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Center for Models of Life
Niels Bohr Institute
University of Copenhagen
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Course: Networks in Biological systems (2016)


Content will be chapter 1 - 8, +chapter 10 and 12 in the book Models of Life: Dynamics and Regulation in Biological Systems, by Kim Sneppen Updated: 21'th November 2016.

Notice that exersize sessions is an important part of the course. Skills in describing algorithms for dealing with couse-effect dynamics in life will be part of the oral examin. The presentation there may contain results obtained by own computer exersizes. Notice corrections to book in end of this page.


Kim Sneppen, office eb1, phone 353 25352
Monday, Lecture: 13:15-15:00 (Aud B, NBI).
Monday, exersize: 15:00-17:00 (Aud B, NBI).
Wednesday, Lecture: 13:15-15:00 (Aud B, NBI).
Wedensday, exersize: 15:00-17:00 (Aud B, NBI).

  • *Mon 21.11.2016: Chapter 1 + Chapter 2.
    Questions Q1.1, Q1.2, Q2.3.1, Q2.3.2, Q2.3.3, Q2.3.4 and Q2.3.5

  • *Wed 23.11.2016: Recapitulating chapter 2 end (in particular eq. 2.3, e.q. 2.9 and eq. 2.12) and chapter 3 (chemical binding, cooperativity, dynamics of simple regulatory links and small RNA regulation),
    Questions Q2.4.1, Q2.4.3, Q.3.2.1, Q3.2.2 and Q3.3.1

  • *Mon 28.11.2016: Beginning of chapter 4,
    Questions Q3.3.2, Q3.3.3 and Q3.3.4, and subsequently Q4.1.1, Q4.1.2 and Q4.1.3, Q4.3.2

  • *Wed 30.11.2016: Chapter 4: Partition function, non-specific binding, DNA looping
    Questions: Q4.3.2, Q4.3.3, Q4.3.4, Q4.4.1

  • *Mon 5.12.2016: Chapter 4: non-specific binding, DNA looping, Chapter 5.1, 5.2 and 5.3
    Questions Q4.4.1, Q4.4.2, Q4.5.2, Q4.5.5, Q5.1.1

  • *Wed 7.12.2016: Chapter 5. start Chapter 6 (Gillespie algorithm)
    Questions Q5.1.2, Q.5.2.1, Q.5.2.3, Q5.3.1, Q5.3.2, Q 5.3.3, Q5.3.4, Q5.4.2, q5.4.3

  • Mon. 12.12.2016: chapter 6.
    Questions Q6.1.1, Q6.1.2, Q6.1.3, Q6.1.4, Q6.2.1, Q6.2.2, Q6.2.3, Q6.2.4

  • *Wed 14.12.2016: Chapter 6 end, Chapter 7 beginning
    Questions Q7.2.1, Q7.2.2, Q7.2.3 (Q7.4.1, Q7.4.2 and Q7.4.3)

  • *Mon 19.12.2016: Chapter 7
    Questions session cancelled. The Question for this week is to re-build the model for olfactoric development, here differentiating between to olfactoric genes.

  • *Wed 21.12.2016: Chapter 7 end, Chapter 8 beginning
    Question section cancelled. The Question for this week is to re-build the model for olfactoric development, here differentiating between to olfactoric genes.

  • *Mon 2.1.2017: Chapter 8: 159-176.
    Questions: Q8.2.1, Q8.2.2, Q8.2.3, Q8.2.6, Q8.3.1, Q8.4.1, Q8.4.2, Q8.4.4

  • *Wed 4.1.2017: Chapter 8 end, Chapter 10 beginning
    Questions Q8.5.1, Q8.5.2, Q8.5.3, Q8.5.6

  • *Mon 9.1.2017: Chapter 10 rest
    Questions Q10.1.1, Q10.1.3, Q10.1.4, Q10.1.5, Q10.2.1, Q10.2.2, Q10.3.1

  • *Wed 11.1.2017: Chapter 10 repetition, Chapter 12. Questions: Q10.3.1, Q10.3.2, Q10.4.1, Q12.1.1, Q12.1.2

  • *Mon 16.1.2017: Chapter 12, Questions: Q12.2.1, Q12.2.2, Q12.2.5, Q12.3.3

  • *Wed 18.1.2017, 13:15 in aud. B: Questions about pensum, (Spørgetime). (Oral examnin, 10 minutes presentation + 15 minutes examination in all of pensum.

