Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student

Size: px
Start display at page:

Download "Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student"

Transcription

1 Cas Stuy 4 PHA 527 Aminoglycosis Answrs provi by Jffry Stark Grauat Stunt Backgroun Gntamicin is us to trat a wi varity of infctions. Howvr, u to its toxicity, its us must b rstrict to th thrapy of lif-thratning infctions an thos for which a l toxic antimicrobial agnt is inffctiv. Gntamicin follows a oncompartmnt boy mol with first-orr limination. Protin bining is low for gntamicin (pning on th tst prform, bining is rport to b -3%. Th volum of istribution is in th rang of -4L an th half-lif is aroun 2 hours (although thr may b consirabl variation in this paramtr. osag is normally. mg/kg vry 8 hours for 7- ays. Th thraputic rang is -6 mg/l. Gntamicin is commonly aministr via short-trm infusions. Howvr, for this cas stuy, aum that th infusions ar sufficintly short as to allow IV bolus quations to b us for any ncary calculations. (on t worry, w ll s all of th infusion xprions soon nough. Prhaps too soon for many of you, spcially th algbraically an xponntially challng. Patint information Mr. I.P. Littl (th nams hav bn chang to protct th innocnt is a 69 yar ol black mal with a history of iabts an hyprtnsion. H is bing trat with gntamicin for an infction in his lowr lg. Th infction was th rsult of a punctur woun which progr u to poor circulation an immun rspons. Aitional patint information is givn blow. hight 5 9 wight 7 lb SCr.3 mg/ml Not: Srum cratinin may also b xpr as.3 mg/l Whil th patint is most likly on othr mications as wll, aum no rug-rug intractions whn aring th following qustions. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc

2 Qustions ( Prict th cratinin claranc of this patint. Is this in th normal rang? If not, xplain an propos a plausibl rason for any viation from th normal valu. Of what importanc is Cl crat in this cas stuy? Why is th ial boy wight (IBW us in th calculation rathr than th actual wight? Calculat Cl crat for this patint. This may b on with th quation, Cl crat (4 ag IBW ( mal 72 crat Not: this is an mpirically riv quation. Ag is in yars, IBW is in kg, an crat is in mg/ml. This rsults in Cl crat in ml/min. First, w must fin IBW: IBW (mal 5 kg kg for ach inch ovr 5 ft. 5 kg + (2.3kg(9 Sinc patint is kg Rturning to th Cl crat calculation. (4 69(7.7 Cl crat ( mal 53.6ml / min (72(.3 Normal GFR 25 ml/min. sinc Cl crat rflcts GFR, w know that thr is som rnal ysfunction in this patint. This GFR is wll blow half th normal valu an coul b u to som unisclos isas stat or simply th ag of th patint. Cl crat is an important consiration in this cas stuy bcaus aminoglycosis ar liminat via glomrular filtration. Any chang in GFR will affct th claranc of gntamicin. W must us IBW in th calculation of Cl crat sinc cratinin is prouc by muscl mtabolism an not fat. Spcial quations ar mploy whn th patint is obs (th ajust boy wight. (2 Prict th k an t /2 of gntamicin starting with th quation which rlats k to cratinin claranc. Thn, calculat ths paramtrs bas on th xprion Clk *V auming a V of, say,5l (which falls within th normal rang. iscu any iffrnc btwn th two valus. Th quation rlating k to Cl crat is k (.293 Cl +.4 crat :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 2

3 Again, this is an mpirically riv quation. Cl crat is in ml/min an k is in hr -. For this patint, k (.293( hr This k woul giv a gntamicin half-lif of t ln k.7hr / 2 4.hr Of cours, w may calculat k if Cl an V ar known (sinc ths two inpnnt paramtrs ictat th limination rat; Cl k V may b rarrang to giv Cl k V Using th cratinin claranc calculat in qustion ( an auming V 5L, w fin k 53.6ml / min L 6min.24hr 5L ml hr With this k, w woul xpct th gntamicin half-lif to b t ln k.24hr / 2 3.2hr Th valus calculat from th two mthos ar rathr clos. A half-lif of 3.7 hr is not that iffrnt from on of 3.2 hr. sinc th first mtho is a rough stimat of k an w gu at th V in th scon mtho, w rally cannot commnt as to which is closst to th actual k. W n actual ata points (gntamicin concntration at iffrnt tim points in orr to calculat th prtinnt pharmacokintic paramtrs for this patint. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 3

