MIT-SCIENCE-Lectures-fa01lec08 (2)
MIT-SCIENCE-Lectures-lec03 (2)
Lecture Notes - 37.24/7.88J/5.48JThe Protein Folding Problem• Reprise RNase refolding• General Features of Globular proteins• Interior PackingRnase RefoldingWe can cartoon the experiments:Assume that reduced form is unfolded and populates an ensemble of unfolded states in 8M urea:[U]Rapidly exchanging statistical ensemble of random coils[I]???[N]Native fold, $ S-S bonds, 1 out of 105 possible sets of S-S bonds [Aggregated]Non-native (no enzymatic activity), non-native (scrambled) disulfide bonds.At the end of the reaction we have native stateSoluble inactive – misfolded or perhaps small oligomersPrecipitated: Anfinsen showed that these were S-S bonded network = he called “scrambled”Critical question is nature of the intermediates as go from here to there:If there was a sequence in which these bonds formed, and one could figure out the sequence or pathway, it might give you considerable information on the steps in the folding pathway.So certainly we need to understand native-fold, and interactions that determine it, stabilize it once formed;However this does not solve problemWe will return to the question after reviewing the general anatomy of globular proteins, which will occupy most of next week.General features of 3-D structures of solved proteins; Globular, Soluble proteins:A. Isolation and CrystallizationThe first crystals of proteins sufficiently large and ordered to diffract X-rays were prepared of the digestive enzyme pepsin:Bernal, J.D., and Dorothy Crowfoot. Nature (1934): 133, 794.This was followed by crystals of insulin, Lactalbumin, hemoglobin, andchymotrypsin:Bernal, Fankuchen, and Perutz (1938)The rise to power of the Nazis in Germany and Italy and the outbreak ofwar brought all these studies to a halt. Bernal led the world scientificcommunity into opposition to the fascists. This was not only with respect to the their persecution of Jewish scientists, but that the notion of Aryanscience different from the general growth of knowledge, represented abroader attack and the growth and communication of knowledge.The rebuilding and repopulating of the civilian biomedical infrastructuretook about ten years, and re-launched in the 1950’s. In England - BritishMedical Research Council, in US - National Institutes of Health.Solution of Myoglobin structure by John Kendrew in 1958 and hemoglobin structure in 1962 by Max Perutz - it became clear that alpha helix actually present in globular proteins. With the solution of the lysozyme structure by David Phillips (1966), revealed that anti-parallel beta-pleated sheet alsopresent in globular proteins.B. Review Criteria (Biases) for the selection of proteins forcrystallization and perhaps into the success or failure ofcrystallization1. Available in large quantities - usually extracellular protein fromextracellular fluids• Hemoglobin from blood• Myoglobin from muscle• Lysozyme from egg white/ tears??• Ribonuclease from stomach??• Insulin from pancreas??• Lactalbumin from milk ??• Chymotrypsin; from saliva, stomach??2. Stable during purification• Resistant to Residual proteases• Does not aggregate• Resistant to Cold denaturation3. Very soluble in aqueous buffersThis excludes:• Fibrous proteins; evolved to interact with each otherto form structures; keratin, collagen• Other Structural proteins; ribosome structuralproteins, histones, actins, tubulins• Membrane proteins4. Must crystallize• Proteins which behave differently than the dogma;take multiple conformations in solutionProtein database sharply under-represents – fibrous proteins, structural proteins, membrane proteinsC. Structures whose atoms have been located at high resolution- Globular aqueous soluble: 1,100 domains(- Membrane: 12)(- Fibrous: 5)This is the class of proteins for which single crystals have been obtained.Clearly the most extensive database is for proteins soluble in aqueoussolutions and which form crystals.D. General Features of Crystallized Globular Proteins1. Surface/Volume RelationshipsGlobular proteins have relatively sharply defined:• Exterior Surface = H20 Interface• Interior volume - Is the interior of a native proteincrystalline or oily?A quantitative answer to this was given by Richards:"The Interpretation of Protein Structures: Total Volumes, Group Volumes and Packing Density" Frederic M. Richards (1974) J. Mol. Biol., 82, 1 - 14.Problem comes down to calculating how densely packed atoms are inprotein molecules?We can define the packing density of a molecule as:Volume of its van der Waals envelopes of its constituent atoms / actual volume of the intact folded moleculeThis value is dimensionless- Close packed hard spheres = 0.74- Close packed infinitely long cylinders = 0.91- Crystals of various small organic molecules 0.70 - 0.78 values (<0.6very rare)The van der Waals radii - from interatomic distances of nonbondedatoms in organic crystals.However calculation of the volume of irregular structures not trivial.Richards’ procedure made use of a geometrical construct calledVoronoi polyhedra.• Draw vector from each atom to closest surroundingatoms.• Draw a plane through it corresponding to intersectionof van der waals radii. This will define a polygon.• When you do this for all atoms space is completelyfilled.• Thus obtain geometrically legitimate volume. Cancompute this from atomic coordinates.For the following solved proteins, the average packing density:• Hen egg white lysozyme = 0.75• Ribonuclease S = 0.74Conclusion: The interior of globular proteins is as tightly packed as areamino acids in organic crystals.Subsequent investigations have supported this general result for thatset of proteins included in crystallized set.Counter argument; rigidity necessary for crystallization is only found inthose proteins which are continuously dense and lack hinges.2. Are there interior cavities or entrained solvent bobs?Careful examination of a larger set of proteins was carried out byA.A. Rashin, Michael Iofin, and Barry Honig (1986) "Internal Cavities and BuriedWaters in Globular Proteins" Biochemistry, 25, 3619-3625.These procedures involve in general:• Construction of Van der Waals radii;• Find places where these radii not buried or in contact with other radii;• Use a spherical probe (water model = sphere radius 1.4A) walkalong van der Waals radii with smaller and smaller probe to findplaces that can walk alongAccessible surface area is defined by center of water molecule rollingover van der Waals surface. Thus there exists inaccessible surface area.Gives an estimate of volume of cavity and accessible surface area.H2Os# Protein MW#VolA3Pancreatic Trypsin Inhibitor 6,000 2 70 4cytochrome c 11,000 5 34 24115ribonuclease 13,000egg lysozyme 14,000 8 190 54019erythrocruorin 14,0001391Myoglobin 17,0002317494trypsin 23,00013chymotrypsin 26,000 26 571 10• Cavities = less than 2% of the volumes of theseproteins.• No single cavity can host a probe of 2A or more.• Almost all cavities become connected to proteinsurface as probe diameter goes down to 0.4 A.What does this suggest?Suggests that these represent channels or hinges.Volume of internal water molecule for larger cavities is about 30AVan der waals radius of water is about 1.4 ASome cavities which appear non-polar can contain a water moleculeforming three hydrogen bonds. This is because the hydrogen bond canbe longer than the sum of the van der waals radius of a polar atom anda probe., and thus some polar atoms with which water forms hydrogenbonds may not contribute to the accessible surface.Note: those cavities that seem to be empty could be contributing boundwater, but if water crystallographically not fixed, smeared out.3. Functional Significance of small cavitiesLargest empty cavity in their sample located between helices B, E, andG, between two domains of the globin.Conserved in six other myoglobin type proteins (Very diverse). May beimportant for relative motions of helices.More than half of cavities in multi-domain proteins are at domaininterfaces.He considers similar, linkage explanation, rather than packing problem.Prediction; Those sequences that have evolved can close pack?Question: WHAT FRACTION OF amino acid sequences is there noclose packed globular structure?For retinal containing pigments models suggest that cavity of 100Awould allow for rotation of chromophore.Further studies carried out by:"Interior and Surface of Monomeric Proteins" Susan Miller, Joel Janin Arthur Lesk and Cyrus Chothia (1987) J. Mol. Biol., 196, 641-656.For example lysines and arginines almost always at surface (<4%buried)4. Additional Features of Inside OutsideGeneral Features of Globular proteins• No Knots• More than half of the polypeptide sequence isorganized into regular secondary structure,predominantly alpha helices and beta sheets• Interiors are densely packed - Extremely rare to burybulk solvent• Buried charges very rareo In rare cases, ion pair, metal complex, oractive site• Interiors are hydrophobic (carbonyls and amides areH-bonded)• A large fraction of the accessible surface of theextended polypeptide chain is buried in the proteininterior.E. Conclusions re protein folding1) Buried side chains truly removed from water: Major energetic contribution toprotein folding; but driving force, as originally proposed by Walter Kauzmann, is entropic effect on water structure; hydrophobic residues cannot H bondwith water; organizes water molecules with respect to own partners.2) These side chains almost always hydrophobic: extremely rare to burycharged side chains; If the inside of a protein is closely packed and excludes water, becomes quite clear that in fact the inside and the outside are verydifferent environments. Therefore the partitioning of residues into the chainbetween interior and surface positions may be very important in defining fold.3) Contradiction: Burying side chains also requires burying backbone; butbackbone has Carbonyl oxygens and amide nitrogens which are hydrophilic, polar groups;4) But in actual fact, largest number of peptide bonds in proteins are partof regular secondary structures, alpha helices and beta sheets: partialcharges are neutralized by maximal hydorgen bond formation:5) SO naively folding processes may have at least two level of organizationFormation of secondary structure, docking against each other to formtertiary structure; Framework model:Now clearly, given the large fraction of chain that is in regular secondarystructure, a substantial fraction of the internal packing of globular proteins is the...So at least two processes that we need to investigate:• Formation of secondary structure;• Next level; packing of secondary structure into tertiary structure: Might be tightly coupled;F. Packing of Secondary StrcuturesOne of the determinants of the shapes of proteins and the folds is thepacking of the units of secondary structure against each other.Short amino acid sequences = peptides > At room temperature in constantmotion; flickering in and out between a variety of conformations;Homopolymers; In solution also flickering in and out between non-regularconformations and mixture of these with alpha helices;Two levels of Packing:• Within units of secondary structure; alpha helix, beta strands• Between units of secondary structure- helix/helix, helix /sheet• Packing Interactions critical for formation of native structure.。
麻省理工MIT(微观经济学)lec01_02_orderings and utility representation
14.123 Lectures 1-2, Page 3
Introduction
• Economics is about explaining and predicting choice. • It is assumed that economic agents choose their most desirable alternative among the set of feasible ones. – Interpret it “as if”, not necessarily “deliberate”. – “This morning I took the shuttle to MIT because this was the best possible way to come in.” Discuss. • Desirability is represented by preferences and/or utility. – Attitudes may be expressed over outcomes never experienced (Would you prefer to be Superman or Spiderman?).
14.123 Lectures 1-2, Page 6
Utility Representation
• DEF. Utility fcn u : X → represents if u(x) ≥ u(y) x y. • THM: If u represents , then is complete and transitive. ■ Follows from the same properties of ≥ on real numbers. ■ • THM: If X is finite and is complete and transitive, then there exists a utility function that represents . ■ u(x) = |{y∈X : xy}|: # of alternatives that x beats weakly.■ • THM: If X is countable and is complete and transitive, then there is a utility function with a bounded range that represents . ■ X ≡ {x1,x2,…}. Let u(x-1)=0, u(x0)=1. For all n=1,2,…, set u(xn) = [max{u(xk)|xnxk,n>k} + min{u(xk)|xkxn,n>k}]/2 .■
MIT-SCIENCE-Lectures-lecture_notes2
∞ �
where βn are arbitrary constants, corresponds to a function vanishing t > |T/2| ,that is, a time-limited function. The surprising import of (2.13) is that the Fourier transform of a time-limited function can be perfectly reconstructed from a knowledge of its values at the Fourier series frequencies alone. That means, in turn, that a knowledge of the countable infinity of Fourier coefficients can reconstruct the original function exactly. Putting it slightly differently, there is no purpose in computing a Fourier transform at frequency intervals closer than 1/T where T is either the
Exercise.
