in the brain of 3xTg-AD and APPswe transgenic mice.

BACKGROUND: Several studies implicate acetylcholinesterase (AChE) in the pathogenesis of Alzheimer's disease (AD), raising the question of whether inhibitors of AChE also might act in a disease-modifying manner. Huprine X (HX), a reversible AChE inhibitor hybrid of tacrine and huperzine A, has shown to affect the amyloidogenic process in vitro. In this study, the aim was to investigate whether HX could affect the AD-related neuropathology in vivo in two mouse models. METHODS: Tg2576 (K670M/N671L) (APPswe) and 3xTg-AD (K670M/N671L, PS1M146V, tauP301L) mice were treated with HX (0.12 µmol/kg, i.p., 21 days) or saline at 6-7 months. Human ß-amyloid (Aß) was measured by ELISA, synaptophysin by Western blot and α7 neuronal nicotinic acetylcholine receptors (nAChRs) were analyzed by [(125)I]α-bungarotoxin autoradiography. RESULTS: Treatment with HX reduced insoluble Aß1-40 (about 40%) in the hippocampus of 3xTg-AD mice, while showing no effect in APPswe mice. Additionally, HX markedly increased cortical synaptophysin levels (about 140%) and decreased (about 30%) the levels of α7 nAChRs in the caudate nucleus of 3xTg-AD mice, while increasing (about 10%) hippocampal α7 nAChRs in APPswe mice. CONCLUSION: The two mouse models react differently to HX treatment, possibly due to their differences in brain neuropathology. The modulation of Aß and synaptophysin by HX in 3xTg-AD mice might be due to its suggested interaction with the peripheral anionic site on AChE, and/or via cholinergic mechanisms involving activation of cholinergic receptors. Our results provide further evidence that drugs targeting AChE affect some of the fundamental processes that contribute to neurodegeneration, but whether HX might act in a disease-modifying manner in AD patients remains to be proven.

Tacrine-based dual binding site acetylcholinesterase inhibitors as potential disease-modifying anti-Alzheimer drug candidates.

Two novel families of dual binding site acetylcholinesterase (AChE) inhibitors have been developed, consisting of a tacrine or 6-chlorotacrine unit as the active site interacting moiety, either the 5,6-dimethoxy-2-[(4-piperidinyl)methyl]-1-indanone fragment of donepezil (or the indane derivative thereof) or a 5-phenylpyrano[3,2-c]quinoline system, reminiscent to the tryciclic core of propidium, as the peripheral site interacting unit, and a linker of suitable length as to allow the simultaneous binding at both sites. These hybrid compounds are all potent and selective inhibitors of human AChE, and more interestingly, are able to interfere in vitro both formation and aggregation of the beta-amyloid peptide, the latter effects endowing these compounds with the potential to modify Alzheimer's disease progression.

Pyrano[3,2-c]quinoline-6-chlorotacrine hybrids as a novel family of acetylcholinesterase- and beta-amyloid-directed anti-Alzheimer compounds.

Two isomeric series of dual binding site acetylcholinesterase (AChE) inhibitors have been designed, synthesized, and tested for their ability to inhibit AChE, butyrylcholinesterase, AChE-induced and self-induced beta-amyloid (Abeta) aggregation, and beta-secretase (BACE-1) and to cross blood-brain barrier. The new hybrids consist of a unit of 6-chlorotacrine and a multicomponent reaction-derived pyrano[3,2-c]quinoline scaffold as the active-site and peripheral-site interacting moieties, respectively, connected through an oligomethylene linker containing an amido group at variable position. Indeed, molecular modeling and kinetic studies have confirmed the dual site binding of these compounds. The new hybrids, and particularly 27, retain the potent and selective human AChE inhibitory activity of the parent 6-chlorotacrine while exhibiting a significant in vitro inhibitory activity toward the AChE-induced and self-induced Abeta aggregation and toward BACE-1, as well as ability to enter the central nervous system, which makes them promising anti-Alzheimer lead compounds.

Novel donepezil-based inhibitors of acetyl- and butyrylcholinesterase and acetylcholinesterase-induced beta-amyloid aggregation.

A novel series of donepezil-tacrine hybrids designed to simultaneously interact with the active, peripheral and midgorge binding sites of acetylcholinesterase (AChE) have been synthesized and tested for their ability to inhibit AChE, butyrylcholinesterase (BChE), and AChE-induced A beta aggregation. These compounds consist of a unit of tacrine or 6-chlorotacrine, which occupies the same position as tacrine at the AChE active site, and the 5,6-dimethoxy-2-[(4-piperidinyl)methyl]-1-indanone moiety of donepezil (or the indane derivative thereof), whose position along the enzyme gorge and the peripheral site can be modulated by a suitable tether that connects tacrine and donepezil fragments. All of the new compounds are highly potent inhibitors of bovine and human AChE and BChE, exhibiting IC50 values in the subnanomolar or low nanomolar range in most cases. Moreover, six out of the eight hybrids of the series, particularly those bearing an indane moiety, exhibit a significant A beta antiaggregating activity, which makes them promising anti-Alzheimer drug candidates.

