[{"data":1,"prerenderedAt":1424},["ShallowReactive",2],{"mdc-3c0a0c-key":3},{"data":4,"body":5},{},{"type":6,"children":7},"root",[8,17,31,38,83,88,92,98,141,146,149,155,160,167,202,207,232,243,248,253,266,269,275,287,293,298,391,394,400,405,410,433,438,461,466,469,475,480,483,489,494,499,505,518,524,537,543,560,571,583,588,591,597,602,620,625,628,634,639,652,664,667,673,678,683,696,701,706,711,719,722,728,733,756,759,765,770,783,788,793,796,802,813,818,841,846,849,855,860,878,883,901,906,919,922,928,933,941,946,959,964,967,973,978,991,996,1004,1007,1013,1018,1036,1039,1045,1050,1068,1073,1076,1082,1087,1095,1100,1108,1111,1117,1122,1135,1140,1153,1163,1168,1198,1201,1207,1212,1217,1229,1234,1246,1249,1255,1260,1266,1272,1300,1306,1377,1382,1385,1391,1396,1401],{"type":9,"tag":10,"props":11,"children":13},"element","h1",{"id":12},"_1-structure-quality-considerations-before-dynamics",[14],{"type":15,"value":16},"text","🧩 1. Structure Quality Considerations Before Dynamics",{"type":9,"tag":18,"props":19,"children":20},"p",{},[21,23,29],{"type":15,"value":22},"Before discussing dynamics, the chapter emphasizes important ",{"type":9,"tag":24,"props":25,"children":26},"strong",{},[27],{"type":15,"value":28},"structural validation aspects",{"type":15,"value":30},":",{"type":9,"tag":32,"props":33,"children":35},"h2",{"id":34},"the-third-backbone-dihedral-angle-ω",[36],{"type":15,"value":37},"🔁 The Third Backbone Dihedral Angle (ω)",{"type":9,"tag":39,"props":40,"children":41},"ul",{},[42,55,67,78],{"type":9,"tag":43,"props":44,"children":45},"li",{},[46,48,53],{"type":15,"value":47},"The ω angle (peptide bond) is ",{"type":9,"tag":24,"props":49,"children":50},{},[51],{"type":15,"value":52},"usually fixed to 180° (trans)",{"type":15,"value":54}," in NMR structure determination.",{"type":9,"tag":43,"props":56,"children":57},{},[58,60,65],{"type":15,"value":59},"Only when experimental evidence supports it is it set to ",{"type":9,"tag":24,"props":61,"children":62},{},[63],{"type":15,"value":64},"0° (cis)",{"type":15,"value":66},".",{"type":9,"tag":43,"props":68,"children":69},{},[70,72,77],{"type":15,"value":71},"Fixing ω creates ",{"type":9,"tag":24,"props":73,"children":74},{},[75],{"type":15,"value":76},"very narrow structural distributions",{"type":15,"value":66},{"type":9,"tag":43,"props":79,"children":80},{},[81],{"type":15,"value":82},"Some refinement protocols allow slight deviations from 180°.",{"type":9,"tag":18,"props":84,"children":85},{},[86],{"type":15,"value":87},"👉 Important: Over-constraining ω artificially reduces structural variability.",{"type":9,"tag":89,"props":90,"children":91},"hr",{},[],{"type":9,"tag":32,"props":93,"children":95},{"id":94},"interatomic-bumps-close-contacts",[96],{"type":15,"value":97},"🚫 Interatomic Bumps (Close Contacts)",{"type":9,"tag":39,"props":99,"children":100},{},[101,112,123],{"type":9,"tag":43,"props":102,"children":103},{},[104,106,111],{"type":15,"value":105},"These occur when ",{"type":9,"tag":24,"props":107,"children":108},{},[109],{"type":15,"value":110},"nonbonded atoms are closer than allowed by van der Waals radii",{"type":15,"value":66},{"type":9,"tag":43,"props":113,"children":114},{},[115,117,122],{"type":15,"value":116},"This is ",{"type":9,"tag":24,"props":118,"children":119},{},[120],{"type":15,"value":121},"energetically very unfavorable",{"type":15,"value":66},{"type":9,"tag":43,"props":124,"children":125},{},[126,128],{"type":15,"value":127},"Structure validation tools:",{"type":9,"tag":39,"props":129,"children":130},{},[131,136],{"type":9,"tag":43,"props":132,"children":133},{},[134],{"type":15,"value":135},"WHAT-IF",{"type":9,"tag":43,"props":137,"children":138},{},[139],{"type":15,"value":140},"MolProbity",{"type":9,"tag":18,"props":142,"children":143},{},[144],{"type":15,"value":145},"👉 A good structure should have very few steric clashes.",{"type":9,"tag":89,"props":147,"children":148},{},[],{"type":9,"tag":32,"props":150,"children":152},{"id":151},"hydrogen-bonding-quality",[153],{"type":15,"value":154},"🔗 