An Introduction to Computational Systems Biology

Systems-Level Modelling of Cellular Networks

Karthik Raman

• Publisher: Chapman and Hall/CRC
• Year: 2021
• Print ISBN:
  9780367752507
  9781138597327
• eBook ISBN:
  9780429944512
• Edition: 1
• Topic: Scienze biologiche
• Subtopic: Probabilità e statistica

This book delivers a comprehensive and insightful account of applying mathematical modelling approaches to very large biological systems and networks—a fundamental aspect of computational systems biology. The book covers key modelling paradigms in detail, while at the same time retaining a simplicity that will appeal to those from less quantitative fields.

Key Features:

• A hands-on approach to modelling
• Covers a broad spectrum of modelling, from static networks to dynamic models and constraint-based models
• Thoughtful exercises to test and enable understanding of concepts
• State-of-the-art chapters on exciting new developments, like community modelling and biological circuit design
• Emphasis on coding and software tools for systems biology
• Companion website featuring lecture videos, figure slides, codes, supplementary exercises, further reading, and appendices: https://ramanlab.github.io/SysBioBook/

An Introduction to Computational Systems Biology: Systems-Level Modelling of Cellular Networks is highly multi-disciplinary and will appeal to biologists, engineers, computer scientists, mathematicians and others.

CHAPTER 1

Introduction to modelling

Contents

• 1.1 What is modelling?
• 1.2 Why build models?
• 1.3 Challenges in modelling biological systems
• 1.4 The practice of modelling
• 1.5 Examples of models
• 1.6 Troubleshooting

Living organisms display remarkable abilities, to adapt and thrive in a variety of environments, fight disease, and sustain life. Underlying every living cell, from the ‘simplest’ prokaryote to human beings and other complex organisms, is an intricate network of biological molecules¹ performing a very wide variety of functions. This network includes complex macromolecules such as DNA, RNA, and proteins, as well as smaller molecules that drive metabolism, such as ATP or even water. In this chapter, we will see why mathematical modelling provides a valuable framework for us to begin unravelling the seemingly interminable complexity of biological systems.

Rapid advancements in sequencing and other high-throughput technologies over the last two decades have generated vast amounts of biological ‘big data’. Spurred by this explosion in data, many computational methods have been developed for analysing such data. Notably, many tools and techniques strive to infer from these data, the complex networks that span metabolism, regulation, and signalling. Simulatable computational models of biological systems and processes, which provide a handle to understand and manipulate the underlying complex networks, form the cornerstone of systems biology.

1.1 What is modelling?

Many definitions exist for modelling, but beyond definitions, it is essential to understand the process of modelling, from one key perspective: what is the overarching goal of the modelling process? What are the important questions we seek to answer through the modelling exercise? Many a time, the clarity of this question decides the success of the modelling exercise. For example, are we interested in the dynamics of the system under consideration? Do we only need to know if certain interactions exist? Or, if some interactions are more important than others (in a qualitative sense)? Do we need to know the exact values of specific parameters in the system? And so on.

¹ See the cover image of the book!

The questions also dictate the resolution of the model. As the famous adage goes, “Don’t model bulldozers with quarks” [1]. Biological systems abound in time-scales and length-scales; therefore, a careful choice of the scale and resolution of the model is critical. If the scales chosen for modelling are incongruent with the questions being asked, the effect(s) we wish to observe may well be lost.

1.1.1 What are models?

Models essentially capture some physical system of interest, say a space shuttle, or a bacterial cell, or a human population where a communicable disease is spreading. Mathematical models capture these systems typically by means of mathematical equations. Models are abstractions of real-world systems; in fact, they are abstractions of (key) parts of a real-world system, capturing features deemed to be essential by the modeller. Modelling is thus a very subjective process, driven by the need to answer specific questions about the real-world system. Models can comprise a bunch of mathematical objects or equations, or even a computer program. Every model is characterised by assumptions on the real-world system, as well as approximations. These assumptions cover:

• variables (things that change),
• parameters (things that do not change, or are assumed to not change), and
• functional forms (that connect the variables and parameters),

Bender [2] defines a model as an “abstract, simplified, mathematical construct related to a part of reality and created for a particular purpose”. This succinct definition harps on several key points:

• Models are abstractions
• Models are simplifications
• Models are incomplete
• Models are question-specific

The last point is very important—it is not unusual to find models that are built or known to be valid only under certain conditions, but are unwittingly applied to other conditions as well. For example, there are models that predict the initial rate of an enzyme-catalysed reaction when no product is present. Often, the same model is used to also predict/fit observations of measurements made at later time-points. There are certain assumptions that have gone into the model building process—if we lose sight of them at some point in time, we are very likely to commit major errors in predictions. Robert May outlines some of these points nicely in his essay titled “Uses and Abuses of Mathematics in Biology” [3].

Models can also be thought to divide the world into three sets [2]:

1. things whose effects are deliberately neglected (things beyond the system boundary),
2. things that are known to affect the model but which the model is not designed to study (things beyond the scope of the model), and
3. things/effects the model is actually designed to study,

In any modelling exercise, we must deliberately choose to neglect several things. Otherwise, we must build a ‘whole-universe model’, for any system to be studied! Therefore, we carefully choose a system boundary and consciously neglect various effects outside of this boundary. For example, while studying bacterial chemotaxis² in an open vessel, we may choose to neglect the effect of wind in the room or the temperature of the environment.

A particular model of chemotaxis may choose to ignore the temperature of the cell suspension, fully knowing that it can have an effect on chemotaxis. That is, these effects are considered to be beyond the scope of the model. The things or effects the model is actually designed to study are the variables of interest. In the chemotaxis example, this would be the concentration of an ‘attractant’, such as glucose. What we choose to neglect—in terms of both the system boundary and model scope—obviously affects both the complexity of a model, and its accuracy/predictive power. As Einstein purportedly remarked [3], “models should be as simple as possible, but not more so”—a practical translation of Occam's razor (see §6.4.1) for modellers.

1.2 Why build models?

Invariably, a key reason why we strive to model any system is the desire to predict its behaviour, typically at another point in time/space, or under different conditions. Modelling drives conceptual clarification and helps reveal knowledge gaps. We create a model by committing to an understanding of a given system, and when the model predictions are off from reality, they point towards assumptions about the system that do not hold.

Modelling can also help prioritise experiments that are most informative and shed light on system function. Further, many experiments are infeasible or difficult to perform, expensive, and may also not be ethical (e.g. while dealing with human/animal subjects).

A key aspect of modelling biological systems, and even biology in general, is the study of systems under perturbation: modelling can potentially answer a number of ‘what-if’ questions, to understand the possible behaviour of the system under a variety of conditions. These could include the removal of a protein, the addition of a drug, or a change in the environment of a cell. Indeed, many models are used to predict the outcomes of the independent removal of every single component from a network, or even combinations of such removals, to clearly understand the key role played by each component in the network.

² The movement of a motile organism, such as a bacterium, in the direction corresponding to the concentration gradient of a particular substance, e.g. glucose.

“All biology is computational biology!”

This box takes its title from the provocative article written by Florian Markowetz in 2017 [4]. The article essentially emphasises the central importance of computation and modelling in modern biology. Nevertheless, there is always a palpable tension between experimentalists and modellers. The la...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Chapter 1 ▪ Introduction to modelling
• Part I Static Modelling
• Part II Dynamic Modelling
• Part III Constraint-based Modelling
• Part IV Advanced Topics
• Index