Bioinformatics III (“Systems biology”) Course will address two areas: - analysis and comparison of whole genome sequences - „systems biology“ – integrated view of cellular networks 1 1. Lecture WS 2003/04 Bioinformatics III
Whole Genomes - Content some topics were already covered in Bioinformatics 1 lecture by Prof. Lenhof genome assembly gene finding genome alignment whole genome comparison (prokaryotes, human mouse) genome rearrangements transcriptional regulation functional genomics phylogeny single nucleotide polymorphisms (SNPs) 2 1. Lecture WS 2003/04 Bioinformatics III
Cellular Networks - Content network topologies: random networks, scale free networks robustness of networks expression analysis metabolic networks, metabolic flow analysis linear systems, non-linear dynamics molecular systems biology: protein-protein interaction networks molecular machines. . . 3 1. Lecture WS 2003/04 Bioinformatics III
Literature whole genome sequences e. g. David Mount, Bioinformatics Chapters 6, 8, 10 € 68 system biology mostly taken from original literature Web-resources Institute of Systems Biology, Seattle, WA http: //www. systemsbiology. org/ - The systems biology institute http: //www. systems-biology. org/ 4 1. Lecture WS 2003/04 Bioinformatics III
assignments 12 weekly assignments planned Homeworks are handed out in the Tuesday lectures and are available on our webserver http: //gepard. bioinformatik. uni-saarland. de on the same day. Solutions need to be returned until Tuesday of the following week 14. 00 in room 1. 05 Geb. 17. 1, first floor, or handed in prior (!) to the lecture starting at 14. 15. In case of illness please send E-mail to: kerstin. gronow-p@bioinformatik. uni-saarland. de and provide a medical certificate. 5 1. Lecture WS 2003/04 Bioinformatics III
Schein = successful written exam The successful participation in the lecture course („Schein“) will be certified upon successful completion of the written exam on Feb. 18, 2004. Participation at the exam is open to those students who have received 50% of credit points for the 12 assignments. Unless published otherwise on the course website until Feb. 4, the exam will be based on all material covered in the lectures and in the assignments. In case of illness please send E-mail to: kerstin. gronow-p@bioinformatik. uni-saarland. de and provide a medical certificate. A „second and final chance“ exam may be offered at the beginning of April 2004 to those who failed the first exam and those who missed the first exam due to illness (medical certificate required). 6 1. Lecture WS 2003/04 Bioinformatics III
tutors Prof. Dr. Volkhard Helms Sprechstunde: Tue 10 -12. Geb. 17. 1, room 1. 06. Generally, I am also available after the lectures. Dr. Tihamer Geyer – assignments for network part Geb. 17. 1, room 1. 09. guest lecturers+tutors 7 1. Lecture WS 2003/04 Bioinformatics III
Tree of Life Bacteria Archaea Eukarya Euryarchaeota l Purple bacteria l Gram-positive l. Cyanobacteria Chlamydiae l. Methanosarcina l Methanobacterium l Methanococcus Thermococcus Crenarchaeota l. Flavobacteria l Spirochetes l Thermotogales Thermoproteus Pyrodictium l. Deinococci l. Green nonsulfur bacteria l Halophiles l Animals l Fungi Thermoplasma l Plants Slime molds Entamoebae Ciliates l Stramenophiles l Trichomonads l Aquifex Microsporidia Diplomonads 8 1. Lecture WS 2003/04 Bioinformatics III
Genomes A genome is the entire genomic material of any of these biological organism. We will review genome organization, known sequences, genome language, sequencing details etc. in the next lecture. Now that we have genome information from multiple organisms I see the following issues: 1 what biological questions do we ask? 2 what bioinformatics tools do we need to find the answers? 3 what are the answers? 9 1. Lecture WS 2003/04 Bioinformatics III
Why mouse? 19 mouse chromosomes. Genetecists have anxiously awaited the recently published draft version of the Mouse genome? Why? Mouse as a close relative to humans is a unique lens through which we can view ourselves. As the leading mammalian system for genetic research over the past century it has provided a model for human physiology and disease. Comparative genomics makes it possible to discern biological features that would otherwise escape our notice. Nature 420, 520 (2002) 10 1. Lecture WS 2003/04 Bioinformatics III
