DNA Reaction System That Acquires Classical Conditioning

Biochemical reaction networks can exhibit plastic adaptation to alter their functions in response to environmental changes. This capability is derived from the structure and dynamics of the reaction networks and the functionality of the biomolecule. This plastic adaptation in biochemical reaction systems is essentially related to memory and learning capabilities, which have been studied in DNA computing applications for the past decade. However, designing DNA reaction systems with memory and learning capabilities using the dynamic properties of biochemical reactions remains challenging. In this study, we propose a basic DNA reaction system design that acquires classical conditioning, a phenomenon underlying memory and learning, as a typical learning task. Our design is based on a simple mechanism of five DNA strand displacement reactions and two degradative reactions. The proposed DNA circuit can acquire or lose a new function under specific conditions, depending on the input history formed by repetitive stimuli, by exploiting the dynamic properties of biochemical reactions induced by different input timings.


peaks of output responces [%]
Supporting Figure S10 Simulation results regarding forgetting the acquired func-
Selected 32-input histories are shown, where input histories that were expected to obtain the conditioned reflex are denoted by shadowed boxes, and output responses that were responsive to the second input are denoted by red lines.
Let the state vector x = [x 1 x 2 • • • x 14 ] T ∈ R 14 of the conditioned reflex circuit shown in Fig. 2 be defined by: where the concentration of a chemical species "X" in a reaction system is expressed by the brackets [X].The ordinary differential equation is then based on reaction kinetics as described by: where the stoichiometric matrix V ∈ R 14×12 and the reaction rate vector r : R → R 12 are given by: where k 1 b , and k (j) d (i, j = 1, 2) are the reaction rates.
Supporting Text S2 Mathematical modeling of generalized conditioned reflex circuit Let the state vector x ∈ R 7n+2 of the generalized conditioned reflex circuit shown in Fig. 5 be defined by: (5) Then, the ordinary differential equation of the form ( 2) is given with the stoichiometric matrix V ∈ R (7n+2)×7n and the reaction rate vector r : R → R 7n as: and where O ∈ R 7×7 is the zero matrix, and k ) are the reaction rates.

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Supporting Text S3 Mathematical modeling of the renewable threshold gate Let the state vector x ∈ R 9 of the threshold gate in Fig. 8B-C of the main text be defined by The ordinary differential equation of the form ẋ = V r under BL irradiation condition is then given with the stoichiometric matrix V ∈ R 9×6 and the reaction rate vector r : R → R 6 as follows: where k ) are the reaction rates.
The initial concentrations were given by [T t ](0)=[T g ](0)=[T f ](0)=100 nM, and the others were 0 nM.The reaction rates (1/nMs) were calculated according to the calculation method, 2 and given by k given with the stoichiometric matrix V ∈ R 9×7 and the reaction rate vector r : R → R 7 as follows: Supporting Text S4 Optimization of learning efficiency The accumulation of memory gate M 2 in the learning condition is an essential condition for learning.In this study, we investigated how the reaction rates in the circuit were related to the updating of the memory gate by evaluating the steady state of the memory gate M 2 upon simultaneous I 1 and I 2 inputs.To this end, we used a structural sensitivity analysis, a straightforward method for performing steady-state analysis for chemical reaction systems. 3r the state vector (1) and the ordinary differential equations (2) of the conditioned reflex circuit, the corresponding augmented matrix A ∈ R 19×19 is derived by: where c n ∈ R 12 (n = 1, ..., 5) and d n ∈ R 14 (n = 1, ..., 7) are the basis vectors of the right and left null space of V , respectively, that is, Ker(V ) and Ker(V T ): (15) Then, the (i, j) element of −A −1 reportedly provides the information on how the perturbation of the reaction r j influences the steady-state concentration of x i . 3In the conditioned reflex circuit, we are interested in how effective the steady-state concentration of x 6 , that is [M 2 ](∞), can be updated, which can be estimated by assessing the (6, * ) element of −A −1 .
Subsequently, we analytically obtained the sixth row vector of −A −1 as:

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Simulation results regarding the learning efficiencies • Supporting Figure S8: Simulation results regarding forgetting the conditioned reflex • Supporting Figure S9: Simulation results regarding forgetting the acquired function • Supporting Figure S10: Simulation results regarding forgetting the acquired function with another setting • Supporting Figure S11: Simulations of the generalized conditional reflection circuit with 4-input channels • Supporting Figure S12: Simulation results of 4-input and 1-output conditioned reflex circuit • Supporting Figure S13: Simulation results of 10-input and 1-output conditioned reflex circuit • Supporting Figure S14: Definition of evaluation values (J (1,2) pk , J (1,2) ss , J (2) pk , and J (2) ss ) in output responses for designing the cost function of the parameter estimation • Supporting Figure S15: Efficiency in learning conditions • Supporting Text S1: Mathematical modeling of conditioned reflex circuit • Supporting Text S2: Mathematical modeling of generalized conditioned reflex circuit • Supporting Text S3: Mathematical modeling of the renewable threshold gate • Supporting Text S4: Optimization of learning efficiency S3 Supporting Figure S1 The chart drawn by Visual DSD. 1 The code is available on GitHub at https://github.com/SYSBIOKYUTECH/conditioned-reflex-circuit.Operating and learning principles.(A) Reactions that occur on input I 1 are highlighted by a red box.(B) Reactions that occur on input I 2 are highlighted by a blue box.(C) Reactions that occur on simultaneous inputs I 1 and I 2 are highlighted by a colored box, where reactions r are represented by a gradient color as they are induced by the fusion of red-and blue-colored reactions.(D-F) Simulation results correspond to the conditions (A-C) in the pre-learning condition, where the upper, middle, and lower panels show the time-course data of inputs, memory gates, and outputs, respectively.Input conditions (nM) are ([I 1 ](0), [I 2 ](0)) = (100, 0) for (D), ([I 1 ](0), [I 2 ](0)) = (0, 100) for (E), and ([I 1 ](0), [I 2 ](0)) = (100, 100) for (F).

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Supporting Figure S6 Simulation results with input patterns of "food (F) bell (B)-B" (A), "FB-FB-B" (B), and "FB-FB-FB-B" (C) Supporting Figure S7 Simulation results regarding the learning efficiencies.Four repetitive and simultaneous inputs were applied to the circuit with [M 1 ](0)=[M 2p ](0)=[S](0)=[R 2 ](0)=200 nM, [R 1 ](0)=50 nM, and k 1 s −1 .The M 2 concentrations updated for each input are indicated in the plot.A Supporting Figure S8 Simulation results regarding forgetting the conditioned reflex.The time-course data of memory gates (A) and output (B) with input patterns are "FB-B-B-B-B-B-B-B-B-B."The detailed data are also shown in Fig. S9.

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= 7.28 × 10 −4 based on 5 nt-toehold mediated reversible reactions, where the lengths of the recognition domains were fixed by 20 nt, and temperature was assumed to be 25 • C.Meanwhile, under UV irradiation conditions, a balance between the forward and backward flows of each reaction is altered due to the obstruction by the cis-type azobenzene.The ordinary differential equation of the form ẋ = V r under UV irradiation condition is then