montagne1

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000315) Biomodels notes: Time courses as in fig 2b of the article. Simulations were performed using Copasi 4.6.33 JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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Programming an in vitro DNA oscillator using a molecular networking strategy.

  • Kevin Montagne
  • Raphael Plasson
  • Yasuyuki Sakai
  • Teruo Fujii
  • Yannick Rondelez
Mol. Syst. Biol. 2011; 7 : 466
Abstract
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.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
60.0 second
1e-09 mole
1e-09 mole litre^(-1.0)
16666666.666666666 mole^(-1.0) litre second^(-1.0)
0.016666666666666666 second^(-1.0)
Id Name Spatial dimensions Size
sample 3.0 1.0
Id Name Initial quantity Compartment Fixed
Inh Inh 0.0 sample
Inh_T1 Inh_T1 0.0 sample
T1 T1 38.5 sample
T1_alpha T1_alpha 0.0 sample
T2 T2 3.89 sample
T2_beta T2_beta 0.0 sample
T3 T3 38.5 sample
T3_Inh T3_Inh 0.0 sample
alpha alpha 10.0 sample
alpha_T1 alpha_T1 0.0 sample
alpha_T1_alpha alpha_T1_alpha 0.0 sample
alpha_T2 alpha_T2 0.0 sample
alpha_T2_beta alpha_T2_beta 0.0 sample
alpha_alpha_T1 alpha_alpha_T1 0.0 sample
alpha_beta_T2 alpha_beta_T2 0.0 sample
beta beta 0.0 sample
beta_Inh_T3 beta_Inh_T3 0.0 sample
beta_T3 beta_T3 0.0 sample
beta_T3_Inh beta_T3_Inh 0.0 sample
empty 0.0 sample

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
ass_aa_l T1 + alpha = alpha_T1

sample * (k0d * T1 * alpha - k0r * alpha_T1)
ass_ab_l alpha + T2 = alpha_T2

sample * (k7d * alpha * T2 - k7r * alpha_T2)
ass_bc_l beta + T3 = beta_T3

sample * (k14d * beta * T3 - k14r * beta_T3)
ass_bc_r T3 + Inh = T3_Inh

sample * (k16d * T3 * Inh - k16r * T3_Inh)
ass_bc_rl beta + T3_Inh = beta_T3_Inh

sample * (k17d * beta * T3_Inh - k17r * beta_T3_Inh)
dis_aa alpha_T1_alpha > alpha + alpha_alpha_T1

sample * k5d * alpha_T1_alpha
dis_ab alpha_T2_beta > beta + alpha_beta_T2

sample * k12d * alpha_T2_beta
dis_bc beta_T3_Inh > Inh + beta_Inh_T3

sample * k19d * beta_T3_Inh
exo_a alpha = empty

sample * k24d * alpha
exo_b beta = empty

sample * k25d * beta
exo_c Inh = empty

sample * k26d * Inh
inh_ac T1 + Inh = Inh_T1

sample * (k21d * T1 * Inh - k21r * Inh_T1)
inh_displ_ac T1_alpha + Inh = alpha + Inh_T1

sample * (k22d * T1_alpha * Inh - k22r * alpha * Inh_T1)
m_ass_aa_lr alpha_T1_alpha = alpha + alpha_T1

sample * (k1d * alpha_T1_alpha - k1r * alpha * alpha_T1)
m_ass_aa_r T1_alpha = T1 + alpha

sample * (k2d * T1_alpha - k2r * T1 * alpha)
m_ass_aa_rl alpha_T1_alpha = alpha + T1_alpha

sample * (k3d * alpha_T1_alpha - k3r * alpha * T1_alpha)
m_ass_ab_lr alpha_T2_beta = alpha_T2 + beta

sample * (k8d * alpha_T2_beta - k8r * alpha_T2 * beta)
m_ass_ab_r T2_beta = T2 + beta

