recent advances in the study of the dynamics of living systems have highlighted the role of reaction networks ( rns ; barabsi and oltvai , 2004 ) . these architectures , in their various genetic , metabolic or signalling implementations , encode many decision - making processes , and thus control cell behaviour ( hartwell et al , 1999 ) . the study of biological networks usually focuses on the relation between the global dynamics of the rn and its topology ( the way the reactions involved are connected to each other ; milo et al , 2002 ; novk and tyson , 2008 ) , with less emphasis on the chemical processes themselves ( bailey , 2001 ) . synthetic biologists have used these topological inferences to reorganize biological elements into artificial in vivo circuits , successfully obtaining the desired dynamic functions : for instance , introducing three repressor genes arranged with their corresponding promoter in a triangular negative - feedback loop in escherichia coli resulted in oscillations in gene expression ( elowitz and leibler , 2000 ) ; in another study , the presence of a positive - feedback loop was shown to increase the robustness of the oscillatory behaviour ( stricker et al , 2008 ) . however successful and promising these attempts have been , the ability to target and predict the overall dynamic behaviour is strongly impaired ( purnick and weiss , 2009 ) by the difficulty of precisely characterizing the kinetics and thermodynamics of the reactions occurring inside a cell ( rosenfeld et al , 2005 ; koide et al , 2009 ) . in vitro systems provide a way towards the rational building of rns in a chemically simpler and more controlled context . at present , however , our ability to assemble rationally test - tube rns lags far behind that for in vivo systems . serious challenges remain , including the cascadability of the various modules ( ackermann et al , 1998 ) , the precise control of the sequence of events ( dadon et al , 2008 ) and the correct balance between production and destruction of the dynamic species ( noireaux et al , 2003 ; kim et al , 2006 ; kim and winfree , 2011 ) . among various biological rns , gene regulatory networks have attracted special interest because of their conceptual simplicity and modularity . taking them as a prototypical example of biological rns , we noticed that their architecture relies mostly on a limited set of basic events : activation , inhibition and destruction . we then searched for an experimental model that would allow the generic in vitro implementation of these three basic events without the need for the complex gene expression machinery . in a second step , the first element , activation , is achieved by a modification of an isothermal linear oligodeoxy - nucleotide ( hereafter  oligomer ' ) amplification scheme based on the repeated extension / nicking of one strand of a short dna duplex ( walker et al , 1992 ) . as the reaction occurs close to the melting temperature ( tm ) of the duplexes ,  input ' and  output ' strands dynamically dehybridize from the template . this , together with the use of a polymerase with strand - displacement ability prevents product inhibition . it also ensures that this element is dynamic and adjusts the output production rate according to changes in input concentration . inhibition is implemented by oligomers capable of repressing , instead of activating , the production of outputs by a template . to that purpose , we propose the use of 3-mismatched oligomers , which are poor substrates for polymerases lacking proofreading ability ; however , given a sufficient number of matching base pairs , they can still form stable duplexes with the templates . such  inhibitors ' displace the correct inputs , but fail to trigger the production of any output . destruction , i.e. , the continuous removal of the dynamic species , is compulsory in order to build complex behaviour . in a closed system recjf , a 5  3 , single - strand specific , processive exonuclease ( han et al , 2006 ) , hydrolyzes oligomers into inactive monomers and is suitable for this purpose . templates should not be destroyed , so they are protected by phosphorothioate bonds at their 5 end . in this overall scheme , inputs , outputs and inhibitors are chemically similar ( all are short oligomers ) , so these network components can be arbitrarily connected : the output of one template simply becomes the input or the inhibitor of another ( box 1 ) . chemical oscillators are prototypical examples of interesting nonlinear systems , but their in vitro design is still difficult ( epstein and pojman , 1998 ; another successful approach is reported by kim and winfree , in this issue ) . we used the aforedescribed components to form a network that includes both a positive and a negative - feedback loop ; hence , it is expected to produce robust oscillations ( stricker et al , 2008 ) . we then proceeded