4 (3 Using th kintic paramtrs foun in th part of qustion (2, calculat th pak an trough lvls for gntamicin xpct from a os of 7mg vry 8 hours. o this for th first os an for th stay-stat conitions. osing rgimn: 7 mg gntamicin vry 8 hrs. In this qustion, w ar ask to calculat pak an trough lvls for gntamicin following th osing rgimn abov. Although short-trm infusions ar us, w will aum th infusions ar short nough as to allow th IV bolus quations to b substitut for th mor complx infusion quations. This may not always b poibl. Howvr sinc you must first larn to walk bfor you bgin to run, w will mak things a bit asir. Start with a simpl sktch At stay stat, thr ar no changs btwn subsqunt paks or troughs. Calculating th pak an trough lvls aftr th first os is asy. Th pak is simply th initial concntration following an IV bolus os of 7 mg: V To us this quation, w n th valu of V. Using th Cl an k valus bas on srum cratin lvls calculat in qustion (2, w fin Cl k V Solving for V to giv V Cl k 53.6ml / min 6min L.7hr hr ml 8. 8 Not: If this is corrct, w unrstimat th V us in th prvious qustion. L :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 4

5 Th is thus, 7mg ( pak 3.7mg 8.8L Th trough occurs 8 hours latr (just prior to th 2 n os ( trough ( pak k τ This is th xact quation w us prviously, ( t V kt kt Sinc w want th at th n of th osing intrval, w st t 8 hours τ. So, ( trough (3.7mg (.7hr (8hr.94mg Th quations for calculating concntrations at stay-stat ar asy to intify. Thy always inclu th accumulation factor ( k τ in th nominator. Th pak at SS is ( pak ( V ( kτ kτ [ 3.7mg (.7hr (8hr ] 4.96 ~ 5.mg Just as with th trough aftr th st os, th trough aftr a os at stay-stat is foun by multiplying th pak valu by a factor to account for limination uring th osing intrval (hr w hav 8 hours for limination. ( trough ( pak k τ (5.mg (.7hr (8hr.3mg :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 5

6 (4 Plasma lvls wr rawn an gntamicin lvls trmin aftr th first os (7mg vry 8 hours. Th concntrations wr 5.8 mg/l an 3.8 mg/l at an 2 hours post infusion, rspctivly. Using this ata, rcalculat th k, t /2, V, an Cl for this patint. rug monitoring allows us to customiz a osing rgimn for a givn patint. Hr w ar givn two ata points following th first os. This will allow us to calculat th pharmacokintic paramtrs for this patint an bttr prict plasma lvls for rpat osing. Th ata points ar. (mg/l t(hr From th ata givn, w can asily calculat k. k (ln 5.8 ln 3.8 m.2hr 2 t ln k.2hr / 2 3.3hr Sinc th first ata point givn is at tim hr, w can fin V with qual as. V Solving this for V givs V 7mg 2. L 5.8mg :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 6

7 W may now calculat claranc: Cl k V (.2hr (2.L 2.55L / hr (5 Using th kintic paramtrs foun in qustion (4, calculat th stay-stat gntamicin concntrations (pak an trough xpct for a osing rgimn of 7mg vry 8 hours. Ar ths lvls within th sir thraputic rang? If not, what changs in th osing rgimn woul you rcommn (kp th osing intrval at 8 hours? trmining pak an trough lvls using th paramtrs just calculat for this patint. Although not rquir in this problm, pak an trough lvls ar shown blow for th st os as wll as osing at stay-stat. pak 5.8mg (on of th ata points givn ( ( trough ( pak k τ (5.8mg (.2hr (8hr.7 ~.mg At stay-stat, ( pak ( ( trough 5.8mg (.2hr [ k τ (8hr ( pak ] (7.mg 7.mg k τ (.2hr (8hr /.3mg Ths ar a littl high. Whil th trough valu is in th thraputic rang of -6 mg/l, th prict pak of 7. mg/l may la to toxic si ffcts. W might rcommn crasing th os to giv a stay-stat pak of 6. mg/l (th uppr limit of th thraputic winow. To calculat this os, w must solv th appropriat quation for. ( pak k τ V ( which rarrang to yil (6.mg (2.L [ 59.2mg ~ 6mg ( pak V ( kτ (.2hr (8hr ] L :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 7

8 A osing rgimn of 6 mg vry 8 hours woul provi stay-stat lvls of ( pak / V ( ( trough (6mg /2.L (.2hr (8hr [ ] k τ ( pak k 6.mg τ (.2hr (8hr (6.mg.mg This osing rgimn shoul b accptabl. Rcall that w ar using IV bolus quations vn though th aministration of th rug is actually via short-trm infusions. Ths IV bolus quations will ovrstimat th lvls. Th gr to which ths quations ovrstimat th concntrations is pnnt on th infusion rat an th rat of limination. :\pha42-527\cas Stuis\cas4gntamicin\ans-cas4-gntamicin.oc 8

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student Cas Stuy Vancomycin Answrs Provi by Jffry Stark, Grauat Stunt h antibiotic Vancomycin is liminat almost ntirly by glomrular filtration. For a patint with normal rnal function, th half-lif is about 6 hours.