Hydrogen Bonding Quality",{"type":9,"tag":18,"props":156,"children":157},{},[158],{"type":15,"value":159},"Hydrogen bonds are crucial structural stabilizers.",{"type":9,"tag":161,"props":162,"children":164},"h3",{"id":163},"how-can-nmr-detect-them",[165],{"type":15,"value":166},"How can NMR detect them?",{"type":9,"tag":168,"props":169,"children":170},"ol",{},[171,181],{"type":9,"tag":43,"props":172,"children":173},{},[174,179],{"type":9,"tag":24,"props":175,"children":176},{},[177],{"type":15,"value":178},"Through-hydrogen-bond J-coupling",{"type":15,"value":180},"\n→ Rarely measured.",{"type":9,"tag":43,"props":182,"children":183},{},[184,189],{"type":9,"tag":24,"props":185,"children":186},{},[187],{"type":15,"value":188},"Indirect methods (more common):",{"type":9,"tag":39,"props":190,"children":191},{},[192,197],{"type":9,"tag":43,"props":193,"children":194},{},[195],{"type":15,"value":196},"Amide H/D exchange rates",{"type":9,"tag":43,"props":198,"children":199},{},[200],{"type":15,"value":201},"Temperature dependence of chemical shifts",{"type":9,"tag":18,"props":203,"children":204},{},[205],{"type":15,"value":206},"⚠ Limitations:",{"type":9,"tag":39,"props":208,"children":209},{},[210,222,227],{"type":9,"tag":43,"props":211,"children":212},{},[213,215,220],{"type":15,"value":214},"Only the ",{"type":9,"tag":24,"props":216,"children":217},{},[218],{"type":15,"value":219},"donor",{"type":15,"value":221}," is identified.",{"type":9,"tag":43,"props":223,"children":224},{},[225],{"type":15,"value":226},"Many donors (Ser, Thr, Tyr hydroxyls) are invisible in NMR.",{"type":9,"tag":43,"props":228,"children":229},{},[230],{"type":15,"value":231},"The complete hydrogen bond network cannot be determined experimentally.",{"type":9,"tag":18,"props":233,"children":234},{},[235,237,242],{"type":15,"value":236},"👉 Therefore, ",{"type":9,"tag":24,"props":238,"children":239},{},[240],{"type":15,"value":241},"force-field refinement is critical",{"type":15,"value":66},{"type":9,"tag":18,"props":244,"children":245},{},[246],{"type":15,"value":247},"Special backbone hydrogen bond potentials improve structure generation.",{"type":9,"tag":18,"props":249,"children":250},{},[251],{"type":15,"value":252},"Quality indicators:",{"type":9,"tag":39,"props":254,"children":255},{},[256,261],{"type":9,"tag":43,"props":257,"children":258},{},[259],{"type":15,"value":260},"Number of unsatisfied donors/acceptors",{"type":9,"tag":43,"props":262,"children":263},{},[264],{"type":15,"value":265},"Computed hydrogen-bonding energy",{"type":9,"tag":89,"props":267,"children":268},{},[],{"type":9,"tag":10,"props":270,"children":272},{"id":271},"_2-protein-dynamics-the-big-picture",[273],{"type":15,"value":274},"🌊 2. Protein Dynamics: The Big Picture",{"type":9,"tag":18,"props":276,"children":277},{},[278,280,285],{"type":15,"value":279},"Proteins are ",{"type":9,"tag":24,"props":281,"children":282},{},[283],{"type":15,"value":284},"ensembles of interconverting states",{"type":15,"value":286},", not static objects.",{"type":9,"tag":32,"props":288,"children":290},{"id":289},"timescales-of-motion",[291],{"type":15,"value":292},"⏳ Timescales of Motion",{"type":9,"tag":18,"props":294,"children":295},{},[296],{"type":15,"value":297},"Energy barriers determine exchange rates:",{"type":9,"tag":299,"props":300,"children":301},"table",{},[302,321],{"type":9,"tag":303,"props":304,"children":305},"thead",{},[306],{"type":9,"tag":307,"props":308,"children":309},"tr",{},[310,316],{"type":9,"tag":311,"props":312,"children":313},"th",{},[314],{"type":15,"value":315},"Motion Type",{"type":9,"tag":311,"props":317,"children":318},{},[319],{"type":15,"value":320},"Timescale",{"type":9,"tag":322,"props":323,"children":324},"tbody",{},[325,339,352,365,378],{"type":9,"tag":307,"props":326,"children":327},{},[328,334],{"type":9,"tag":329,"props":330,"children":331},"td",{},[332],{"type":15,"value":333},"Local