Blocking stable motifs may obstruct specific attractors | To evaluate if this intervention is longterm successful we compare the probabilities that an arbitrary initial condition ends in A3 with and without the intervention. |
Blocking stable motifs may obstruct specific attractors | We find that the intervention makes it more likely for an arbitrary initial condition to reach .43, so this intervention is not longterm successful. |
Blocking stable motifs may obstruct specific attractors | To validate an intervention target, we compare the probabilities that an arbitrary initial condition ends in the target attractor with and without the intervention (see Methods). |
General asynchronous updating scheme | In the general asynchronous scheme, the state of the nodes is updated at discrete time steps starting from an initial condition at t: 0. |
Intervention target validation | To validate an intervention target, we fix the node states prescribed by the intervention, choose a random (uniformly chosen) initial condition , and evolve the system using the general asynchronous updating scheme for a sufficiently large number of time steps so that the system reaches an attractor. |
Intervention target validation | We find that, for our test cases, temporal evolution for 10,000 time steps ensures reaching an attractor from any initial condition considered with stable motif control intervention or without an intervention; to be safe, we choose to evolve for 50,000 time steps in all cases. |
Intervention target validation | We repeat this for a large number of initial conditions (100,000) and calculate the probability of reaching each attractor from an arbitrary (uniformly chosen) initial condition . |
Stable motif control implies network control | Normally, the sequence of stable motifs is chosen autonomously by the system based on the initial conditions and timing. |
The control targets transcend the logical modeling framework | We test the effectiveness of the stable motif control interventions in the translated ODE models by comparing the probability for an uniformly chosen initial condition to reach the target attractor with and without the intervention (see S6 Text). |
Compounds that drive insulin signaling | Effects of initial conditions on LN229 simulations. |
Compounds that drive insulin signaling | Varying initial conditions in the model showed that the insulin system is highly sensitive to reduced oxygen concentrations and elevated IGFI concentrations compared to the default initial conditions (control). |
Compounds that drive insulin signaling | For the remaining initial conditions , the insulin signaling system in glioblastoma was robust over changes in initial HIFloc concentrations and the (IGFI-IGFBPZ) complex concentration. |
Discussion | Sensitivity analysis on initial conditions found the insulin signaling pathway to be most sensitive to IGFI concentration and oxygen levels. |
Fitting model parameters | The estimated initial conditions and fitted rate constants are shown in Tables 1 and 2. |
Fitting model parameters | The glioblastoma growth rates were found for two distinct experiments (U87 and LN229) by fitting the same model and obtaining different initial conditions and growth rates for the two cell lines. |
Fitting model parameters | Initial conditions were also determined from experiments. |
Supporting Information | Sensitivity analysis of initial conditions and rate constants on IGFI, IGFBPZ, HIFloc and glioblastoma diameter for both U87 and LN229 glio-blastoma cell lines for 24 hour simulation. |
Simulations of dI/Cact dynamics | In the model, however, the initial conditions for each interphase include newly-formed nuclei that are devoid of any dl, Cact, or dl/Cact complex. |
Simulations of dI/Cact dynamics | In other words, even if the nuclear import rates of Cact and dl/Cact complex were zero, the initial conditions for each interphase would include nonzero levels of these species in the nuclei. |
dI/Cact model formulation | The simulation begins at the onset of NC10 interphase with the initial conditions for each molecular species uniform in space. |
Bow-tie architectures evolve when the goal is rank deficient | We studied goals of dimension D = 6—8 consisting of L = 4—6 matrices, tested 4—8 different goals for each dimension, and evolved networks towards each goal in 100—3000 repeated simulations, each starting from different random initial conditions . |
Bow-tie architectures evolve when the goal is rank deficient | We repeated the simulation 700 times for each goal starting from different random matrix initial conditions . |
Data analysis | Consequently, each run starts from different initial conditions and uses different mutational realizations. |
Results | Nevertheless, using the multiplicative properties of branching processes, we can calculate the probability of escape and the (conditional) average time to resistance for any given initial conditions of tumor size or metastases (see derivation details in 81 Text). |
Results | Similar results are obtained using different initial conditions , despite that resistance evolution is more likely (and sooner) to occur When the sensitive cell is initially placed in the sanctuary compartment than in the drug-containing compartment (cf. |
Results | This result is mainly due to the initial condition used: lesion 1 is much larger than lesion 0 that the influx of escaping cells to the sanctuary exceeds the number of cells in situ. |