More information

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300

More information

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here.

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here. PHA 5127 Dsigning A Dosing Rgimn Answrs provi by Jry Stark Mr. JM is to b start on aminophyllin or th tratmnt o asthma. H is a non-smokr an wighs 60 kg. Dsign an oral osing rgimn or this patint such that

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

PHA 5128 Answer CASE STUDY 3 Question #1: Model

PHA 5128 Answer CASE STUDY 3 Question #1: Model PHA 5128 Answr CASE STUDY 3 Spring 2008 Qustion #1: Aminoglycosids hav a triphasic disposition, but tobramycin concntration-tim profil hr is dscribd via a 2-compartmnt modl sinc th alpha phas could not

More information

PHA Final Exam Fall 2007

PHA Final Exam Fall 2007 PHA 5127 Final Exam Fall 2007 On my honor, I hav nithr givn nor rcivd unauthorizd aid in doing this assignmnt. Nam Plas transfr th answrs onto th bubbl sht. Th qustion numbr rfrs to th numbr on th bubbl

More information

PHA Final Exam Fall 2001

PHA Final Exam Fall 2001 PHA 5127 Final Exam Fall 2001 On my honor, I hav nithr givn nor rcivd unauthorizd aid in doing this assignmnt. Nam Qustion/Points 1. /12 pts 2. /8 pts 3. /12 pts 4. /20 pts 5. /27 pts 6. /15 pts 7. /20

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

Case Study VI Answers PHA 5127 Fall 2006

Case Study VI Answers PHA 5127 Fall 2006 Qustion. A ptint is givn 250 mg immit-rls thophyllin tblt (Tblt A). A wk ltr, th sm ptint is givn 250 mg sustin-rls thophyllin tblt (Tblt B). Th tblts follow on-comprtmntl mol n hv first-orr bsorption

More information

First order differential equation Linear equation; Method of integrating factors

First order differential equation Linear equation; Method of integrating factors First orr iffrntial quation Linar quation; Mtho of intgrating factors Exampl 1: Rwrit th lft han si as th rivativ of th prouct of y an som function by prouct rul irctly. Solving th first orr iffrntial

More information

Higher order derivatives

Higher order derivatives Robrto s Nots on Diffrntial Calculus Chaptr 4: Basic diffrntiation ruls Sction 7 Highr ordr drivativs What you nd to know alrady: Basic diffrntiation ruls. What you can larn hr: How to rpat th procss of

More information

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula

u x v x dx u x v x v x u x dx d u x v x u x v x dx u x v x dx Integration by Parts Formula 7. Intgration by Parts Each drivativ formula givs ris to a corrsponding intgral formula, as w v sn many tims. Th drivativ product rul yilds a vry usful intgration tchniqu calld intgration by parts. Starting

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination Mathmatics H Calculus I: Limits, rivativs, an Intgrals Trnt Univrsity, Summr 8 Solutions to th Actual Final Eamination Tim-spac: 9:-: in FPHL 7. Brought to you by Stfan B lan k. Instructions: Do parts

More information

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)

More information

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06 Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim

More information

Brief Introduction to Statistical Mechanics

Brief Introduction to Statistical Mechanics Brif Introduction to Statistical Mchanics. Purpos: Ths nots ar intndd to provid a vry quick introduction to Statistical Mchanics. Th fild is of cours far mor vast than could b containd in ths fw pags.