librations",{"type":9,"tag":329,"props":335,"children":336},{},[337],{"type":15,"value":338},"picoseconds",{"type":9,"tag":307,"props":340,"children":341},{},[342,347],{"type":9,"tag":329,"props":343,"children":344},{},[345],{"type":15,"value":346},"Side chain motions",{"type":9,"tag":329,"props":348,"children":349},{},[350],{"type":15,"value":351},"ps–ns",{"type":9,"tag":307,"props":353,"children":354},{},[355,360],{"type":9,"tag":329,"props":356,"children":357},{},[358],{"type":15,"value":359},"Global tumbling",{"type":9,"tag":329,"props":361,"children":362},{},[363],{"type":15,"value":364},"ns",{"type":9,"tag":307,"props":366,"children":367},{},[368,373],{"type":9,"tag":329,"props":369,"children":370},{},[371],{"type":15,"value":372},"Conformational exchange",{"type":9,"tag":329,"props":374,"children":375},{},[376],{"type":15,"value":377},"μs–ms",{"type":9,"tag":307,"props":379,"children":380},{},[381,386],{"type":9,"tag":329,"props":382,"children":383},{},[384],{"type":15,"value":385},"Large rearrangements",{"type":9,"tag":329,"props":387,"children":388},{},[389],{"type":15,"value":390},"seconds",{"type":9,"tag":89,"props":392,"children":393},{},[],{"type":9,"tag":32,"props":395,"children":397},{"id":396},"global-tumbling",[398],{"type":15,"value":399},"🌀 Global Tumbling",{"type":9,"tag":18,"props":401,"children":402},{},[403],{"type":15,"value":404},"Proteins rotate in solution.",{"type":9,"tag":18,"props":406,"children":407},{},[408],{"type":15,"value":409},"Correlation time ( \tau_m ):",{"type":9,"tag":39,"props":411,"children":412},{},[413,423],{"type":9,"tag":43,"props":414,"children":415},{},[416,418],{"type":15,"value":417},"Derived from ",{"type":9,"tag":24,"props":419,"children":420},{},[421],{"type":15,"value":422},"Stokes–Einstein–Debye equation",{"type":9,"tag":43,"props":424,"children":425},{},[426,428],{"type":15,"value":427},"Typically ",{"type":9,"tag":24,"props":429,"children":430},{},[431],{"type":15,"value":432},"several to hundreds of ns",{"type":9,"tag":18,"props":434,"children":435},{},[436],{"type":15,"value":437},"Key concept:",{"type":9,"tag":39,"props":439,"children":440},{},[441,451],{"type":9,"tag":43,"props":442,"children":443},{},[444,446],{"type":15,"value":445},"Motions faster than τm → ",{"type":9,"tag":24,"props":447,"children":448},{},[449],{"type":15,"value":450},"internal fast motions",{"type":9,"tag":43,"props":452,"children":453},{},[454,456],{"type":15,"value":455},"Motions slower than τm → ",{"type":9,"tag":24,"props":457,"children":458},{},[459],{"type":15,"value":460},"collective conformational exchange",{"type":9,"tag":18,"props":462,"children":463},{},[464],{"type":15,"value":465},"The figure on page 2 (Fig. 4.13) beautifully summarizes this hierarchy.",{"type":9,"tag":89,"props":467,"children":468},{},[],{"type":9,"tag":10,"props":470,"children":472},{"id":471},"_3-nmr-observables-affected-by-dynamics",[473],{"type":15,"value":474},"📡 3. NMR Observables Affected by Dynamics",{"type":9,"tag":18,"props":476,"children":477},{},[478],{"type":15,"value":479},"NMR reports on dynamics via multiple observables.",{"type":9,"tag":89,"props":481,"children":482},{},[],{"type":9,"tag":32,"props":484,"children":486},{"id":485},"chemical-shift-and-exchange",[487],{"type":15,"value":488},"🧪 Chemical Shift and Exchange",{"type":9,"tag":18,"props":490,"children":491},{},[492],{"type":15,"value":493},"Chemical shifts are sensitive to environment.",{"type":9,"tag":18,"props":495,"children":496},{},[497],{"type":15,"value":498},"For two-state exchange (A ⇌ B):",{"type":9,"tag":161,"props":500,"children":502},{"id":501},"fast-exchange-kex-δν",[503],{"type":15,"value":504},"🟢 Fast exchange (kex >> Δν)",{"type":9,"tag":39,"props":506,"children":507},{},[508,513],{"type":9,"tag":43,"props":509,"children":510},{},[511],{"type":15,"value":512},"One averaged peak",{"type":9,"tag":43,"props":514,"children":515},{},[516],{"type":15,"value":517},"Position = population-weighted