How Accurately do Current Force Fields Predict. Experimental Peptide Conformations? An Adiabatic Free Energy Dynamics Study:

Size: px
Start display at page:

Download "How Accurately do Current Force Fields Predict. Experimental Peptide Conformations? An Adiabatic Free Energy Dynamics Study:"

Transcription

1 How Accurately do Current Force Fields Predict Experimental Peptide Conformations? An Adiabatic Dynamics Study: Supplementary Information (SI) Alexandar T. Tzanov, Michel A. Cuendet,, and Mark E. Tuckerman,, Department of Chemistry, New York University, New York, NY 13, USA, Swiss Institute of Bioinformatics, UNIL Sorge, 115 Lausanne, Switzerland, and Courant Institute of Mathematical Sciences, New York University, New York, New York 13, USA 1 Supplementary Information As Supplementary Information, we provide additional tables and figures with information that is not necessary to point of the main text. Supplementary tables include quantitative information about the position and height of FES minima for each of the system considered in this study. We also provide numerical values for the macrostate populations obtained from the clustering approach and Eq. () and represented in Figures 5 and. In addition, the statistical uncertainty related to both FES minima and macrostate populations are given for each system. To whom correspondence should be addressed Department of Chemistry, New York University, New York, NY 13, USA Swiss Institute of Bioinformatics, UNIL Sorge, 115 Lausanne, Switzerland Courant Institute of Mathematical Sciences, New York University, New York, New York 13, USA 1

2 Supplementary figures show the FES and clusters obtained for all systems and force fields, as represented in the middle and lower panels of Figure 3.

3 1.1 Supplementary Tables NAAMA in Solution Table S1: Calculated coordinates in degrees, free energy values and barriers in between conformers for NA-A-MA in solution. FE FE CHARMM3 CHARMM7 α R C P II C7 eq C7 ax α L C5->P II P II ->α L 7..5 C7 ax ->α 5.3. α R ->α L AMBER99SB FUJI α R C P II C7 eq C7 ax α L C5->P II.9. P II ->α L C7 ax ->α. 5. α R ->α L OPLS AA/L GROMOS 5a7 α R C P II C7 eq C7 ax α L C5->P II P II ->α L C7 ax ->α R.7.3 α R ->α L α R ->α

4 Table S: Calculated fractional populations vs. average experimental populations from Ref. 3 per conformer for NA-A-MA in solution. An asterisk (*) denotes deviation from averaged experimental data. C5 P II α R C5 PII αr Experimental CHARMM CHARMM AMBER FUJI FF OPLS-AA/L GROMOS

5 1.1. NATMA in Solution Table S3: Calculated macrostates and conformers for NA-T-MA in solution with CHARMM7 Macrostate Conformer χ 1 χ FE [] C5 (AP) C5 (AP) P II (AΦ) C7 eq (ΦP) α R (ΦA) C7 ax (AA) C7 ax (PA) α L Table S: Calculated macrostates and conformers for NA-T-MA in solution with CHARMM3 Macrostate Conformer χ 1 χ FE [] C5 (AP) C5 (AP) P II (AΦ) C7 eq (ΦP) α R (ΦA) C7 ax (PA) α L Table S5: Calculated macrostates and conformers for NA-T-MA in solution with AMB99SB Macrostates Conformer χ 1 χ FE [] C5 (AP) C5 (AΦ) P II (AΦ) C7 eq (ΦP) α R (AP) α R (ΦA) C7 ax (AP) C7 ax (PA) α L

6 Table S: Calculated macrostates and conformers for NA-T-MA in solution with FUJI FF Macrostate Conformer χ 1 χ FE [] C5 (AP) C5 (AP) PII (AΦ) C7 eq (ΦP) α R (AP) C7 ax (AP) α L Table S7: Calculated macrostates and conformers for NA-T-MA in solution with OPLS-AA/L Macrostates Conformer χ 1 χ FE [] C5 (AP) C5 (AP) P II (AΦ) C7 eq (ΦP) C7 eq (ΦP) α R (ΦA) C7 ax (AP) C7 ax (PA) α L Table S: Calculated macrostates and conformers for NA-T-MA in solution with GROMOS Macrostates Conformer χ 1 χ FE [] C5 (AP) P II (AΦ) C7 eq (ΦP) α R (ΦA) C7 ax (PAP) α L Table S9: Calculated fractional populations of NA-T-MA macrostates in solution vs. experimental data. An asterisk (*) denotes deviation from experimental results. C5 P II α R C5 PII αr Experimental 5 CHARMM CHARMM AMB99SB FUJI FF OPLS-AA/L GROMOS

