Signal transduction pathways modulated by the D2 subfamily of dopamine receptors.

The D2 subfamily of dopamine receptors includes D2A, D2B, D3, and D4 dopamine receptors. These receptors activate cellular effector systems, principally through pertussis toxin-sensitive G-proteins. Historically, D2-like receptors in brain tissues were recognized as the dopamine receptor subtypes that inhibit adenylyl cyclase. Recent studies, reviewed here, have shown that multiple effector systems can be activated by these receptors, and the potential involvement of these in dopaminergic neutrotransmission is discussed.

Synthesis and pharmacological evaluation of thiopyran analogues of the dopamine D3 receptor-selective agonist (4aR,10bR)-(+)-trans-3,4,4a,10b-tetrahydro-4-n-propyl-2H,5H [1]b enzopyrano[4,3-b]-1,4-oxazin-9-ol (PD 128907).

Benzopyranoxazine (+)-7 (PD 128907) is the most dopamine (DA) D3 receptor-selective agonist presently known. The only structural feature which distinguishes 7 from the analogous nonselective naphthoxazines is an oxygen atom in the 6-position. To extend this series of tricyclic DA agonists we used a classic bioisoster approach and synthesized thiopyran analogues of 7, which have a sulfur atom in the 6-position. We prepared trans-4-n-propyl-3,4,4a,10b-tetrahydro-2H,5H-[1]benzothiopyrano[4, 3-b]-1,4-oxazin-9-ol (9, trans-9-OH-PTBTO), its enantiomers ((+)-9 and (-)-9), the racemic cis-analogue (10), and the racemic trans-sulfoxide (11) and studied the potency and selectivity for DA receptors of these compounds. As with other rigid DA agonists, the highest affinity for DA receptors resided in one of the enantiomers, in this case the (-)-enantiomer of 9. On the basis of a single-crystal X-ray analysis of a key intermediate, the absolute configuration of (-)-9 was found to be 4aS,10bR, which is homochiral with (+)-(4aR,10bR)-7. In contrast to (+)-7 however, (-)-9 displayed no selectivity for any of the DA receptors. In addition, it has affinity for 5HT1A receptors. (+/-)-cis-4-n-Propyl-3,4,4a,10b-tetrahydro-2H,5H-[1]benzothiopyrano++ +[4,3-b]-1,4-oxazin-9-ol (10), which was expected to be inactive, displayed affinity and selectivity for the DA D3 receptor, whereas the sulfoxide 11 displayed some DA D3 selectivity, but with a lower affinity. Further pharmacological evaluation revealed that (-)-9 is a very potent full agonist at DA D2 receptors and a partial agonist at DA D3 receptors. The cis-analogue (+/-)-10 displayed the same profile, but with lower potency. These findings were confirmed in vivo: in reserpinized rats (-)-9 displayed short-acting activation of locomotor activity (DA D2 agonism) and also lower lip retraction and flat body posture, (5HT1A agonism). Compound (+/-)-10 had no effect on locomotor activity. In unilaterally 6-OH-DA lesioned rats, (-)-9 gave short-acting locomotor activation. Furthermore, in microdialysis studies in rat striatum, (-)-9 potently decreased DA release, confirming its activation of presynaptic DA D2 receptors.

Thiazoloindans and thiazolobenzopyrans: a novel class of orally active central dopamine (partial) agonists.

The 2-aminothiazole moiety has proven its value in medicinal chemistry as a stable and lipophilic bioisosteric replacement of a phenol group. This approach has provided dopamine (DA) agonists with good oral availability. To further explore its use in the development of DA agonists, we have combined the 2-aminothiazole moiety with 2-aminoindans and 3-aminobenzopyrans, which are known templates for DA agonists. In this study we have synthesized 6-amino-3-(N,N-di-n-propylamino)-3,4-dihydro-2H-thiazolo[5, 4-f]-[1]benzopyran (12) and 6-amino-2-(N, N-di-n-propylamino)thiazolo[4,5-f]indan (20) and several analogues (13, 17, and 21). The affinity of the thiazolobenzopyrans and thiazoloindans for DA receptors was evaluated, which revealed compound 20 to have high affinity for DA D(3) receptors. In addition, the compounds were screened for their potential to inhibit lipid peroxidation, to determine their radical scavenging properties. Compounds 12, 20, and 21 were subjected to further pharmacological evaluation in a functional assay to determine intrinsic activity. Compound 20 was also studied with microdialysis (to determine effects on DA turnover in striatum) and in unilaterally 6-OH-DA lesioned rats (to determine their potential as DA agonists). These studies selected compound 20 (GMC 1111) as particularly interesting. Compound 20 caused a rotation activation in unilaterally 6-OH-DA lesioned rats and an increase in DA turnover in rat striatum. This dual agonist/antagonist action is best accounted for by its partial agonism at striatal DA D(2) receptors. Interestingly, 20 displayed long-lasting activity and excellent oral availability in 6-OH-DA lesioned rats, making this compound potentially useful for the treatment of Parkinson's disease.