How do we compare genomes? Conservation of synteny between human and mouse. 558, 000 highly conserved, reciprocally unique landmarks were detected within the mouse and human genomes, which can be joined into conserved syntenic segments and blocks. A typical 510 -kb segment of mouse chromosome 12 that shares common ancestry with a 600 -kb section of human chromosome 14 is shown. Blue lines connect the reciprocal unique matches in the two genomes. In general, the landmarks in the mouse genome are more closely spaced, reflecting the 14% smaller overall genome size. Nature 420, 520 (2002) 11 1. Lecture WS 2003/04 Bioinformatics III
Genome rearrangements Segments and blocks >300 kb in size with conserved synteny in human are superimposed on the mouse genome. Each colour corresponds to a particular human chromosome. The 342 segments are separated from each other by thin, white lines within the 217 blocks of consistent colour. Genome rearrangments have functional implications (will be discussed later). Nature 420, 520 (2002) 12 1. Lecture WS 2003/04 Bioinformatics III
Review: Pairwise sequence alignment • dynamic programming: Needleman-Wunsch, Smith Waterman • sequence alignments • substition matrices • significance of alignments • BLAST, algorithmn – parameters – outputhttp: //www. ncbi. nih. gov • This part of lecture taken from • O’Reilly book on “BLAST” by Korf, Yandell, Bedell • see also Bioinformatik I lecture by Prof. Lenhof • weeks 3 and 5 13 1. Lecture WS 2003/04 Bioinformatics III
Sequence alignment • When 2 or more sequences are present one would like - to detect quantitatively their similarities - discover equivalences of single sequence motifs - observe regularities of conservation and variability - deduce historical relationships - important goal: annotation of structural and functional properties assumption: sequence, structure, and function are inter-related. 14 1. Lecture WS 2003/04 Bioinformatics III
Search in databases • Identify similarities between • a new test sequence, of • unknown and uncharacterized structure and function • and sequences in (public) sequence databases with known structure and function. • N. B. The similar regions can encompass the entire sequence or parts of it! • Local alignment global alignment 15 1. Lecture WS 2003/04 Bioinformatics III
Sequence Alignment The purpose of a sequence alignment is to arrange all those residues of a deliberate number of sequences beneath eachother that are derived from the same residue position in an ancestral gene or protein. gap = Insertion oder Deletion J. Leunissen
Needleman-Wunsch Algorithm - general algorithm for sequence comparison - maximises a similarity score - maximum match = largest number of residues of one sequence that can be matched with another allowing for all possible deletions - finds the best GLOBAL alignment of any two sequences - NW involves an iterative matrix method of calculation all possible pairs of residues (bases or amino acids) – one from each sequence – are represented in a two-dimensional array all possible alignments (comparisons) are represented by pathways through this array. Three main steps 1 initialization 2 fill (induction) 3 trace-back 17 1. Lecture WS 2003/04 Bioinformatics III
Needleman-Wunsch Algorithm: Initialization task: align words “COELACANTH” and “PELICAN” of length m=10 and n=7. Construct (m+1) (n+1) matrix. Assign values – m gap and – n gap to elements m and n of first row and first column. Here, gap = -1. Arrows of these fields point back to origin. C 0 P N T H -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -6 N A -5 A C -4 C A -3 I L -2 L E -1 E O -7 18 1. Lecture WS 2003/04 Bioinformatics III
Needleman-Wunsch Algorithm: Fill all matrix fields with scores and pointers using a simple operation that requires the scores from the diagonal, vertical, and horizontal neighboring cells. Compute - match score: value of upper left diagonal cell + score for a match (+1 or -1) - horizontal gap score: value of cell to the left + gap score (-1) - vertical gap score: value of cell to the top + gap score (-1) assign maximum of these 3 scores to cell. point arrow in direction of maximum score. C max(-1, -2) = -1 max(-2, -3) = -2 0 P -1 O E L A C A N T H -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -1 -2 (make arbitrary, consistent choice – e. g. always choose the diagonal over a gap. 19 1. Lecture WS 2003/04 Bioinformatics III
