Systems Biology (Methods in Molecular Biology)

It is worth noting the high fit of the model (r¼0.89) and that the main contribution (higher regression coefficient) to PolB com ...

5 Conclusions System’s parameter estimation in biology asks for a continuous feedback between biological and procedural informat ...

Chapter 6 Inverse Problems in Systems Biology: A Critical Review Rodolfo Guzzi, Teresa Colombo, and Paola Paci Abstract Systems ...

under very specific conditions. A good example of an inverse prob- lem is the derivation of the structure of a molecule from the ...

reconciliation of the underlying hypothesis with experimental data. In the context of systems biology, this implies, in most of ...

Under the hypothesis of homogeneity of the solution where reactions occur, the mass action law asserts that the time evolution o ...

biology is a bifurcation phenomenon of the model equations. These bifurcations are tuned by the conservation law constants of th ...

JxðÞ¼,θ ∂Yðx,θÞ ∂ðx,θÞ ¼ ∂y ∂x 1  ∂y ∂xn  ∂y ∂θ 1  ∂y ∂θn ⋮⋮⋮⋮ ∂ynu ∂x 1  ∂ynu ∂xn  ∂ynu ∂θ 1  ∂ynu ∂θn 0 B B ...

whereF:X!Yis an ill-posed operator between Hilbert spaces X,Y. The inverse problem is to identify the model parameters observed ...

given set of parameters from the experimental data. The precise function is a sum of squared differences between the model and t ...

and the Jacobian is referred to as the Design Matrix for the linear- ized approximation of the full model [20]. Sloppy models ar ...

The time differential equations are: dC 2 dt ¼k 8 notPC 2 ðtÞþk 9 CPðtÞþk 6 MðtÞ dCP dt ¼k 8 notPC 2 ðtÞk 9 CPðtÞk 3 CP ...

3.2 Identifiability In general a mathematical model helps to better understand the biological phenomenon studied. It enables exp ...

3.3 Sloppiness In order to detect the level of sloppiness of the parameters involved in the Tyson’ model we applied the procedur ...

3.5 Inverse Bifurcation Bifurcation analysis has proven to be a powerful method for under- standing the qualitative behavior of ...

Lu et al. [25], applying a methodology based on the inverse map from the space of bifurcation diagrams to biological space param ...

scale dynamic biological models generally may have many unknown, non-measurable parameters and their tuning may appear unrealist ...

A.2 Bifurcation Concepts A bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameter ...

to make a change of variables from the dependent variablexto a local variable. Now let: xðtÞ¼xþEðtÞ, ð 23 Þ where it is assumed ...

We now consider each of the two solutions forr>0, and examine their linear stability in the usual way. First, we add a small ...