Skolan för
och datavetenskap
KTH / CSC / Kurser

Quantitative Systems Biology

This is the course web page for the Academic Year 2015-2016.

Location: Room 112:028
AlbaNova University Center
Roslagstullsbacken 11
Stockholm, Sweden
Same building as: Nordita "South" building
First lecture: Wednesday April 13, 10.15-11.00


The schedule will be decided with the students following the course.


This year no tutorials will be organized.


The purpose of the course is to present molecular biology from a mechanistic perspective, and on topical problems and methods in Systems Biology. The focus of the course is describing gene regulation and regulatory networks.


After the course the student should be able to

  • formulate mathematical models of gene regulatory networks on the level of kinetic equations
  • simulate such systems and compare to experimental data
  • discuss network properties in genomic data
  • compute simple graph theoretical properties of such data
so that they will be able to
  • independently construct computer programs that model melecular mechanisms of gene regulation
  • in professional life, identify biological problems for which sufficiently well described mathematical modeling and simulation could be of added value


The basic circuitry in transcription regulation, and other biological networks, including examples. The principle of robustness in biological systems of control. Kinetic proofreading and other error-correcting mechanisms in biological information-processing. Principles of kinetic equations in gene regulatory modelling. Motifs in biological and other networks.


The courses in the basic block on mathematics, computer science and numerical analysis on the D-, E- or F-programme.
The course SK2530 Introduction to Biomedicine, or equivalent.


Uri Alon, 2007
An Introduction to Systems Biology: Design Principles of Biological Circuits
Chapman & Hall/CRC Mathematical and Computational Biology Series
ISBN-10: 1-58488-642-0
ISBN-13: 978-158488-642-6

Additional material

For e.g. graduate students taking the course, the following papers may give valuable additional perspectives to the ones presented in the book (a fair amount of papers are also cited in the book).


Diffusion is the erratic motion of small particles forced by random collisions with molecules e.g. water molecules in a solution. Diffusion is characterized by the mean square displacement increasingly linearly in time. Compare motion in a straight line where the mean square displacement increases quadratically in time. One consequence of diffusion is the the Smoluchowski formula for the time it takes (on the average) for a diffusing particle to find a target of size a in a volume V (proportional to V/(aD), where D is the diffusion coefficient. This time is on the order of second or tenths of seconds for a not too large protein looking for a typical target on the DNA in a bacterial cell.

A nice book covering diffusion from a biological perspective is Howard C Berg "Random Walks in Biology" (Princeton University Press, 1983). The number of books and reviews written about diffusion from a physical or mathematical perspective is very large. Wikipedia (English) on Diffusion is short and does not cover as much as one would like, but the Wikipedia entry on Brownian Motion is quite OK. A historical overview, with many details and modern developments, is Bertrand Duplantier Brownian Motion, "Diverse and Undulating" (2007).

Random graphs and networks [Alon, App C]

The mathematical theory of random graphs started with Erdos and Renyi. The canonical reference is Bela Bollobas "Random Graphs" (Academi Press, NY, 1985); a more recent (but more mathematical) one is Svante Janson "Random Graphs" (Wiley-Interscience, 2000). Real-world network data are not always well described by the models of Erdos and Renyi; a phenomenon often referred to as "scale-free" neworks. Many models exist that explain real-world network data better (or much better) than the Erdös-Renyi theory, at the price of greater model complexity, fewer mathematical results, and the danger of over-fitting. This has been a very active field over the last 15 years.

Transcriptional regulation [Alon, App. A and B]

T.~Hwa's lab has investigated the computational properties of transcription regulation; the two-part review in Curr. Opin. Genet. Dev. is a useful summary of what has been done in the field.

The E coli operons

In the course (for instance in first tutorial and in Homework assignment 1) we use the RegulonDB data base on transcriptional regulation in E coli, but this is not the only source available: other examples are OperonDB, Prodoric, and ODB OperonDB and Prodoric contain operons (including transcription factor binding sites) in many bacterial species, and ODB also data on other organism. Going a bit further, yet another example, focusing on eukaryotic transcription factors (and only partially publically available) is TRANSFAC. All these data bases needs to be used with care, because they contain so much and diverse types of information There is for instance typically both experimentally validated data and computational predictions. More material on the E coli operons have now been collected in a separate document.

Noise and cell-cell variation [Alon, App D]

The Elowitz et al paper is referenced and described in Alon's book; the other papers are more recent.

Bacterial chemotaxis [Chapter 7]

The discussion in this chapter is based on work from Stan Leibler's lab (where Alon worked at the time) and can be found in Bacterial chemotaxis (motion of bacteria in response to chemical cues) has been studied by many groups and the adaptation problem which is the focus in [Alon, chapter 7] is only one that has interested theorists and experimentalists. The leading authority has been Howard C. Berg (Harvard) who has written a monograph on the rotary motor which drives the flagella: (this review is however difficult to access on some platforms).

A 2010 paper giving a game theoretic perspective on chemotaxis (a bacterium plays a game against other bacteria and/or nature, in deciding how to measure and react to density gradients in its near environment) is

The main conclusion of this paper is that the integrated response kernel of the bacterium should be zero, a property which entails adaptation for small changes in the concentration of attractants and repellants (linear response regime). The connection between the game theoretic approach and the modelling of the methylation-demethylation pathway is made in A very recent paper shows that there is adaptation also on the level of the interaction between CheY and the flagellar motor: This paper hence gives a possible mechanism for adaptation on a slow time scale in mutants that lack the methylation-demethylation pathway enzymes CheR and CheB, and in thermotaxis where the integrated response kernel is not zero (one-lobe kernel).