to the step - by - step experimental assembly of this system , nicknamed  oligator ' . we first built a one - node network , implementing the positive - feedback loop , by using a single template ( t1 ) that consists of a dual repeat of its input 's (  ) complementary sequence . this template is incubated in the presence of a polymerase and a nicking enzyme , and we monitor the reaction using a double - strand intercalating dye . as expected , this elementary network produces an exponential amplification of . however , when the same reaction is combined with the exonuclease destruction reaction , a steady state , where  is dynamically produced and destroyed , is reached after the initial transient phase ( figure 1a ) . we designed the 3-mismatched inhibitor ( inh ) to displace  from t1 : inh 's higher binding constant and toeholds ( zhang and winfree , 2009 ) allow it to bind strongly and quickly to t1 even in the presence of . experimentally , increasing ( inh ) significantly decreased the amplification rate of  ( figure 1b ) . however , inh can be destroyed in the presence of the exonuclease , resulting in an eventual release of the inhibition ( supplementary figure s1 ) . finally , we connected the production of inh to the presence of  to close the negative - feedback loop . because stable oscillations require a delay in this loop ( novk and tyson , 2008 ) , we inserted an intermediate species ,  , between  and inh : template t2 produces  from  and template t3 gives inh from . altogether , t1 , t2 and t3 experimentally encode the network shown in figure 1f . after assembling all components and triggering the reaction , sustained oscillations indeed emerge ( figure 1c ) . depending on experimental conditions , we could detect up to 40 cycles with a period ranging from one to several hours ; eventually , the reaction either stabilized or diverged . note that , in a closed system , only transient oscillations can be expected : in any case , the exhaustion of available chemical fuel ( here dntps ) will eventually lead to the stabilization of the system , but other causes can also participate ( supplementary information s4 and supplementary figure s8 ) . the kinetic behaviour of this system can be described by a combination of hybridization / melting equilibria and irreversible enzymatic reactions , as shown in figure 2a . assuming first order kinetics for all the enzymatic reactions ( see supplementary information s5 for validation ) , we directly obtain a realistic yet simple  raw model ' that depends only on 11 kinetic parameters ( supplementary information s5 and supplementary figures s9 and s10 ) . moreover , all these parameters could be independently measured in separate experiments : melting curves gave the thermodynamic hybridization constants ; the kinetic association rates for each template / oligomer pair were extracted from temperature jump experiments ( supplementary information s1 , supplementary figure s2 and supplementary table sii ) ; and finally the three enzymatic catalyses were analysed one by one : each satisfyingly conformed to the standard michaelis  menten model , from which a first - order rate constant , valid for small substrate concentrations , was calculated ( table i and supplementary information s2 , supplementary figures s3s5 and supplementary table siii ) . using these independent experimental parameters , it became possible to numerically integrate the  raw model ' . in figure 1d , we plot the calculated evolution of the total concentration of base pairs in solution , which is assumed to be proportional to the fluorescent signal emitted by the intercalating dye : the period and overall behaviour agrees remarkably well with the experimental data . however , this fluorescent signal only gives a global indication of the amount of dna in the system , and results from contributions of many species . to precisely describe the system , one needs to know individually the evolution of each dynamic species  ,  and inh . to do so , samples were taken and quenched at various time intervals over three cycles . the low concentration of the oligomers made gel analysis difficult ( supplementary figure s6 ) , but we could successfully use a dna amplification method to individually quantify  ,  and inh in each aliquot ( figure 2b and supplementary information s3 , supplementary figure s7 and supplementary table siv ) : we found that all three concentrations oscillate over time , with  first reaching its maximum , followed by  , then inh . inh then slowly decays , until  is able to recover and the cycle starts again . without any adjustment in the parameters , this is not surprising given the relatively large experimental uncertainties associated with the parameter values . optimized model ' that includes these uncertainties , by allowing all parameters to drift within a 30% window around their input values . similarly , the