Dopamine D(3) receptor antagonists. 1. Synthesis and structure-activity relationships of 5,6-dimethoxy-N-alkyl- and N-alkylaryl-substituted 2-aminoindans.

5,6-Dimethoxy-2-(N-dipropyl)-aminoindan (3, PNU-99194A) was found to be a selective dopamine D(3) receptor antagonist with potential antipsychotic properties in animal models. To investigate the effects of nitrogen substitution on structure-activity relationships, a series of 5,6-dimethoxy-N-alkyl- and N-alkylaryl-substituted 2-aminoindans were synthesized and evaluated in vitro for binding affinity and metabolic stability. The results indicate that substitution at the amine nitrogen of the 2-aminoindans is fairly limited to the di-N-propyl group in order to achieve selective D(3) antagonists. Thus, combinations of various alkyl groups were generally inactive at the D(3) receptor. Although substitution with an N-alkylaryl or N-alkylheteroaryl group yields compounds with potent D(3) binding affinity, the D(2) affinity is also enhanced, resulting in a less than 4-fold preference for the D(3) receptor site, and no improvements in metabolic stability were noted. A large-scale synthesis of the D(3) antagonist 3 has been developed that has proven to be reproducible with few purification steps. The improvements include the use of 3,4-dimethoxybenzaldehyde as a low-cost starting material to provide the desired 5,6-dimethoxy-1-indanone 5c in good overall yield (65%) and the formation of a soluble silyl oxime 17 that was reduced efficiently with BH(3).Me(2)S. The resulting amino alcohol was alkylated and then deoxygenated using a Lewis acid and Et(3)SiH to give the desired product 3 in good overall yield of ( approximately 65%) from the indanone 5c.

Selective cyclooxygenase-2 inhibitors: heteroaryl modified 1,2-diarylimidazoles are potent, orally active antiinflammatory agents.

A series of heteroaryl modified 1,2-diarylimidazoles has been synthesized and found to be potent and highly selective (1000-9000-fold) inhibitors of the human COX-2. 3-Pyridyl derived COX-2 selective inhibitor (25) exhibited excellent activity in acute (carrageenan induced paw edema, ED(50) = 5.4 mg/kg) and chronic (adjuvant induced arthritis, ED(50) = 0.25 mg/kg) models of inflammation. The relatively long half-life of 25 in rat and dog prompted investigation of the pyridyl and other heteroaromatic systems containing potential metabolic functionalities. A number of substituted pyridyl and thiazole containing compounds (e.g., 44, 46, 54, 76, and 78) demonstrated excellent oral activity in every efficacy model evaluated. Several orally active diarylimidazoles exhibited desirable pharmacokinetics profiles and showed no GI toxicity in the rat up to 100 mg/kg in both acute and chronic models. The paper describes facile and practical syntheses of the targeted diarylimidazoles. The structure-activity relationships and antiinflammatory properties of a series of diarylimidazoles are discussed.

A comprehensive method for the quantitative determination of dopamine receptor subtypes.

We have demonstrated that three subtypes of dopamine receptors can be characterized using several radioligand binding techniques. Indirect binding assays in which several competing ligands were used to inhibit the binding of the nonselective radioligand spiroperidol resulted in shallow displacement curves with Hill coefficients less than 1. Nonlinear regression analysis of these curves also indicated that there were two subtypes of the D-2 receptor present in a ratio of approximately 3 to 1. Direct binding assays with [3H]alpha-flupenthixol showed that this radioligand nonselectively labeled D-2A, D-2B, and D-1 receptors. Inhibition of the binding of [3H]alpha-flupenthixol by spiroperidol revealed that spiroperidol had a much higher affinity for D-2A and D-2B receptors than for D-1 receptors. Masking D-2 receptors with nanomolar concentrations of spiroperidol permitted characterization of D-1 receptors with the radioligand [3H]alpha-flupenthixol. Indirect binding assays of D-1 receptors with numerous competing ligands resulted in steep displacement curves with Hill coefficients of 1. This is consistent with the existence of a single, homogeneous population of D-1 receptors.

