MAT 27A: Linear Algebra with Applications to Biology Winter Course PDF

Linear algebra deals with matrices and Winter Course: vectors. MAT 27A: Linear Algebra with...

Linear algebra deals with matrices and Winter Course: vectors. MAT 27A: Linear Algebra with It is central to Applications to Biology nearly all quantitative data analysis methods.  Co-developed by Math, Science, & Engineering faculty as a national model for math training It is the mathematics that  Topics same as MAT 22A, and satisfies MAT 22A & describes network 22AL requirement, but with focus on real-world interactions of all applications to biological & biochemical systems types (e.g., biochemical, neural,  Computational lab teaches critical math modeling physiological, techniques ecological). Lecture: MWF 12:10-1pm, TLC 2216 Computer lab: R 12:10-2 pm, TLC 2216 Prerequisites: MAT 17C or 21C or 21CH Questions? Contact [email protected] or [email protected] Computer simulation of a reaction-diffusion system Assignment 2 and MT2 Lecture assignment 2 (graded) Same logistics as lecture assignment 1 Opens today 11/6 at noon; due Monday 11/11 11:59 pm Same as Assignment 1: 2 untimed attempts, keep highest score; open book, individual work MT2 Same logistics as MT1 Wed 11/13 in class, 50 min, 25 questions One double-sided letter-sized “cheat-sheet” allowed Regular or scientific calculator allowed—not graphing, not your phone Covers lectures 9-18 (redox to translation, included) Always choose the best (most complete) answer. No partial credit is given. Always assume a common-sense, straightforward interpretation. The correct answer will not be based on a semantic trick. (But always read carefully, especially higher/lower, positive/negative, 5’-3’, coding/template, etc. These topics are inherently prone to confusion.)  BIS2A Lecture 23 Translation DALL-E: “A DNA translation machine in the style of Da Vinci” Learning objectives Describe the features of the genetic code Explain the significance of reading frames Describe the two adaptor steps for translation (tRNAs and tRNA synthetases) Explain how a polypeptide is formed, both chemically and in the ribosome Describe the features of ribosomes Explain ribosome initiation, elongation and termination in prokaryotes and eukaryotes Central dogma DNA RNA Protein Transcription Translation Central dogma DNA RNA Protein Transcription Translation Copying, same Changing from one language, slightly language (words) to different format another (cake) How is a linear sequence of RNA translated into a linear sequence of amino acids? Different “languages” 4 bases, 20 amino acids  combinations of nucleotides? Genetic “code”! 41 = 4, 42 = 16, 43 = 64  How is a linear sequence of RNA translated into a linear sequence of amino acids? Each group of three consecutive nucleotides (codon) specifies an amino acid, or a stop to translation The code is almost universal across the tree of life The genetic code is redundant (but not ambiguous) Codon wheel Codon table  An RNA sequence can in principle be translated in three different reading frames Frame 3 reading frames, based on where 1 the decoding process begins Would result in 3 very different proteins (sequence/length) Frame 2 The cell must be able to determine the correct frame for translation initiation! Frame 3 Proper start codon Nonsense, missense and silent mutations * Silent: the new codon codes for the same amino acid (redundancy) * Missense: the new codon codes for different amino acid (changes the meaning/sense) * Nonsense: the new codon codes for a stop codon (there is no amino acid, no meaning/sense) Translation via codons in a particular frame, but HOW? Some kind of adaptor molecule that can link the nucleotide codon message with a specific amino acid? transferRNAs (tRNA)  tRNAs: adaptors between codons and aa RNA-based adaptor tRNA binds a specific (“cognate”) aa on one end Has an anti-codon on another end Anti-codon base pairs with the codon on the mRNA, placing the aa in line for polymerization 5’ 3’ mRNA xx x codon nt = nucleotideaa = amino acid  Question What’s the codon for Phe shown here? a) CUU b) UUC c) GAA d) TTG 5’ 3’ 3’ CUU 5’ 5’ UUC 3’ RNA is always written 5’ to 3’!  Practice question Which is the 3’ and 5’ end of the anticodons shown here? Figure it out with the codon table! Two different molecules are shown here, phenylalanine tRNA (PDB entry 4tna ) and aspartate tRNA (PDB entry 2tra ).  