Technical University of Denmark

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1 1 of 13 Technical University of Denmark Written exam, 15 December 2007 Course name: Introduction to Systems Biology Course no Aids allowed: Open Book Exam Provide your answers and calculations on separate paper. Remember to provide the required information on each of these pages, i.e. name, student number and signature on the final page. The contribution of each question to the overall score is marked for each question (out of 100 points). Short questions (34 points): 1) In the network below, which node has the highest in-degree? How many feed forward loops are in the network? (2 points) ANSWER: C and 1 FFL 2) If you know that the node degree distribution of a given network follows a power law, what additional relationship is used to determine whether it is hierarchical or not? (2 points) ANSWER: Clustering coefficient versus degree relationship. If the clustering coefficient of a node is a function of degree, inversely related, then the network is hierarchical to some extent. 3) Based on data from a single mass-spec pull down experiment, a network is drawn using the spoke representation (with no self-interacting proteins). In this network, a total of 7 interactions are drawn. How many interactions should be drawn in a matrix representation (with no self-interacting proteins)? (2 points)

2 2 of 13 ANSWER: 7 interactions imply 7 proteins were pulled-down with the tagged protein. All pair-wise interactions between the 7 neighbours is calculated by choose(7, 2) = (49 7)/2 = 21. If we then add in the 7 initial interactions gives 28. 4) At what repression coefficient is the response time of a Type 1 incoherent feed forward network with an AND gate (as defined by Uri Alon in An Introduction to Systems Biology page 47, Fig 4.3) equivalent to that of simple gene induction by a single factor (i.e. X -> Y)? (2 points) ANSWER: Repression coefficient = 0 5) Name the three vocabularies used in the Gene Ontology resource. (2 points) ANSWER: Molecular Function, Biological Process, Cellular Component 6) Which vocabulary from question #6 will contain protein kinase activity? (2 points) ANSWER: Molecular Function 7) If we define a dynamic system by the change in mrna and protein levels over time, if the environment is kept constant, what are the possible characterizations of the state space trajectories (ignoring cell division)? (The state space is defined by the levels of the mrnas and proteins) (2 points) ANSWER: Fixed point or limit cycle. Oscillations or periodic expression should also give partial credit. 8) What network statistics should you know to assess how unlikely it is that two proteins are connected by a common intermediate protein (i.e. in a social network, how surprising is it that your friend has a particular friend)? (2 points) ANSWER: The all pair s shortest-path distribution would help here. 9) It is impossible to infer the regulatory role of the edges of the following network with only the perturbation of A activity (e.g. A levels up or down or the A gene deleted) and the resulting response of C. What additional information would you need to determine the regulatory roles of edges A-B and B-C? (2 points) ANSWER: The response of C when B is perturbed or the activity of B (response of B) when A is perturbed.

3 3 of 13 10) Describe how you can use Flux Balance Analysis (FBA) for identifying drug targets for combating microbial infections. Briefly comment on major limitations and pitfalls of the suggested approach. (2 points) ANSWER: FBA can be used to predict the effect of metabolic gene deletions/repressions on the growth of pathogenic micro-organisms. Thus, the genetic targets that are predicted to, either decrease the growth rate or to completely stop the growth will be good candidates as drug targets against the micro-organism under study. Few of the major limitations/pitfalls of this approach are; i) predictive power of FBA depends on the objective function used and the complexity of the network under study; ii) identified drug targets should be such that they do not interfere with the human metabolic network. Since metabolic networks are highly conserved, (ii) is a major challenge. 11) Describe the principles behind the chip-chip method? (2 points) ANSWER: Chromatin immunoprecipitation of a transcription factor (TF) that is tagged with an epitope and/or immunoprecipitate with an antibody specific to your TF or epitope after cells have been treated with formaldehyde to cross-link proteins to DNA. Genomic DNA is then fragmented, labelled cdna or crna is made and this is hybridized to a microarray. This profile is compared to sample prepared without immunoprecipitation (whole cell extract). 12) Which types of protein interactions can be interpreted as directional? (2 points) ANSWER: Protein-DNA interactions (regulatory interaction), protein-kinase kinase-target interactions, drug-protein interactions, 13) Based on the Christian von Mering paper [Nature (417), 2002] that compared different protein-protein interaction measurement techniques, what performance statistic is expected to improve the most when integrating data from different techniques? (2 points) ANSWER: Specificity should improve the most. Area under ROC would also be okay. 14) Describe how the GRAM approach of Bar-Joseph et al. [Nature Biotecnology (21) 2003] defines regulatory modules and (briefly) how they are found. (2 points) ANSWER: Regulatory modules are defined as the set of transcription factors and the associated set of (coexpressed) regulated target genes. Coexpressed genes are identified for a set of genes found to be bound by a common set of TFs. This seed set is then used to find additional genes and regulatory interactions with a relaxed criterion for regulatory interactions.

