oligonucleotides were synthesized on an expedite automated dna / rna synthesizer ( applied biosystems , foster city , ca ) using nucleoside phosphoramidites purchased from glen research ( sterling , va ) . all oligonucleotides were purified by denaturing polyacrylamide gel electrophoresis ( page ) and desalted using a c18 sep - pak cartridge ( waters , milford , ma ) . histidine - tagged t7 rna polymerase was purified from e. coli strain bl21 containing plasmid pbh161 ( kindly provided by william mcallister , state university of new york , brooklyn ) . thermus aquaticus dna polymerase was cloned from total genomic dna and purified as described previously30 . m1 rna , the catalytic subunit of rnase p , was obtained from e. coli genomic dna ( sigma - aldrich , st . louis , mo ) by pcr amplification and subsequent in vitro transcription , as described previously1 . calf intestine phosphatase and t4 polynucleotide kinase were purchased from new england biolabs ( ipswich , ma ) , yeast inorganic pyrophosphatase was from sigma - aldrich , and bovine pancreatic dnase i was from roche applied science ( indianapolis , in ) . nucleoside and deoxynucleoside 5-triphosphates , theophylline , and fmn were purchased from sigma - aldrich , [ -p]atp ( 7 ci / pmol ) was from perkin elmer ( waltham , ma ) , and caffeine was from mp biomedicals ( solon , oh ) . photinus pyralis ( firefly ) luciferase , saccharomyces cerevisiae adenosine-5-triphosphate sulfurylase , adenosine 5-phosphosulfate , and d - luciferin were from sigma - aldrich . bovine calf serum was from omega scientific ( tarzana , ca ) and superasin ( rnase inhibitor ) was from ambion ( austin , tx ) . all rna enzymes and substrates were prepared by in vitro transcription in a reaction mixture containing 0.4 m dna template , 0.8 m synthetic oligodeoxynucleotide having the sequence 5-ggactaatacgactcactata-3  ( t7 rna polymerase promoter sequence underlined ) , 2 mm each of the four ntps , 15 u/l t7 rna polymerase , 0.001 u/l inorganic pyrophosphatase , 15 mm mgcl2 , 2 mm spermidine , 5 mm dithiothreitol , and 50 mm tris - hcl ( ph 7.5 ) . the mixture was incubated at 37 c for 2 h , quenched by adding an equal volume of 15 mm na2edta , treated with 1 u/l dnase i , and extracted with a 1:1 mixture of phenol : chloroform . transcription of m1 rna was performed similarly , except employing a double - stranded dna template that was generated by pcr . the a and a  substrates could not be obtained reliably by in vitro transcription due to heterogeneity at the 3  end of the transcripts . instead , these substrates were prepared from the corresponding e or e  molecules by cleaving off the b or b  portion using e. coli m1 rna , as described previously1 . the external guide sequence rna for cleavage of etheo and efmn had the sequence 5-cguaaguugcggucucacca-3  , and for etheo and efmn had the sequence 5-auauucaugcggucucacca-3  ( nucleotides complementary to the target rna underlined ) . for the second pair of etheo and etheo molecules used in the multiplex experiments , the external guide sequence rnas had the sequence 5-cguaguaugcggucuacca-3  and 5-gaauaucauugcggucucacca-3  , respectively . the a and a  substrates were [ 5-p]-labeled by first dephosphorylating using calf intestine alkaline phosphatase , then phosphorylating using t4 polynucleotide kinase and [ -p]atp . the labeled substrates were purified by page and desalted using a nensorb 20 cartridge ( nen life sciences , waltham , ma ) . rna - catalyzed rna ligation was performed in a reaction mixture containing 5 m e or e  , 0.1 m [ 5-p]-labeled a  or a , 6 m b  or b , 25 mm mgcl2 , and 50 mm epps ( ph 8.5 ) , which was incubated at 42 c . aliquots were taken at various times and quenched by adding an equal volume of gel - loading buffer containing 50 mm na2edta and 18 m urea . the products were separated by page and quantitated using a pharosfx molecular imager ( bio - rad , hercules , ca ) . the data were fit to the equation : ft = fmax(a1ek1t)(a2ek2t ) , where ft is the fraction reacted at time t , fmax is the overall maximum extent of the reaction , a1 and k1 are the amplitude and rate of the initial fast phase , and a2 and k2 are the amplitude and rate of the subsequent slow phase , respectively . in the presence of 5 mm theophylline , the reaction catalyzed by etheo exhibited a fast phase with an amplitude of 0.57 and rate constant of 1.4 min , followed by a slow phase with an amplitude of 0.24 and rate constant of 0.044 min ; the reaction catalyzed by etheo had an amplitude of 0.52 and rate constant of 0.59 min in the fast phase , and an amplitude of 0.26 and rate constant of 0.045 