average",{"type":9,"tag":161,"props":519,"children":521},{"id":520},"slow-exchange-kex-δν",[522],{"type":15,"value":523},"🔴 Slow exchange (kex \u003C\u003C Δν)",{"type":9,"tag":39,"props":525,"children":526},{},[527,532],{"type":9,"tag":43,"props":528,"children":529},{},[530],{"type":15,"value":531},"Two separate peaks",{"type":9,"tag":43,"props":533,"children":534},{},[535],{"type":15,"value":536},"Intensities reflect populations",{"type":9,"tag":161,"props":538,"children":540},{"id":539},"intermediate-exchange",[541],{"type":15,"value":542},"🟡 Intermediate exchange",{"type":9,"tag":39,"props":544,"children":545},{},[546,550,555],{"type":9,"tag":43,"props":547,"children":548},{},[549],{"type":15,"value":512},{"type":9,"tag":43,"props":551,"children":552},{},[553],{"type":15,"value":554},"Line broadening (exchange broadening)",{"type":9,"tag":43,"props":556,"children":557},{},[558],{"type":15,"value":559},"May become undetectable",{"type":9,"tag":18,"props":561,"children":562},{},[563,565],{"type":15,"value":564},"📌 Peak width at half height:\n",{"type":9,"tag":566,"props":567,"children":568},"span",{},[569],{"type":15,"value":570},"\nT_2^{-1} = pi Delta\nu_{1/2}\n",{"type":9,"tag":18,"props":572,"children":573},{},[574,576,581],{"type":15,"value":575},"Exchange affects ",{"type":9,"tag":24,"props":577,"children":578},{},[579],{"type":15,"value":580},"T₂",{"type":15,"value":582},", not T₁.",{"type":9,"tag":18,"props":584,"children":585},{},[586],{"type":15,"value":587},"Figure 4.14 (page 3) clearly illustrates these regimes.",{"type":9,"tag":89,"props":589,"children":590},{},[],{"type":9,"tag":10,"props":592,"children":594},{"id":593},"_4-relaxation-and-linewidth",[595],{"type":15,"value":596},"📉 4. Relaxation and Linewidth",{"type":9,"tag":18,"props":598,"children":599},{},[600],{"type":15,"value":601},"Linewidth (T₂) depends on:",{"type":9,"tag":168,"props":603,"children":604},{},[605,610,615],{"type":9,"tag":43,"props":606,"children":607},{},[608],{"type":15,"value":609},"Exchange broadening",{"type":9,"tag":43,"props":611,"children":612},{},[613],{"type":15,"value":614},"Tumbling correlation time (τm)",{"type":9,"tag":43,"props":616,"children":617},{},[618],{"type":15,"value":619},"Fast internal motions",{"type":9,"tag":18,"props":621,"children":622},{},[623],{"type":15,"value":624},"T₂ increases almost linearly with τm (Fig. 4.15).",{"type":9,"tag":89,"props":626,"children":627},{},[],{"type":9,"tag":32,"props":629,"children":631},{"id":630},"t-relaxation",[632],{"type":15,"value":633},"🔄 T₁ Relaxation",{"type":9,"tag":18,"props":635,"children":636},{},[637],{"type":15,"value":638},"T₁ depends on:",{"type":9,"tag":39,"props":640,"children":641},{},[642,647],{"type":9,"tag":43,"props":643,"children":644},{},[645],{"type":15,"value":646},"Tumbling",{"type":9,"tag":43,"props":648,"children":649},{},[650],{"type":15,"value":651},"Motions faster than tumbling",{"type":9,"tag":18,"props":653,"children":654},{},[655,657,662],{"type":15,"value":656},"It does ",{"type":9,"tag":24,"props":658,"children":659},{},[660],{"type":15,"value":661},"not",{"type":15,"value":663}," depend on slow conformational exchange.",{"type":9,"tag":89,"props":665,"children":666},{},[],{"type":9,"tag":32,"props":668,"children":670},{"id":669},"distance-averaging-in-exchange",[671],{"type":15,"value":672},"📏 Distance Averaging in Exchange",{"type":9,"tag":18,"props":674,"children":675},{},[676],{"type":15,"value":677},"For dipolar-coupled nuclei:",{"type":9,"tag":18,"props":679,"children":680},{},[681],{"type":15,"value":682},"If exchange is:",{"type":9,"tag":39,"props":684,"children":685},{},[686,691],{"type":9,"tag":43,"props":687,"children":688},{},[689],{"type":15,"value":690},"Fast on chemical shift timescale",{"type":9,"tag":43,"props":692,"children":693},{},[694],{"type":15,"value":695},"Slower than tumbling",{"type":9,"tag":18,"props":697,"children":698},{},[699],{"type":15,"value":700},"Relaxation depends on ⟨r⁻⁶⟩.",{"type":9,"tag":18,"props":702,"children":703},{},[704],{"type":15,"value":705},"If