4 4 of 13 15) The feedback repression motif discussed in Uri Alon s book is interpreted as being important for what biological reason? (2 points) ANSWER: Optimal concentrations of the target can be reached more quickly. The production of the target can be fast without fear of over-producing due to the feedback inhibition. 16) Based on yeast two-hybrid experiments, the following interactions among 6 proteins are found: {A-B, A-D, B-C, B-D, C-E, C-F, D-E}. What is the reliability score of the least reliable (i.e. lowest scoring) interaction? (4 points) ANSWER: S bin = - log 10 ((N A + 1) * (N B + 1)) A-B: - log 2 A-D: - log 2 B-C: - log 9 B-D: - log 4 C-E: - log 6 C-F: - log 3 D-E: - log 6 Section II: Multi-part questions (38 points) 17) Dr. Eager is very keen on studying gene deletion phenotypes in a microbe. He decided to use FBA and MOMA for simulating the effects of single gene deletions. When he plotted the results of FBA versus MOMA for the mutant growth rates, it looked like the one in the figure below. Would you advice him to trust his results? Justify your answer. (4 points)

5 5 of 13 ns1a,b,c ANSWER: The results do not seem trustworthy. The reason is that a set of three gene deletion predictions (ns1a, B, C) do not confer to the stoichiometric limitations. This is evident from the fact that the MOMA predicted growth rates for these cases is higher than FBA-predicted, which is not feasible, FBA always predicts the maximum possible growth rate. 18) A systems biologist decides to design a synthetic regulatory circuit and they want to construct a system using only transcriptional inducers. a. What would be the challenges of building an inducilator circuit that exhibits periodic behavior with 3 transcription factors that normally have long half-lives (i.e. protein is stable)? (2 points) b. In what way could you engineer each component to over come this? (you may use more factors than the 3 required inducers) (4 points) ANSWERS: a) The long half life of the inducers means that the circuit will tend to not oscillate, i.e. it will converge quickly to a fixed point. b) As with the repressilator, the decay of the proteins (transcription factors) is important and must be fast enough to get oscillations (limit cycle regime). This could be addressed if each component was a feed-forward network that implemented a delay.

6 6 of 13 where co-factors 3,4,5 have short half-lives. 19) Protein production from mrna can be approximated by a simple model under a certain set of simplifying assumptions as shown in the following figure. S Stimulation, linear rate constant Ks P Degradation, linear rate constant Kd a. Assume that the stimulation of protein synthesis by mrna (S) is the rate limiting factor for the production of the protein (P). Write the differential equation that describes the concentration of P as a function of the concentration of S and derive the relation between P and S at steady state. (4 points) b. Would you recommend modeling this system by using a Boolean model? If not, illustrate a signal-response curve that may be suitable for making a binary behaviour assumption. (2 points) ANSWERS: a) dp = K s. S! K d. P dt At steady state the time derivative can be set equal to zero. Thus we get: K s P = S K d b) Since the signal-response relationship for this case is linear, Boolean approximation is not advisable. An example of signal-response curve where the Boolean approximation will be useful is given below.

7 7 of 13 20) All of these network modules (components) provide evidence of protein complexes. A B C a. Which of the 3 has the most network evidence to support it being a protein complex? (2 points) b. Which component was most likely derived from TAP based mass-spec data? (2 points) c. What component has the lowest average clustering coefficient? (2 points) ANSWERS: a) A, b) C, c) B, calculations A: (1+1+1)/3=1, B: (0+0+0)/3=0, C: (1+1+1/3+1+1)/5= ) A recent paper claims that a novel protein complex composed of eight proteins plays a role in colon cancer development (see the network below). However, the identification of the protein complex composition is controversial.

