Simulation of Biological Processes phần 6 doc

Subramaniam: Not necessarily. You can have emergent properties as a conse￾quence of integration.

Noble: And you may even be puzzled as to why. This is not yet an explanation.

Boissel: The next term is ‘robustness’. Yesterday, again, I heard two di¡erent

de¢nitions. First, insensitivity to parameter values; second, insensitivity to uncer￾tainty. I like the second but not the ¢rst.

Noble: In some cases you would want sensitivity. No Hodgkin^Huxley analysis

of a nerve impulse would be correct without it being the case that at a certain critical

point the whole thing takes o¡. We will need to have sensitivity to some parameter

values.

Boissel: For me, insensitivity to parameter values means that the parameters are

useless in the model.

Cassman: In those cases (at least, the fairly limited number where this seems to be

true) it is the architecture of the system that determines the output and not the

speci¢c parameter values. It seems likely this is only true for certain characteristic

phenotypic outcomes. In some cases it exists, in others it doesn’t.

Hinch: Perhaps a better way of saying this is insensitivity to ill-de¢ned parameter

values. In some models there are parameters that are not well de¢ned, which is the

case in a lot of signalling networks. In contrast, in a lot of electrophysiology they

are well de¢ned and then the model doesn’t have to be robust to a well de¢ned

parameter.

Loew: Rather than uncertainty, a better concept for our discussion might be

variability. That is, because of di¡erences in the environment and natural

variability. We are often dealing with a small number of molecules. There is there￾fore a certain amount of uncertainty or variability that is built into biology. If a

biological system is going to work reliably, it has to be insensitive to this

variability.

Boissel: That is di¡erent from uncertainty, so we should add variability here.

Paterson:It is the di¡erence between robustness of a prediction versus robustness

of a system design. Robustness of a system design would be insensitivity to

variability. Robustness of a prediction, where you are trying to make a prediction

based on a model with incomplete data is more the uncertainty issue.

Maini: It all depends what you mean by parameter. Parameter can also refer to the

topology and networking of the system, or to boundary conditions. There is a link

between the parameter values and the uncertainty. If your model only worked if a

certain parameter was 4.6, biologically you could never be certain that this

parameter was 4.6. It might be 4.61. In this case you would say that this was not a

good model.

Boissel: There is another issue regarding uncertainty, which is the strength of

evidence of the data that have been used to parameterize the model. This is a

di⁄cult issue.

GENERAL DISCUSSION II 127

References

Boyd CAR, Noble D 1993 The logic of life. Oxford University Press, Oxford

Loew L 2002 The Virtual Cell project. In: ‘In silico’ simulation of biological processes. Wiley,

Chichester (Novartis Found Symp 247) p 151^161

Winslow RL, Helm P, Baumgartner W Jr et al 2002 Imaging-based integrative models of the

heart: closing the loop between experiment and simulation. In: ‘In silico’ simulation of

biological processes. Wiley, Chichester (Novartis Found Symp 247) p 129^143

128 GENERAL DISCUSSION II