Chapter 6
Inverse Problems in Systems Biology: A Critical Review
Rodolfo Guzzi, Teresa Colombo, and Paola Paci
Abstract
Systems Biology may be assimilated to a symbiotic cyclic interplaying between the forward and inverse
problems. Computational models need to be continuously refined through experiments and in turn they
help us to make limited experimental resources more efficient. Every time one does an experiment we know
that there will be some noise that can disrupt our measurements. Despite the noise certainly is a problem,
the inverse problems already involve the inference of missing information, even if the data is entirely reliable.
So the addition of a certain limited noise does not fundamentally change the situation but can be used to
solve the so-called ill-posed problem, as defined by Hadamard. It can be seen as an extra source of
information. Recent studies have shown that complex systems, among others the systems biology, are
poorly constrained and ill-conditioned because it is difficult to use experimental data to fully estimate their
parameters. For these reasons was born the concept of sloppy models, a sequence of models of increasing
complexity that become sloppy in the limit of microscopic accuracy. Furthermore the concept of sloppy
models contains also the concept of un-identifiability, because the models are characterized by many
parameters that are poorly constrained by experimental data. Then a strategy needs to be designed to
infer, analyze, and understand biological systems. The aim of this work is to provide a critical review to the
inverse problems in systems biology defining a strategy to determine the minimal set of information needed
to overcome the problems arising from dynamic biological models that generally may have many unknown,
non-measurable parameters.
Key wordsSystems biology, Inverse problems, Sloppy models, Identifiability, Reverse engineering1 Introduction
1.1 The Rationale
of Systems Biology
and the Inverse
Problems
Systems biology is a relatively young discipline that considers the
cells as holistic entities. In his paperSequences and Consequences
Brenner [1], a founding father of molecular biology, strikes at what
he sees as the heart of the goal of systems biology. After reminding
us that the systems approach seeks to generate viable models of
living systems, Brenner goes on to say that: “Even though the
proponents seem to be unconscious of it, the claim of systems
biology is that it can solve the inverse problem of physiology by
deriving models of how systems work from observations of their
behavior. It is known that inverse problems can only be solvedMariano Bizzarri (ed.),Systems Biology, Methods in Molecular Biology, vol. 1702,
https://doi.org/10.1007/978-1-4939-7456-6_6,©Springer Science+Business Media LLC 2018
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