The organization, regulation and dynamical responses of biological systems are in
many cases too complex to allow intuitive predictions and require the support of mathematical
modeling for quantitative assessments and a reliable understanding of system functioning.
All steps of constructing mathematical models for biological systems are challenging,
but arguably the most difficult task among them is the estimation of model parameters
and the identification of the structure and regulation of the underlying biological
networks. Recent advancements in modern high-throughput techniques have been allowing
the generation of time series data that characterize the dynamics of genomic, proteomic,
metabolic, and physiological responses and enable us, at least in principle, to tackle
estimation and identification tasks using 'top-down' or 'inverse' approaches. While
the rewards of a successful inverse estimation or identification are great, the process
of extracting structural and regulatory information is technically difficult. The
challenges can generally be categorized into four areas, namely, issues related to
the data, the model, the mathematical structure of the system, and the optimization
and support algorithms. Many recent articles have addressed inverse problems within
the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these
tasks because of its unique structural flexibility and the fact that the structure
and regulation of a biological system are mapped essentially one-to-one onto the parameters
of the describing model. The proposed methods mainly focused on various optimization
algorithms, but also on support techniques, including methods for circumventing the
time consuming numerical integration of systems of differential equations, smoothing
overly noisy data, estimating slopes of time series, reducing the complexity of the
inference task, and constraining the parameter search space. Other methods targeted
issues of data preprocessing, detection and amelioration of model redundancy, and
model-free or model-based structure identification. The total number of proposed methods
and their applications has by now exceeded one hundred, which makes it difficult for
the newcomer, as well as the expert, to gain a comprehensive overview of available
algorithmic options and limitations. To facilitate the entry into the field of inverse
modeling within BST and related modeling areas, the article presented here reviews
the field and proposes an operational 'work-flow' that guides the user through the
estimation process, identifies possibly problematic steps, and suggests corresponding
solutions based on the specific characteristics of the various available algorithms.
The article concludes with a discussion of the present state of the art and with a
description of open questions.