Quantitative Systems BiologyThis is the course web page for the Academic Year 20152016.
ScheduleThe schedule will be decided with the students following the course. TutorialsThis year no tutorials will be organized.PurposeThe 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. GoalsAfter the course the student should be able to
ContentsThe basic circuitry in transcription regulation, and other biological networks, including examples. The principle of robustness in biological systems of control. Kinetic proofreading and other errorcorrecting mechanisms in biological informationprocessing. Principles of kinetic equations in gene regulatory modelling. Motifs in biological and other networks. Prerequisites
The courses in the basic block on mathematics, computer science and numerical analysis on the D, E or Fprogramme. Literature
Uri Alon, 2007 Additional materialFor 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). DiffusionDiffusion 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" (WileyInterscience, 2000). Realworld network data are not always well described by the models of Erdos and Renyi; a phenomenon often referred to as "scalefree" neworks. Many models exist that explain realworld network data better (or much better) than the ErdösRenyi theory, at the price of greater model complexity, fewer mathematical results, and the danger of overfitting. 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 twopart review in Curr. Opin. Genet. Dev. is a useful summary of what has been done in the field.
The E coli operonsIn 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 cellcell 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
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
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.
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 followup, 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 fitnessMathematical 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
Global properties of gene regulationIn 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 autoregulated 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:
ExaminationExamination is by homework assignments, mandatory for all grades, and an individual examination, mandatory for the highest grade only. The grading criteria are
The individual examination is conducted by the examiner with one assistant under at least 30 minutes and at most 60 minutes per student. Contact
Erik Aurell, tel: 790 69 84, email: eaurell@kth.se