rates of similar but distinct reactions ( e.g. , polymerization of .t1 versus that of .t3 ) were allowed to take independent values within the same 30% window . this created a slightly more complex , but also more realistic model , whose final parameters were optimized by fitting , simultaneously , all the data in figure 3 . under these conditions , the optimized model ' precisely describes the period , amplitude and phase position of the experimental observables ( average parameter drift 15% , resulting in a  of 13 for the adjustment of concentration evolutions ; figure 2b and supplementary information s5 and supplementary table sv ) . while the structure of the network is encoded at the dna sequence level , it is possible to tune its behaviour by changing the template concentrations . to test the robustness of our predictions in other locations of its control parameter space , we used the optimized model to calculate the phase diagram in the [ t1][t3 ] plane ( figure 3 ) . a stable steady state is predicted for low values of t3 , but , increasing [ t3 ] , critical values distributed along a hyperbolic - shaped curve are reached . beyond these values amplitudes and periods continuously increase with [ t3 ] and no other stable points are observed . in parallel , we experimentally explored the same area by reproducing the oscillating experiment with 48 different [ t1]/[t3 ] conditions ( figure 3 ) . we observed a good qualitative agreement with calculations , over a large area of the [ t1][t3 ] plane ( see supplementary figure s13 for investigation along the [ t2 ] axis ) . moreover , within the oscillatory region , the periods were correctly predicted in most cases . dna strands , with their predictable base pairing , together with computable thermodynamic ( santalucia and hicks , 2004 ) and kinetic ( zhang and winfree , 2009 ) features enable unambiguous encoding at the molecular level . this has been used to create spatial static structures at the nanometre scale ( seeman , 2003 ; rothemund , 2006 ) , as well as chemical ( yin et al , 2008 ; soloveichik et al , 2010 ) and biochemical ( bath et al , 2005 ; win et al , 2009 ) machines . here , we have extended this strategy to the experimental assembly of dynamic systems by implementing complete rns . however , we have built the system using only simple in vitro biochemical reactions based on dna polymerization / depolymerization . in this first demonstration , we selected a network topology that was compatible with oscillations and could be implemented with a minimum number of templates ( only three ) . we chose the parameters ( tm of the sequences , enzyme concentrations or working temperature ) using mixed empirical and computational approaches : we first designed the activating oligomers with a tm close to  or below the working temperature , to insure that oligomers dynamically hybridize and dehybridize ; we then tested various sequences for their capacity to inhibit the self - amplification of the activator , as in figure 2c ; subsequently , we assembled the whole network and searched for experimental conditions compatible with oscillations ; we were then able to measure the kinetic and thermodynamic parameters in these conditions and used the model to guide our search towards a more stable oscillatory behaviour . for this specific topology to produce oscillations , we found that the inhibitor should possess a tm much higher than the activator ( typically 10c higher ) . while we have not yet entirely clarified all the design rules of such systems and especially the role of the network 's structure , it should be emphasized that this in vitro approach gives a large freedom to the molecular network designer . the connectivity of the network can be simply reorganized by matching the sequence of the various sub - elements . the thermodynamic parameters can be tuned by adjusting their length and/or gc content and , importantly , this can be done in a predictive manner using well - known algorithms . finally , the kinetic parameters can be controlled by adjusting the concentrations of enzymes and/or by positioning toehold sequences on the templates ( zhang and winfree , 2009 ) . this versatility suggests that more elaborate systems , containing maybe tens of nodes , might be feasible . this would open the unexplored territory of large synthetic networks , displaying complex dynamic functions ( purnick and weiss , 2009 ) . therefore , we expect that such designs will be useful to rapidly assess various hypotheses concerning the structure  function relationships at the level of rns ( nakajima et al , 2005 ; novk and tyson , 2008 ) . recently , the design requirements to obtain oscillations have been experimentally investigated in e. coli ( stricker et al , 2008 ; mather et al , 2009 ) , focusing on the role of the positive and negative feedback . comparing such in vivo results with equivalent