Needleman-Wunsch Algorithm: Trace-back trace-back lets you recover the alignment from the matrix. start at the bottom-right corner and follow the arrows until you get to the beginning. C O E L A C A N T H 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 P -1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 E -2 -2 -2 -1 -2 -3 -4 -5 -6 -7 -8 L -3 -3 -3 -2 0 -1 -2 -3 -4 -5 -6 I -4 -4 -4 -3 -1 -1 -2 -3 -4 -5 -6 C -5 -3 -4 -4 -2 -2 0 -1 -2 -3 -4 A -6 -4 -4 -5 -3 -1 -1 1 0 -1 -2 N -7 -5 -5 -5 -4 -2 -2 0 2 1 0 COELACANTH -PELICAN-- 20 1. Lecture WS 2003/04 Bioinformatics III
Smith-Waterman-Algorithm Smith-Waterman is a local alignment algorithm. SW is a very simple modification of Needleman-Wunsch. Only 3 changes: - edges of the matrix are initialized to 0 instead of increasing gap penalties. - maximum score is never less than 0. No pointer is recorded unless the score is greater than 0. - trace-back starts from highest score in matrix and ends at a score of 0. ELACAN C ELICAN O E L A C A N T H 0 0 0 P 0 0 0 E 0 0 0 1 0 0 0 0 L 0 0 2 1 0 0 0 I 0 0 1 1 0 0 0 C 0 1 0 0 2 0 0 A 0 0 0 1 0 3 2 1 0 N 0 0 0 0 1 4 3 2 21 1. Lecture WS 2003/04 Bioinformatics III
Differences Needleman-Wunsch Smith-Waterman 1 Global alignments 1 Local alignments 2 requires alignment score for a pair 2 Residue alignment score may be of residues to be 0 positive or negative 3 no gap penalty required 3 requires a gap penalty to work efficiently more suited for alignment of eukaryotic sequences with exons and introns 22 1. Lecture WS 2003/04 Bioinformatics III
Algorithmic complexity Dynamic programming methods such as Needleman-Wunsch and Smith. Waterman have O(mn) complexity in both time and memory. Variation: just use 2 rows at a time and don’t allocate the whole matrix. The alignment algorithm becomes O(n) in memory. 23 1. Lecture WS 2003/04 Bioinformatics III
Scoring - or Substition Matrices – serve to better score the quality of sequence alignments. – for protein/protein comparison: a 20 x 20 matrix for the probabilities that certain amino acids are exchange others by random mutations – the exchange of amino acids of similar character (Ile, Leu) is more likely (receives higher score) than for exchanging amino acids of dissimilar character (e. g. Ile Asp) – scoring matrices are assumed to be symmetrical (exchange Ile Asp has the same probability as Asp Ile). Therefore they are triangular matrices. 24 1. Lecture WS 2003/04 Bioinformatics III
Substitution matrices • Not all amino acids are similar – some can be replaced more easily than others – some mutations occur more frequently than others – some mutations are more long-lived than others • Mutations prefer certain exchanges – some amino acids have similar 3 -letter codons – those residues are more replaced by random DNA mutation • Selection prefers certain exchanges – some amino acids have similar properties and structure (E. g. Trp cannot be inserted in the protein interior. ) 25 1. Lecture WS 2003/04 Bioinformatics III
PAM 250 Matrix 26 1. Lecture WS 2003/04 Bioinformatics III
Example Score The Score of an alignment is the sum of all invidual scores of the amino acid (base) pairs of the alignment. • Sequence 1: TCCPSIVARSN • Sequence 2: SCCPSISARNT • 1 12 12 6 2 5 -1 2 6 1 0 => Alignment Score = 46 27 1. Lecture WS 2003/04 Bioinformatics III
Dayhoff Matrix (1) – derived by M. O. Dayhoff who collected statistical data for probabilities of amino acid exchanges – data set for closely related protein sequences (> 85% identity). – advantage: these can be aligned to high certainty. – derive 20 x 20 matrix for probabilities of amino acid mutations from the observed frequency of exchanges – This matrix is called PAM 1. An evolutionary distance of 1 PAM (point accepted mutation) means that 1 point mutations occur per 100 residues. Or: both sequences are 99% identical. 28 1. Lecture WS 2003/04 Bioinformatics III
Dayhoff Matrix (2) • Log odds Matrix: contains logarithms of PAM matrix entries. • • Score of mutation i j • observed mutation rate i j = log( expected mutation rate according to amino acid frequency ) • The probability of two independent mutational events is the product of the individual probabilities. • When using a log odds Matrix (i. e. using the logarithm of all values) one obtains the total alignment score as sum of the scores for every residue pair. 29 1. Lecture WS 2003/04 Bioinformatics III