Behavioral and neurochemical data suggest functional differences between dopamine D2 and D3 receptors.

In an in vitro model for mitogenic activity in cloned Chinese hamster ovary (CHO) cells expressing rat dopamine D2 or D3 receptors, the EC50D2/EC50D3 ratios for the agonists, apomorphine, (+)-3-hydroxy-N-n-propyl-phenylpiperidine ((+)-3-PPP), quinpirole, R-(+)-7-hydroxy-2-(di-n-propylamino)tetralin (R-(+)-7-OH-DPAT) and pramipexole (SND919) were found to be 0.36, 0.41, 1.3, 3.7 and 7.0, respectively. In locomotor activity experiments with actively exploring rats, the more dopamine D3 preferring agonists, R-(+)-7-OH-DPAT and pramipexole, were most efficacious to reduce locomotion. The hypoactivity was also observed at doses that did not affect brain dopamine synthesis rate (DOPA accumulation) or release (measured in in vivo dialysis experiments). In contrast, for apomorphine, (+)-3-PPP and quinpirole there was a closer correlation between doses that reduced exploratory activity and doses that reduced brain dopamine release and synthesis. The present data support the hypothesis that the functional dopamine D3 receptor is a postsynaptic receptor inhibitory on rat locomotion.

Pramipexole binding and activation of cloned and expressed dopamine D2, D3 and D4 receptors.

Pramipexole (SND 919; 2-amino-4,5,6,7-tetrahydro-6-propylamino-benzthiazole-dihydrochlor ide) is a potent dopamine autoreceptor agonist. We have carried out an analysis of the binding affinities of dopamine D2L, D2S, D3, and D4 receptors for pramipexole using both [3H]pramipexole and [3H]spiperone as radioligands at cloned and heterologously expressed receptors. Studies were carried out using rat and human D2L, D2S and D3 receptors with equivalent results. When the binding of pramipexole to the high affinity, guanine nucleotide-sensitive state of each receptor was analyzed, pramipexole is most selective for D3 compared to D2 and D4 receptors. These results indicate a 5-fold selectivity of pramipexole for D3 receptors, while quinpirole and bromocriptine are non-selective or more D2/D4 receptor selective. Two measurements of receptor activation for dopamine D2, D3, and D4 receptors also show that pramipexole is most potent for activation of D3 receptors. The dopamine D3 receptor selectivity of pramipexole may explain the previously described properties of this drug, including its potent autoreceptor preference.

Pre- and postsynaptic dopaminergic activities of U-86170F.

The biochemical, endocrine, receptor binding, and behavioral effects of the putative dopamine autoreceptor agonist, U-86170F, were evaluated in various in vivo and in vitro models. U-86170F and apomorphine were shown to cause a significant reversal of the effects of gamma-butyrolactone (GBL) on dopamine accumulation in mouse striata. In contrast to apomorphine, U-86170F had a ceiling effect on the extent of the reversal of GBL effects (55%), whereas apomorphine had an 82% reversal. The effect on striatal homovanillic acid (HVA) levels was also monitored, and both compounds exerted a similar and significant reduction in striatal HVA. A comparison was made between the effects of intraperitoneal (i.p.) and oral administration of U-86170F in the alpha-methyl-p-tyrosine (alpha-MPT)/prolactin model in rats. When administered by the i.p. route, U-86170F suppressed the effects of alpha-MPT on prolactin level increase, having an ED50 of about 0.03 mg/kg, and when administered by the oral route, its ED50 was approximately 0.1 mg/kg. U-86170F has been shown to be a potent dopamine autoreceptor agonist in the GBL, prolactin, and HVA models, with an effective i.p. dose of approximately 0.03 mg/kg. When evaluated for postsynaptic dopaminergic activity in the reserpinized mouse model, and compared to apomorphine, U-86170F was found to increase locomotor activity, but its maximum effect was only 65% of that attained with apomorphine. Higher doses were needed for postsynaptic effects. In receptor binding studies using cloned D2 receptor preparations, U-86170F was found to exhibit agonist binding properties similar to dopamine as demonstrated by their inhibition of 3H-raclopride binding.(ABSTRACT TRUNCATED AT 250 WORDS)

Quantitative determination of dopamine receptor subtypes not linked to activation of adenylate cyclase in rat striatum.