7 1.1.3 NATMA in the Gas Phase Table S1: Calculated conformers of NA-T-MA in gas phase with the CHARMM7 force field vs. data from Ref.. In Ref., relative free energies of the 1 lowest-energy minima are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C7 eq (AP) C7 eq (AΦ) C5 (ΦP) C5 (AΦ) A C7 eq (ΦP) C α R C7 ax Table S11: Calculated conformers of NA-T-MA in gas phase with CHARM3 force field vs. data from Ref. and their relation to Macrostates. In Ref., relative free energies are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C7 eq (AP) C5 (AΦ) A C5 (ΦP) C7 eq (ΦP) C C7 eq (AΦ) α R C7 ax Table S1: Calculated conformers of NA-T-MA in gas phase with AMBER99SB force field vs. data from Ref. and their relation to macrostates. In Ref., relative free energies of the 1 lowestenergy minima are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C7 eq (AP) C5 (AΦ) A C7 eq (ΦP) C α R C7 ax

8 Table S13: Calculated conformers of NA-T-MA in gas phase with FUJI force field vs. data from Ref. and their relation to Macrostates. In Ref., relative free energies of the 1 lowest-energy minima are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C7 eq (AP) C5 (AΦ) A C5 (ΦP) C7 eq (ΦP) C α R C7 eq (AΦ) C7 ax Table S1: Calculated conformers of NA-T-MA in gas phase with OPLS-AA/L force field vs. data from Ref.. In Ref., relative free energies of the 1 lowest-energy minima are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C5 (AΦ) A C7 eq (ΦP) C C7 ax α R Table S15: Calculated conformers of NA-T-MA in gas phase with GROMOS 5a7 force field vs. data from Ref. and their relation to Macrostates. In Ref., relative free energies are calculated at the DFT Becke3LYP/-31+GG* level of theory. Structure Conformer χ 1 χ FE [] Ref. Macrostate C5 (AP) B C5 (ΦP) C7 eq (AP) C5 (AΦ) A C7 eq (ΦP) C α R C7 eq (AΦ) C7 ax

9 Table S1: Calculated fractional populations vs experimental data for NATMA in gas phase. * denotes difference to experimental findings. A B C A B C Experimental 5 3 CHARMM CHARMM3 5 - AMB99SB FUJI FF - - OPLS-AA/L GROMOS

10 1.1. Statistical Uncertainties on FES and Macrostate Populations Table S17: Variability of FES per FF for NAAMA in solution. SE and CI denote confidence interval of calculated free enrgy and confidence interval of this energy per macrostate. NAAMA in SOLUTION C5 PII α R C7 SE [] CI [] Population C3 SE [] CI [] Population AMB99 SE [] CI [] Poulation FUJI-FF SE [] CI [].9..1 Poulation OPLS SE [] CI [] Population GROMOS SE [] Population CI

11 Table S1: Variability of FES per FF for NATMA in solution. Popultation denotes confidence interval of populations per macrostate, SE and CI denote confidence interval of calculated free enrgy and confidence interval of this energy per macrostate. NATMA in SOLUTION C5 PII α R C7 SE [] CI [] Population C3 SE [] CI [] Population AMB99 SE [] CI [] Poulation FUJI-FF SE(cal/mol) CI [] Poulation OPLS SE [] CI [] Population GROMOS SE [] CI [] Population

12 Table S19: Variability of FES per FF for NATMA in gas phase. Popultation denotes confidence interval of populations per macrostate, SE and CI denote confidence interval of calculated free energy and confidence interval of this energy per macrostate. NATMA in GAS PHASE A B C C7 SE [] CI [] Population C3 SE [] CI [] Population AMB99 SE [] CI [] Poulation FUJI-FF SE [] CI [] Poulation OPLS SE [] CI [] Population GROMOS SE [] CI [] Population

13 1. Supplementary Figures (a) (b) (c) (d) (e) (f) Figure S1: FES of NA-A-MA in solution (a,b) with CHARMM7 (c,d) with CHARMM3 (e,f) with AMBER99SB (g,h) with FUJI FF (i,j) with OPLS-AA/L. (k,l) with GROMOS 5a7 13

14 (g) (h) (i) (j) (k) (l) Figure S1: (continued) 1

15 χ (a) (b) (c) χ (d) (e) χ χ (f) (g) (h) (i) Figure S: FES of NA-T-MA in solution with CV projected in the (Φ, Ψ) plane, clusters projected in the (Φ, Ψ) plane and FES projected in the (, χ ) plane, for: (a,b,c) with CHARMM7 (d,e,f) with CHARMM3 (g,h,i) with AMBER99SB (j,k,l) with FUJI FF (m,n,o) with OPLS-AA/L (p,q,r) with GROMOS 5a7 15

16 (j) (k) 1 (l) χ (m) (n) 1 15 (o) χ χ χ (p) 5 (q) Figure S: (continued) (r)

17 χ (a) (b) (c) χ (d) (e) χ (g) (f) (h) (i) Figure S3: FES of NA-T-MA in the gas phase with CV projected in the (Φ, Ψ) plane, clusters projected in the (Φ, Ψ) plane and FES projected in the (, χ ) plane, for: (a,b,c) with CHARMM7 (d,e,f) with CHARMM3 (g,h,i) with AMBER99SB (j,k,l) with FUJI FF (m,n,o) with OPLS-AA/L (p,q,r) with G5a7 17