in vitro prototypes will provide more insight on the role of various design features of biological networks . for example , one might use the approach reported here to quickly evaluate the importance of loops , delay mechanisms or other nonlinear phenomena on the occurrence and robustness of oscillations . an important aspect of in vivo systems , e.g. , gene regulatory networks , is that they are chemically much more complex than the simple biochemical reactions used in this study . moreover , biological networks take place in the intricate context of the cellular inner medium and are intrinsically connected to its metabolic functions . therefore , mathematical analyses of biological networks generally involve a coarse description and rough estimates of the parameters . in contrast , we have shown that the oligator 's behaviour can be predicted accurately from a straightforward kinetic model and a small set of easy - to - obtain parameters . after refinement , the numerical analysis provides a reliable and precise understanding of its dynamics ( supplementary figures s11 and s12 ) . this fact has proven extremely valuable during the assembly process , allowing us to find our way in a complex multi - parameter space . it also opens the possibility to assess the importance of quantitative aspects on the emergence of complex dynamic functions . all reactions ( except quantitative isothermal amplifications described in supplementary information s3 ) were assembled in buffer a containing 45 mm tris  hcl , 50 mm nacl , 10 mm kcl , 10 mm ( nh4)so4 , 7 mm mgcl2 , 6 mm dtt , ph=8.0 , 100 g ml bsa ( new england biolabs ) , 410 mm trehalose ( included to stabilize recjf during long experiments ) , complemented with 1  evagreen ( biotium ) and dntps ( 100 m each ) when necessary . oligonucleotides  ,  , inh , t1 , t2 , t3 were obtained from idt and ordered with hplc purification . templates t1 , t2 and t3 were phosphorylated at their 3 end to prevent any unexpected polymerization and bore two phosphorothioates at their 5 end to protect them from hydrolysis by recjf . bst dna polymerase , large fragment , nt.bstnbi nickase and recjf were purchased from neb . when not specified otherwise , they were used at 16 , 200 and 30 u ml , respectively . fluorescence was recorded with a real - time thermocycler ( either a miniopticon ( bio - rad ) , an iq5 ( bio - rad ) or a 7500 real - time pcr system ( applied biosystems ) ) set at a constant temperature of 38.5c . melt curves at 260 nm were recorded with a v630bio uv - vis spectrometer ( jasco ) equipped with a peltier cell . the model in sbml format can be accessed in biomodels database under the i d the length of  was fixed at 11 bases and its sequence ( 5-tcgagtctgtt-3 ) chosen to ( 1 ) have a nicking enzyme recognition sequence ( in bold ) ( 2 ) have a melting temperature ( tm=39.5c , calculated in buffer a at 100 nm strand concentration ) close to the working temperature and ( 3 ) display no secondary structure . ( 5-atgagtcatgc-3 , tm=37.9c ) was designed with similar constraints and the absence of cross - binding with  or . inh ( agtctgtttcgagtaa , tm=50.2c ) was made to bind t1 with a tm higher than  , but with two mismatches at its 3 end . the length of  was fixed at 11 bases and its sequence ( 5-tcgagtctgtt-3 ) chosen to ( 1 ) have a nicking enzyme recognition sequence ( in bold ) ( 2 ) have a melting temperature ( tm=39.5c , calculated in buffer a at 100 nm strand concentration ) close to the working temperature and ( 3 ) display no secondary structure . ( 5-atgagtcatgc-3 , tm=37.9c ) was designed with similar constraints and the absence of cross - binding with  or . inh ( agtctgtttcgagtaa , tm=50.2c ) was made to bind t1 with a tm higher than  , but with two mismatches at its 3 end .
living organisms perform and control complex behaviours by using webs of chemical reactions organized in precise networks . this powerful system concept , which is at the very core of biology , has recently become a new foundation for bioengineering . remarkably , however , it is still extremely difficult to rationally create such network architectures in artificial , non - living and well - controlled settings . 
 we introduce here a method for such a purpose , on the basis of standard dna biochemistry . 
 this approach is demonstrated by assembling de novo an efficient chemical oscillator : we encode the wiring of the corresponding network in the sequence of small dna templates and obtain the predicted dynamics . 
 our results show that the rational cascading of standard elements opens the possibility to implement complex behaviours in vitro . 
 because of the simple and well - controlled environment , the corresponding chemical network is easily amenable to quantitative mathematical analysis . 
 these synthetic systems may thus accelerate our understanding of the underlying principles of biological dynamic modules .