More information

Unit 6: Solving Exponential Equations and More

Unit 6: Solving Exponential Equations and More Habrman MTH 111 Sction II: Eonntial and Logarithmic Functions Unit 6: Solving Eonntial Equations and Mor EXAMPLE: Solv th quation 10 100 for. Obtain an act solution. This quation is so asy to solv that

More information

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d Aitional Math (07) Prpar b Mr Ang, Nov 07 Fin th valu of th constant k for which is a solution of th quation k. [7] Givn that, Givn that k, Thrfor, k Topic : Papr (00 marks) Tim : hours 0 mins Nam : Aitional

More information

MSLC Math 151 WI09 Exam 2 Review Solutions

MSLC Math 151 WI09 Exam 2 Review Solutions Eam Rviw Solutions. Comput th following rivativs using th iffrntiation ruls: a.) cot cot cot csc cot cos 5 cos 5 cos 5 cos 5 sin 5 5 b.) c.) sin( ) sin( ) y sin( ) ln( y) ln( ) ln( y) sin( ) ln( ) y y

More information

SPH4U Electric Charges and Electric Fields Mr. LoRusso

SPH4U Electric Charges and Electric Fields Mr. LoRusso SPH4U lctric Chargs an lctric Fils Mr. LoRusso lctricity is th flow of lctric charg. Th Grks first obsrv lctrical forcs whn arly scintists rubb ambr with fur. Th notic thy coul attract small bits of straw

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr Dtails of th ot St #19 Rading Assignmnt: Sct. 7.1.2, 7.1.3, & 7.2 of Proakis & Manolakis Dfinition of th So Givn signal data points x[n] for n = 0,, -1

More information

Examples and applications on SSSP and MST

Examples and applications on SSSP and MST Exampls an applications on SSSP an MST Dan (Doris) H & Junhao Gan ITEE Univrsity of Qunslan COMP3506/7505, Uni of Qunslan Exampls an applications on SSSP an MST Dijkstra s Algorithm Th algorithm solvs

More information

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables.

Partial Derivatives: Suppose that z = f(x, y) is a function of two variables. Chaptr Functions o Two Variabls Applid Calculus 61 Sction : Calculus o Functions o Two Variabls Now that ou hav som amiliarit with unctions o two variabls it s tim to start appling calculus to hlp us solv

More information

A Propagating Wave Packet Group Velocity Dispersion

A Propagating Wave Packet Group Velocity Dispersion Lctur 8 Phys 375 A Propagating Wav Packt Group Vlocity Disprsion Ovrviw and Motivation: In th last lctur w lookd at a localizd solution t) to th 1D fr-particl Schrödingr quation (SE) that corrsponds to

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Cor rvision gui Pag Algbra Moulus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv blow th ais in th ais. f () f () f

More information

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark.

Note If the candidate believes that e x = 0 solves to x = 0 or gives an extra solution of x = 0, then withhold the final accuracy mark. . (a) Eithr y = or ( 0, ) (b) Whn =, y = ( 0 + ) = 0 = 0 ( + ) = 0 ( )( ) = 0 Eithr = (for possibly abov) or = A 3. Not If th candidat blivs that = 0 solvs to = 0 or givs an tra solution of = 0, thn withhold

More information

Where k is either given or determined from the data and c is an arbitrary constant.

Where k is either given or determined from the data and c is an arbitrary constant. Exponntial growth and dcay applications W wish to solv an quation that has a drivativ. dy ky k > dx This quation says that th rat of chang of th function is proportional to th function. Th solution is

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Exiting from QE. Fumio Hayashi and Junko Koeda. for presentation at SF Fed Conference. March 28, 2014

Exiting from QE. Fumio Hayashi and Junko Koeda. for presentation at SF Fed Conference. March 28, 2014 Fumio Hayashi an Junko Koa Exiting from QE March 28, 214, 1 / 29 Exiting from QE Fumio Hayashi an Junko Koa for prsntation at SF F Confrnc March 28, 214 To gt start... h^ : Fumio Hayashi an Junko Koa Exiting

More information

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.

4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon. PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also

More information

Indeterminate Forms and L Hôpital s Rule. Indeterminate Forms

Indeterminate Forms and L Hôpital s Rule. Indeterminate Forms SECTION 87 Intrminat Forms an L Hôpital s Rul 567 Sction 87 Intrminat Forms an L Hôpital s Rul Rcogniz its that prouc intrminat forms Apply L Hôpital s Rul to valuat a it Intrminat Forms Rcall from Chaptrs

More information

Schematic of a mixed flow reactor (both advection and dispersion must be accounted for)

Schematic of a mixed flow reactor (both advection and dispersion must be accounted for) Cas stuy 6.1, R: Chapra an Canal, p. 769. Th quation scribin th concntration o any tracr in an lonat ractor is known as th avction-isprsion quation an may b writtn as: Schmatic o a mi low ractor (both

More information

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c. MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ

More information

Differentiation of Exponential Functions

Differentiation of Exponential Functions Calculus Modul C Diffrntiation of Eponntial Functions Copyright This publication Th Northrn Albrta Institut of Tchnology 007. All Rights Rsrvd. LAST REVISED March, 009 Introduction to Diffrntiation of