min in the slow phase . cross - catalytic exponential amplification was performed in a reaction mixture containing 0.02 m each of e and e  , 5 m each of [ 5-p]-labeled a and a  , 5 m each of b and b  , 25 mm mgcl2 , and 50 mm epps ( ph 8.5 ) , which was incubated at 42 c . the reaction was initiated by mixing equal volumes of two solutions , one containing the enzymes and substrates , and the other containing the mgcl2 and epps buffer . aliquots were taken at various times , quenched , and the amounts of newly - synthesized e and e  were quantitated as described above . the data were fit to the logistic growth equation , as described in the main text . known concentrations of inorganic pyrophosphate or samples taken from the cross - replication reaction were diluted 10-fold into a reaction mixture containing 0.15 g/l luciferase , 0.00045 u/l atp sulfurylase , 10 m adenosine 5-phosphosulfate , 0.5 mm d - luciferin , 25 mm magnesium acetate , 0.1% bovine serum albumin , 1 mm dithiothreitol , 0.4 g/l polyvinylpyrrolidone ( mw 360,000 ) , and 100 mm tris - acetate ( ph 7.75 ) . the pyrophosphate standards were prepared in a solution identical to that employed in cross - replication , but lacking the rna enzymes and substrates . luminescence was detected using a perkin elmer ls55 luminescence spectrometer operating in bioluminescence mode , with a pmt voltage of 900 v , cycle time of 200 ms , gate time of 180 ms , and delay time of 0 . the flash count was set to 1 , the emission filter was fully open , and the emission slit width was 12 nm . following addition of the sample to the luciferase mixture , luminescence was monitored for 5 min with a 0.1 s integration time . the amount of light generated was linear over a pyrophosphate concentration range of 0.110 m . oligonucleotides were synthesized on an expedite automated dna / rna synthesizer ( applied biosystems , foster city , ca ) using nucleoside phosphoramidites purchased from glen research ( sterling , va ) . all oligonucleotides were purified by denaturing polyacrylamide gel electrophoresis ( page ) and desalted using a c18 sep - pak cartridge ( waters , milford , ma ) . histidine - tagged t7 rna polymerase was purified from e. coli strain bl21 containing plasmid pbh161 ( kindly provided by william mcallister , state university of new york , brooklyn ) . thermus aquaticus dna polymerase was cloned from total genomic dna and purified as described previously30 . m1 rna , the catalytic subunit of rnase p , was obtained from e. coli genomic dna ( sigma - aldrich , st . louis , mo ) by pcr amplification and subsequent in vitro transcription , as described previously1 . calf intestine phosphatase and t4 polynucleotide kinase were purchased from new england biolabs ( ipswich , ma ) , yeast inorganic pyrophosphatase was from sigma - aldrich , and bovine pancreatic dnase i was from roche applied science ( indianapolis , in ) . nucleoside and deoxynucleoside 5-triphosphates , theophylline , and fmn were purchased from sigma - aldrich , [ -p]atp ( 7 ci / pmol ) was from perkin elmer ( waltham , ma ) , and caffeine was from mp biomedicals ( solon , oh ) . photinus pyralis ( firefly ) luciferase , saccharomyces cerevisiae adenosine-5-triphosphate sulfurylase , adenosine 5-phosphosulfate , and d - luciferin were from sigma - aldrich . bovine calf serum was from omega scientific ( tarzana , ca ) and superasin ( rnase inhibitor ) was from ambion ( austin , tx ) . all rna enzymes and substrates were prepared by in vitro transcription in a reaction mixture containing 0.4 m dna template , 0.8 m synthetic oligodeoxynucleotide having the sequence 5-ggactaatacgactcactata-3  ( t7 rna polymerase promoter sequence underlined ) , 2 mm each of the four ntps , 15 u/l t7 rna polymerase , 0.001 u/l inorganic pyrophosphatase , 15 mm mgcl2 , 2 mm spermidine , 5 mm dithiothreitol , and 50 mm tris - hcl ( ph 7.5 ) . the mixture was incubated at 37 c for 2 h , quenched by adding an equal volume of 15 mm na2edta , treated with 1 u/l dnase i , and extracted with a 1:1 mixture of phenol : chloroform . transcription of m1 rna was performed similarly , except employing a double - stranded dna template that was generated by pcr . the a and a  substrates could not be obtained reliably by in vitro transcription due to heterogeneity at the 3  end of the transcripts . instead , these substrates were prepared from the corresponding e or e  molecules by cleaving off the b or b  portion using e. coli m1 rna , as described previously1 . the external guide sequence rna for cleavage of etheo and efmn had the sequence 5-cguaaguugcggucucacca-3  , and for etheo and efmn had