The synergies that exist between mathematics and the life sciences are becoming more and more apparent. This is reflected in their prominent role in the current development of both disciplines. Many candidate applications of mathematics in the life sciences remain unexplored. In this minisymposium we will address some of those open problems; focussing on the mathematical analysis of cellular systems. We will specifically invite speakers with a track record in this area and request them to discuss challenging mathematical problems in the field of cellular systems biology.
The mini-symposium is scheduled during 5ECM on Thursday July, 17th, in two slots: 13.25-14.55 and 15.25-16.55, separated by a coffee break. There will be four talks of 30 minutes each, leaving room for 15 minutes of discussion with each talk.Speakers (titles and abstracts as far as currently known):
Jens Timmer (Freiburg): Data-based Identifiability Analysis of Non-Linear Dynamical Models
Mathematical models of the dynamics of cellular processes promise to yield new insights into the underlying cell biology and their systems' properties. Since the processes are usually high-dimensional and time-resolved experimental data of the processes are sparse, parameter estimation faces the challenges of structural and practical non-identifiability of the parameters. Non-identifiability result in, in general, non-linear dependencies of the estimated parameters. To infer (non-)identifiability elegant analytical approaches exist which are, however, due to their computational complexity limited to low-dimensional systems. Established methods for high-dimensional systems rely on linear approximations which renders the interpretation of their results difficult. We propose a data-based non-parametric approach for identifiability analysis that is based on the bootstrap. It applies the alternating conditional expectation algorithm (ACE) to estimate so-called optimal transformations. Statistical analysis of the optimal transformations allows for identifiability analysis regardless of model size or complexity. The algorithm identifies dependent, i.e. non-identifiable, groups of parameters, as well as the identifiable ones. We exemplify the proposed procedure by applications to dynamical models of cellular signaling pathways. We show how identifiability analysis supports the iterative cycle between modeling and experimentation in modern Systems Biology.
Pauline Hogeweg (Utrecht University)
Johan Paulsson (Harvard Medical School)
David Rand (Warwick): Global sensitivity and summation laws for cellular network dynamics
The development of analytical tools to understand and predict the behaviour of regulatory, signalling and metabolic networks is challenging because their dynamics are highly nonlinear, have high-dimensional state spaces and depend on large numbers of parameters. I develop a more global approach to sensitivity analysis that studies the variation of the whole solution rather that focusing on just one output variable. Such an approach is practicable for cellular networks because such systems have a local geometric rigidity. This leads to new approaches to sensitivity analysis, parameter reduction and experimental optimisation. A key result is that all the sensitivities of such a complex dynamical system can be represented in terms of a pair of graphical objects. In addition, I will discuss a new summation theorem which substantially generalises previous results for oscillatory and other dynamical phenomena. This theorem can be interpreted as a mathematical law stating the need for a balance between fragility and robustness in such systems.
Organizers: Frank Bruggeman (Centrum voor Wiskunde en Informatica, Amsterdam) and Mark Peletier (Eindhoven)