8 8 of 13 a. Calculate the clustering coefficient of each protein in the network. (4 points) b. Use the MCODE algorithm to identify which proteins should be included in the complex under the assumption that the vertex weight of a given protein is equal to its clustering coefficient, the inclusion cut-off (VWP) is 0.4 and that all proteins in the resulting protein complex must have a degree of at least three. (4 points) ANSWERS: a) S: 4/12 = 1/3 T: 0/2 = 0 U: 0 V: 4/6 W: 1 X: 8/12 = 2/3 Y: 8/12=2/3 Z: 12/20 b) W, Y, Z, X, (V goes out because its degree is only 2) 22) The activity of the entire protein complex is controlled by the activity of protein Z, which is regulated through a Type 1 coherent feed forward loop (as defined by Uri Alon in An introduction to Systems Biology page 47, Fig 4.3). Z is dependent on transcription factors A and B through an AND gate. Transcription factor A regulates the transcription of B with an activation threshold K AB =0 and Z with an activation threshold K AZ =0. Both transcription factors are always in their active state. Transcription factor B has a production rate β B = 1, a degradation rate α B = 0.8. Transcription of Z begins when B reaches 80% of its steady state concentration. a. When A is transcribed, what is the steady state concentration of B? (4 points) b. By genetic manipulation, the degradation rate of B has been reduced to 0.6. All other parameters are unaffected by the genetic manipulation. At time zero, transcription factor B becomes transcribed. At what time does transcription of Z begin? (4 points) ANSWERS: a) B ST =β/α = 1/0.8 = 1.25 b) T= 1/α Y ln[1/(1-k BZ /B ST )] T=1/α Y ln[1/(1-0.8)]=ln5/0.6 = 2.68 Long questions (28 points) 23) The following figure shows a simplified metabolic network of an antibiotic-producing micro-organism. In this model there is only one substrate, S, which can either be incorporated into biomass X or secreted out as antibiotic P. For ease of the model

9 9 of 13 formulation, X is divided into two conceptual metabolites, intra-cellular, Xin, and extra-cellular Xout. Also note that the stoichiometry for the reaction v9 is: B + E 2 Xin. For all calculations, unless otherwise stated differently and if necessary, you can assume that the substrate uptake rate is fixed at 1 millimole (g-biomass) -1 (hr) -1. a. What will be the FBA predicted optimal growth rate for this model? Will the FBA solution be unique? Justify your answer. (4 points) b. Assuming a steady-state for all intra-cellular metabolites, prepare a plot showing the relation between the biomass formation rate and productivity (in this case, product formation rate * biomass formation rate ). What is the specific biomass production rate (i.e. growth rate) at which the maximum productivity will be achieved? (4 points) c. List two sets of reactions that are synthetically lethal; and two sets of reactions that are directly flux coupled. (2 points) ANSWERS: a) FBA predicted optimal growth rate for this model will be 1 hr -1. This will be the case when all of the substrate S will go to biomass and none to product P. The FBA solution in this case will not be unique since any distribution of flux between v2 and v3 will result in the same growth rate as long as (v2 + v3) is constant. Here, (v2+v3) needs to be non-zero for obtaining non-zero growth. b) The stoichiometry of the network dictates that: v10 + v8 = v1 = 1. Here, v10 = biomass formation rate and v8 = product formation rate. Using this information, and noting that the lower and upper limits for v10 are 0 and 1, we can prepare the following plot.