Binding of 13-amidohuprines to acetylcholinesterase: exploring the ligand-induced conformational change of the gly117-gly118 peptide bond in the oxyanion hole.

The acetylcholinesterase (AChE) inhibitory activity of a series of 13-amido derivatives of huprine Y, designed to enlarge the occupancy of the catalytic binding site by mimicking the piridone moiety present in (-)-huperzine A, has been assessed. Although both 13-formamido and 13-methanesulfonamido derivatives are more potent human AChE inhibitors than tacrine and (-)-huperzine A, none of them equals the potency of huprine Y. Molecular modeling studies show that the two derivatives effectively trigger the Gly117-Gly118 conformational flip induced upon binding of (-)-huperzine A, leading to a similar pattern of interactions as that formed by the pyridone amido group of (-)-huperzine A. The detrimental effect on the binding affinity relative to the 13-unsubstituted huprine could be ascribed to a sizable deformation cost associated with the ligand-induced peptide flip. This finding can be interpreted as a mechanism selected by evolution to ensure the preorganization of the functionally relevant oxyanion hole in the binding site of AChE, where residues Gly117 and Gly118 play a relevant role in mediating substrate recognition.

Synthesis and pharmacological evaluation of huprine-tacrine heterodimers: subnanomolar dual binding site acetylcholinesterase inhibitors.

A series of huprine-tacrine heterodimers has been developed by connection of huprine Y, a compound with one of the highest affinities for the active site of acetylcholinesterase yet reported, with tacrine, a compound with known affinity for the peripheral site of the enzyme, through a linker of appropriate length to allow simultaneous interaction with both binding sites. These compounds exhibit human acetylcholinesterase and butyrylcholinesterase inhibitory activities with IC(50) values in the subnanomolar and low nanomolar range, respectively.

Characterisation of the anticholinesterase activity of two new tacrine-huperzine A hybrids.

The effects of two tacrine-huperzine A hybrids, (+/-)-huprine Y and (+/-)-huprine Z, have been evaluated. Bovine and human acetylcholinesterase (AChE) and human butyrylcholinesterase (BChE) inhibition were assayed by Ellman's method. The two huprines were more active than both tacrine and (-)-huperzine A as inhibitors of both human and bovine AChE, and they acted as mixed-type AChE inhibitors. Moreover, (+/-)-huprine Y exhibited a tight binding character seen in the experiments of reversibility of bovine AChE inhibitory activity. In addition, both compounds were more active toward AChE than toward BChE. Also, the selectivity for the human AChE was greater than for the bovine enzyme. In ex vivo studies performed in mice, both drugs showed a clear inhibitory activity of brain AChE, 20 min after i.p. injection, (+/-)-huprine Y being more potent than (+/-)-huprine Z [ID(50) 1.09 (0.39-2.98) vs. 5.77 (3.29-10.30) micromol/kg]. The time-course study of the inhibitory effect displayed a t(1/2) of 1 h for the two compounds. These results show that these drugs are two potent, central AChE inhibitors of potential interest in the treatment of AD.

Synthesis and muscarinic activities of O-[(benzyl- or benzoyl-pyrazolyl)propynyl]-oximes of N-methylpiperidinone, 3-tropinone, and 3-quinuclidinone.

The synthesis of O-propynyloximes of N-methylpiperidinone, 3-tropinone, and 3-quinuclidinone, containing several pyrazole frameworks is described, together with their muscarinic receptor affinities. Compounds derived from N-methylpiperidinone or 3-tropinone and N-(4-methoxybenzyl)- or N-(2,4,6-trimethylbenzoyl)pyrazole showed moderate activity for muscarinic receptors in the rat central nervous system. A semi-empirical AM1 calculation has shown that the O-[(benzoyl-pyrazolyl)propynyl]-oximes of tropinone fit a previously described muscarinic pharmacophoric model, revealing structural features useful for the development of new muscarinic agents.

Changes in electrophysiological properties in the prostatic portion of vas deferens from spontaneously hypertensive rats.