Dayhoff Matrix (3) • Derive Matrices for larger evolutionary distances by multiplying the PAM 1 matrix with itself. • PAM 250: – 2, 5 mutations per residue – corresponds to 20% matches between two sequences, – i. e. mutations are observed at 80% of all residue positions. – This is the default matrix of most sequence analysis packages. 30 1. Lecture WS 2003/04 Bioinformatics III
BLOSUM Matrix • limitation of Dayhoff-Matrix: the matrices based on the Dayhoff model of evolutionary rates are of limited value because the substitution rates were derived from sequence alignments of sequences that are more than 85% identical. • A different path was taken by S. Henikoff and J. G. Henikoff who used local multiple alignments of distantly related sequences. • Advantages: - larger data sets - multiple alignments are more robust 31 1. Lecture WS 2003/04 Bioinformatics III
BLOSUM Matrix (2) • The BLOSUM matrices (BLOcks SUbstitution Matrix) are based on the BLOCKS database. • The BLOCKS database uses the concept of blocks (ungapped amino acid signatures) that are characteristic for protein families. • Derive probabilities of exchange for all amino acid pairs from the observed mutations inside the blocks. Convert into log odds BLOSUM matrix. • Different matrices are obtained by varying the lower requirement for the level of sequence identity. • e. g. the BLOSUM 80 matrix is derived from blocks with > 80% identity. 32 1. Lecture WS 2003/04 Bioinformatics III
Which matrix to use? • Close relationship (low PAM, high Blosum) Distant relationship (High PAM, low Blosum) • reasonable default parameters: PAM 250, BLOSUM 62
Gap penalties • Besides substitution matrices we need a method to score gaps • Which relevance do insertions or deletions have relative to substitutions? • distinguish introduction of gaps: • aaagaaa • aaa-aaa • from extension of gaps: • aaaggggaaa • aaa----aaa • different programs (CLUSTAL-W, BLAST, FASTA) recommend different default parameters which should be used as a first guess.
Significance of Alignments (1) • When is an alignment statistically significant? In other words: • How different is the obtained score of an alignment from scores that would result from alignments of the test sequence with random sequences? • Or: • What is the probability that an alignment of this score occured randomly? 35 1. Lecture WS 2003/04 Bioinformatics III
Significance of Alignments (2) • size of database = 20 x 106 letters • Peptide #hits • A 1 x 106 (if equally distributed) • AP 50000 • IAP 2500 • LIAP 125 • WLIAP 6 • KWLIAP 0, 3 • KWLIAPY 0, 015 36 1. Lecture WS 2003/04 Bioinformatics III
BLAST – Basic Local Alignment Search Tool • finds the highest-scored local optimal alignment of a test sequence with all sequences of a database. • Very fast algorithm. Ca. 50 times faster than dynamical programming. • because BLAST uses pre-indexed database, BLAST can be used to search very large databases. • is sufficiently sensitive and selective for most purposes. • Is robust – default parameters usually work fine. 37 1. Lecture WS 2003/04 Bioinformatics III
BLAST Algorithm, Step 1 • For given word of length w (usually 3 for proteins) and for a given scoring matrix • construct list of all words (w-mers) which get score > T if compared to w-mer of input sequence. test sequence LNKCKTPQGQRLVNQ P Q G 18 P E G 15 P R G 14 P K G 14 P N G 13 P D G 13 P M G 13 below cut-off (T=13) word related words P Q A 12 P Q N 12 etc. 38 1. Lecture WS 2003/04 Bioinformatics III
BLAST Algorithm, Step 2 • each related word points to positions in data base (hit list). P Q G 18 P E G 15 P R G 14 P K G 14 P N G 13 P D G 13 P M G 13 PMG Database 39 1. Lecture WS 2003/04 Bioinformatics III
BLAST Algorithm, Step 3 • Program tries to extend suitable segments (seeds) in both directions by adding pairs of residues. • Residues are added until score sinks below cut-off. 40 1. Lecture WS 2003/04 Bioinformatics III
different BLAST algorithms • BLASTN – compares nucleotide sequence against nucleotide database • BLASTP – compares protein sequence against protein database • BLASTX – compares nucleotide sequences translated in all 6 open reading frames against protein sequence database • TBLASTN • TBLASTX 41 1. Lecture WS 2003/04 Bioinformatics III
BLAST Output (1) • Small probability shows that hit is likely not random 42 1. Lecture WS 2003/04 Bioinformatics III