  • Pensum

    Examin in Aud B (monday 23) respectively Aud B (wedensday 25) at NBI Blegdamsvej.
    Chapters 1,2,3,4,5,6,7,8,10, and 12 in "Models of Life", including all exersizes mentioned above.

    Exam questions (Examin consist of 10 minutes presentation of one randomly chosen topic below + 15 minutes questions across all pensum):
    1) Transcription-translation, and content of E.coli. Ribosome numbers in E.coli with growth conditons, Monod Growth law for bacteria. (chapter 2).
    2) Dynamics of regulatory links, Transcription and translation regulation, protein-protein binding (chapter 3 + chapter 10.1).
    3) The partition function formalism for calculating promoter strength (chapter 4).
    4) Diffusion inside cells, timescales in protein-DNA binding, timescales for gene regulation (chapter 5).
    5) Noise and dynamics of Transcription factors and RNA polymerase activity. Describe basic transcription initiation process, and how it is influenced by transcription factors. Discuss interference between two promoters, with emphasis on what properties that makes promoters most sensitive to interference from another promoter (chapter 5).
    6) Gillespie algorithm and modeling stability of a genetic switch. (Describe how to select next reaction, an how to update time. Use it to describe the dynamics of a genetic switch. What constitute the noise. Decribe how noise could be made larger inn a real system, and describe how stability change with noise level), (Chapter 6).
    7) Nucleosome mediated epigenetics. Discuss basic 3 state model for gene silencing with methylated nucleosomes. Pinpoint constraints due to cell division. What is needed to make epigenetics. Discus how the model may be simplified to a two state cooperative model, and prove that cooperativity is needed. Discuss role of space in the recruitment process (Chapter 7).
    8) Feedback, shock responses and oscillations. Describe basic motifs for gene regulation, and pinpoint what sets timescale for typical response. Mention difference in architecture between positive and negative feedback circuits. (chapter 3.2 and chapter 8.1-8.4).
    9) Excitable media and minimal models of inflamation responce. Describe basic idea, and its implementation. Discuss other ways to couple cells in space (turing pattern, growth instabbilities) (chapter 8.5)
    10) Signal propagation on networks: signaling cascades and adaptation. Describe a phosphorylation event, and the basic sequation. Derrive the simples push-pull reaction. Discuss the implementation of an adaptation network. (chapter 10.2-10.3)
    11) Metabolic fluxes and some regulatory motifs in that regards (chapter 8.4 and chapter 10.4).
    12) Phage biology in ecological perspetive. Predator prey models for one bacteria and one phage, respective two bacteria and one phage. Cexistence of phage and bacteria. Lysogeny as bet hedging (chapter 12).

    Other topics to be included under the 15 minutes teacher directed examination time: Timescale for gene regulation, on-and off rates for protein-DNA binding. Explain why local rules in 1-d models cannot give bistability. Discuss differentiation in Olfactoric neurons. DNA looping in lambda, and estimate of looping frequency. CII's role in phage lambda. Derivation of Monods growth equation. The promoter, rate limiting step and its regulation. Ultrasensitivity of gene regulation by using protein sequestration. Compare network architecture of Turing and excitable media. Bistability and epigenetics. Economy of operones, noise minimization. Metabolic flux balance. Plaque formation and phage spreading. Bacterial defence systems against phages. Models for bacterial-phage ecology. The workings of restriction-modification systems and relation between their failure rate and activity of their enzymes. How a slow growing bacteria can eliminate a fast growing one by use of a phage.

    Exam will be in Aud B, Monday 23, Wedensday 25.
    Tirsdag the 24 Januarry (Auditorium B, NBI):
    14.00: Karen
    14.30: Sylvester
    Wedensday the 25 Januarry (Auditorium B, NBI):
    13.30: Buster
    14.00: Anna-Freya
    14.30: Frederik
    15.00: Heidi
    15.30: Jonas Dalgaard
    If other, please contact Kim Sneppen.