�
x ˆ (s) =
ignoring all convergence issues. We thus have the nice result that a periodic function has a Fourier transform; it has the property of vanishing except precisely at the usual Fourier series frequencies where its value is a δ−function with amplitude equal to the complex Fourier series coefficient at that frequency.
MIT-SCIENCE-Lectures-lec09 (2)
7.88 Lecture Notes - 97.24/7.88J/5.48JThe Protein Folding Problem• Fluorescence spectroscopy• Denaturation and Denaturing agents• Denatured State as a random coil (First Approx.)• Renaturation/Refolding Protocols• Detection of partially folded IntermediatesSo far we have examined the experimental evidence for three cases• Ribonuclease S• Heptad Repeat protein -Tropomyosin ; Coil <> helix transition in aqueous solution:• S-peptide coil >helix transition in solutionHowever, as we noted earlier the 22,000 + proteins in the protein database are primarily soluble globular proteins; And probably more than half to 3/4 of the proteins encoded by genomes are in this class:So need to understand how sequence drives fold, or to be A probably the majority of proteins encodedMethods for the study of the conformation of folding intermediatesA. Fluorescence SpectroscopyJ. R. Lakowicz Ch 23 pp518-567Many molecules that absorb light in the UV or visible spectra, also re-emit photons, at longer wavelength: FluorescencePhe Tyr and Tryp absorb in the region of:Amino Acid Abs max (nm) Molar absorbance M-1 cm-1197 Phe 257.41420 Tyr 274.65600 Tryp 279.8Absorbance A =log10(I o/I):I o is transmittance by reference solution, I is transmittance by sample.Molar absorbance is = A/bc, where b is path length in centimeters, and c is concentration in moles/liter280mu. Phe peak is about 255 but 1/20 that of tryp peak at 280.Absorption in this region of the spectrum is due to changes in electronic energy levels, levels of orbital electrons.Photon absorption occurs in 10(-15) seconds, so short that nucleus doesn't change much in time interval; so goes up in energy level almost instantaneously , but lifetime is much longer, 10(-8) seconds.Return to ground state usually multi-step:• small losses of energy in atomic collisions >> Goes back to lowest vibrational energy level state of excited electronic state (faster than emission);If molecule doesn't blow up, then after short period of time,• returns to lowest energy level emitting a photon; since excited state has lost a little energy, then photon emitted will be lower energy, longer wavelength thanphoton absorbed;Lambda max for fluorescence:2820.04Phe0.21303Tyr0.20Tryp340Emission occurs on nanosecond time scale; Process occurs like radioactive decay I = I o e (-t/g), where t is time after end of light, g is average lifetime of fluorescent state; Because emission is a property of valence electrons, sensitive to environment;Fluorescence; tryptophane: in water 350; buried in proteins 330.Native florescent spectrumDenatured fluorescent spectrum:B. Denaturation and the Denatured StateThese studies were carried on purified chains refolding in vitro; of course in cell s chainsreleased from ribosomes, but some 20 years passed before it was possible to studyprotein folding intermediates in vivo:Now let’s consider studying this problem for a complete polypeptide chain of a globularprotein in the general case, for example globin with its 7 helices; to examine the foldingpathway for the globin chain in the test tube, we would need unfolded molecules;We also need to reach the unfolded or partially unfolded state to recover active forms of incorrectly or misfolded molecules; Eli Lilly manufactures human insulin by expressingthe cloned gene in E. coli. When they harvest the cells the insulin chains accumulate asan insoluble mass called an “inclusion body”. In order to obtain biologically activeinsulin the chains must be solubilized and then refolded in vitro.It turns out that maintaining an unfolded state of biologically evolved polypeptide chains is not trivial In order to investigate how chains reach their native state, need access to some definedunfolded –denatured state.In order to recover correctly folded forms of incorrectly folded or misfolded proteins, alsoneed denatured statePractical;To maintain proteins active, need to understand processes of denaturation.To recover proteins from denatured states, need some knowledge thereof. IN factgeneral result of cloning gene into expression vector, is generation of non nativeaggregated state called an inclusion body:Obtaining native protein requires successfully refolding in vitro;• Requires access to soluble state• Method to study basis of stability of native conformation.• To study folding pathway, need defined unfolded starting state.Denaturation; Process of the loss of nature structure: associated with unusual phasetransition associated with structure loss: upon mild treatment:The denatured state is usually identified by the• Loss of biological functionso Loss of catalytic activityo Loss of ligand binding propertieso Loss of antibody recognition: and• Change in solution propertieso Increased viscosityo Aggregates large enough to scatter lighto Change in spectroscopic properties.Under conditions in which Covalent modification not detectable - The term denatured refers to an operation: it’s the description of a state in terms of having passed through operation.Denaturing Agents:Globular proteins can be denatured with a wide variety of agents:• Heato Denatured chains usually partially structured and aggregated (treatment with additional denaturing agents causes further changes).o Often not reversible on cooling outside very narrow set of conditions.o Covalent side reactions as temperature increases.Tropomyosin is an exception!• pHo Ionization of side chains breaking ion pairs, salt bridgeso Denatured chains highly charged:o Increased charge density leads generalized electrostatic repulsion;o Unfolded chain is structured• Organic solventso Benzeneo Phenolo Trichloroethyleneo Acetoneo Ethanolo Chloroformo Acetonitrile- Often neither native nor denatured state soluble in these solvents- Difficult to compare conformations between immiscible solvents- Some induce alpha-helicity, like TFE• Detergentso sodium dodecyl sulfate- Enormously important for analysis; denatured state binds1.4gm/gram of detergent - denatured state is highly structured:- Often is micellar form that is strongly denaturing; so detergent must be above cmc, critical micelle concentration;- Difficult to remove detergents rapidly and efficientlyo Lithium bromideo Sodium bromideo potassium thiocynate (KSCN)- However, not general ionic strength, NaCl, KCl don't do it.