sample * (k9d * T2_beta - k9r * T2 * beta)
m_ass_ab_rl alpha_T2_beta = alpha + T2_beta

sample * (k10d * alpha_T2_beta - k10r * alpha * T2_beta)
m_ass_bc_lr beta_T3_Inh = beta_T3 + Inh

sample * (k15d * beta_T3_Inh - k15r * beta_T3 * Inh)
m_inh_displ_ca alpha + Inh_T1 = alpha_T1 + Inh

sample * (k23d * alpha * Inh_T1 - k23r * alpha_T1 * Inh)
nick_aa alpha_alpha_T1 > alpha_T1_alpha

sample * k6d * alpha_alpha_T1
nick_ab alpha_beta_T2 > alpha_T2_beta

sample * k13d * alpha_beta_T2
nick_bc beta_Inh_T3 > beta_T3_Inh

sample * k20d * beta_Inh_T3
pol_aa alpha_T1 > alpha_alpha_T1

sample * k4d * alpha_T1
pol_ab alpha_T2 > alpha_beta_T2

sample * k11d * alpha_T2
pol_bc beta_T3 > beta_Inh_T3

sample * k18d * beta_T3

Global parameters

Id Value
Bp_concentration <assignment rule> nM
Inh_total <assignment rule> nM
alpha_total <assignment rule> nM
beta_total <assignment rule> nM
fluorescence 0.0
k0d 0.0294
k0r 3.43457943925 per_min
k10d 3.43457943925 per_min
k10r 0.0294
k11d 11.8408 per_min
k12d 9.2239832 per_min
k13d 2.60186 per_min
k14d 0.0171
k14r 0.610714285714 per_min
k15d 0.00186296832954 per_min
k15r 0.027
k16d 0.027
k16r 0.00186296832954 per_min
k17d 0.0171
k17r 0.610714285714 per_min
k18d 17.024 per_min
k19d 5.566848 per_min
k1d 3.43457943925 per_min
k1r 0.0294
k20d 3.2064 per_min
k21d 0.027
k21r 0.00608108108108 per_min
k22d 0.021546
k22r 0.0000415391351351
k23d 0.0000415391351351
k23r 0.021546
k24d 0.411 per_min
k25d 0.485802 per_min
k26d 1.7262 per_min
k2d 3.43457943925 per_min
k2r 0.0294
k3d 3.43457943925 per_min
k3r 0.0294
k4d 15.2 per_min
k5d 11.8408 per_min
k6d 3.34 per_min
k7d 0.0294
k7r 3.43457943925 per_min
k8d 0.610714285714 per_min
k8r 0.0171
k9d 0.610714285714 per_min
k9r 0.0171

Local parameters

Id Value Reaction

Assignment rules

Definition
alpha_total = alpha + alpha_T1 + T1_alpha + 2.0 * alpha_T1_alpha + alpha_T2 + alpha_T2_beta + alpha_T2
beta_total = beta + T2_beta + alpha_T2_beta + beta_T3 + beta_T3_Inh
Inh_total = Inh + T3_Inh + beta_T3_Inh + Inh_T1
fluorescence = -0.38 + 0.00093 * (11.0 * (alpha_T1 + T1_alpha + alpha_T2 + T2_beta + beta_T3) + 16.0 * (T3_Inh + Inh_T1) + 22.0 * (alpha_T1_alpha + alpha_alpha_T1 + alpha_T2_beta + alpha_beta_T2) + 27.0 * (beta_T3_Inh + beta_Inh_T3))
Bp_concentration = 11.0 * (alpha_T1 + T1_alpha + alpha_T2 + T2_beta + beta_T3) + 16.0 * (T3_Inh + Inh_T1) + 22.0 * (alpha_T1_alpha + alpha_alpha_T1 + alpha_T2_beta + alpha_beta_T2) + 27.0 * (beta_T3_Inh + beta_Inh_T3)

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments