Electric field due to a point charge The electric field in the xy-plane due to a point charge at 10, 02 is a gradient field with a potential function V1x, y2 = k 2x2 + y2 , where k 7 0 is a physical constant. a. Find the components of the electric field in the x- and y-directions, where E1x, y2 = -_V1x, y2. b. Show that the vectors of the electric field point in the radial direction (outward from the origin) and the radial component of E can be expressed as Er = k>r2, where r = 2x2 + y2. c. Show that the vector field is orthogonal to the equipotential curves at all points in the domain of V.
Chapter 11: Cell communication 2/29/16 Cell needs receptor to receive signal If receptor isn't in cytosol then nothing changes, if it is then it enterns through nuclear pore into nucleus Target gene DNA is what hornome receptor. Hormonegene bonding alters gene expression Every cell has the same DNA sequence, but it is the expression of these genes via the hormonereceptor complex that allows the gene to be expressed in the gene Signal processing Not all hormones/peptides can diffuse. Receptor protein embedded in lipid bilayer allow signal transduction pathway o Hormone binds to receptor, signal is sent through cytosol and amplified o G proteins: can bind GDP (guanasine diphosphate) or GTP (guanasine triphosphate) triggers a cell response; inside on periphery of membrane (attached to membrane with a lipid tail). Receptor has G protein bound to it GPCR G protein coupled receptor When signal binds to receptor it changes the G protein making it detach and go from GDP to GTP which activates the protein and it splits to bind to enzyme (transmembrane protein) which produces the second messenger Second messenger: molecules made in the cell that carry signals to trigger a cell response o Enzymelinked receptor: triggers protein activation within cell Intrercellular signal is sent > transmembrane protein receptor in bilayer (ectodomain; pokes inside and outside of bilayer) > signal is tranduced to intracellular signal > signal is picked up by other molecules with amplifies it > cell activity changes causing the cell to respond cAMP is a secondary messenger that can stimulate the activity of protein kinase A and other proteins o First messenger > receptor > G protein > enzyme (adenylyl cyclase (catalyzes the conversion of ATP to cyclic AMP (cAMP))) > secondary messenger (cAMP) > protein kinase A > target proteins BE ABLE TO DRAW THIS PROCESS IP3 (inasonal triphosphate) and Ca2+ secondary messengers DRAW THIS PROCESS o Signal molecule >receptor > g protein activation > phospholipase C enzyme to cleave PIP2 to DAG (dyasal glycerol) and IP3 (second messenger) > diffuse through cytosol and binds to smooth ER > smooth ER stores calcium and IP3 acts as a gated channel which allows Ca to leave ER as second messenger > proteins are activated in cytosol > cellular response Amplification: a single hormone can stimulate the production of many secondary messengers RTKs (receptor tirosine kinases): are enzyme linked, not G protein linked. Able to phosphorylate other proteins. It's a dimer (has two pieces to it). Two pieces must collide in order for it to be activated. Signal binds to one part and the other is attracted to it and then it dimerizes (comes together) Ectodomain: outside part that receives signal Transmembrane: holds receptor in membrane Signal transduction o Signal binds and it dimerizes > RTK autophosphorylates (adds a phosphate group to itself) > Ras protein (a G protein because it is GDP when innactive and GTP when active) with one subunit is activated (GTP) because it's bound to RTK via bridging proteins > RAS protein activates a protein by bringing in the protein to activate the other protein Chapter 11: Signaling 3/2/2016 Adenylyl cyclase (in the membrane) catalyzes the conversion of ATP to cyclin AMP (cAMP) Kinase: an enzyme that phosphorylates other proteins Receptor tyrosine kinase (RTK): only phosphorylate the amino acid tyrosine (has a free OH group for phosphate group to be added to). auto phosphorylates and then acts as a docking site for other proteins (Ras) 1 Signal binds outside of cell to a transmembrane receptor 2 Conformational change triggers receptor phosphorylation inside of cell 3 Causes Ras (not a kinase) to bind GTP and remove GDP; Ras in now activated 4 Acivates Ras triggers a phosphorylation cascade (every protein after Ras is a kinase): kinases are sequentially activated Signal responses: signal transduction changes activity of target cell at a distance (cells are far apart) Gene expression a change in which genes are being expressed in the cell Activation/deactivation of a particular target protein that already exists in the cell Signal deactivation: allow cell to remain sensitive to changes in order to stop producing secondary messengers G proteins convert GTP back to GDP; changes the shape so cannot bind anymore Extracellular signal is no longer produced Phosphatases: enzymes that remove phosphate groups from proteins (may not always inactivate a protein) Crosstalk: integrates diverse signals a cell receives interactions between signaling pathways. Elements or products from one pathway may afeect another Adjacent cells: gap junctions, desmosomes MAKE A MAP FOR A RECEPTOR TYROSINE KINASE PATHWAY AND A GPROTEIN COUPLED RECEPTOR PATHWAY Chapter 8: Energy 3/4/2016 Kinetic: energy in movement Potential: energy in position; more unstable = higher Ep Further electron is from nucleus the more Ep Free energy: amount available to do work *spontaneous reactions have lower potential energy and higher entropy than the reactants Potential energy drops when electros are held more tightly in products than reactants o Unequal electronegativities = low Ep o Equal electronegativities = high Ep Gibbs freeenergy change: indicates whether a reaction is spontaneous or requires energy Delta G = delta H T delta S G = spontaneous (exergonic) +G = requires energy (endergonic) G=0 = reaction at equilibrium Enzymes don't effect the delta G of reaction Catalysis: acceleration of chemical change in order for reaction to happen Enzymes bring molecules together so that they may react; lowers activation energy *reaction rates depend on the kinetic energy of the reactants and the activation energy (Ea) required to achieve the transition state *Delta G does not say anything about speed of reaction Induced fit model: when the enzyme binds to the substrate, causing the enzyme to change shape Enzyme catalyzed reaction steps 1. initiation, reactants are corrently oriented and bind to active site 1 Transition state facilitated: enzyme facilitated chemical reaction 2 Termination: products are released from enzyme Enzyme phosphorylation: causes a conformation change in the protein Cofactors: inorganic ions that bind to enzyme to make it change shape Coenzymes: organic molecules bind to active site to help with correct shape of enzyme active site for substrate Competitive inhibition: a molecule similar to substrate that fits into active site and prevents the actual substrate from binding with enzyme Allosteric regulation: binding sites other than active site that a molecule binds to change shape of enzyme to either activate or deactivate it Limiting the rate of catalysis when substrate concentration is low the speed of enzyme catalyzed reaction is linear; at high substrate concentration the reaction rate plateaus at maximum speed