- Ammonium sulfate is stabilizing• High Pressureo Useful for multimeric proteins; dissociation reaction• Organic soluteso UreaNH2 - C=0 - NH2- Not an electrolyte: effects sensitive to pH and ionic strengtho Guanidinium HydrochlorideNH2 - C = (NH2+Cl-) - NH2- Strong electrolyte. So denaturation always coupled with high ionicstrengthExperimental work on protein unfolding as a pre-condition for establishing an unfolding refolding equilibrium is dominated by two reagents;C. What is the State of these Denatured Molecules?In both of these solvents -urea and GuHCL - a wide variety of proteins are denatured to species that approximate very closely to random coils. For example, for a true random coil, whose end to end to distance or radius of gyration is described by:Sensitive measure of molecular volume is viscosity; unfolded chains occupy largervolume than folded, and so interfere with fluid flow, increasing viscosity; Viscosity is a measure of work done to produce a given rate of liquid flow; represents resistance toliquid flow;Add solute, viscosity generally increases.When protein denatures, interaction –binding- surface with solvent increases sharply, >> viscosity increases;Intrinsic viscosities of native and GuHCl (5.0 -7.5M) denatured reduced chains(b-MeTh) –25Certain inorganic salts•Protein MW Native Denatured/Reduced RNase 13,700 3.3 16.6 9.4Lysozyme 14,300 2.7 17.1 6.5Hemoglobin 64,500 3.6 18.9beta lactoglobulin 36,800 3.4 22.8 19.8tropomysosin 76,000 45 33For a truly random coil, intrinsic viscosity is directly related to molecular weight throughan equation of the general form[Have to extrapolate to zero shear to make sure molecules aren't orienting in solution.]etaMo = An bWhere Mo is the mean molecular weight of the amino acid residues;n = number of residuesFinding of a straight line relating log of etaMo to log of Anb Determination of viscosityversus molecular weight after denaturation is good evidence for a random coilconformation in the resulting chainsC. Tanford, K. Kawaharas, and S. Laopanje (1967)Proteins as Radnom Coils. I. Intrinsic viscosities and sedimentation coefficients in concentrated guanidine hydrochloride JACS 89 729.For GuHCl Tanford found A = 77.3, b =0.666If plot logarithmically log {viscosity] M versus logn [n] get linear relationshipHere is data from Charles Tanford on the linear variation of intrinsic viscosity as afunction of chain length for polypeptide chains in high concentrations (5 - 7.5 M GuHCl)at 25°C.log[eta]M olog nA similar result is obtained with the same proteins in 8M urea, with very smalldifferences in parameters, A =76, b =0.655.One care need to take with urea, at neutral and alkaline pH decomposes slowly to form cyanate ion. This reacts with free amino groups to form carbamyl derivatives.D. An Equilibrium Denaturation ExperimentNative protein in buffer: dilute to increasing concentrations of urea: examine properties; for example enzyme activity and fluorescence quenching of tryptophanesIncubate until no further changes:Cautions: urea decomposes to reactive cyanates; watch out for metals contamination: need to re-crystallize ultra-pure stuff;In folded state, prolyl peptide bonds stabilized by folded structure; in unfolded state, isomerization proceeds in solution; very slow; at equilibrium cis trans prolyl peptide bonds different than in first few minutes after unfolding:The general nature of the denaturation process, somewhat independent of method is that it is usually highly cooperative, showing a steep change in the state with the variable. Looks like sloppy phase transition;That is, the molecules are either native or denatured, with limited evidence of intermediates. Thus in the transition state have mixture of native and denatured. Like phase change.The Mechanism of Urea and Guanidinium Denaturation:Large literature on action of GdHCl on proteins, but still no mechanism. This is flip side of the very limited ability to assess what is holding the protein together - high concentrations necessary Organic solutes -Strong electrolyte. So denaturation always coupled with high ionic strength for denaturation, for example 6M, these reagents are occupying roughly half the solvent volume. General notion is that they are acting changing the structure of water.Two studies that give some notion of what is going on:Hibbard and Tulinsky Biochemistry 17, 5460-5468. Equilibrated crystal of alpha-chymotrypsin with 2MGuHCl or with 3M urea and examined diffraction pattern. Obviously this is below denaturation transition, but approaching it.GDHCl disrupted primarily surface of molecules in crystal. Solvent becomes better solvent for surface chains.Urea appeared to diffuse into molecule; perhaps solvates non-polar groups otherwise buried. non-polar M.What about proteins lacking disulfide bonds:E. Criteria for existence of partially folded intermediatesDuring equilibrium unfolding and refolding experiments:Protein diluted into various concentrations of denaturant: incubated until no change in signal; (determine empirically)Renaturation: Fully denatured protein diluted back to increasing concentrations of buffer; samples it until no further change in signal;In reading for Thursday you will see that time this sample has incubated in denaturant isa critical variable in refolding kinetics”1. Complex Equilibrium denaturationHere is equilibrium denaturation/renaturation experiment:If curve has a break in slope, normally interpreted as due to presence of apartially folded intermediate at intermediate denaturant concentrations: This isdata forIn the middle of the transition at last three species populated to some extent, U, I, and N2. Non coincidence of signalsHere is denaturation curve for a protein, in which experimenters following twodifferent signals: fluorescence and circular dichroism;Fluorescence groups being exposed to solvent at lower GdHCl concentration that overall backbone unfolding:Suggests that partially folded species formed, with region around tryp disordered, but most of protein intact:3. Occasionally see third class of curvesHere is one for RNase T from Pace et al RNase T: fluorescence increases, then decreases; Can have other kinds of curvesNow of the utmost importance to distinguish kinetic experiments - initiate reaction follow course, under conditions that back reaction not significant, and equilibrium experiment, in which ignore pathway, examine only distribution of end states:In a kinetic experiment evidence for more than two states would come frompresence of more than one kinetic phase:• If only one transition, U >>N, then expect single rate process:• If in studying kinetics observe complex kinetics, for example:- Initial fast rate followed by slow rate followed by much slower rate, evidence that more than one process going on, must be at leastone other species present;Let’s review point about intermediates:If only two states, then fluorescence either 2 (native) or 1 (quenched) (tryp 59)Lets say monitor some other signal, CD alpha helicity: value is 2 or 5; Then both curves will of necessity have same shape; all values simply sum of two populations:If partially folded intermediate, its properties could differ from N and U: Its tryp could be buried, as in N (f=2), but its helices only partially formed - say CD value three:Then CD curve would differ from fluorescence curve:Then as proceed through folding transition, these values follow distribution of partitioning;Part C。