    Book corrections;

    Large scale correction. Each questions section have a subsection number, which is confucing. Please remove. (nucleosome is good, chapter 8 is good) Give example on code in a few questions, have 30 min blackboard in beginning of each exersize. Maybe some help to matlab.

    question 2.4.1 mu-->nu
    Michaelis-Menten growth curves--> Michaelis-Menten like behaviour
    question 2.4.3: Eqs. (2.5),(2.6),(2.7) --> Eqs. (2.6),(2.7)
    Page 39 unpleasent, describe in words in detail, in particular eq. 3.13.
    3.14. remove factor 2 from denominator (RT is in fact equal RM).
    Remove small tau in fig 3.5 panel b.
    Question 3.2.1: ....evolution. First investigate the case tau=1. Hint: For simple repression this amounts to C(t+dt)=C(t)+(1/(R+1)-C(t))*dt, with dt=0.01. Start at time t=0 by setting R=0.1 and C=0 and iterate until time t=10.
    page 62 -3 kcal mol bp-1 --> -3kcal/mol/bp
    page 62: Question 4.3.3: Write an equation for the distribution of the number of proteins n that is bound the to DNA.
    page 62: Question 4.4.4-->4.3.4 Consider an operator that is regulated by a transcriptional repressor, and assume that the repressor showul leave the operator open when there is 10 copies in the cell, and repressed when there is 1000 copies in the cell. What would be the binding energy betwen the repressor and the operator.
    Page 63: Lack an index for G in second line of figure 4.12.
    page 64: Fig. 4.13 error: Black RNAP on PRM should be yellow, and with number -11.5 inside. On RNAP on PR then change DG=-10.5 to -12.5
    page 65: After 3 lines just after eq 4.18 insert: In general, the activity of a promoter depend on the occupation state of the relevant operators, and the rate of mRNA production will accordingly be given by the weighted sum Activity = (Activity if state 1)*P(state 1) + (Activity in state 2)*P(state 2) +... where each probability is given by equations similar to eq. 4.17.
    page 67: question 4.4.2. a total concentration of 100 CI with appropriate number of dimesr would have done.
    Page 69: misses an exp(-Gs) in end of equation....
    Page 72, eq,4.30 and the one just after: Put in kB together with T in exponentials.
    Page 78: [A][B][B].-->[A][B][C].
    Chapter 5 heed to be explained better, more coherent, what is point.
    Page 81, bottom equation, misses a d in front of rho. Should be soft d by the way.
    page 84, give correct reference on in-vitro on rate for RNAP.
    page 84, give one more equation in footnote, that rho(r)=N/V+J/(4pi*D*epsilon) with rho(epsilon)=0 and J measured as current away from absorbing sphere of radius epsilon.
    page 93, question 5.3.1 ..that RNAP needs time Omega l/v to .. ------> ..that a bound RNAP needs time l/v to .. Hint: Solve eq. 5.25 while taking into account that RNAP cannot enter promoter during time l/v after previous RNAP have elongated.
    page 99, 5.4.2: Consider a simplified production of proteins, ------> Simulate the production and decay of proteins, where mRNA is assumed to be short lived and each mRNA on average gives one protein. mRNA production rate could be assumed to be one per 10 minutes, whereas proteins decay time is 30 minutes. First assume that there is exactly one protein per mRNA by simply converting the mRNA to one protein at nstance of production. Second asssume that the mRNA lifetime is exponentially distributed, and simulate this by converting each produed mRNA to a number of protein drawn for an exponential distribution with average equal to one. CORRECT ANSWER NOTES.
    page 99, 5.4.3 Exponentially distributed ``burst" of proteins. ------> is converted into a burst that contain an exponentially distributed number of proteins.
    page 102, before equation 5.47 replace: on rates on the order of ------> on rates that scale as
    Chapter 6, to much programming languege in Gillespie algorthm. Last half of chapter maybe eliminated.
    page 107, after eq. 6.11: Here 1/r will be the average time until next event. r will depend on current state of the system, and should typically be re-calculated after each event.
    Equation 5.47 replace = with similarity sign (~)
    Page 130: Question 7.2.3 at... ------> question 7.2.4 at...
    Page 131: Middle figure in panel 7.8 is in fact show bimodality, which is not due to an the mean drift, but due to increased noise when A and M are similar.(Jafarpour et al. PRL 115 (2015) 158101.
    Page 134: Question 7.2.1 ...are local, whereas recruitments A--> U and M-->U are global. This model needs two parameters, the parameter alpha fo how often one chose recruitment, and a parameter beta=0.5 for the probability that a given recruitment attempt should be global. When attempting a global attempt, select one recruiting nuclesome and another that it acts on anywhere in the system. The move can only be performed if the two chosen nuleosomes are of type M and A, or A and M. Similarly a local move involves selection of two neighbor nucleosomes where the nucleosome to be changed have to start in U state. Use an L=60....
    Page 144, Question 7.4.1 remove equation label 7.12, and write before equation: ....reduces the rate ``R" of recruitment from S to A: Rate(S-->A) = R/(1+r*P) where P is the total activity of all olfactoric genes and ``r" is a constant.
    page 150: reference list [25,116,142,175,238,360-378].
    page 153: fig 8.4 panel B a half self repression link should be fixed. panel C, the complex between red and blue should be reintroduced.
    Page 160: Make a question 8.3.2 that simulate the Frank model for chirality symmetry breaking in early life (f.C.Frank, Biochim. Biophys. Acta 11, 459 (1953)). in a form suggested by Jafapour et al, PRL 115 (2015) 158101. Here recruiting life forms M and A recruits from U, but when M meets A they are both transformed to 2 U.
    page 161, fig 8.10 specify that it is log on the axes.
    page 166, question 8.4.1 specify hat main dynamics is between e**3 and e**9.
    page 172: Add references To Dagmar Iber, for limb development.
    page 173, fig caption 8.16: ...separated from 2.6mm from this... ------> ...separated by 2.6mm from this...
    page 175: corection to last equation in 8.5.1, replace T(x)-->T(x,t) everywhere and set: T(x,t+dt)=T(x,t)+DeltaT(x)*dt and R(x,t+dt)=R(x,t)+DeltaR(x)*dt
    New section just after 8.5.3 before 8.5.4 where I brieffly (hb, Kr, Kn, G) mention minimal modle for GAP genes with bicoid as input, i.e. reading a gradient, emphasizing that one could get a lot from a passive morphogen. Show picture with whitout mutual repression (of everybody with everybody), reference to 1) Bejsovec and Weischaus (1993), Development 119, 2) Reinitz and to 3) Papatchenko
    page 210: small kij should be changed to big Kij in eq. 10.1, 10.2 and 10.2
    page 212: To simplify the analysis one often assumes that external enzyme concentrations I and F are always much smaller than intrinsic enzyme concentrations ([F]<<[X]). -------> To simplify the analysis one often assumes that enzyme concentration F are always much smaller than reactant concentration ([F]<<[X]).
    page 212: rephrase to normal Michaelis nomenclature: KM and kcat.
    page 214: Eq. 10.13, in lower reaction then the arrow on subscript R should point the other way
    10.2.1 there is an epsilon like sign in nominator in end of first line. Should be E.
    end this section with Ferrell paper on positive feeback switch related to cell cycle arrest , i.e. that the phosphorylated enzyme favor production of itself and inhibit drain by producing its non phosphoryated variant (Nature 2003)