The main objective of this study has been to analyse the electrophysiological differences in the prostatic portion of vas deferens between spontaneously hypertensive (SHR) and Wistar Kyoto rats (WKY). Resting membrane potentials (RMP) recorded in SHR (-63.8+/-0.3 mV) and WKY (-68.1+/-0.3 mV) were significantly different. Bath applications of suramin (30 microM), alpha,beta-methylene adenosine 5'-triphosphate (alpha,beta-meATP; 30 microM) or prazosin (0.1 microM) did not modify the control values of RMP. In control conditions, spontaneous excitatory junction potentials (SEJPs) were recorded in preparations from both groups of animals. SEJPs registered in SHR were greater than those in WKY in amplitude (7.0+/-0.4 mV vs. 2.6+/-0.1 mV) and frequency (0.25+/-0.02 Hz vs. 0.14+/-0.01 Hz). SEJP amplitude was abolished by bath applications of suramin (30 microM) or alpha,beta-meATP (30 microM). However, tetrodotoxin (TTX; 1 microM) and prazosin (0.1 microM) had no effect on this spontaneous activity. Electrical-field stimulation (EFS; 0.1 ms, 20 V, 0.2 Hz) induced an enhanced excitatory junction potential (EJP) in SHR but not in WKY (16.0+/-0.6 mV vs. 12.2+/-0.5 mV) which was abolished by TTX (1 microM), suramin (30 microM) and alpha,beta-meATP (30 microM). The degree of inhibition of both SEJP and EJP produced by alpha,beta-meATP (0.3-30 microM) was greater in SHR than in WKY. This study demonstrates an altered purinergic contribution to the co-transmission process in the prostatic portion of vas deferens from SHR.

Synthesis of new 1-(but-2-ynyl)pyrazoles: containing a pyrrolidine or diethylamine moiety and their muscarinic properties.

The synthesis of two series of 1-(but-2-ynyl)pyrazole containing a pyrrolidine or a diethylamine moiety, respectively, is described, together with their muscarinic receptor affinities.

Synthesis and acetylcholinesterase/butyrylcholinesterase inhibition activity of 4-amino-2, 3-diaryl-5, 6, 7, 8-tetrahydrofuro(and thieno)[2, 3-b]-quinolines, and 4-amino-5, 6, 7, 8, 9-pentahydro-2, 3-diphenylcyclohepta[e]furo(and thieno)-[2, 3-b]pyridines.

The acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE) inhibition activities of a series of 4-amino-2, 3-diaryl-5, 6, 7, 8-tetrahydrofuro[2, 3-b]quinolines (10-12)/4-amino-5, 6, 7, 8-tetrahydro-2, 3-diphenylthieno[2, 3-b]quinoline (14) and 4-amino-5, 6, 7, 8, 9-pentahydro-2, 3-diphenylcyclohepta[e]furo[2, 3-b]pyridine (13)/4-amino-5, 6, 7, 8, 9-pentahydro-2, 3-phenylcyclohepta[e]thieno[2, 3-b]pyridine (15) are described. These compounds are tacrine (THA) analogues which have been prepared either from readily available 2-amino-3-cyano-4, 5-diarylfurans (16-18) or from 2-amino-3-cyano-4, 5-diphenylthiophene (19), via Friedländer condensation with cyclohexanone or cycloheptanone. These compounds are competitive inhibitors for acetylcholinesterase, the more potent being compound (13) which is three-fold less active than tacrine. The butyrylcholinesterase inhibition activity is significant only in compounds 10 and133, which are ten-fold less active than tacrine. It is found that the products 11 and 12 strongly inhibit acetylcholinesterase, and show excellent selectivity regarding butyrylcholinesterase.

Assessing the (a)symmetry of concentration-effect curves: empirical versus mechanistic models.

Modeling the shape of concentration-effect curves is of prime importance in pharmacology. Geometric descriptors characterizing these curves (the upper and lower asymptotes, the mid-point, the mid-point slope, and the point of inflection) are used for drug comparison or for assessing the change in agonist function after a system modification. The symmetry or asymmetry around the mid-point of a concentration-effect curve is a fundamental property that, regretfully, is often overlooked because, generally, models yielding exclusively symmetric curves are used. In the present review, empirical and mechanistic models are examined in their ability to fit experimental data. The geometric parameters of a survey of empirical models, the Hill equation, a logistic variant that we call the modified Hill equation, the Richards function, and the Gompertz model are determined. To analyze the relationship between asymmetry and mechanism, some examples from the ionic channel field, in an increasing degree of complexity, are used. It is shown that asymmetry arises from ionic channels with multiple binding sites that are partly occupied. The operational model of agonism is discussed both in its empirical general formulation and including the signal transduction mechanisms through G-protein-coupled receptors. It is shown that asymmetry results from systems where receptor distribution is allowed. Developed mathematical models are compared for describing experimental data on alpha-adrenoceptors. The existence or not of a relationship between the shape of the curves and receptor reserve is discussed.