Fitting model parameters | The estimated initial conditions and fitted rate constants are shown in Tables 1 and 2. |
Fitting model parameters | The rate constants were simultaneously fitted using data of IGFI and IGFBP2 levels as a function of each other and time (see Fig 3A, Slomiany et al. |
Glioblastoma growth reduction | To simulate the effect of using different drug targeting factors in glioblastoma, we set each rate constant to 0 separately, modeling the effects of removing each interaction, with the exception of the basal production and degradation of HIFloc. |
Glioblastoma growth reduction | Setting the rate constant to 0 simulated the removal of each reaction from the system. |
Global sensitivity analysis | In addition to varying the rate constants individually, we simultaneously explored the entire parameter space of the rate constants (varying between 0.1X—10X of the fitted values) using the Latin Hypercube Sampling method [75]. |
Global sensitivity analysis | From this sampling, 500 sets of rate constants were simulated in the model for glioma growth over 40 days where the glioblastoma diameter was |
Global sensitivity analysis | Variable Description 60,, Glioblastoma diameter at final time point using varied rate constant GDO Glioblastoma diameter at final time point at optimized value |
Parameter fitting | Unknown rate constants were found by fitting existing literature data. |
Sensitivity analysis | The sensitivity of glioblastoma growth to changes in kinetic rate constants was determined for kinetic rates of 0.1X-10X the fitted values individually. |
Introduction | A quasi-steady-state assumption for these intermediates is commonly employed to this end [3], yielding a final expression function of microscopic rate constants and reactant concentrations. |
Introduction | Some of the rate constants are related to the apparent equilibrium constant of the overall reaction by the Haldane relationships, directly linking kinetics with thermodynamics [5]. |
Introduction | Moreover the rate constants can be converted into macroscopic kinetic constants [6], which can be measured and estimated from subsequent enzymatic assays. |
Parameterization and sampling of the catalytic mechanism | Where k is a microscopic rate constant , x is the reactant concentration and e is the concentration of enzyme intermediate involved in the elementary step. |
Parameterization and sampling of the catalytic mechanism | Rate laws can be derived from the enzyme mechanism and the microscopic rate constants using the King-Altman’s method [4]. |
Parameterization and sampling of the catalytic mechanism | In order to sample kinetics, we can in principle sample the rate constants directly. |
Sampling functional contributions: catalytic and regulatory effects | If the reference values for the total enzyme and metabolite concentrations are known, they can be used to transform the set of scaled rate constant into absolute constants. |
Precise transcription cycle times, despite inherent molecular noise, can cause transient transcriptional oscillations at the population level | We chose realistic values for the rate constants and protein abundances (see S3 Text and 83—85 Tables). |
Reversible assembly of large protein complexes can take tens of minutes | The mean assembly time for a protein complex of n factors, with identical kinetics, depends on the reversibility of complex formation (K13) and the first-order association rate constant (k’F) as: if factors have different association rate constants , this time is given by 23:.1211/kjD 1.. |
Reversible assembly of large protein complexes can take tens of minutes | In these equations, k3, denotes the effective first order rate constant (unit: min'l) for the binding of a regulatory factor to a partially assembled complex. |
Reversible assembly of large protein complexes can take tens of minutes | It equals the multiplication of a (diffusion-limited) second-order rate constant for binding (unit: nM'1 min'l) with the (nuclear) concentration of the regulatory factor (unit: nM). |
Reversible equilibrium-binding mechanisms for gene regulation become ineffective when many regulatory factors are involved | CD(T) = 1 = H; qbi(Ti), with v as the transcription rate and k’ as the apparent transcription rate constant . |
Supporting Information | Mechanisms of protein complex assembly and their duration depending on the sequence and association rate constant . |
Supporting Information | The rate constant for the final irreversible acetylation of lysine 9 and lysine 14 kmod = 60 min'l, i.e. |
Supporting Information | A customary algorithm was used to calculate rate constants for the corresponding protein association and dissociation reactions. |
Definition of kinetic signatures | The peak and dip signature functions require a rate constant 6 which is not an explicit parameter of the model. |
Definition of kinetic signatures | This formulation ensures that the initial rise or fall in expression shows an exponential characteristic that is not limited to the almost linear characteristic that might otherwise result from a small value of the rate constant 6. |
Results | The peak and dip signature functions require a rate constant 6 which is not an explicit parameter of the model. |
Results | This formulation ensures that the initial rise in expression shows an exponential characteristic that is not limited to the almost linear initial change in expression that might otherwise result from a small value of the rate constant 6. |