    Simple Adaptation motifs
    Extra figure to chapter 10 adaptation, summarizing feed forward relative to feed back:
    Feed forward send two signals to C that cancels each other after some time.
    Feed back uses the buffer to restore previous level of C.

    10.3 adaptation, start with simplest incoherent forward one da=(x-a)/2 db=x-a-b and then mention complications in exersize with full equations da=(x/(x+1000)-c)/2, db=1000*x/(x+1000)-1000*[ab]-b, where binding cosnstnt between a and b is 1/1000. and mention possibility to put in a sensor dc=(1000*b/(b+1000)-c)/30 c dd=1000*b(1-d)/((1-d)a+eff+b)-1000*c*d/(1000*c+1+d) the continue with the buffer equation.
    page 216: afetr eq. 10.16 it should be F much less than B+KFB (maybe work more on making this simpler)
    page 217: simplify eq. 10.15 and 10.16 by removing all small kCB,kFB,kLC and kBC, remove F from KFB term in the equation 10.15 but insert it in the figure. remove L from KLC term in the equation 10.16 but insert it in the figure. in sentence before write ....a negative feedback system of the form (from [545]) remove small kBC and kCB later in text. (Kep the big ones)
    replace sentence just after eq. 10.16 with: which is simplified by assuming small values of L and F.
    Page 219: host consumption ------> host digestive fraction
    page 220: Fig 10.11 should be moved to just before 10.3.1, Fig. 10.12 just after (if needed make fig. 10.12 smaller).
    remove small ? below bottom of Fig. 12.2
    page 252: question 12.1.2 replace: ..within 1 minute ------> all times that is later than 1 minute after the infection.
    Page 259: rewrite equation 12.13 in terms of eta', dont use r at all.
    page 281, Figure caption 13.3, Eliminate this last sentence: Calculation was done at mutation rate mu=0.005.
    Question answer: 2.4.1: lambda to Big lambda, and go one more step.
    2.4.3: there is a repeated lambda/nu instead of Q/T.
    3.2.1: Set the decay time tau=1.
    question 7.4.2, R(S-->A) equation have a (1-a) factor to much in an intermediate step.