10 10 of 13 The optimal point for this curve lies at v10 = 0.5. The optimal point can either be calculated numerically, or estimated from the plot or be deduced from the fact that for any variable x that lies between 0 and 1, the maximum of x*(1-x) occurs when x = 1-x. c) Synthetic lethal sets: i) {v2,v3} ii) {v5, v6} iii) {v2, v6} iii) {v3, v5} Directly flux coupled sets: i) {v2, v5} ii) {v4, v7} iii) {v3, v6} iv) {v9, v10} 24) Apart from the stoichiometric constraints, there are many dynamic regulatory features of the systems described in question #23 that are important for survival of the organism. The following figure shows results from a growth experiment of this organism in a liquid media. Biomass, Substrate Product X S P

11 11 of 13 a. What regulatory rule or rules for the antibiotic production can be inferred from this data? Comment on biological implications of your answer. Based on this, what information can we postulate about the organism s evolutionary history in relation to the antibiotic production? (4 points) b. In an adaptive evolution experiment, this micro-organism was subjected to several serial dilutions so that the substrate concentration was always kept >80 g/l. What is your expectation regarding the evolved organism s capacity for making antibiotics? What will be the result if the concentration is kept at chosen to be 45 g/l instead? Justify your answer. (2 points) c. Expression of the enzyme catalyzing reaction v8 (let s say E8) obviously has a cost in terms of reduced growth rate. Assuming that the flux through v8 is directly proportional to the concentration of E8, derive expression for this cost function (assume steady state operation again), where the cost is given as the fractional reduction in the growth rate compared with the maximum growth rate. (4 points) ANSWERS: a) One can infer that the antibiotic production is under the regulation of substrate inhibition-type regulatory circuit. It can also be postulated that the antibiotic production is initiated only when a critical level of total biomass concentration is reached. The first scenario (substrate inhibition) may imply that the antibiotic production is started by the micro-organism to combat the competing microbes in the environment, the competition being sensed as the depletion of the substrate S. In the second case (critical biomass) the reason may be the inter-cellular communication through certain signal metabolites that triggers the production of P. Since the production of antibiotic appears to be regulated (for whatever reasons), it may be postulated that the cost of maintaining and running the regulatory mechanism, plus that of antibiotic production, must be lower than the benefit gained by the timely induction of antibiotic production. Furthermore, it can also be postulated that the cost of producing antibiotic all the time is not affordable in light of the benefit gained. Overall, these postulates can be combined together and one may hypothesize that during the evolution, the organism has benefited from the antibiotic production only for a fraction of the time. This fraction is not large enough to justify continuous production, neither small enough to justify loosing the production capability over the evolutionary time-scale. b) (i) S>80 g/l: In this case it can be hypothesized that the organism s capability of antibiotic production may be lost over time. If this happens, it will be evidence for the substrate inhibition scenario from the first sub-question. (ii) S ~ 45 g/l: In this case it can be hypothesized that the organism s capability of regulating the antibiotic production may be lost over time and thus the production will be ON all the time (independent of S) in the evolved strain. Again, it will be evidence for the substrate inhibition scenario from the first sub-question.

12 12 of 13 NOTE: It is possible to provide alternate but acceptable answers to (a) & (b). In such cases, examiner should judge the points to be given based on the logic of the arguments presented. max µ! µ c) Cost = max µ Where µ denotes growth rate. At steady state, the stoichiometry of the network dictates that: v10 + v8 = v1 = 1. Here v10 = µ. Hence we have µ = 1-v8. Further more µ max = 1. Cost = v8 = k. E8 Using the given information that the flux is directly proportional to the enzyme concentration. 25) To understand the transcriptional regulation in the metabolism of the microbe in question #23, DNA microarray analysis were performed between two different conditions. The results from the analysis are summarized in the following table, in terms of the p-values (and Z-scores) calculated by using a statistical significance test. Using this data, identify the top-scoring reporter metabolite (i.e. metabolite around which the most significant collective transcriptional changes are observed). The background distribution of Z-scores at the whole genome level is given by the following equations, background µ = 0.5 n background 1! = n n where n is number of neighbours. (8 points) Reaction Gene P-Value Z-Score v1 G v2 G v3 G v4 G v5 G v6 G v7 G v8 G v9 G v10 G ANSWER: The top-scoring reporter metabolite is I with score of The calculations for all of the metabolites are shown in the following table.

13 13 of 13 Metabolite Number of neighbors Neighbors Average Z- Score (AZ) Background mean (Bm) Background standard deviation (Bstd) Corrected Z-score = (AZ-Bm)/Bstd S 1 v I 4 v1,v2,v3,v A 2 v2,v B 3 v5,v6,v C 2 v3,v D 2 v4,v E 3 v7,v8,v P 1 v XIN 2 v9,v XOUT 1 v