exchange is faster than tumbling:\nRelaxation depends on ⟨r⁻³⟩².",{"type":9,"tag":18,"props":707,"children":708},{},[709],{"type":15,"value":710},"For NH bonds:",{"type":9,"tag":39,"props":712,"children":713},{},[714],{"type":9,"tag":43,"props":715,"children":716},{},[717],{"type":15,"value":718},"r is fixed → distinction irrelevant.",{"type":9,"tag":89,"props":720,"children":721},{},[],{"type":9,"tag":32,"props":723,"children":725},{"id":724},"noe-and-dynamics",[726],{"type":15,"value":727},"🔁 NOE and Dynamics",{"type":9,"tag":18,"props":729,"children":730},{},[731],{"type":15,"value":732},"Steady-state NOE depends on:",{"type":9,"tag":39,"props":734,"children":735},{},[736,741,746,751],{"type":9,"tag":43,"props":737,"children":738},{},[739],{"type":15,"value":740},"T₁",{"type":9,"tag":43,"props":742,"children":743},{},[744],{"type":15,"value":745},"Dipolar interaction correlation time",{"type":9,"tag":43,"props":747,"children":748},{},[749],{"type":15,"value":750},"τm",{"type":9,"tag":43,"props":752,"children":753},{},[754],{"type":15,"value":755},"Fast internal motion",{"type":9,"tag":89,"props":757,"children":758},{},[],{"type":9,"tag":32,"props":760,"children":762},{"id":761},"rdcs-and-dynamics",[763],{"type":15,"value":764},"🧲 RDCs and Dynamics",{"type":9,"tag":18,"props":766,"children":767},{},[768],{"type":15,"value":769},"Residual Dipolar Couplings report on:",{"type":9,"tag":39,"props":771,"children":772},{},[773,778],{"type":9,"tag":43,"props":774,"children":775},{},[776],{"type":15,"value":777},"Orientation of bond vectors",{"type":9,"tag":43,"props":779,"children":780},{},[781],{"type":15,"value":782},"Motions from ps → ms",{"type":9,"tag":18,"props":784,"children":785},{},[786],{"type":15,"value":787},"Internal motion averages vector orientations → averaged RDC values.",{"type":9,"tag":18,"props":789,"children":790},{},[791],{"type":15,"value":792},"Thus:\n👉 RDCs encode dynamic information.",{"type":9,"tag":89,"props":794,"children":795},{},[],{"type":9,"tag":10,"props":797,"children":799},{"id":798},"_5-nmr-experiments-for-dynamics",[800],{"type":15,"value":801},"🧠 5. NMR Experiments for Dynamics",{"type":9,"tag":18,"props":803,"children":804},{},[805,807,812],{"type":15,"value":806},"Dynamic information comes from ",{"type":9,"tag":24,"props":808,"children":809},{},[810],{"type":15,"value":811},"relaxation measurements",{"type":15,"value":66},{"type":9,"tag":18,"props":814,"children":815},{},[816],{"type":15,"value":817},"Relaxation arises from:",{"type":9,"tag":39,"props":819,"children":820},{},[821,826,831],{"type":9,"tag":43,"props":822,"children":823},{},[824],{"type":15,"value":825},"Fluctuating magnetic fields",{"type":9,"tag":43,"props":827,"children":828},{},[829],{"type":15,"value":830},"Caused by molecular motion",{"type":9,"tag":43,"props":832,"children":833},{},[834,836],{"type":15,"value":835},"Frequency dependence described by ",{"type":9,"tag":24,"props":837,"children":838},{},[839],{"type":15,"value":840},"spectral density J(ω)",{"type":9,"tag":18,"props":842,"children":843},{},[844],{"type":15,"value":845},"J(ω) is the Fourier transform of time correlation functions.",{"type":9,"tag":89,"props":847,"children":848},{},[],{"type":9,"tag":10,"props":850,"children":852},{"id":851},"_6-n-relaxation-experiments",[853],{"type":15,"value":854},"🧬 6. ¹⁵N Relaxation Experiments",{"type":9,"tag":18,"props":856,"children":857},{},[858],{"type":15,"value":859},"The backbone ¹H–¹⁵N amide bond is ideal because:",{"type":9,"tag":168,"props":861,"children":862},{},[863,868,873],{"type":9,"tag":43,"props":864,"children":865},{},[866],{"type":15,"value":867},"Present in all non-Pro residues",{"type":9,"tag":43,"props":869,"children":870},{},[871],{"type":15,"value":872},"Approximates two-spin system",{"type":9,"tag":43,"props":874,"children":875},{},[876],{"type":15,"value":877},"Easy to measure in HSQC",{"type":9,"tag":18,"props":879,"children":880},{},[881],{"type":15,"value":882},"Measured parameters:",{"type":9,"tag":39,"props":884,"children":885},{},[886,891,896],{"type":9,"tag":43,"props":887,"children":888},{},[889],{"type":15,"value":890},"¹⁵N T₁",{"type":9,"tag":43,"props":892,"children":893},{},[894],{"type":15,"value":895},"¹⁵N T₂",{"type":9,"tag":43,"props":897,"children":898},{},[899],{"type":15,"value":900},"¹H–¹⁵N NOE",{"type":9,"tag":18,"props":902,"children":903},{},[904],{"type":15,"value":905},"They probe:",{"type":9,"tag":39,"props":907,"children":908},{},[909,914],{"type":9,"tag":43,"props":910,"children":911},{},[912],{"type":15,"value":913},"ps–ns motions",{"type":9,"tag":43,"props":915,"children":916},{},[917],{"type":15,"value":918},"μs–ms exchange",{"type":9,"tag":89,"props":920,"children":921},{},[],{"type":9,"tag":10,"props":923,"children":925},{"id":924},"_7-extracting-tumbling-correlation-time",[926],{"type":15,"value":927},"🧮 7. Extracting Tumbling Correlation Time",{"type":9,"tag":18,"props":929,"children":930},{},[931],{"type":15,"value":932},"For isotropic tumbling:",{"type":9,"tag":18,"props":934,"children":935},{},[936],{"type":9,"tag":566,"props":937,"children":938},{},[939],{"type":15,"value":940},"\nau_m = \frac{1}{2\nu_N} sqrt{\frac{6T_1}{T_2} - 7}\n",{"type":9,"tag":18,"props":942,"children":943},{},[944],{"type":15,"value":945},"But proteins are often:",{"type":9,"tag":39,"props":947,"children":948},{},[949,954],{"type":9,"tag":43,"props":950,"children":951},{},[952],{"type":15,"value":953},"Nonspherical",{"type":9,"tag":43,"props":955,"children":956},{},[957],{"type":15,"value":958},"Anisotropically rotating",{"type":9,"tag":18,"props":960,"children":961},{},[962],{"type":15,"value":963},"Thus T₁/T₂ may vary per residue even without internal motion.",{"type":9,"tag":89,"props":965,"children":966},{},[],{"type":9,"tag":10,"props":968,"children":970},{"id":969},"_8-model-free-formalism-lipariszabo",[971],{"type":15,"value":972},"🧩 8. Model-Free Formalism (Lipari–Szabo)",{"type":9,"tag":18,"props":974,"children":975},{},[976],{"type":15,"value":977},"Goal:\nSeparate:",{"type":9,"tag":39,"props":979,"children":980},{},[981,986],{"type":9,"tag":43,"props":982,"children":983},{},[984],{"type":15,"value":985},"Overall tumbling",{"type":9,"tag":43,"props":987,"children":988},{},[989],{"type":15,"value":990},"Internal motion",{"type":9,"tag":18,"props":992,"children":993},{},[994],{"type":15,"value":995},"Assumption:\nInternal and overall motions are separable:",{"type":9,"tag":18,"props":997,"children":998},{},[999],{"type":9,"tag":566,"props":1000,"children":1001},{},[1002],{"type":15,"value":1003},"\nC(t) = C_0(t) C_i(t)\n",{"type":9,"tag":89,"props":1005,"children":1006},{},[],{"type":9,"tag":32,"props":1008,"children":1010},{"id":1009},"basic-model-free-parameters",[1011],{"type":15,"value":1012},"Basic Model-Free Parameters",{"type":9,"tag":18,"props":1014,"children":1015},{},[1016],{"type":15,"value":1017},"Three parameters:",{"type":9,"tag":168,"props":1019,"children":1020},{},[1021,1026,1031],{"type":9,"tag":43,"props":1022,"children":1023},{},[1024],{"type":15,"value":1025},"τm – global tumbling",{"type":9,"tag":43,"props":1027,"children":1028},{},[1029],{"type":15,"value":1030},"S² – order parameter",{"type":9,"tag":43,"props":1032,"children":1033},{},[1034],{"type":15,"value":1035},"τe – internal motion timescale",{"type":9,"tag":89,"props":1037,"children":1038},{},[],{"type":9,"tag":161,"props":1040,"children":1042},{"id":1041},"order-parameter-s",[1043],{"type":15,"value":1044},"📌 Order Parameter S²",{"type":9,"tag":18,"props":1046,"children":1047},{},[1048],{"type":15,"value":1049},"Measures amplitude of motion:",{"type":9,"tag":39,"props":1051,"children":1052},{},[1053,1058,1063],{"type":9,"tag":43,"props":1054,"children":1055},{},[1056],{"type":15,"value":1057},"S² = 1 → completely rigid",{"type":9,"tag":43,"props":1059,"children":1060},{},[1061],{"type":15,"value":1062},"S² = 0 → fully