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Thomas Whitham Sith Form Pur Mathmatics Unit C Algbra Trigonomtr Gomtr Calculus Vctor gomtr Pag Algbra Molus functions graphs, quations an inqualitis Graph of f () Draw f () an rflct an part of th curv

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

10. EXTENDING TRACTABILITY

10. EXTENDING TRACTABILITY Coping with NP-compltnss 0. EXTENDING TRACTABILITY ining small vrtx covrs solving NP-har problms on trs circular arc covrings vrtx covr in bipartit graphs Q. Suppos I n to solv an NP-complt problm. What

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by D. Klain Vrsion 207.0.05 Corrctions and commnts ar wlcom. Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix A A k I + A + k!

More information

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES

A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES A RELATIVISTIC LAGRANGIAN FOR MULTIPLE CHARGED POINT-MASSES ADRIAAN DANIËL FOKKER (1887-197) A translation of: Ein invariantr Variationssatz für i Bwgung mhrrr lctrischr Massntilshn Z. Phys. 58, 386-393

More information

The Matrix Exponential

The Matrix Exponential Th Matrix Exponntial (with xrciss) by Dan Klain Vrsion 28928 Corrctions and commnts ar wlcom Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial of A to b th matrix () A A k I + A + k!

More information

The second condition says that a node α of the tree has exactly n children if the arity of its label is n.

The second condition says that a node α of the tree has exactly n children if the arity of its label is n. CS 6110 S14 Hanout 2 Proof of Conflunc 27 January 2014 In this supplmntary lctur w prov that th λ-calculus is conflunt. This is rsult is u to lonzo Church (1903 1995) an J. arkly Rossr (1907 1989) an is

More information

Principles of Humidity Dalton s law

Principles of Humidity Dalton s law Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid

More information

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression

Applied Statistics II - Categorical Data Analysis Data analysis using Genstat - Exercise 2 Logistic regression Applid Statistics II - Catgorical Data Analysis Data analysis using Gnstat - Exrcis 2 Logistic rgrssion Analysis 2. Logistic rgrssion for a 2 x k tabl. Th tabl blow shows th numbr of aphids aliv and dad

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

a 1and x is any real number.

a 1and x is any real number. Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars

More information

Grade 12 (MCV4UE) AP Calculus Page 1 of 5 Derivative of a Function & Differentiability

Grade 12 (MCV4UE) AP Calculus Page 1 of 5 Derivative of a Function & Differentiability Gra (MCV4UE) AP Calculus Pag of 5 Drivativ of a Function & Diffrntiabilit Th Drivativ at a Point f ( a h) f ( a) Rcall, lim provis th slop of h0 h th tangnt to th graph f ( at th point a, f ( a), an th

More information

EEO 401 Digital Signal Processing Prof. Mark Fowler

EEO 401 Digital Signal Processing Prof. Mark Fowler EEO 401 Digital Signal Procssing Prof. Mark Fowlr ot St #18 Introduction to DFT (via th DTFT) Rading Assignmnt: Sct. 7.1 of Proakis & Manolakis 1/24 Discrt Fourir Transform (DFT) W v sn that th DTFT is

More information

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator.

Exam 1. It is important that you clearly show your work and mark the final answer clearly, closed book, closed notes, no calculator. Exam N a m : _ S O L U T I O N P U I D : I n s t r u c t i o n s : It is important that you clarly show your work and mark th final answr clarly, closd book, closd nots, no calculator. T i m : h o u r

More information

Problem Set 6 Solutions

Problem Set 6 Solutions 6.04/18.06J Mathmatics for Computr Scinc March 15, 005 Srini Dvadas and Eric Lhman Problm St 6 Solutions Du: Monday, March 8 at 9 PM in Room 3-044 Problm 1. Sammy th Shark is a financial srvic providr

More information

4 x 4, and. where x is Town Square

4 x 4, and. where x is Town Square Accumulation and Population Dnsity E. A city locatd along a straight highway has a population whos dnsity can b approimatd by th function p 5 4 th distanc from th town squar, masurd in mils, whr 4 4, and

More information

First derivative analysis

First derivative analysis Robrto s Nots on Dirntial Calculus Chaptr 8: Graphical analysis Sction First drivativ analysis What you nd to know alrady: How to us drivativs to idntiy th critical valus o a unction and its trm points