Significance of BLAST alignment P-value (probability) – probability that alignment score could result from alignment of random sequences – the closer P equals 0, the higher is certainty that a hit is a true hit (homologous sequence) E-value (expectation value) – E = P * number of sequences in database – E is the number of alignments of a particular score that can be expected to occur randomly in a sequence database of this size – if e. g. E=10, one expects 10 random hits with the same score. Such an alignment is not significant. Use appropriate threshold in BLAST. 43 1. Lecture WS 2003/04 Bioinformatics III
Rough guide • P-value (probability) – A. M. Lesk – P 10 -100 sequences are identical – 10 -100 < P < 10 -50 sequences are almost identical, e. g. alleles or SNPs – 10 -50 < P < 10 -10 closely related sequences, homology is certain – 10 -10 < P < 10 -1 sequences are usually distantly related – P > 10 -1 similarity probably not significant • E-value (expectation value) • E 0, 02 sequences probably homologous • 0, 02 < E < 1 Homology possible • E 1 good agreement most likely random. 44 1. Lecture WS 2003/04 Bioinformatics III
Rough guide Level of sequence identity with optimal alignment Ø> 45% proteins have very similar structure Ø Ø> 25% Ø 18 – 25% Øbelow and most likely the same function proteins probably possess similar fold Twilight-Zone - assuming homology is tempting alignment has little significance 45 1. Lecture WS 2003/04 Bioinformatics III
Twilight-Zone (1) • myoglobin from whale and Leghemoglobin of lupins are 15% identical with optimal alignment • both have very similar tertiary structure. • both contain heme group and bind oxygen • they are remotely related, though homologous proteins Left: Whale Mb Right: Leg Hb www. rcsb. org 46 1. Lecture WS 2003/04 Bioinformatics III
Twilight-Zone (2) • the N- and C-terminal halfs of thiosulfate-transferase have 11% sequence identity. • Because they belong to the same protein assumption that they resulted from gene duplication and divergent evolution. • Indeed both 3 D structures show large similarity. 2 ORA Rhodanese www. rcsb. org 47 1. Lecture WS 2003/04 Bioinformatics III
Twilight-Zone (3) • serine proteases chymotrypsin and subtilisin • have 12% identity with optimal alignment • both have same function, same catalytic triad of 3 amino acids (Ser – His – Asp) • However, the two folds are completely different and the proteins are not related. Example for convergent evolution. Left: 1 AB 9 Bovine Chymo Trypsin Right: 1 GCI Bacillus Lentus Subtilisin www. rcsb. org 48 1. Lecture WS 2003/04 Bioinformatics III
Summary Pairwise alignment of sequences is routine but not trivial. Dynamic programming guarantees finding the alignment with optimal score (Smith-Waterman, Needleman-Wunsch). Much faster but reliable tools are: FASTA, (PSI) BLAST Deeper functional insight into sequences and relationships from multiple sequence alignments (see lecture on phylogenies). 49 1. Lecture WS 2003/04 Bioinformatics III
Growth of Proteomic Data vs. Sequence Data 50 1. Lecture WS 2003/04 Bioinformatics III
Systems biology is an emergent field that aims at system-level understanding of biological systems. Cybernetics, for example, aims at describing animals and machines from the control and communication theory. Unfortunately, molecular biology had just started at that time, so that only phenomenological analysis has been possible. With the progress of genome sequence project and range of other molecular biology project that accumulate in-depth knowledge of molecular nature of biological system, we are now at the stage to seriously look into possibility of system-level understanding solidly grounded on molecular-level understanding. http: //www. systems-biology. org/000/ 51 1. Lecture WS 2003/04 Bioinformatics III
Systems biology What does it mean to understand at "system level"? Unlike molecular biology which focusses on molecules, such as the sequences of nucleotide acids and proteins, systems biology focusses on systems that are composed of molecular components. Although systems are composed of matters, the essence of systems lies in the dynamics and cannot be described merely by enumerating components of the system. At the same time, it is misleading to believe that only the system structure, such as network topologies, is important without paying sufficient attention to diversities and functionalities of components. Both the structure of the system and its components play indispensable roles forming a symbiotic state of the system as a whole. http: //www. systems-biology. org/000/ 52 1. Lecture WS 2003/04 Bioinformatics III