The binding of [3H]domperidone and [3H]spiroperidol was examined in membranes prepared from rat striatum. Scatchard analysis of the binding of [3H]domperidone resulted in curvilinear plots consistent with the presence of multiple classes of binding sites. Nonlinear regression analysis of untransformed data showed that the curvature was best explained by the presence of two populations of binding sites. Scatchard plots of the binding of [3H]spiroperidol were linear, suggesting that this radioligand binds to a single class of receptors. However, results obtained in studies of the inhibition of [3H]spiroperidol binding by a number of competing ligands were not consistent with the interaction of these agents with a single class of binding sites. Computer-assisted analysis of the Hofstee plots of six competing ligands gave the same relative proportion for two classes of sites as determined by analysis of the binding of [3H]domperidone. The two classes of receptors labeled with [3H]spiroperidol had affinities for domperidone that were similar to those of the two populations of binding sites for [3H]domperidone. Furthermore, the number of binding sites for [3H]spiroperidol was equal to the total number of binding sites for [3H]domperidone. These findings suggest that the two radioligands bind to the same two classes of binding sites. It is unlikely that either of the two classes of striatal sites are receptors for serotonin. The approach described will make it possible to assess the effects of physiological or pharmacological manipulations on the densities or properties of subtypes of dopamine receptors.

Subunit interactions of native and ADP-ribosylated alpha 39 and alpha 41, two guanine nucleotide-binding proteins from bovine cerebral cortex.

Bovine cerebral cortex contains two major substrates for ADP-ribosylation by pertussis toxin: a 39-kDa protein, alpha 39, and a 41-kDa protein, alpha 41 (Neer, E. J., Lok, J. M., and Wolf, L. G. (1984) J. Biol. Chem. 259, 14222-14229). Both of these proteins bind guanosine 5'-(3-O-thio)triphosphate (GTP gamma S) with a similar affinity (Kd = 30 +/- 10 nM for alpha 39, Kd = 32 +/- 14 nM for alpha 41). Both proteins associate with a beta X gamma subunit made up of a 36-kDa beta component and a 6-kDa gamma component. We have previously shown that the beta X gamma unit is required for pertussis toxin-catalyzed ADP-ribosylation (Neer et al. (1984)). By measuring the amount of beta X gamma required for maximal incorporation of ADP-ribose, we now find that the EC50 for beta X gamma in this reaction is 3 +/- 1 times lower for alpha 41 than for alpha 39. ADP-ribosylation by pertussis toxin does not prevent dissociation of alpha 41 X beta X gamma or alpha 39 X beta X gamma by GTP gamma S. GTP gamma S decreases the sedimentation coefficient of ADP-ribosylated alpha 41 from 4.2 S to 3.0 S and the sedimentation coefficient of ADP-ribosylated alpha 39 from 4.3 S to 2.9 S. The conclusion that GTP gamma S dissociates both ADP-ribosylated heterotrimers was confirmed by the observation that GTP gamma S blocks precipitation of ADP-ribosylated alpha 39 or alpha 41 by anti-beta antibody. Neither alpha 41 X beta X gamma nor alpha 39 X beta X gamma is dissociated by GTP whether or not the proteins are ADP-ribosylated. The observation that alpha 41 more readily associates with beta X gamma than does alpha 39 may explain our earlier observation that alpha 41 is more readily ADP-ribosylated than alpha 39. In most intact membranes, only a 41-kDa ADP-ribosylated protein is seen. However, alpha 39 is also present in most tissues since we can detect it with anti-alpha 39 antibody. The functional consequences of pertussis toxin treatment may depend on whether one or both proteins are ADP-ribosylated. This in turn may depend on the ratio of alpha 41 and alpha 39 to beta X gamma in a given tissue.

Assay of dopamine receptors with [alpha-3H]flupenthixol.