More information

EXST Regression Techniques Page 1

EXST Regression Techniques Page 1 EXST704 - Rgrssion Tchniqus Pag 1 Masurmnt rrors in X W hav assumd that all variation is in Y. Masurmnt rror in this variabl will not ffct th rsults, as long as thy ar uncorrlatd and unbiasd, sinc thy

More information

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005

PHYS ,Fall 05, Term Exam #1, Oct., 12, 2005 PHYS1444-,Fall 5, Trm Exam #1, Oct., 1, 5 Nam: Kys 1. circular ring of charg of raius an a total charg Q lis in th x-y plan with its cntr at th origin. small positiv tst charg q is plac at th origin. What

More information

Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration

More information

Constants and Conversions:

Constants and Conversions: EXAM INFORMATION Radial Distribution Function: P 2 ( r) RDF( r) Br R( r ) 2, B is th normalization constant. Ordr of Orbital Enrgis: Homonuclar Diatomic Molculs * * * * g1s u1s g 2s u 2s u 2 p g 2 p g

More information

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH.

COMPUTER GENERATED HOLOGRAMS Optical Sciences 627 W.J. Dallas (Monday, April 04, 2005, 8:35 AM) PART I: CHAPTER TWO COMB MATH. C:\Dallas\0_Courss\03A_OpSci_67\0 Cgh_Book\0_athmaticalPrliminaris\0_0 Combath.doc of 8 COPUTER GENERATED HOLOGRAS Optical Scincs 67 W.J. Dallas (onday, April 04, 005, 8:35 A) PART I: CHAPTER TWO COB ATH

More information

Quasi-Classical States of the Simple Harmonic Oscillator

Quasi-Classical States of the Simple Harmonic Oscillator Quasi-Classical Stats of th Simpl Harmonic Oscillator (Draft Vrsion) Introduction: Why Look for Eignstats of th Annihilation Oprator? Excpt for th ground stat, th corrspondnc btwn th quantum nrgy ignstats

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY

SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY SIGNIFICANCE OF SMITH CHART IN ANTENNA TECHNOLOGY P. Poornima¹, Santosh Kumar Jha² 1 Associat Profssor, 2 Profssor, ECE Dpt., Sphoorthy Enginring Collg Tlangana, Hyraba (Inia) ABSTRACT This papr prsnts

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

2. Laser physics - basics

2. Laser physics - basics . Lasr physics - basics Spontanous and stimulatd procsss Einstin A and B cofficints Rat quation analysis Gain saturation What is a lasr? LASER: Light Amplification by Stimulatd Emission of Radiation "light"

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

ph People Grade Level: basic Duration: minutes Setting: classroom or field site

ph People Grade Level: basic Duration: minutes Setting: classroom or field site ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:

More information

1 Minimum Cut Problem

1 Minimum Cut Problem CS 6 Lctur 6 Min Cut and argr s Algorithm Scribs: Png Hui How (05), Virginia Dat: May 4, 06 Minimum Cut Problm Today, w introduc th minimum cut problm. This problm has many motivations, on of which coms

More information

1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h.

1 1 1 p q p q. 2ln x x. in simplest form. in simplest form in terms of x and h. NAME SUMMER ASSIGNMENT DUE SEPTEMBER 5 (FIRST DAY OF SCHOOL) AP CALC AB Dirctions: Answr all of th following qustions on a sparat sht of papr. All work must b shown. You will b tstd on this matrial somtim

More information

(1) Then we could wave our hands over this and it would become:

(1) Then we could wave our hands over this and it would become: MAT* K285 Spring 28 Anthony Bnoit 4/17/28 Wk 12: Laplac Tranform Rading: Kohlr & Johnon, Chaptr 5 to p. 35 HW: 5.1: 3, 7, 1*, 19 5.2: 1, 5*, 13*, 19, 45* 5.3: 1, 11*, 19 * Pla writ-up th problm natly and

More information

Homework #3. 1 x. dx. It therefore follows that a sum of the

Homework #3. 1 x. dx. It therefore follows that a sum of the Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-

More information

Problem Set #2 Due: Friday April 20, 2018 at 5 PM.