Kinetic proofreading [Chapter 9]

This topic is a classic in Biophysics. The basic problem is how copying of one informational moelcule to another (DNA to DNA, DNA to RNA, RNA to protein) can be much more accurate than any plausible association energy differences could allow them to be. The fundamental paper is by John Hopfield from 1974. For a slightly later, more detailed, theoretical analysis, see Ehrenberg and Blomberg, 1980, and for an experimental paper on the fidelity of DNA replication in prokaryotes, from about the same time, see Fersht et al (1982). The detailed mechanisms behind the fidelity of bacterial protein synthesis are still under active investigation, see the recent review (Johansson et al, 2008) from Ehrenberg's lab. Alon adopts the point of that many other recognition processes in biology also relies on kinetic proofreading. The example put forward in the book is T-cell recognition of non-self from self proteins, following the paper of McKeithan, 1995. This (possible) use of the kinetic proofreading mechanism is much less well established than the classical cases of DNA replication, transcription and translation; for a recent contribution, see e.g. Altan-Bonnet and Germain (2005) New dynamic regimes of kinetic proofreading were pointed out in

Molecular evolution, optimal design and Savageau's demand rule [Chapters 9 and 10]

In an experiment began in the 1980ies, strains of E.~coli have been propagated for tens of thousands of generations in defined media, and many evolutionary changes monitored; one (of many) publication(s) from this group is Lensky et al(1998). The paper Deker and Alon (2005), cited in the book, has a more recent follow-up, Kalisky et al, (2007). Links to the two papers on the demand rule by Savageau (1998) are given last.

Models of evolution, selection, Price equation and fitness

Mathematical models of evolution is a very wide field, very little covered in Alon's book. Evolution is normally taken to be shaped by selection, mutations and genetic drift. The last term is perhaps somewhat unfortunate as it refers to the inherent randomness as to which individuals, even with identical traits and fitness, which actually propagate their genomes from one generation to the next. In very large and homogeneously mixed populations genetic drift is absent, but in small populations it is significant. Often it is therefore also refered to as the founder effect, as survival of which genotypes in a small group populating a new niche is partly due to chance. Evolution without selection is called neutral theory and has been a very active field since the 1960ies. Mathematically the theory of neutral evolution shares many techniques with statistical physics. Although the main reference is and remains the book The Neutral Theory of Molecular Evolution by M Kimura a later readable and more compact review (from the viewpoint of physics) is The modern theory of selection is due to George R. Price and is formalized by Price equation. Wikipedia is a good reference in this case as most of Price's papers are not accessible from KTH and the later papers in the field do not add much; two papers of Price which can nevertheless currently (May 8, 2012) be found on-line are An effect directly derivable from Price's equation was recently demonstrated to give rise to "altruism" in bacterial communities A review of these experiments and related theory has appeared in From Price equation it is clear that fitness is a difficult subject in evolutionary theory (this material was discussed during lecture 11). On the one hand fitness can be defined as the ratio of offspring to parents, either as absolute fitness or as relative fitness but this measure refers to the future and is not observable at the time of the parents. Alternatively, fitness can be taken as a propensity of an individual to propagate its genome to the next generation, but this will then only be a proxy for fitness. While average relative fitness is trivially always equal to one, the average change of a proxy for fitness obeys the Price equation as any other trait. A large literature exists on fitness landscapes where the change in fitness is supposed to be proportional a gradient. In general evolution will not be described by fitness landscapes as the change of fitness is not gradient-like. A recent paper on the theoretical side working instead with fitness flux is Whether this particular theoretical advance will be practically useful remains to be seen. In summary, evolutionary theory has been a very active field in mathematical biology for a long time which is set to have more and more real-world applications as sequencing in time (along a process) and across communities (metagenomics) will continue to advance.

Global properties of gene regulation

In the last few years there have been a renewed interest in global regularities in gene regulation in E coli. The most well known of these is an empirical law that the fraction of resources devoted by the cell to ribosomes is linearly proportional to the growth rate. There are also several old (and new) empirical laws stating how gene expression of e.g. constutively expressed genes and positively and negatively regulated genes depend on the growth rate. One finding is that negatively regulated genes and also negatively auto-regulated genes have expression levels fairly independent on the growth rate. This gives a new perspective on the main material in the course. Main papers in this line are: Two recent reviews are Two very recent additional contributions are


Examination is by homework assignments, mandatory for all grades, and an individual examination, mandatory for the highest grade only. The grading criteria are

  • 0/4 correctly solved homework assignments give grade F
  • 1/4 correctly solved homework assignments give grade E
  • 2/4 correctly solved homework assignments give grade D
  • 3/4 correctly solved homework assignments give grade C
  • 4/4 correctly solved homework assignments give grade B
  • 4/4 correctly solved homework assignments and successfully passed individual examination give grade A
Students having registered for the course, but who have not signed the attendance list, nor otherwise given sign to the lecturer that they are follwing the course, will be given grade X.

The individual examination is conducted by the examiner with one assistant under at least 30 minutes and at most 60 minutes per student.


Erik Aurell, tel: 790 69 84, e-mail:
Nicolas Innocenti, tel: 790 62 71 , e-mail:

Copyright © Sidansvarig: Erik Aurell <>
Uppdaterad 2016-04-11