tRNA synthetases: adaptors between tRNAs and their aa aaxyz Aminoacyl-tRNA For the code to work, crucial step is sythetase to properly attach each tRNA to its aa Aminoacyl-tRNA synthetases covalently attach the correct aa to charged the end of each tRNA tRNAxyz empty Tri-partite system: enzyme + tRNA + tRNAxyz aa tRNA synthetases: adaptors between tRNAs and their aa Translation actually has 2 adaptor steps: tRNA synthetases (tRNA, aa) tRNA (aa, codon) An error in either adaptor would 2 case the wrong aa to be incorporated into the protein tRNA synthetases have proof- reading capabilities charged tRNA Protein formation via pairing of mRNA codon and the anti-codon of an aa- charged tRNA, but HOW? Chemical basis of polypeptide formation How the cell does it in ribosomes Polypeptide formation: amino acid recap Protein chain (polypeptide) grows by stepwise addition of each amino acid Polypeptide formation (1): chemical bond Protein chain (polypeptide) grows by stepwise addition of each amino acid Amino acids are linked by peptide bonds between amino and carboxyl ends of aa Peptides grow from the N to the C terminus carboxyl end amino end (C terminus) (N terminus)  Polypeptide formation (2): charged tRNAs N+ 1 N+ N 1 N The aa and growing polypeptides are not “floating”, but charged on tRNAs The N terminus of aa on tRNAn+1 attacks the C terminus of the growing polypeptide on tRNAn Peptide bond is formed, tRNAn is released and the extended polypeptide is now attached to the tRNAn+1  Polypeptide formation (3): ribosomes The charged tRNA that undergo peptide bond formation are not “floating” either: peptide formation occurs in the ribosome (in the cytoplasm) Ribosomes are large molecular assemblies of multiple proteins and ribosomal RNA (rRNA) Ribosomes: large assemblies of multiple proteins and ribosomal RNA (rRNA) Prokaryotic ribosome (70S) Large subunit Small (50S) subunit (30S) 5S 5SrRNA + 23S rRNA + 23S 16S rRNA rRNA + 34+proteins rRNA 34 + 21 proteins proteins Overall structure: “small subunit” and “large subunit” (each with various proteins/rRNAs) Ribosomes: large assemblies of multiple proteins and ribosomal RNA (rRNA) Prokaryotic Eukaryotic ribosome ribosome (70S) (80S) Large subunit Small Large subunit Small subunit (50S) subunit (60S) (40S) (30S) 5S 5SrRNA + 23S rRNA + 23S 16S rRNA 5S rRNA + 28S rRNA 18S rRNA rRNA + 34+proteins rRNA 34 + 21 +5.8S rRNA +49 + 33 proteins proteins proteins proteins Overall structure: “small subunit” and “large subunit” (each with various proteins/rRNAs) Eukaryotic ribosome is more complex (more components), but general principles are the same Small/large subunits have distinct functions in translation Prokaryotic Eukaryotic ribosome ribosome (70S) (80S) Large subunit Small Large subunit Small subunit (50S) subunit (60S) (40S) (30S) 5S 5SrRNA + 23S rRNA + 23S 16S rRNA 5S rRNA + 28S rRNA 18S rRNA rRNA + 34+proteins rRNA 34 + 21 +5.8S rRNA +49 + 33 proteins proteins proteins proteins Small subunit for codon:anti-codon pairing Large subunit for peptide bond formation Small and large subunits come together for mRNA translation and then separate The ribosome is a ribozyme! (RNA enzyme) Prokaryotic Eukaryotic ribosome ribosome (70S) (80S) Large subunit Small Large subunit Small subunit (50S) subunit (60S) (40S) (30S) 5S 5SrRNA + 23S rRNA + 23S 16S rRNA 5S rRNA + 28S rRNA 18S rRNA rRNA + 34+proteins rRNA 34 + 21 +5.8S rRNA +49 + 33 proteins proteins proteins proteins Catalytic activity for peptide bond formation provided by the rRNA, not the protein subunits Bacterial ~20 aa/s; eukaryotic ~4 aa/s Polypeptide formation (3): ribosomes Small subunit is for codon:anti-codon Large subunit is for peptide bond formation 4 sites for RNA binding 1 for mRNA 3 for tRNA (A, P, E sites) These sites are mostly formed by rRNA Peptidyl transferase activity also catalyzed by rRNA Polypeptide formation (3): ribosomes A (aminoacyl) site: tRNAn+1 with incoming aa P (peptidyl) site: tRNAn with growing chain E (exit) site: emptied tRNAn-1 Ribosome catalyzes bond formation and moves over to the next codon  Polypeptide formation (3): ribosomes Binding Conformational of tRNAn+1 change: large subunit and tRNAs move over 1 position Peptide Conformationa bond l change: between small subunit tRNAn moves over; and tRNAn ejected tRNAn+1 Polypeptide formation (3): ribosomes Peptidyl transfer + conformational change N+ 1 N+ N 1 N P site A site E site Peptide bond formation (peptidyl transfer) is happening in the ribosome P site It is catalyzed by the rRNA in the large subunit Efficient and accurate translation is aided by elongation factors (GTP hydrolysis) Polypeptide formation (3): ribosomes Peptidyl transfer + conformational change P site N+ 1 N+ N 1 N P site A site E site The ribosome cannot break the peptide bond if the wrong n+1 aa-tRNA is used BUT ribosome does have initial control over the n+1 aminoacyl—tRNA Initial selection (fit of the codon:anticodon base pair interaction) “kinetic proofreading” (favours the cognate aa-tRNA through energy-requiring, irreversible step; cognate aa-tRNA can hydrolyse GTP and lead to required conformational change much faster than the near-cognate --details NOT covered in this course)  All good for elongation, what about initiation? WHEN YOU READ YOU BEGIN WITH A, B, C Proper initiation is crucial, as