flexible",{"type":9,"tag":43,"props":1064,"children":1065},{},[1066],{"type":15,"value":1067},"Typical backbone: 0.7–0.95",{"type":9,"tag":18,"props":1069,"children":1070},{},[1071],{"type":15,"value":1072},"Represents angular restriction of bond vector.",{"type":9,"tag":89,"props":1074,"children":1075},{},[],{"type":9,"tag":161,"props":1077,"children":1079},{"id":1078},"spectral-density-basic-model",[1080],{"type":15,"value":1081},"Spectral Density (Basic Model)",{"type":9,"tag":18,"props":1083,"children":1084},{},[1085],{"type":15,"value":1086},"[\nJ(\nu) = \frac{2}{5} left( \frac{S^2 \tau_m}{1+\nu^2 \tau_m^2}",{"type":9,"tag":39,"props":1088,"children":1089},{},[1090],{"type":9,"tag":43,"props":1091,"children":1092},{},[1093],{"type":15,"value":1094},"\frac{(1-S^2)\tau}{1+\nu^2 \tau^2}\right)\n]",{"type":9,"tag":18,"props":1096,"children":1097},{},[1098],{"type":15,"value":1099},"with:",{"type":9,"tag":18,"props":1101,"children":1102},{},[1103],{"type":9,"tag":566,"props":1104,"children":1105},{},[1106],{"type":15,"value":1107},"\nau^{-1} = \tau_m^{-1} + \tau_e^{-1}\n",{"type":9,"tag":89,"props":1109,"children":1110},{},[],{"type":9,"tag":10,"props":1112,"children":1114},{"id":1113},"_9-extended-model-free-clore",[1115],{"type":15,"value":1116},"🧠 9. Extended Model-Free (Clore)",{"type":9,"tag":18,"props":1118,"children":1119},{},[1120],{"type":15,"value":1121},"Accounts for:",{"type":9,"tag":39,"props":1123,"children":1124},{},[1125,1130],{"type":9,"tag":43,"props":1126,"children":1127},{},[1128],{"type":15,"value":1129},"Fast internal motion (τf)",{"type":9,"tag":43,"props":1131,"children":1132},{},[1133],{"type":15,"value":1134},"Slow internal motion (τs)",{"type":9,"tag":18,"props":1136,"children":1137},{},[1138],{"type":15,"value":1139},"With separate order parameters:",{"type":9,"tag":39,"props":1141,"children":1142},{},[1143,1148],{"type":9,"tag":43,"props":1144,"children":1145},{},[1146],{"type":15,"value":1147},"S²f",{"type":9,"tag":43,"props":1149,"children":1150},{},[1151],{"type":15,"value":1152},"S²s",{"type":9,"tag":18,"props":1154,"children":1155},{},[1156,1158],{"type":15,"value":1157},"Total:\n",{"type":9,"tag":566,"props":1159,"children":1160},{},[1161],{"type":15,"value":1162},"\nS^2 = S_f^2 S_s^2\n",{"type":9,"tag":18,"props":1164,"children":1165},{},[1166],{"type":15,"value":1167},"Up to six fitting parameters:",{"type":9,"tag":39,"props":1169,"children":1170},{},[1171,1175,1179,1183,1188,1193],{"type":9,"tag":43,"props":1172,"children":1173},{},[1174],{"type":15,"value":750},{"type":9,"tag":43,"props":1176,"children":1177},{},[1178],{"type":15,"value":1147},{"type":9,"tag":43,"props":1180,"children":1181},{},[1182],{"type":15,"value":1152},{"type":9,"tag":43,"props":1184,"children":1185},{},[1186],{"type":15,"value":1187},"τf",{"type":9,"tag":43,"props":1189,"children":1190},{},[1191],{"type":15,"value":1192},"τs",{"type":9,"tag":43,"props":1194,"children":1195},{},[1196],{"type":15,"value":1197},"Rex",{"type":9,"tag":89,"props":1199,"children":1200},{},[],{"type":9,"tag":10,"props":1202,"children":1204},{"id":1203},"_10-conformational-exchange-rex",[1205],{"type":15,"value":1206},"⚡ 10. Conformational Exchange (Rex)",{"type":9,"tag":18,"props":1208,"children":1209},{},[1210],{"type":15,"value":1211},"Rex contributes to T₂ only.",{"type":9,"tag":18,"props":1213,"children":1214},{},[1215],{"type":15,"value":1216},"Captures:",{"type":9,"tag":39,"props":1218,"children":1219},{},[1220,1224],{"type":9,"tag":43,"props":1221,"children":1222},{},[1223],{"type":15,"value":918},{"type":9,"tag":43,"props":1225,"children":1226},{},[1227],{"type":15,"value":1228},"Chemical shift modulation",{"type":9,"tag":18,"props":1230,"children":1231},{},[1232],{"type":15,"value":1233},"Exchange affects:",{"type":9,"tag":39,"props":1235,"children":1236},{},[1237,1241],{"type":9,"tag":43,"props":1238,"children":1239},{},[1240],{"type":15,"value":580},{"type":9,"tag":43,"props":1242,"children":1243},{},[1244],{"type":15,"value":1245},"Not T₁",{"type":9,"tag":89,"props":1247,"children":1248},{},[],{"type":9,"tag":10,"props":1250,"children":1252},{"id":1251},"final-conceptual-takeaways",[1253],{"type":15,"value":1254},"🎯 Final Conceptual Takeaways",{"type":9,"tag":18,"props":1256,"children":1257},{},[1258],{"type":15,"value":1259},"This chapter builds a powerful conceptual framework:",{"type":9,"tag":161,"props":1261,"children":1263},{"id":1262},"proteins-are-dynamic-ensembles",[1264],{"type":15,"value":1265},"Proteins are dynamic ensembles.",{"type":9,"tag":161,"props":1267,"children":1269},{"id":1268},"nmr-observables-encode-motion-through",[1270],{"type":15,"value":1271},"NMR observables encode motion through:",{"type":9,"tag":39,"props":1273,"children":1274},{},[1275,1280,1285,1290,1295],{"type":9,"tag":43,"props":1276,"children":1277},{},[1278],{"type":15,"value":1279},"Chemical shift averaging",{"type":9,"tag":43,"props":1281,"children":1282},{},[1283],{"type":15,"value":1284},"Line broadening",{"type":9,"tag":43,"props":1286,"children":1287},{},[1288],{"type":15,"value":1289},"Relaxation rates",{"type":9,"tag":43,"props":1291,"children":1292},{},[1293],{"type":15,"value":1294},"NOE values",{"type":9,"tag":43,"props":1296,"children":1297},{},[1298],{"type":15,"value":1299},"RDC averaging",{"type":9,"tag":161,"props":1301,"children":1303},{"id":1302},"timescale-mapping",[1304],{"type":15,"value":1305},"Timescale Mapping:",{"type":9,"tag":299,"props":1307,"children":1308},{},[1309,1324],{"type":9,"tag":303,"props":1310,"children":1311},{},[1312],{"type":9,"tag":307,"props":1313,"children":1314},{},[1315,1319],{"type":9,"tag":311,"props":1316,"children":1317},{},[1318],{"type":15,"value":320},{"type":9,"tag":311,"props":1320,"children":1321},{},[1322],{"type":15,"value":1323},"Technique",{"type":9,"tag":322,"props":1325,"children":1326},{},[1327,1339,1351,1364],{"type":9,"tag":307,"props":1328,"children":1329},{},[1330,1334],{"type":9,"tag":329,"props":1331,"children":1332},{},[1333],{"type":15,"value":351},{"type":9,"tag":329,"props":1335,"children":1336},{},[1337],{"type":15,"value":1338},"¹⁵N T₁, T₂, NOE",{"type":9,"tag":307,"props":1340,"children":1341},{},[1342,1346],{"type":9,"tag":329,"props":1343,"children":1344},{},[1345],{"type":15,"value":377},{"type":9,"tag":329,"props":1347,"children":1348},{},[1349],{"type":15,"value":1350},"Rex, CPMG",{"type":9,"tag":307,"props":1352,"children":1353},{},[1354,1359],{"type":9,"tag":329,"props":1355,"children":1356},{},[1357],{"type":15,"value":1358},"ms–s",{"type":9,"tag":329,"props":1360,"children":1361},{},[1362],{"type":15,"value":1363},"EXSY",{"type":9,"tag":307,"props":1365,"children":1366},{},[1367,1372],{"type":9,"tag":329,"props":1368,"children":1369},{},[1370],{"type":15,"value":1371},"ps–ms",{"type":9,"tag":329,"props":1373,"children":1374},{},[1375],{"type":15,"value":1376},"RDCs",{"type":9,"tag":18,"props":1378,"children":1379},{},[1380],{"type":15,"value":1381},"(Figure 4.13 visually summarizes this hierarchy.)",{"type":9,"tag":89,"props":1383,"children":1384},{},[],{"type":9,"tag":10,"props":1386,"children":1388},{"id":1387},"big-insight",[1389],{"type":15,"value":1390},"🧠 Big Insight",{"type":9,"tag":18,"props":1392,"children":1393},{},[1394],{"type":15,"value":1395},"Structure determination is incomplete without dynamics.",{"type":9,"tag":18,"props":1397,"children":1398},{},[1399],{"type":15,"value":1400},"Relaxation analysis allows:",{"type":9,"tag":39,"props":1402,"children":1403},{},[1404,1409,1414,1419],{"type":9,"tag":43,"props":1405,"children":1406},{},[1407],{"type":15,"value":1408},"Quantifying flexibility (S²)",{"type":9,"tag":43,"props":1410,"children":1411},{},[1412],{"type":15,"value":1413},"Extracting timescales (τe)",{"type":9,"tag":43,"props":1415,"children":1416},{},[1417],{"type":15,"value":1418},"Detecting conformational exchange (Rex)",{"type":9,"tag":43,"props":1420,"children":1421},{},[1422],{"type":15,"value":1423},"Understanding protein function through motion",1775084302730]