CS2220 Introduction to Computational Biology Assignment #3 To be submitted electronically before 2pm on Thurs 25 March 2010 This assignment contributes 10% to the final course grade The purposes of this assignment are (a) to reinforce lessons on sequence comparison, and (b) to give practice at identifying problems that can be posed in terms of optimization. Please provide only your answers and not the instructions or situational texts in your submission. PROBLEM ONE: Dynamic Programming and Edit Distance between Strings. [Associated Reading: The Practical Bioinformatician, chapter 10, and Algorithms on Strings, Trees and Sequenc (...), chapter 11] Since the trace-back paths in a dynamic programming table correspond one-to-one with the optimal alignments, the number of distinct co-optimal alignments can be obtained by computing the number of distinct trace-back paths. (1a) [4 marks] Specify an algorithm (e.g., in pseudo-code) to compute the number of co-optimal alignments, performed using dynamic programming or another method of your choice. (1b) [1 mark] What is the asymptotic run time of your algorithm? PROBLEM TWO: [1 mark] Global and Local Alignments (2a) If using the same score/penalty function for all types of alignments, with higher scores indicating greater similarity, then how will the local score for aligning sequences S and T compare with the global score? (i) always less (ii) always less than or equal (iii) always equal (iv) always greater than or equal (v) always greater than (vi) none of the above (2b) How will the local alignment for S and T compare with the global alignment? (i) The positions aligned in the local alignment are always a strict subset of the positions aligned in the global alignment (ii) always a subset (iii) always the same set (iv) always a superset (v) always a strict superset (vi) none of the above (2c) [Optional/ExtraCredit] Can you think of a new, atypical score function that would change either or both of the answers you have given above? Explain very briefly. PROBLEM 3: Applications of Optimization. [Associated Reading: BMC Systems Biology 2008, 2:47 doi:10.1186/1752-0509-2-47 This article is available from: http://www.biomedcentral.com/1752-0509/2/47] In this exercise you must venture into reading unfamiliar texts from unfamiliar fields with insufficient background and incomplete information, but still be able to “smell” which aspects of a problem contain optimization issues. You must be familiar with PCR and evolution, but otherwise you do not need to do further reading or background study before answering these questions. For this exercise, you should use terms like optimal and optimize according to their mathematical meanings. Non-mathematical and non-computational optimization, such as choosing the "optimal" color scheme to complement your personality, is absolutely not considered a type of optimization in this exercise. Please state yes/no whether optimization is a good way to approach each of the problems listed below. If yes, please describe how optimization could be set up to address the problem, by giving brief English text for i. what is the objective, ii. what are the decision variables (and their domains or constraints, if relevant) iii. what part of the goals would be achieved by performing this optimization. Situation 2A: [2 marks] DRUG DEVELOPMENT “Our goal is to improve the drug-like qualities of chemical compounds ("leads") that show initial positive results during primary screening, so as to create modified compounds with efficacy and low toxicity, likely succeed in pre-clinical and clinical trials. Because of the improved efficiency in primary screening, refinement of lead compounds is now the major bottleneck in the drug discovery process. Traditionally, the process of refining leads would utilize manual, benchtop biological research that includes secondary screens, studies of the relationship between the structure and activity of compounds and cellular toxicity measurements. This slow and expensive process usually employs single measurements of biological activity without capturing both time and space data from cells. Time and space data, which we call high content data, is important to the understanding of complex cell functions. Without cellular analysis systems which provide high content data on cell functions, the pharmaceutical and biotechnology industries have historically been focused on a narrow range of targets, primarily the receptors on the surface of cells. However, cell functions involve not only the number and distribution of specific receptors localized on the surface of cells, but also the distribution and activity of other molecules on and within the cells. For example, the cycle of internalization of receptors to the inside of cells and back to the surface that regulates the responsiveness of many cells, involves numerous proteins in different locations within cells and exhibits different activities. The ability to measure the time and space activities of these proteins in relationship to specific cell functions, such as receptor-based stimulation, is an important challenge for lead optimization.” [Text adapted from the "Business Description" of the IPO statement of Cellomics Inc. according to ipoportal.edgar-online.com, and from www.aapspharmaceutica.com] SITUATION 2B: [2 marks] IMAGE ALIGNMENT Image alignment is the process of matching one image called the template with another image. Image alignment is one of the most widely used techniques in computer vision and it is widely applicable to many goals including analysis of microscopy data in cell biology. To automate image alignment, we must first determine the appropriate mathematical model relating pixel positions in one image to pixel positions in another. Next, we must somehow estimate the correct alignments relating pairs of images. The mathematical relationships that map pixel coordinates from one image to another are typically chosen from a variety of parametric motion models including simple 2D transforms, to planar perspective models, 3D camera rotations, lens distortions, and the mapping to non-planar surfaces. To facilitate working with images at different resolutions, we use normalized device