the sequence 5-auauucaugcggucucacca-3  ( nucleotides complementary to the target rna underlined ) . for the second pair of etheo and etheo molecules used in the multiplex experiments , the external guide sequence rnas had the sequence 5-cguaguaugcggucuacca-3  and 5-gaauaucauugcggucucacca-3  , respectively . the a and a  substrates were [ 5-p]-labeled by first dephosphorylating using calf intestine alkaline phosphatase , then phosphorylating using t4 polynucleotide kinase and [ -p]atp . the labeled substrates were purified by page and desalted using a nensorb 20 cartridge ( nen life sciences , waltham , ma ) . rna - catalyzed rna ligation was performed in a reaction mixture containing 5 m e or e  , 0.1 m [ 5-p]-labeled a  or a , 6 m b  or b , 25 mm mgcl2 , and 50 mm epps ( ph 8.5 ) , which was incubated at 42 c . aliquots were taken at various times and quenched by adding an equal volume of gel - loading buffer containing 50 mm na2edta and 18 m urea . the products were separated by page and quantitated using a pharosfx molecular imager ( bio - rad , hercules , ca ) . the data were fit to the equation : ft = fmax(a1ek1t)(a2ek2t ) , where ft is the fraction reacted at time t , fmax is the overall maximum extent of the reaction , a1 and k1 are the amplitude and rate of the initial fast phase , and a2 and k2 are the amplitude and rate of the subsequent slow phase , respectively . in the presence of 5 mm theophylline , the reaction catalyzed by etheo exhibited a fast phase with an amplitude of 0.57 and rate constant of 1.4 min , followed by a slow phase with an amplitude of 0.24 and rate constant of 0.044 min ; the reaction catalyzed by etheo had an amplitude of 0.52 and rate constant of 0.59 min in the fast phase , and an amplitude of 0.26 and rate constant of 0.045 min in the slow phase . cross - catalytic exponential amplification was performed in a reaction mixture containing 0.02 m each of e and e  , 5 m each of [ 5-p]-labeled a and a  , 5 m each of b and b  , 25 mm mgcl2 , and 50 mm epps ( ph 8.5 ) , which was incubated at 42 c . the reaction was initiated by mixing equal volumes of two solutions , one containing the enzymes and substrates , and the other containing the mgcl2 and epps buffer . aliquots were taken at various times , quenched , and the amounts of newly - synthesized e and e  were quantitated as described above . the data were fit to the logistic growth equation , as described in the main text . known concentrations of inorganic pyrophosphate or samples taken from the cross - replication reaction were diluted 10-fold into a reaction mixture containing 0.15 g/l luciferase , 0.00045 u/l atp sulfurylase , 10 m adenosine 5-phosphosulfate , 0.5 mm d - luciferin , 25 mm magnesium acetate , 0.1% bovine serum albumin , 1 mm dithiothreitol , 0.4 g/l polyvinylpyrrolidone ( mw 360,000 ) , and 100 mm tris - acetate ( ph 7.75 ) . the pyrophosphate standards were prepared in a solution identical to that employed in cross - replication , but lacking the rna enzymes and substrates . luminescence was detected using a perkin elmer ls55 luminescence spectrometer operating in bioluminescence mode , with a pmt voltage of 900 v , cycle time of 200 ms , gate time of 180 ms , and delay time of 0 . the flash count was set to 1 , the emission filter was fully open , and the emission slit width was 12 nm . following addition of the sample to the luciferase mixture , luminescence was monitored for 5 min with a 0.1 s integration time . the amount of light generated was linear over a pyrophosphate concentration range of 0.110 m .
rna enzymes have been developed that undergo self - sustained replication at a constant temperature in the absence of proteins1 . 
 these rna molecules amplify exponentially through a cross - replicative process , whereby two enzymes catalyze each other s synthesis by joining component oligonucleotides . 
 other rna enzymes have been made to operate in a ligand - dependent manner by combining a catalytic domain with a ligand - binding domain ( aptamer ) to provide an  aptazyme2,3 . 
 the principle of ligand - dependent rna catalysis now has been extended to the cross - replicating rna enzymes so that exponential amplification occurs in the presence , but not the absence , of the cognate ligand . 
 the exponential growth rate of the rna depends on the concentration of the ligand , enabling one to determine the concentration of ligand in a sample . 
 this process is analogous to quantitative pcr ( qpcr ) , but can be generalized to a wide variety of targets , including proteins and small molecules that are relevant to medical diagnostics and environmental monitoring .