Quantitative Systems Biology
This is the course web page for the Academic Year 2012-2013.
The following lecture schedule can be changed if necessary
(within reasonable limits).
The lectures will be held in room RB35. The entrance door to the building from the
side of Roslagstullsbacken will be open from the hour sharp, before
|First lecture||Monday|| April 8||10.15-12.00|
|Second lecture||Wednesday|| April 10||10.15-12.00 ==> Moved to 13.15-15.00 |
|Third lecture||Friday|| April 12||13.15-15.00|
|Fourth lecture||Monday|| April 15||10.15-12.00|
|Fifth lecture||Wednesday|| April 17||13.15-15.00|
|Sixth lecture||Friday|| April 19||10.15-12.00==> Moved to |April 22 - 10.15-12.00 April 25th - 13.15-15.00
|Seventh lecture||Monday|| April 29||10.15-12.00|
|Eighth lecture||Thursday|| May 2||10.15-12.00|
|Nineth lecture||Friday|| May 3||10.15-12.00 |
|Tenth lecture||Monday|| May 6||10.15-12.00==> Moved to April 24 - 13.15-15.00 ||
|Eleventh lecture||Wednesday|| May 8||10.15-12.00|
|Twelveth lecture ||Friday|| May 10||13.15-15.00 ==> Moved to May 13 - 13.15-15.00 |
Two tutorials will be organized in the course.
First tutorial will be Tuesday April 16 9.00-12.00.
Second tutorial will be Monday April 22 14.00-17.00.
For more information on the tutorials, follow the link in the upper left corner.
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
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
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
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
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
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.
- On schemes of combinatorial transcription logic.
Buchler NE, Gerland U, Hwa T. Proc Natl Acad Sci U S A. 2003 100:5136-41.
- Transcriptional regulation by the numbers: models.
Bintu L, Buchler NE, Garcia HG, Gerland U, Hwa T, Kondev J, Phillips R.
Curr Opin Genet Dev. 2005 15:116-24.
Transcriptional regulation by the numbers: applications.
Bintu L, Buchler NE, Garcia HG, Gerland U, Hwa T, Kondev J, Kuhlman T, Phillips R.
Curr Opin Genet Dev. 2005 15:125-35.
The E coli operons
In the course (for instance in first tutorial and in Homework assignment 1) we use the
base on transcriptional regulation in E coli
, but this is not the
only source available: other examples are
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)
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.
Stochastic Gene Expression in a Single Cell
Elowitz MB, Levine AJ, Siggia ED, Swain PS.
Science. 2002 297:1183-6.
Transcriptome-wide noise controls lineage choice in mammalian progenitor cells.
Chang HH, Hemberg M, Barahona M, Ingber DE, Huang S.
Nature 2008 453:544-7.
Dynamic Proteomics of Individual Cancer Cells in Response to a Drug.
A. A. Cohen,1 N. Geva-Zatorsky, E. Eden, M. Frenkel-Morgenstern, I. Issaeva, A. Sigal, R. Milo, C. Cohen-Saidon, Y. Liron, Z. Kam, L. Cohen, T. Danon, N. Perzov, U. Alon
Science 322:1511-1516 (2008)
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
Robustness in simple biochemical networks
Barkai N, Leibler S
Nature 1997 387:913-917.
Robustness in bacterial chemotaxis
Alon U., Surett M.G, Barkai N., Leibler S.
Nature 397:168-171 (1999)
Response regulator output in bacterial chemotaxis
Alon U., Camarena L, Surette M.G., Aguera y Arcas B., Liu Y., Leibler S.,
The EMBO Journal 17:4238-4248 (1998)
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
The detailed mechanisms behind the fidelity of bacterial
are still under active investigation,
see the recent review (Johansson et al
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)
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
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.
Evolution of competitive fitness in experimental populations of E. coli: what makes one genotype a better competitor than another?
Lenski RE, Mongold JA, Sniegowski PD, Travisano M, Vasi F, Gerrish PJ, Schmidt TM.
Antonie Van Leeuwenhoek. (1998) 73:35-47.
Negative epistasis between beneficial mutations in an evolving bacterial population
A. I. Khan, D. M. Dinh, D. Schneider, R. E. Lenski, and T. F. Cooper.
Science (2011) 332:1193-1196.
Second-order selection for evolvability in a large Escherichia coli population .
R. J. Woods, J. E. Barrick, T. F. Cooper, U. Shrestha, M. R. Kauth, and R. E. Lenski.
Science (2011) 331:1433-1436.
Genome evolution and adaptation in a long-term experiment with Escherichia coli.
J. E. Barrick, D. S. Yu, S. H. Yoon, H. Jeong, T. K. Oh, D. Schneider, R. E. Lenski, and J. F. Kim.
Nature. (2009) 461:1243-1247.
Optimality and evolutionary tuning of the expression level of a protein.
Dekel E, Alon U.
Nature. (2005) 436:588-92.
Cost-benefit theory and optimal design of gene regulation functions.
Kalisky T, Dekel E, Alon U.
Phys Biol. (2007) 4:229-45.
Demand theory of gene regulation. I. Quantitative development of the theory.
Genetics. (1998) 149:1665-76.
Demand theory of gene regulation. II. Quantitative application to the lactose and maltose operons of Escherichia coli.
Genetics. (1998) 149:1677-91.
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
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
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
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.
Examination is by homework assignments, mandatory for all
grades, and an
individual examination, mandatory for the highest grade only.
The grading criteria
- 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: email@example.com
Nicolas Innocenti, tel: 790 62 71 , e-mail: firstname.lastname@example.org