3946. Partial derivatives Find the first partial derivatives of the following functions. f 1x, y, z2 = ex + 2y + 3z
EXAM 3 STUDY GUIDE Chapter 15: Carbohydrates Terms to Know Biomolecules exist in living organisms Carbohydrates occurring OH groups with a ketone or aldehyde o Monosaccharides= simple sugar= 37 carbons o Disaccharides= 2 monosaccharides= 614 carbons o Polysaccharides= complex many monosaccharides combined Chiral 4 different atoms attached to the same carbon Achiral at least one atom bonded to the same carbon MORE THAN ONCE Enantiomers mirror images Fisher Projections 2 dimensional that has bonds that goes back and forward Haworth structures formed by a reaction between a carbonyl and hydroxyl group Anomers cyclic sugar that differs at the carbon atom where an OH and OR group is attached Hyperglycemia blood glucose concentration higher than 90 mg Excessive thirst and urination Can be caused by diabetes Hypoglycemia blood glucose concentration lower than 70mg Dizziness, weakness, Can be caused by overproduction of insulin by pancreas Naming Carbohydrates 1. Find highest functional group Ketone or Aldehyde 2. Count # of carbons 3. Add –ose ending Drawing Haworth structures 1. Draw Fisher Projection 2. Turn 90 degrees clockwise 3. Curve carbons into hexagon shape 4. Figure if the molecule is a D or L by looking at the OH group on the last chiral carbon - If it points to the right its D, if it points to the left its L 5. Rotate carbon 6 either up for D molecule or down for L molecule 6. Make hemiacetal by closing the loop Reactions Oxidation of Monosaccharides - Just add an O to the H - Replace –ose ending with –onic acid Oxidation of Fructose > Glucose - Benedicts solution - Ketose > Aldose Reduction of Monosaccharides - Only aldehydes - Produce sugar alcohols - Aldehydes > 1 degree alcohol - Replace –ose ending with –itol DGlucose - Most common - Source of energy for brain - Found in fruits, vegetables, honey, corn syrup DGalactose - Component of lactose - Found in milk DFructose - Very sweet - Found in honey and fruits Forming Disaccharides Glucose + Glucose = Maltose (Malt sugar) - From hydrolysis of starch - Reducing sugar - Found in cereals, candies, brewing Glucose + Galactose = Lactose (Milk sugar) - Milk and milk products - Reducing sugar Glucose + Fructose = Sucrose (Table sugar) - Not reducing sugar Polysaccharides: I. Starch - Insoluble - Found in plants, rice, wheat, potatoes, and beans Amylose vs. Amylopectin - Better for us - 80% of starch - Harder to digest - unbranched alpha 1-4 bond and branched alpha 1-6 bond - 20% or starch - Unbranched alpha 1-4 bond II. Glycogen - Stored in liver and muscles - Unbranched alpha 1-4 bond and branched alpha 1-6 bond - Maintain blood glucose level - Provide energy between meals III. Cellulose - Unbranched beta 1-4 bond - Insoluble - Used for plant structure Chapter 17: Lipids Lipids= from plant or animal - soluble in nonpolar solvents - insoluble in water A. Fatty Acids - Carboxylic acids - Fats and oils - 12-18 carbons - Saturated= single bonds, o bad for us, solid at room temp., clog arteries - Unsaturated= double bonds o Cis= large kinks/bends, fewer interactions, low melting point, liquid at room temp. o Trans= straight line, more interactions, higher melting point, solid at room temp. o I. Wax= ester of a saturated fatty acid and alcohol - Found in fruits, leaves, stems = prevent loss of water - Found in skin, fur, and animal feathers = provide waterproof coating II. Triacylglycerol - Fats or oils - Glycerol and 3 fatty acids - Energy storage III. Glycerophospholipids - 2 fatty acids + PO4 + amino alcohol - Lecithin and Cephalin o Brain and nerve tissues o Found in egg yolk, wheat germ, yeast - Polar head and nonpolar tail IV. Sphingomyelin - Sphingosine + 1 fatty acid + PO4 + choline - Made of myelin sheath - Surround nerve cells - Increase nerve impulses - Insulates/ protects nerve cells B. Steroids - All consist of steroid nucleus ( 3 cyclohexane and 1 cyclopentane ring ) I. Cholesterol - OH on carbon3, double bond between carbon 5 & 6, methyl group on carbon 10 & 13, and alkyl chain off carbon 17 - Polar and nonpolar - Made in liver - Found in meats, milk, eggs - Maintain cell, membrane structure - Too much can clog arteries or gallstones II. Bile Salts - Polar and nonpolar - Made in liver - Stored in gallbladder - Helps absorb cholesterol Lipoproteins - Chylomicrons o Transport lipids from diet - VLDS’s o Carry triacylglycerol from liver to peripheral tissues o Storage and energy - LDL’s = bad cholesterol o Transport cholesterol from liver to peripheral tissues o Used in cell membranes and to make steroids o Can cause arterial plagues - HDL’s = good cholesterol o Transport cholesterol back to liver o Convert cholesterol to bile salts III. Steroid hormones - From cholesterol - Communication system C. Eicosanoids - 20 carbons - Unsaturated - Made throughout body - “short-lived chemical messengers” I. Prostaglandins - Lowering/raising blood pressure - Stimulate contraction/relaxation - Produce inflammation, pain, swelling Chapter 19: Amino Acids and Proteins Terms to Know Amino acids- an alpha carbon bonded to a NH3+, COO-, H, and a R group - Essential Amino Acids o Histidine, Isoleucine, Leucine, Lysine, Methionine, Phenylalanine, Threonine, Tryptophan, and Valine Zwitterions- overall net charge of zero - Can form crystals= high melting point - Soluble in water Isoelectric= PI= PH when negative and positive charges balance evenly Cationic- positive net charge, low PH= more H+ Anionic- negative net charge, high PH= more OH- Peptide bond- forms between COO- group and a NH3+ group - Naming Peptides o Combine first 3 letters of amino acids used and separate with hyphens Protein Structures 1. Primary= actual amino acid sequence - Cannot denature= stay the same 2. Secondary= coiling and folding of backbone interaction - Two repeating patterns (alpha –helix=hydrogen bonds between amino acids or Beta –sheet=hydrogen bonds side to side) Ex. Collagen 3. Tertiary= overall 3D shape of R groups -Hydrophilic interaction= noncovalent, must interact with H2O -Hydrophobic interactions= noncovalent, between nonpolar particles -Salt Bridges= noncovalent, between charged particles -Hydrogen bonding- noncovalent, between polar w/ polar, acidic, or basic particles -Disulfide bonding= covalent, must have (-s-s-) interactions Ex. Myoglobin 4. Quaternary= 2+ polypeptides come together Ex. Hemoglobin Protein Hydrolysis= peptide bonds --> amino acids - Break down w/presence of digestive enzyme Protein Denature= disruption of noncovalent interactions - Secondary, tertiary, and quaternary - Due to temp. increase, change in pH, heavy metals