MIT-SCIENCE-Lectures-00f_mid1
14.12Game Theory–Midterm IInstructions.This is an open book exam;you can use any written material.You have one hour and 20minutes.Each question is33points.Good luck!1.Consider the following game.1\2L M RT3,24,01,1M2,03,30,0B1,10,22,3a.Iteratively eliminate all the strictly dominated strategies.b.State the rationality/knowledge assumptions corresponding to each elimination.c.What are the rationalizable strategies?d.Find all the Nash equilibria.(Don’t forget the mixed-strategy equilibrium!)2.Consider the following extensive form game.Xa.Find the normal form representation of this game.b.Find all pure strategy Nash equilibria.c.Which of these equilibria are subgame perfect?3.Consider two agents£1,2¤owning one dollar which they can use only after they divide it.Eachplayer’s utility of getting x dollar at t is-t x for- 0,1 .Given any n 0,consider thefollowing n-period symmetric,random bargaining model.Given any date t £0,1,T,n"1¤, we toss a fair coin;if it comes Head(which comes with probability1/2),we select player1;if it comes Tail,we select player2.The selected player makes an offer x,y ¡0,1¢2such that x y t1.Knowing what has been offered,the other player accepts or rejects the offer.If the offer x,y is accepted,the game ends,yielding payoff vector -t x,-t y .If the offer is rejected, we proceed to the next date,when the same procedure is repeated,except for t n"1,after which the game ends,yielding(0,0).The coin tosses at different dates are stochasticallyindependent.And everything described up to here is common knowledge.pute the subgame perfect equilibrium for n 1.What is the value of playing this gamefor a player?(That is,compute the expected utility of each player before the coin-toss,given that they will play the subgame-perfect equilibrium.)pute the subgame perfect equilibrium for n pute the expected utility of eachplayer before the first coin-toss,given that they will play the subgame-perfect equilibrium.c.What is the subgame perfect equilibrium for n u3.。
MIT-SCIENCE-Lectures-fa01ps01
– O O P O – O H H 2C C O C O CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 C O O C H
H C H O C O CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 C O O C H H
H C
– O O P O – H O C H2C
O O C O C CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2 CH2
*Minoxidil is uncharged in its active state
H2 N
N N H2 N N NH 2 2
Minoxidil
a) Below is a schematic of a Minoxidil binding site on a hypothetical protein. i) Draw the side chains at amino acid positions 51, 129, 134, and 167. ii) Draw Minoxidil as shown above binding in the site. Be sure to consider the interactions between Minoxidil and the side chains when orienting Minoxidil within the binding site.
MIT-SCIENCE-Lectures-fa01lec06 (2)
24.00: Problems of PhilosophyProf. Sally HaslangerOctober 3, 2001RacismsI. Racist PropositionsAppiah distinguishes three importantly different ideas relevant to race and racism:Racialism:...there are heritable characteristics, possessed by members of our species, that allow us to divide them into a small set of races, in such a way that all the members of these races share certain traits and tendencies with each other that they do not share with members of any other race. These traits and tendencies characteristic of a raceconstitute, on the racialist view, a sort of racial essence; and it is part of the content of racialism that the essential heritable characteristics...account for more than the visible morphological characteristicsskin color, hair type,facial featureson the basis of which we make our informal classifications. (5)In other words: A racialist is one who maintains that people who appear similar on the basis of certain inherited physical characteristics (such as skin color, hair type, facial features) share a distinctive "racial essence" that is responsible for a range of psychological and behavioral traits and tendencies.ï Appiah argues (elsewhere) that racialism is false: There is no "racial essence" (genetic or otherwise) underlying the morphological features shared by members of what we count as races that is responsible for (supposed) similarities in traits and tendencies among members of racial groups. In other words, even if there are what we might call superficial races,i.e., groups of people who share certain inherited visible features, there are no racial kinds, i.e., groups unified by sharing a racial essence.ï A consequence of Appiah's denial of racialism is that if there are any psychological/behavioral similarities ("common traits and tendencies") among members of "superficial races", this is due either to historical/cultural/social causes, or it is due to contingent natural correlations, e.g., it might be that the members of genetically isolated groups are similar in many ways, both visibly and psychologically, but in such cases one cannot assume that there is an underlying "nature" or "essence" that explains all the similarities. The correlation of visible and psychological features may be accidental, or due to contextual features, and may break down immediately when the group disperses or when the group's genetic isolation ends.ï Appiah maintains that racialists are wrong in the sense that the hold a false or incorrect view, but because racialism makes no moral or evaluative claims (it doesn't say anything about what's good or bad, what we ought to do or not do), there is nothing wrong morally speaking in being a racialist. As he puts it, racialism "seems to be a cognitive rather than a moral problem." (5)Extrinsic racism:...extrinsic racists make moral distinctions between members of different races because they believe that the racial essence entails certain morally relevant qualities. The basis for the extrinsic racists' discrimination between people is their belief that members of different races differ in respects that warrant the differential treatment,respectssuch as honesty or courage or intelligencethat are uncontroversially held...to be acceptable as a basis fortreating people differently. (5)In other words: An extrinsic racist maintains that people of racial group X tend to have the property P, and P is a morally objectionable property (such as dishonesty, laziness, irrationality, etc.) So we are warranted in treating people of racial group X differently (i.e., worse) than others (for at least some apparent racial group X).Intrinsic racism:intrinsic racists..are people who differentiate morally between members of different races because they believe that each race has a different moral status, quite independent of the moral characteristics entailed by its racialessence....an intrinsic racist holds that the bare fact of being the same race is a reason for preferring one person to another. (5-6)In other words: An intrinsic racists maintains that people of racial group X are inherently morally inferior (for at least some apparent racial group X).