coordinates. For a typical (rectilinear) image or video frame, we let the pixel coordinates range from [−1, 1] along the longer axis, and [−x, x] along the shorter, where x is the inverse of the aspect ratio. Once we have chosen a suitable pixel representation system and a motion model to describe the range of possible alignments, we need to devise some method to estimate the parameter values for the motion model alignment. One approach is to shift or warp the images relative to each other and to look at how much the pixels agree. Approaches that use pixel-to-pixel matching are often called direct methods, as opposed to the feature-based methods. SITUATION 2C: [2 marks] PHYLOGENETIC TREES A phylogenetic tree is a graphical representation of the evolutionary relationships among entities that share a common ancestor. Those entities can be species, genes, genomes, or any other operational taxonomic unit (OTU). More specifically, a phylogenetic tree, with its pattern of branching, represents the descent from a common ancestor into distinct lineages. It is critical to understand that the branching patterns and branch lengths that make up a phylogenetic tree can rarely be observed directly, but rather they must be inferred from other information. The principle underlying phylogenetic inference is quite simple: Analysis of the similarities and differences among biological entities can be used to infer the evolutionary history of those entities. However, in practice, taking the end points of evolution and inferring their history is not straightforward….The concept of descent with modification tells us that organisms sharing a recent common ancestor should, on average, be more similar to each other than organisms whose last common ancestor was more ancient. Therefore, it should be possible to infer evolutionary relationships from the patterns of similarity among organisms. This is the principle that underlies the various distance methods of phylogenetic reconstruction, all of which follow the same general outline. First, a distance matrix (i.e., a table of “evolutionary distances” between each pair of taxa) is generated. In the simplest case, the distances represent the dissimilarity between each pair of taxa (mathematically, they are 1 – S, where S is the similarity). The resultant matrix is then used to generate a phylogenetic tree. [Quoted from http://evolution-textbook.org] SITUATION 2D: [2 marks] DETECTING GENOMIC LESIONS Recent work has developed a new experimental protocol for detecting structural variation in genomes with high efficiency. It is particularly suited to cancer genomes where the precise breakpoints of alterations such as deletions or translocations vary between patients. The problem of designing PCR primers is challenging because a large number of primer pairs are required to detect alterations in the hundreds of kilobases range that can occur in cancer. Good primer pairs must achieve high coverage of the region of interest, while avoiding primers that can dimerize with each other, and while satisfying the traditional physico-chemical constraints of good PCR primers Established experimental techniques for detecting structural genomic changes include array-CGH (Pinkel and Albertson, 2005), FISH (Perry et al., 1997) and End-sequence Profiling (ESP) (Volik et al., 2006), but array-CGH will detect only copy number changes, FISH is laborintensive, and ESP is costly. PCR provides one possible solution to this problem because appropriately designed primer pairs within 1 kb of the fusing breakpoints will amplify only in the presence of the mutated DNA, and can amplify even with a small population of cells. Such PCRbased screening has been useful in isolating deletion mutants in Caenorhabditis elegans (Jansen et al., 1997). We seek a PCR method with multiple simultaneous primers whose PCR products cover a region in which breakpoints may occur. Every primer upstream of one breakpoint is in the same orientation, opposite to the primers downstream of the second breakpoint. A primer pair can form a PCR product only if a genomic lesion places the pair in close proximity. If the primer pairs are spatially distinct, then any lesion will cause the amplification of exactly one primer–pair. Primers must be selected which adequately cover the entire region, the primers must be chosen from a unique region of the genome, and not allowed to dimerize with each other. Finally, a selected primer must satisfy physico-chemical characteristics that allow it to prime the polymerase reaction. The dimerization and physic-chemical characteristics of good primers are well-studied problems with pre-existing methods available. SITUATION 2E: [2 marks] NETWORK RECONSTRUCTION In many complex systems found across disciplines, such as biological cells and organisms, social networks, economic systems, and the Internet, individual elements interact with each other, thereby forming large networks whose structure is often not known. In these complex networks, local events can easily propagate, resulting in diverse spatio-temporal activity cascades, or avalanches. Examples of such cascading activity are the propagation of diseases in social networks, cascades of chemical reactions inside a cell, the propagation of neuronal activity in the brain, and e-mail forwarding on the Internet. Exploring all possible topological configurations for a complete network with N nodes is a daunting task, since that number is on the order of exp(2, N*N). Using a variety of methods and assumptions, correlations in the dynamics between nodes have been successfully used to identify functional links in relatively large networks such as obtained from MEG or fMRI recordings of brain activity. A pure correlation approach, however, is prone to induce false connectivities. For example, it will introduce a link between two un-connected nodes, if their activities are driven by common inputs. More elaborate approaches such as Granger Causality, partial Granger Causality, partial directed coherence, and transfer entropy partially cope with the problem of common input, however, these methods require extensive data manipulations and data transformations and have been mainly employed for small networks.