Two major classes of dopamine receptors, called D-1 receptors and D-2 receptors, have been identified. [alpha-3H]Flupenthixol has been used as a radioligand for the study of D-1 receptors, which are thought to act through stimulation of adenylate cyclase activity. Previous studies in our laboratory have shown that the D-2 receptors in rat caudate labeled by [3H]spiroperidol also have a high affinity for alpha-flupenthixol. The present experiments show that although Scatchard analysis of the binding of [alpha-3H]flupenthixol is consistent with the presence of a homogeneous population of receptors, subpopulations of these sites can be distinguished by their differing affinities for spiroperidol, which has a Kd for D-1 receptors of about 0.3 microM and a Kd for D-2 receptors of approximately 50 pM. The number of D-1 receptors in rat striatum is approximately 4 times the number of D-2 receptors. D-1 receptors can be studied by including 10 nM spiroperidol in assays carried out with [alpha-3H]flupenthixol, thus blocking the binding of [alpha-3H]flupenthixol to D-2 receptors. The affinity of these receptors for dopamine is decreased by GTP, as has been observed in studies of other receptors whose effects are mediated through changes in adenylate cyclase activity. In the presence of spiroperidol, the Hill coefficients determined from dose-response curves of the inhibition of the binding of [alpha-3H]flupenthixol by antagonists or by agonists in the presence of GTP suggest that the binding reaction obeys simple Michaelis-Menten kinetics for a single class of binding sites.

Anion-exchange high-performance liquid chromatographic analysis of inositol phosphates.

The analysis of inositol phosphates by anion-exchange HPLC is described. The method employs a citrate buffer gradient to resolve several inositol phosphates including inositol 1-phosphate, inositol 1,4-bisphosphate (IP2), and inositol 1,4,5-trisphosphate (IP3), as well as some of the isomers of these compounds. Since the buffer system does not contain any phosphate, we can use a phosphate assay to examine the chromatographic behavior of phosphate-containing compounds. The method shows good resolution and recovery (greater than 95% for IP2 and IP3). Total analysis time, including reequilibration, is about 90 min. In addition, an isocratic system that can rapidly (less than 10 min) measure IP3 is described. The HPLC system was used to characterize inositol phosphate turnover in thrombin-stimulated platelets and formylmethionyl-leucyl-phenylalanine-stimulated HL-60 cells.

Physical and immunological characterization of a guanine nucleotide-binding protein purified from bovine cerebral cortex.

ADP-ribosylation by pertussis toxin has been used to identify the alpha subunit of Ni, the guanine nucleotide-binding protein which mediates hormone and GTP inhibition of adenylate cyclase. Two proteins have been purified from bovine cerebral cortex which are substrates for ADP-ribosylation by pertussis toxin, a 41-kDa protein (alpha 41) and a 39-kDa protein (alpha 39). The 41-kDa protein is very similar to the subunit of Ni purified from other tissues while the function of the 39-kDa protein is unknown (Neer, E. J., Lok, J. M., and Wolf, L. G. (1984) J. Biol. Chem. 259, 14222-14229; Sternweis, P. C., and Robishaw, J. D. (1984) J. Biol. Chem. 259, 13806-13813). We now show that the purified alpha 39 protein from bovine brain is a relatively hydrophilic protein which associates with a hydrophobic beta gamma component. The complex can be dissociated by guanosine 5'-(3-O-thio)triphosphate. The alpha 39 component binds guanosine 5'-(3-O-thio)triphosphate with a KD of 27 nM. We have developed polyclonal antibodies to alpha 39 and beta. The antibodies to alpha 39 cross-react weakly with alpha 41 in an immunoblot assay indicating some homology between the two proteins but making it unlikely that alpha 39 is derived from alpha 41. Using the antibodies for quantitation we found that alpha 39 is 0.5% and beta is 0.7% of membrane proteins. While the antibodies cross-react with alpha 39 and beta proteins in many different species, central nervous system tissues always have more immunoreactivity than membranes from peripheral organs. Anti-beta antibody recognizes the beta subunit when it is associated with alpha 39 or alpha 41 and can immunoprecipitate both alpha . beta gamma trimers. The guanine nucleotide-dependent dissociation of the alpha 39 . beta gamma trimer suggests that the complex could inhibit adenylate cyclase by liberating free beta gamma units. The function of alpha 39 may not, however, be exclusively to regulate adenylate cyclase but may include coupling hormone receptors to other effectors. Antibodies specific for alpha 39 and beta will be useful tools in determining the functions of alpha 39 and beta in hormone-responsive cells.

D2 dopamine receptor stimulation of mitogenesis in transfected Chinese hamster ovary cells: relationship to dopamine stimulation of tyrosine phosphorylations.