ï Appiah points out, however, that it would be "odd" to call someone a "racist" if they just happened to be ignorant of all the facts. E.g., someone brought up in a remote location might have only false information about X's and so come to hold what look like racist beliefs; but if in the face of new (and better) evidence she easily corrects her beliefs, then even if she holds some racist beliefs, there is a sense in which she is not a racist.ï So, he suggests, racism is not just a matter of what you believe, but how you believe it: does your belief rest on the evidence you have available to you (or could easily get), or are you unable or unwilling to take advantage of the available evidence? Those who exhibit a pattern in their inadequate attention to the evidence have a "cognitive incapacity"on Appiah's view this is a form of irrationality--and this "cognitive incapacity" is the source of their racism. They exhibit "distortions of judgement" (8) possibly due to self-interest, self-deception, internalized racist stereotypes, etc.II. Racial PrejudiceGiven these observations, Appiah defines "racial prejudice" as follows:Racial prejudice consists in "the deformation of rationality in judgment [viz., their systematic "incapacity" to collect and assess evidence responsibly] that characterizes those whose racism is more than a theoretical attachment to certain propositions about race." (8) On this view, racial prejudice is a kind of cognitive flaw. For those who are ignorant and hold racist propositions because they have not been exposed to all the evidence, there is hope that more information will lead them to see the error in their views. But those who suffer from racial prejudice need more than information; they need to learn skills of critical reflection that enable them to see through the distortions of ideology and self-interest. (9-10)III. Racism and MoralityAppiah suggests that racism is symptomatic of a kind of irrationality. In the case of extrinsic racists, it consists in a failure to be responsive to evidence concerning the (supposedly inferior) racial group in question, e.g., to evidence whether they really have the questionable property P, and to reasoning concerning the link between generalizations about the group and moral judgements.In the case of intrinsic racists, however, the racism does not lie in the incorrect attribution of certain observable properties to members of a group (it is not like miscalculating whether Whites can jump, or whether Blacks "have rhythm"); the attribution in question concerns moral worth. The intrinsic racist asserts that some groups have greater moral worth than others (or that some individuals, because of their race alone, are more worthy of my regard or loyalty, etc.). Is the intrinsicracist's failing, if it is a failing, a cognitive error? Is it a failure of rationality? Or is it, as Appiah sometimes suggests, (also?) a kind of moral failure?Appiah suggests that the intrinsic racist exhibits a kind of distorted rationality insofar as he under the influence of an ideology that serves the dominant group (8) and uses the racist beliefs "as a basis for inflicting harm" (10). Sometimes intrinsic racism is not used as a basis for harm and is not connected to the power of the dominant group, in which case it is not clearly racism, and not clearly irrational. For example, racially subordinate groups sometimes build solidarity with each otherAppiah mentions Zionists and Black Nationalistsby maintaining that race, in and of itself, is morally significant. Although one might argue that at least some members of these groups use race as a basis for inflicting harm, the relevant question is whether it is ever permissible to hold views that are intrinsically racist. Appiah suggests that it is. Do you agree? Are intrinsic racist beliefs less problematic for some groups than others?But the "distorted rationality" Appiah is trying to point out in the case of intrinsic racists is nothing like a failure to appreciate evidence. Ultimately Appiah's argument is that intrinsic racists misunderstand the nature of public morality. It may be that we are allowed to form special attachments to others, attachments that are based on arbitrary likes and dislikes, in the private domain, e.g., of family. But these special attachments are not allowed to influence us in contexts where morality is at stake. It may be OK to give a birthday gift to your mother and not your professor; but it is not OK to keep your promise to your mother and not to your professor. You must keep all your promises. What the intrinsic racist fails to understand is that from the moral point of view, race is not a legitimate basis for making distinctions between individuals. So the intrinsic racist, on Appiah's view, doesn't simply exhibit a cognitive failure, but also a moral failure.Questions:ï On what basis does Appiah claim that race is not morally relevant? He suggests that it to deny this is to go "against the mainstream of the history of Western moral philosophy" (14). But does he have an argument for it? Does he have evidence for it? How could one go about arguing that race is not morally relevant?ï Could an intrinsic racist charge that Appiah's reliance on the idea that race is morally irrelevant is itself a bit of ideology, i.e., that it is the articulation of a particular "practical consciousness" found in the West? Does saying this show that the idea is false or distorted or problematic?IV. Return to PragmatismIs Pragmatism a good guide to what is epistemically justified? Is it a good guide to what is practically justified? Consider first epistemic justification, using this instance of the Pragmatist principle:Faced with a genuine choice about whether or not to believe extrinsic racism, where there is no compellingevidence in favor of either extrinsic racism or not, we are "free" to decide whether or not to believe extrinsicracism.When is there "no compelling evidence" to settle the matter?(a) when I lack compelling evidence?(b) when no one has found compelling evidence (so far)?