this sets the reading frame Highly regulated! Translation starts at the first AUG codon (methionine) after a ribosomal recruiting sequence WHEN YOU TRANSLATE YOU BEGIN WITH A, U, G  All good for elongation, what about initiation? WHEN YOU READ YOU BEGIN WITH A, B, C Initiation players: AUG Initiator tRNA (met) Initiation factors bound to mRNA Ribosome subunits must come together mRNA features that help recruit/position the ribosome: Eukaryotes: 5’ cap, Kozak sequence WHEN YOU TRANSLATE YOU BEGIN WITH A, U, G Prokaryotes: Shine-Dalgarno sequence Kozak/S-D position the ribosome relative to the start codon  The Shine-Dalgarno sequence is a ribosome binding/recruitment sequence in prokaryotes Upstream of the start site Recruits ribosome, positions it close to the start site Ribosome will first bind SD, then start ”scanning” for the start site SD is found in prokaryotes How does the ribosome recognize SD sequence is part of the transcript, but not of the the recruitment sequence? protein The transcript contains 5’ Where is the promoter Base pairing interactions! and 3’ untranslated regions (DNA) relative to the 5’ important for translation UTR? regulation (more later) John Shine and Lynn  SD sequence recognized by base- pairing with small-subunit rRNA Small subunit recognizes “Shine- Dalgarno sequence” (AGGAGGU) upstream of AUG start codon Recognized by base-pairing of rRNA of small subunit rRNA This positions the small subunit/ribosome close to the start codon so translation can begin No mRNA cap (important for recognition in eukaryotes) Translation initiation in prokaryotes recruited 1. Initiator tRNA-Met (tRNAi-Met) is loaded in P site of small subunit 2. Small subunit is recruited to mRNA and scans for Shine-Dalgarno sequence 3. Once SD is found, large subunit joins small subunit 4. Additional proteins (initiation factors) are involved Multiple SD sequences (and the lack of 5’ cap) allow for translation of polycistronic mRNAs Shine-Dalgarno sequences (SD) Ribosomes are recruited to each SD of the polycistronic mRNA Ribosome must know where to start, but also where to stop! (stop codon)  Translation initiation in eukaryotes Conceptually similar to prokaryotes, but more complex: more initiation factors and regulatory steps involved Complex finds 1. Load small subunit with tRNAi-Met AUG within Kozak 2. Recruit small subunit to mRNA by interacting with initiation factors bound to 5’ cap and 3’ polyA tail 3. Scan for start codon embedded in Kozak sequence 4. Recruit large subunit  Translation initiation in eukaryotes Initiator tRNA-Met Initiator tRNA loads up with methionine: tRNAi-Met Small subunit Eukaryotic initiation factor2 (eIF2) brings tRNAi-Met to small subunit P site  Translation initiation in eukaryotes Initiator tRNA-Met Initiation factors bound to mRNA’s cap and polyA tail recruit the small subunit Small subunit The 5’ caps plays crucial role in recruiting and positioning the small subunit Mature mRNA Other eIFs Translation initiation in eukaryotes Small subunit with tRNAi scans for first AUG AUG must be in the context of a consensus sequence (“Marilyn Kozak sequence”: ACCAUGG) for efficient recognition Small subunit rRNA base pairs with Kozak sequence and stops there Large subunit is recruited –full ribosome is in place Translation initiation in eukaryotes First peptide bond between aa in A and P sites Translation proceeds Lastly, termination End of encoded protein signalled by stop codons: UAA, UAG, UGA Not recognized by any tRNAs Instead, recognized by release factors Lastly, termination Release factor binds to stop in A site Then moves to P site (GTP is expended) Lastly, termination Catalysis with H2O, releasing peptide from tRNA in E site Ribosome releases mRNA, separates Proteins are made on polyribosomes Multiple ribosomes can latch on to single mRNA at the same time >80 nt apart Leads to faster protein production In humans, actively translated mRNAs have avarage 10-20 ribosomes Today we learned The features of the genetic code The significance of reading frames The two adaptor steps for translation (tRNAs and tRNA synthetases) How a polypeptide is formed, both chemically and in the ribosome The features of ribosomes Ribosome initiation, elongation and termination in prokaryotes and eukaryotes Readings Alberts B, Johnson A, Lewis J, et al. Molecular Biology of the Cell. 4th edition. New York: Garland Science; 2002. From RNA to Protein. Available from: https://www.ncbi.nlm.nih.gov/books/NBK26829/ Practice question Based on the DNA strand below, and assuming the promoter for this gene is located to the left, which protein sequence below does this DNA sequence encode? (Assume the first nucleotide above is the start of the first codon.) 5’-ATGTTGAAAATGCCGTAGAGGC-3’ A. Met-Leu-Lys-Met-Pro-Arg B. Met-Leu-Lys-Met-Pro C. Met-Leu-Lys-Met-Pro-stop-Arg D. Met-Pro E. Pro-Met-Lys-Leu-Met. (B)