Problem Set #2 Due: Friday April 20, 2018 at 5 PM. 1 EE102B Spring 2018 Signal Procssing and Linar Systms II Goldsmith Problm St #2 Du: Friday April 20, 2018 at 5 PM. 1. Non-idal sampling and rcovry of idal sampls by discrt-tim filtring 30 pts) Considr

More information

SOLAR SYSTEM STABILITY EXPLAINED UNDER THE N-BODY PROBLEM SOLUTION

SOLAR SYSTEM STABILITY EXPLAINED UNDER THE N-BODY PROBLEM SOLUTION SOLAR SYSTEM STABILITY EXPLAINED UNDER THE N-BODY PROBLEM SOLUTION Jorg A Franco R E-ail: gorgafr@gailco Abstract: Th priction of th ovnt of a group of N gravitationally attracting bois aroun its cntr

More information

EECE 301 Signals & Systems Prof. Mark Fowler

EECE 301 Signals & Systems Prof. Mark Fowler EECE 301 Signals & Systms Prof. Mark Fowlr ot St #21 D-T Signals: Rlation btwn DFT, DTFT, & CTFT 1/16 W can us th DFT to implmnt numrical FT procssing This nabls us to numrically analyz a signal to find

More information

PROBLEM SET Problem 1.

PROBLEM SET Problem 1. PROLEM SET 1 PROFESSOR PETER JOHNSTONE 1. Problm 1. 1.1. Th catgory Mat L. OK, I m not amiliar with th trminology o partially orr sts, so lt s go ovr that irst. Dinition 1.1. partial orr is a binary rlation

More information

2. Finite Impulse Response Filters (FIR)

2. Finite Impulse Response Filters (FIR) .. Mthos for FIR filtrs implmntation. Finit Impuls Rspons Filtrs (FIR. Th winow mtho.. Frquncy charactristic uniform sampling. 3. Maximum rror minimizing. 4. Last-squars rror minimizing.. Mthos for FIR

More information

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises

Chapter 3 Exponential and Logarithmic Functions. Section a. In the exponential decay model A. Check Point Exercises Chaptr Eponntial and Logarithmic Functions Sction. Chck Point Erciss. a. A 87. Sinc is yars aftr, whn t, A. b. A A 87 k() k 87 k 87 k 87 87 k.4 Thus, th growth function is A 87 87.4t.4t.4t A 87..4t 87.4t

More information

Chapter 13 Aggregate Supply

Chapter 13 Aggregate Supply Chaptr 13 Aggrgat Supply 0 1 Larning Objctivs thr modls of aggrgat supply in which output dpnds positivly on th pric lvl in th short run th short-run tradoff btwn inflation and unmploymnt known as th Phillips

More information

64. A Conic Section from Five Elements.

64. A Conic Section from Five Elements. . onic Sction from Fiv Elmnts. To raw a conic sction of which fiv lmnts - points an tangnts - ar known. W consir th thr cass:. Fiv points ar known.. Four points an a tangnt lin ar known.. Thr points an

More information

Prod.C [A] t. rate = = =

Prod.C [A] t. rate = = = Concntration Concntration Practic Problms: Kintics KEY CHEM 1B 1. Basd on th data and graph blow: Ract. A Prod. B Prod.C..25.. 5..149.11.5 1..16.144.72 15..83.167.84 2..68.182.91 25..57.193.96 3..5.2.1

More information

Gradebook & Midterm & Office Hours

Gradebook & Midterm & Office Hours Your commnts So what do w do whn on of th r's is 0 in th quation GmM(1/r-1/r)? Do w nd to driv all of ths potntial nrgy formulas? I don't undrstand springs This was th first lctur I actually larnd somthing

More information

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles.

Content Skills Assessments Lessons. Identify, classify, and apply properties of negative and positive angles. Tachr: CORE TRIGONOMETRY Yar: 2012-13 Cours: TRIGONOMETRY Month: All Months S p t m b r Angls Essntial Qustions Can I idntify draw ngativ positiv angls in stard position? Do I hav a working knowldg of

More information

CS 491 G Combinatorial Optimization

CS 491 G Combinatorial Optimization CS 49 G Cobinatorial Optiization Lctur Nots Junhui Jia. Maiu Flow Probls Now lt us iscuss or tails on aiu low probls. Thor. A asibl low is aiu i an only i thr is no -augnting path. Proo: Lt P = A asibl

More information

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation.

