2.1.3 Modelling biology

The biological processes that surround us possess a complexity that can not be explained and figured out only from pure observation and deduction.

Mathematical modelling allows us to understand the nature, dynamics and development of biological systems and to make plausible and useful predictions about how those system will behave in the future.

The task of modelling is indispensable for research and for the scientific method as a tool to understand the physical reality of our world.

What is a model? Definition and purposes

A model is a simplified representation of reality able to describe and explain an existing phenomenon.

The key concept in that definition is "simplified" since all models are simplifications.

They only try to represent a particular aspect or area of a real process.

Considering this, modelling becomes a subjective procedure.

A model needs to be developed with a specific purpose, which sets what magnitudes and variables are important for that purpose and what can be disregarded or at least de-emphasized.

Therefore a model explains only some aspects of a process, under certain environmental conditions and only for a particular degree of accuracy.

A model that aims at predicting a system’s output can be based and developed around a precise description of input-output variables.

However, if finding out the function of an object or the mechanisms of a system is the purpose of the model, then the relations between its parts must be included and described carefully.

Some models in biology are quite general such as Michaelis-Menten kinetics (that aims to explain the dynamics of many different enzymes) and some can be very specific (for instance the structure of a protein, the sequence of a gene or the bio-energetics of mitochondria).

Models obtain the data to fill its structure from experiments.

Therefore, a model can only be as precise and potent as the experimental data is based on.

However, the process of modelling has some advantages when done in parallel or in an iterative way along experiments.

First, modelling helps to clarify concepts.

Detecting data inconsistencies and knowledge gaps are typical outcomes of good models.

Secondly, it is cheaper, easier and faster to try out some test or hypothesis with a good model than to perform experiments.

Good models save money and time.

Finally, and this is probably the key point, models assist and guide experimentation.

Different perturbations, long time courses, virtually endless repetitions can lead research to the most promising possibilities.

Cells as modelling environment

Biological models are as diverse as biology itself.

Planet-level ecosystems, complex organisms, particular organs, tissues, cells, sub-cellular systems, pathways, molecular interactions, molecular sequence and structure.

The size and scope of the models used in biology can vary dramatically.

As it was mentioned before, systems biology deals usually with individual cells.

Furthermore, this thesis focuses mainly on cellular metabolism and cellular protein interactome analysis.

There are two main reasons to circumscribe systems biology to cell-level modelling.

First, there is still massive amount of information that we do not know yet.

Although high-throughput techniques have multiplied the cellular data available to test and study, much needs to be done to improve our knowledge of cell functions and structure.

Information about some metabolic or signalling pathways or gene and protein functions is still partial and fragmented and sometimes even contradictory.

The second reason arises from the inherent complexity of biological system.

Genomes contain thousands of genes, poly-peptides have thousands of residues, proteinprotein interaction networks have tens of thousands of interactions.

Assuming the information needed to construct models for those elements is known, the sheer complexity of the system makes the model implementation and interpretation very difficult.

There is a general understanding that at this moment cells are complex enough for the experimental data and the modelling tools available.

Classification of biological models

There are different classes of models depending on the purpose of the model and the amount and nature of the experimental data available.

Theory-based or data driven.

Theory-based models draw their mathematical structure from first principle knowledge from the system.

Data-driven models are based solely on the relation and dependency of the data.

This thesis shows examples of both types.

Parametric or non parametric.

Parametric models need the presence of parameters fitted by the experimental data.

If the model does not need parameter fitting then it is non parametric.

Static or dynamic.

Static models represent the system at specific time instants or snapshots and assume steady state.

Dynamic models display the evolution of the system variables over time.

Black box or white box.

A black box model or approximation represents a system which can be viewed in terms of its inputs and outputs, without any information inner elements are available for study and testing.

Homogeneous or heterogeneous.

Homogeneous models consider cell populations homogeneous in its functions, mechanisms and structures.

Heterogeneous models distinguish between different cell sub-population that show different features.

Modelling questions

Building a model is a subjective endeavour.

However, the process of modelling, in particular modelling in biology, can be broken down in a series of simple steps that is relevant to point out here.

The next questions serve more of a series of issues that is generally useful to address when modelling than an exhaustive roadmap.

Problem and purpose.

What problem or process do we want to explain or study? What particular aspect of that problem should we focus on? Available data.

What kind of available information we do have to build the model? Is there some pre-existing structural knowledge about the problem? Are the knowledge gaps? Do we know all the components and interactions that form the system? Model structure.

Which structure should the model have? Dynamic or static? Deterministic or stochastic? How many variables, parameters and equations should have? Testing.

Do the model agrees with the experimental data? Is it able to predict results from new experiments? Do the model make easy predictions to test? Refinement.

Which parts of the models should we adapt to better represent the phenomenon? Does it need more parameters? Different variables? Bigger or smaller scope? Modelling, like any process in research, highly benefits from preparation and thinking ahead.

It is a fine balance between having a solid approach to the problem and the aim of the model and the flexibility of expand it or limit it in scope and shape.