Systems biology Key milestones are: (1) understanding of structure of the system, such as gene regulatory and biochemical networks, as well as physical structures, (2) understanding of dynamics of the system, both quantitative and qualitative analysis as well as construction of theory/models with powerful prediction capability, (3) understanding of control methods of the system, and (4) understanding of design methods of the system. There are numbers of exciting and profound issues that are actively investigated, such as robustness of biological systems, network structures and dynamics, and applications to drug discovery. Systems biology is in its infancy, but this is the area that has to be explored and the area that we believe to be the main stream in biological sciences in this century. http: //www. systems-biology. org/000/ 53 1. Lecture WS 2003/04 Bioinformatics III
Systems Biology Nat. Biotech. Nov. 2000, 1147 54 1. Lecture WS 2003/04 Bioinformatics III
From Genomics to Genetic Circuits The relationship between the genotype and the phenotype is complex, highly non-linear and cannot be predicted from simply cataloging and assigning gene functions to genes found in a genome. http: //gcrg. ucsd. edu/presentations/hougen/l 2. pdf 55 1. Lecture WS 2003/04 Bioinformatics III
Genetic Circuits Engineering 56 1. Lecture WS 2003/04 Bioinformatics III
Analysis of Genetic Circuits 57 1. Lecture WS 2003/04 Bioinformatics III
Reconstructing Metabolic Networks 58 1. Lecture WS 2003/04 Bioinformatics III
Translating Biochemistry into Linear Algebra 59 1. Lecture WS 2003/04 Bioinformatics III
DOE initiative: Genomes to Life a coordinated effort slides borrowed from talk of Marvin Frazier Life Sciences Division U. S. Dept of Energy 60 1. Lecture WS 2003/04 Bioinformatics III
Facility I Production and Characterization of Proteins Estimating Microbial Genome Capability • Computational Analysis – Genome analysis of genes, proteins, and operons – Metabolic pathways analysis from reference data – Protein machines estimate from PM reference data • Knowledge Captured – Initial annotation of genome – Initial perceptions of pathways and processes – Recognized machines, function, and homology – Novel proteins/machines (including prioritization) – Production conditions and experience 61 1. Lecture WS 2003/04 Bioinformatics III
Facility II Whole Proteome Analysis Modeling Proteome Expression, Regulation, and Pathways • Analysis and Modeling – Mass spectrometry expression analysis – Metabolic and regulatory pathway/ network analysis and modeling • Knowledge Captured – Expression data and conditions – Novel pathways and processes – Functional inferences about novel proteins/machines – Genome super annotation: regulation, function, and processes (deep knowledge about cellular subsystems) 62 1. Lecture WS 2003/04 Bioinformatics III
Facility III Characterization and Imaging of Molecular Machines Exploring Molecular Machine Geometry and Dynamics • Computational Analysis, Modeling and Simulation – Image analysis/cryoelectron microscopy – Protein interaction analysis/mass spec – Machine geometry and docking modeling – Machine biophysical dynamic simulation • Knowledge Captured – Machine composition, organization, geometry, assembly and disassembly – Component docking and dynamic simulations of machines 63 1. Lecture WS 2003/04 Bioinformatics III
Facility IV Analysis and Modeling of Cellular Systems Simulating Cell and Community Dynamics • • Analysis, Modeling and Simulation – Couple knowledge of pathways, networks, and machines to generate an understanding of cellular and multi-cellular systems – Metabolism, regulation, and machine simulation – Cell and multicell modeling and flux visualization Knowledge Captured – Cell and community measurement data sets – Protein machine assembly time-course data sets – Dynamic models and simulations of cell processes 64 1. Lecture WS 2003/04 Bioinformatics III
Computing and Information Infrastructure Capabilities GTL Computing Roadmap Protein machine Interactions Molecule-based cell simulation Molecular machine classical simulation Cell, pathway, and network simulation Community metabolic regulatory, signaling simulations Constrained rigid docking Constraint-Based Flexible Docking Current U. S. Computing Genome-scale protein threading Comparative Genomics Biological Complexity 65 1. Lecture WS 2003/04 Bioinformatics III
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