Fourier Transforms and the Wave Equation. Key Mathematics: More Fourier transform theory, especially as applied to solving the wave equation. Lur 7 Fourir Transforms and th Wav Euation Ovrviw and Motivation: W first discuss a fw faturs of th Fourir transform (FT), and thn w solv th initial-valu problm for th wav uation using th Fourir transform

More information

Solution of Assignment #2

Solution of Assignment #2 olution of Assignmnt #2 Instructor: Alirza imchi Qustion #: For simplicity, assum that th distribution function of T is continuous. Th distribution function of R is: F R ( r = P( R r = P( log ( T r = P(log

More information

Einstein Equations for Tetrad Fields

Einstein Equations for Tetrad Fields Apiron, Vol 13, No, Octobr 006 6 Einstin Equations for Ttrad Filds Ali Rıza ŞAHİN, R T L Istanbul (Turky) Evry mtric tnsor can b xprssd by th innr product of ttrad filds W prov that Einstin quations for

More information

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012

The van der Waals interaction 1 D. E. Soper 2 University of Oregon 20 April 2012 Th van dr Waals intraction D. E. Sopr 2 Univrsity of Orgon 20 pril 202 Th van dr Waals intraction is discussd in Chaptr 5 of J. J. Sakurai, Modrn Quantum Mchanics. Hr I tak a look at it in a littl mor

More information

Coupled Pendulums. Two normal modes.

Coupled Pendulums. Two normal modes. Tim Dpndnt Two Stat Problm Coupld Pndulums Wak spring Two normal mods. No friction. No air rsistanc. Prfct Spring Start Swinging Som tim latr - swings with full amplitud. stationary M +n L M +m Elctron

More information

SER/BER in a Fading Channel

SER/BER in a Fading Channel SER/BER in a Fading Channl Major points for a fading channl: * SNR is a R.V. or R.P. * SER(BER) dpnds on th SNR conditional SER(BER). * Two prformanc masurs: outag probability and avrag SER(BER). * Ovrall,

More information

3 2x. 3x 2. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

3 2x. 3x 2.   Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB Math B Intgration Rviw (Solutions) Do ths intgrals. Solutions ar postd at th wbsit blow. If you hav troubl with thm, sk hlp immdiatly! () 8 d () 5 d () d () sin d (5) d (6) cos d (7) d www.clas.ucsb.du/staff/vinc

More information

4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16.

4. (5a + b) 7 & x 1 = (3x 1)log 10 4 = log (M1) [4] d = 3 [4] T 2 = 5 + = 16 or or 16. . 7 7 7... 7 7 (n )0 7 (M) 0(n ) 00 n (A) S ((7) 0(0)) (M) (7 00) 8897 (A). (5a b) 7 7... (5a)... (M) 7 5 5 (a b ) 5 5 a b (M)(A) So th cofficint is 75 (A) (C) [] S (7 7) (M) () 8897 (A) (C) [] 5. x.55

More information

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved.

6.1 Integration by Parts and Present Value. Copyright Cengage Learning. All rights reserved. 6.1 Intgration by Parts and Prsnt Valu Copyright Cngag Larning. All rights rsrvd. Warm-Up: Find f () 1. F() = ln(+1). F() = 3 3. F() =. F() = ln ( 1) 5. F() = 6. F() = - Objctivs, Day #1 Studnts will b

More information

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory

Ch. 24 Molecular Reaction Dynamics 1. Collision Theory Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic

More information

Greenfield Wind Farm. Visual Simulation 1. Affinity Renewables Inc. Figure As viewed from Trans Canada Highway 104.

Greenfield Wind Farm. Visual Simulation 1. Affinity Renewables Inc. Figure As viewed from Trans Canada Highway 104. Affinity Rnwabls Inc. Figur 6.12 Grnfil Win Farm Visual Simulation 1 As viw from Trans Canaa Highway 104 Easting: 487,437 Northing: 5,029,060 Photograph Dat: Octobr 28, 2013 Viw Angl: 163 Dgrs Imag Manufacturr:

More information

Pipe flow friction, small vs. big pipes

Pipe flow friction, small vs. big pipes Friction actor (t/0 t o pip) Friction small vs larg pips J. Chaurtt May 016 It is an intrsting act that riction is highr in small pips than largr pips or th sam vlocity o low and th sam lngth. Friction

More information

Appendix 2.3 General Solutions for the Step Response of Third- and Fourth-Order Systems (with some unpleasant surprises!)

Appendix 2.3 General Solutions for the Step Response of Third- and Fourth-Order Systems (with some unpleasant surprises!) P.Stariè, E.Margan Appnix 2. A2..1 A2..2 Contnts: Appnix 2. Gnral Solutions for th Stp Rspons of Thir- an Fourth-Orr Systms (with som unplasant surpriss!) Thr is no such thing as instant xprinc! ( Oppnhimr

More information

4.2 Design of Sections for Flexure

4.2 Design of Sections for Flexure 4. Dsign of Sctions for Flxur This sction covrs th following topics Prliminary Dsign Final Dsign for Typ 1 Mmbrs Spcial Cas Calculation of Momnt Dmand For simply supportd prstrssd bams, th maximum momnt

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information