(c) when there is, in principle, no compelling evidence?If (a) or (b), then it would seem that the lack of compelling evidence may be due to systematic distortion (my irrationality, or the ideological influences in society that prevent evidence from being properly collected and evaluated). But if systematic distortion is a plausible hypothesis, shouldn't we say that we should withhold belief, and that belief either way is not rationally permissible? However, if we strengthen the Pragmatist principle to require that we withhold belief until all possible evidence is collected (so going for (c)), then we would miss out on many of the advantages James mentions (e.g.,in love) and it isn't clear how far Pragmatism offers an improvement over Evidentialism. Thus it seems that Pragmatism is not a good guide to what's rationally permissible, understood as a matter of epistemic rationality, i.e., how we should proceed in our search for knowledge.Consider pragmatic justification using a different instance of the principle:Faced with a genuine choice (at time t) about whether or not to believe intrinsic racism, where there is nocompelling evidence (at t) in favor of either intrinsic racism or not, we are "free" to decide whether or not tobelieve intrinsic racism.According to Appiah, intrinsic racism is not refutable by (scientific) evidence (8). On his view, however, it is a distorted ideology that can be used to support injustice. If it is sometimes a genuine choice whether to accept intrinsic racism, and if there is no compelling evidence one way or the othereven in principlethen it would seem that according to Pragmatism it is rationally permissible to accept intrinsic racism. But to continue with Appiah, one who endorses this sort of intrinsic racism can be charged with a deep moral failing. Appiah suggests this is not a "cognitive incapacity", but a "moral error"(12). If the intrinsic racist holds the racist beliefs "unthinkingly" then it is unclear that we have a case of autonomous rational behavior at all (see Appiah, 9). Alternatively, if the intrinsic racist is autonomous in this choice of belief (and harmful action based on it), then we should say that Pragmatism allows that morally reprehensible beliefs (and the actions they justify?) are rationally permitted. Is this enough to show that Pragmatism is not a good guide to what's rationally permissible, understood as a matter of practical rationality, i.e., of how we should proceed in our efforts to act rationally?Question: Is there some way to understand or modify Pragmatism to avoid these conclusions?Summary: The phenomena of wishful thinking, ideological distortion, irrational adherence to unfounded beliefs, all call into question our ability to determine if and when we have come to a point when we can be confident there is no evidence to settle the matter and that we're permitted to just choose what to believe. Even if we do reach such a point, we must be aware that our choice of what to believe may have problematic moral consequences. So Pragmatism is not without problems. All things considered is Evidentialism the better choice? Are there further alternatives to these two approaches?。
MIT-SCIENCE-Lectures-essay_1
21L007 After ColumbusTopics for the first essay1. Montaigne’s essay, although it claims otherwise, is based on writtensources, of which Léry’s text is an important one. Pick a topic in Montaigne’s account of the Tupi – making war, religion, ethics, food customs, gender roles – and identify as many differences as you can between the essay and the first-hand account in Léry. Concentrating on those differences which seem to you most significant, lay out for your reader their net effects -- what is the total effect of these differences in each text? In your conclusion, you mightspeculate on why or to what end Montaigne might have altered his account in these ways; or you might consider how Léry evaluates/responds to theinformation Montaigne alters or excludes.2. Léry stands out for his relative open-mindedness, and his willingness (atleast in some areas) to meet the Tupi on equal terms. At the same time, hecondemns other Frenchmen who “forget themselves” so far as to participate fully in Tupi culture, to abandon their different status as Frenchmen. Pick a few places in the text which seem important or interesting in this light, trace how and where, Léry moves along the axes of judgement (does he praise,condemn, or simply report?), differentiation (does he see the Tupi as alien or similar to himself and his kind?), and participation (does he enter the culture or stand outside it?). In your conclusion, you might pick one moment ofLéry’s response as either especially representative, or especially important to you as a reader – then argue for the first, or explain the second.3. According to Paul Lejeune, the Montagnais avoid anger above all;according to Jean de Brébeuf, the Hurons also avoid showing anger orvengeance (JR, 33 51). These observations seem to contrast with Léry andMontaigne’s emphasis on the centrality of vengeance and inveterate hatred in Tupi culture (Léry, 112). What can be learned by examining this apparentpoint of difference? This examination might proceed in several stages,considering the observation, the culture is being observed, and those who aredoing the observing. To begin with, fine-tune the observation (these avoidanger, these rely on it): how do the Tupi encourage or reward anger, forinstance? How do the Hurons discourage it? Then, as you look more broadly at the culture is being observed, consider how much the hypothesis fits andhow much you might want to qualify it: Is anger encouraged in all areas of Tupi life or only some? If the Hurons don't believe in vengeance, whatmotivates them to go to war? Are these cultures really different, and howmuch? Finally, you might ask yourself about the values of the observer and how these might affect their representation of the topic under discussion: do the Jesuits appear to value things that Lery does not care about, for instance, and vice versa? You may take on this topic (anger and vengeance) as it is, or use it as a template for thinking about some other observation or hypothesis. Length: 5 pages, double-spaced (ca. 1500 words).Due date (essay): Monday, Sept. 29Due date (revision): 10/15How to format your paper:Typed/printed, double-spaced, 1” margins. Paragraphs indented 5 spaces at left; do not separate paragraphs by extra blank lines. Quotations of 10 words or less should be integrated into the text; longer quotations should be indented 5 spaces at left and right margins, single spaced, and set off from the text of the essay by a blank line before and after the quotation. (Please see examples below).How to title your paper:Your essay should have a fairly specific title – one which will suggest what you’ve concluded about the differences between Montaigne and Lery, for instance --e.g., “Saintly Savages and Subhuman Cannibals” or “Truth-telling versus Total Fabrication”. (Note: unlike these two, your titles will probably be more subtle and represent viable arguments). “Jean de Léry’s Voyage to Brazil” would not be a good title. It’s worth taking a little thought over the title, not only because it creates the first impression of your essay (that, too); coming up with a phrase which encapsulates your argument can help in focusing that argument.How to quote:Short Quotation (2 kinds)1/ When Montaigne claims that his servant “had lived ten or twelve years in that other world” (115), he is referring to ....