Several neurotransmitters that act through G protein-linked receptors have been shown to affect the growth rate of dividing cells. An analysis of the early signaling events that mediate this response revealed some novel activities for G protein-linked receptors. Activation of D2 receptors heterologously expressed in CHO cells also stimulates the synthesis of DNA, which results in increased proliferation. Pertussis toxin pretreatment abolishes D2 agonist-stimulated mitogenesis, which indicates the need for a G protein. D2 receptor-stimulated mitogenesis occurs in the presence of a membrane-soluble cyclic AMP analog and, in Chinese hamster ovary cells with a mutated protein kinase A, which is resistant to the growth effects of cyclic AMP. Therefore, the proliferative response is independent of changes in cyclic AMP. It was determined that a number of other signaling pathways commonly used by Gi-linked receptors are not involved in the D2-mediated mitogenic response. These include arachidonic acid release, stimulation of protein kinase C, stimulation of inositol phosphates, opening of K+ channels and activation of amiloride sensitive Na+/H+ exchange. D2 receptor-stimulated mitogenesis is blocked by genistein, a tyrosine kinase inhibitor, at the same concentrations that block thrombin-stimulated mitogenesis. In fact, dopamine and thrombin stimulate a rapid increase in tyrosine phosphorylation of a number of substrates in the transfected Chinese hamster ovary cells. These results reveal a novel signaling event for D2 dopamine receptors, activation of tyrosine phosphorylations. They suggest the importance of these events for D2 dopamine receptor-stimulated mitogenesis.

Activation of heterologously expressed D3 dopamine receptors: comparison with D2 dopamine receptors.

Recombinant rat D3 dopamine receptors heterologously expressed in Chinese hamster ovary (CHO) cells are functionally coupled to endogenous G proteins. The affinity of the receptors for agonists is regulated by guanine nucleotides in the same manner as that of other G protein-linked receptors. The magnitude of the change in affinity induced by GTP is much less, however, than what is observed for recombinant rat D2 receptors expressed in CHO cells at similar densities. The striking difference is that the low affinity state (uncoupled D3 receptors) has a much higher affinity for agonists than does the low affinity state (uncoupled) of D2 receptors. Both receptors in the high affinity state (G protein coupled) have similar affinities for dopamine. Three functional responses result from activation of D3 or D2 receptors expressed in CHO cells. Both receptor subtypes mediate inhibition of adenylyl cyclase activity, increases in extracellular acidification rates that are prevented by removal of external Na+ and by amiloride analogs, and stimulation of cell division. However, these three functional results of D3 and D2 receptor activation are both quantitatively and qualitatively different. Dopamine activation of D3 receptors is always 2-5-fold less efficacious than dopamine activation of D2 receptors, despite similar densities of receptors. Both D3 and D2 receptor-mediated increases in extracellular acidification rates are blocked by pertussis toxin; however, the D3 response and not the D2 response is partially attenuated by membrane-soluble cAMP analogs. D3 and D2 receptor-mediated stimulation of mitogenesis is blocked by pertussis toxin and unaffected by cAMP analogs. The results show that D2 and D3 dopamine receptors mediate similar signaling events and are additional examples of G protein-linked receptors that can activate more than one pathway. Having functionally coupled D2 and D3 receptors expressed in the same cell type enabled determinations of agonist potencies at both D2 and D3 receptors. Comparison of the potencies at the two receptors reveals that none of the agonists is as selective for D3 receptors as was previously thought based on radioligand binding data.

Planning the purification process of active cDNA in expression cloning strategies.

In principle, it is possible to clone the gene for any receptor that can be expressed in the Xenopus laevis frog oocyte and assayed electrophysiologically (E. S. Levitan, 1988, TINS 11, 41-43). Repeated fractionation of a lambda vector cDNA library made from mRNA which encodes the receptor protein will eventually lead to a single cDNA clone. This strategy poses the question as to how large should a lambda vector cDNA aliquot be at any fractionation stage in order that one may be relatively certain that the aliquot contains the clone of interest, and how many times should the fractionation be repeated in order that one isolate the single clone of interest? The purification of active cDNA is an iterative process. At each fractionation stage we specify the probability of at least one active cDNA in the total aliquot to be high. The required size of the aliquot taken depends upon this specified probability and the additional probability of selecting at random an individual cDNA which is active. We require an estimate of the latter probability for the initial stage. For subsequent stages Baye's estimators of these probabilities are used in the formula for calculating the aliquot size at each stage. We show how to perform this calculation when there is equal amplification of the active and remaining sequences and when the active sequence has a non-representative (unequal) amplification. When equal amplification holds a relatively simple formula is provided for calculating the expected number of stages needed in the process. When unequal amplification holds there is no simple calculation for this quantity and the entire sequence of calculations leading to termination of the process must be performed. In either case the minimum lambda vector amplification (growth) factor required at each stage to yield an adequate amount of cDNA for analysis is calculable.