[NOTE: when the quotation is integrated into your own sentence, as here -- your words “his servant” are the subject of Montaigne’s verb “had lived” -- make sure the grammar works. To check whether it does, remove the quotation marks and see if the sentence looks right.]2/ Montaigne writes: “skill is a dead and physical possession” (115).Long QuotationHere I am, writing along in my essay, along and along and along. Here comes a quotation, beginning now.They get up with the sun, and immediately after rising they eat for the whole day, forthey have no other meal (111).Okay, quotation’s over. Back to the essay now, with double-spacing and regular margins again. One other thing: anytime you include a long chunk of text, be sure to talk about its details and what, specifically, we should understand from reading it. If there is not enough to say, the quotation should probably be shorter.。
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24.00: Problems of PhilosophyProf. Sally HaslangerOctober 15, 2001Personal Identity IThere are several questions that might arise concerning personal identity. When we ask "Who am I?" we might be wondering about what "makes us tick", what we ultimately value, what matters to us. We might also be asking what sort of being we are, what our possibilities are, under what conditions "I" would continue to exist. We'll begin our discussion of personal identity with the latter set of questions.Consider a parallel set of questions:(Id) Under what conditions are baseball-events events in the same game? E.g., under what conditions are aparticular batter batting and a particular runner running parts of the same game?Break (I) into two questions. First, the question of synchronic identity:(SI) Under what conditions are simultaneous baseball-events events in the same game?Let a baseball "stage" consist of all the events at a given time that are part of a single game. Then we can formulate the question of diachronic identity as follows:(DI) Under what conditions are two baseball stages stages in the same game? E.g., what makes the beginning of the third inning and the end of the eighth inning stages of the very same baseball game?Restate the questions for persons:Synchronic identity: under what conditions are two simultaneous person-events events in the life of the same person? Diachronic identity: under what conditions are two person-stages stages in the life of a single person. In particular, what makes a particular person-stage a continuation of me as I am right now?Synchronic unity relation: the relation that unites simultaneous person-events into a stage of a single person.Diachronic unity relation: the relation that unites person-stages into a single temporally-extended person.Perry Dialogue, First Night:1. (Weirob) Is survival of death possible?ï What we want is survival of me (not the molecules of my body...).ï What survives must do justice to possibility of anticipation and memory.2. (Miller) Postulation of soul.Soul criterion: x is the same person as y iff x and y have the same soul.ï What is a soul? The subject of consciousness? A spiritual/disembodied self? The ghost in the machine?3. (Weirob) Practical applicability condition on adequate response:ï An adequate account of the survival/identity of persons must also be able to justify our practices of recognizing and identifying each other.4. (Weirob) The soul not a good basis for recognition.ï We can recognize each othersí bodies, but not each othersí souls.5. (Miller) Body-soul correlations provide a basis for recognition.ï We do observe the soul indirectly by observing the behavior of each others' bodies.6. (Weirob) But how do you know that there is a body-soul correlation? By observation?ï Chocolate example shows that correlation between body and soul untestable; if not testable, it must just be a matter of faith.7. (Miller) Personality-Soul correlations provide a basis for body-soul correlations.ï If the soul is the subject of mental states, the soul must be what explains the pattern of mental states, i.e., it must be what provides us with our personality or character. So there must be a correlation between soul and personality.8. (Weirob) But even if soul does account for personality, thereís no reason that one must have the same soul to exhibit the same personality.ï We can't infer from sameness/similarity of personality to sameness/similarity of soul.ï River analogy: rivers have the same appearance even though the water molecules are constantly changing; better example: Martians/God/mad scientist could make a duplicate of you with the same personality, but without the same soul. ï [Also, don't people sometimes undergo changes in their personality, e.g., after a conversion, a tragic experience, falling in love, etc.?]9. (Miller) But maybe the relevant correlations must be established by 1st person observations.ï I know of myself that there is a body-personality-soul correlation.10. (Weirob) But how do you know that even in your own case?ï All that you introspect is thoughts and feelings, but isnít this compatible with a sequence of souls passing through? How do you know that God doesnít give your body a new soul each morning? How would you tell if when you woke up there was a new soul responsible for your thoughts, or just the old one?11. (Weirob) Does the postulation of soul really help? Doesnít it push the question back?ï E.g., suppose I say that a flower blooming in my garden is the same one that was blooming yesterday; someone asks: on what basis do you say that? I say that it has the same flower-spirit as the previous one. Doesnít the question arise: what are the identity conditions for flower spirits? What does it take for a flower-spirit to continue to exist?12. Gretchenís bodily solution:ï Do I doubt my own soul? Not in the sense of doubting that Iím conscious. But my consciousness is a property of a body, and that body is me. But if I am my body, then the destruction of my body is the destruction of me. So:Body criterion: x is the same person as y iff x and y have the same living human body.In other words:Person-stage x is part of the same person as person-stage y iff x and y are person stages linked by bodily continuity (where bodily continuity is understood in terms of the continuity of a living human body).。