18 (j) (k) 1 15 (l) χ (m) (n) 1 15 (o) χ (p) gas kcal/mol 1 χ (q) Figure S3: (continued) (r)

Free energy calculations and the potential of mean force

Free energy calculations and the potential of mean force Free energy calculations and the potential of mean force IMA Workshop on Classical and Quantum Approaches in Molecular Modeling Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science

More information

5.1 Triangle Congruence Postulates

5.1 Triangle Congruence Postulates 5.1 Triangle Congruence Postulates Congruent Figures: Figures that are the same shape and size. All corresponding angles are congruent All corresponding sides are congruent Name: How are congruent figures

More information

Lecture 8: Introduction to Density Functional Theory

Lecture 8: Introduction to Density Functional Theory Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science

More information

ELECTRONIC SUPPLEMENTARY INFORMATION. Nonlinear machine learning and design of. reconfigurable digital colloids

ELECTRONIC SUPPLEMENTARY INFORMATION. Nonlinear machine learning and design of. reconfigurable digital colloids Electronic Supplementary Material (ESI) for Soft Matter. This journal is The Royal Society of Chemistry 2016 ELECTRONIC SUPPLEMENTARY INFORMATION Nonlinear machine learning and design of reconfigurable

More information

J JUL - 25-JUL 2016 HOUSEHOLD FINANCES RESEARCH

J JUL - 25-JUL 2016 HOUSEHOLD FINANCES RESEARCH J00 JUL JUL 0 Table XF0 In terms of your finances, how often if at all, do you and your household find yourselves without enough money to buy enough food? BASE: ALL ADULTS AGED + IN GREAT BRITAIN Page

More information

0811ge. Geometry Regents Exam

0811ge. Geometry Regents Exam 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

More information

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2.

Mathematics. Exercise 6.4. (Chapter 6) (Triangles) (Class X) Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. () Exercise 6.4 Question 1: Let and their areas be, respectively, 64 cm 2 and 121 cm 2. If EF = 15.4 cm, find BC. Answer 1: 1 () Question 2: Diagonals of a trapezium ABCD with AB DC intersect each other

More information

G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2

G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2 Regents Exam Questions www.jmap.org Name: 1 In square GEOM, the coordinates of G are (2, 2) and the coordinates of O are ( 4,2). Determine and state the coordinates of vertices E and M. [The use of the

More information

G.CO.6-9 ONLY COMMON CORE QUESTIONS

G.CO.6-9 ONLY COMMON CORE QUESTIONS Class: Date: G.CO.6-9 ONLY COMMON CORE QUESTIONS Multiple Choice Identify the choice that best completes the statement or answers the question. 1 The image of ABC after a rotation of 90º clockwise about

More information

2.4 Algebraic and Congruence Properties

2.4 Algebraic and Congruence Properties 2.4 Algebraic and Congruence Properties Learning Objectives Understand basic properties of equality and congruence. Solve equations and justify each step in the solution. Use a 2-column format to prove

More information

= (, ) V λ (1) λ λ ( + + ) P = [ ( ), (1)] ( ) ( ) = ( ) ( ) ( 0 ) ( 0 ) = ( 0 ) ( 0 ) 0 ( 0 ) ( ( 0 )) ( ( 0 )) = ( ( 0 )) ( ( 0 )) ( + ( 0 )) ( + ( 0 )) = ( + ( 0 )) ( ( 0 )) P V V V V V P V P V V V

More information

SUPPORTING INFORMATION. Table S1: Use of different functionals and variation of HF exchange on IS/HS splitting

SUPPORTING INFORMATION. Table S1: Use of different functionals and variation of HF exchange on IS/HS splitting SUPPORTING INFORMATION List of Contents Table S1: Use of different functionals and variation of HF exchange on IS/HS splitting S2 Table S2: Structural parameters using the B3LYP** functional for the IS

More information

ψ j φ j+1 Motif position

ψ j φ j+1 Motif position 1.0 % Occupancy 0.8 0.6 0.4 0.2 0.0 ψ i-1 φ i ψ j φ j+1 ψ k-1 Motif position φ Supplementary Figure 1 Residue profiles for the positions in the β-sheet motif. Residue types as percentages for the six positions

More information

the coordinates of C (3) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places. (4)

the coordinates of C (3) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places. (4) . The line l has equation, 2 4 3 2 + = λ r where λ is a scalar parameter. The line l 2 has equation, 2 0 5 3 9 0 + = µ r where μ is a scalar parameter. Given that l and l 2 meet at the point C, find the

More information

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below.

0611ge. Geometry Regents Exam Line segment AB is shown in the diagram below. 0611ge 1 Line segment AB is shown in the diagram below. In the diagram below, A B C is a transformation of ABC, and A B C is a transformation of A B C. Which two sets of construction marks, labeled I,

More information

Hierarchical Coupling of First Principles. Molecular Dynamics with Advanced Sampling. Methods: Supplementary Information

Hierarchical Coupling of First Principles. Molecular Dynamics with Advanced Sampling. Methods: Supplementary Information Hierarchical Coupling of First Principles Molecular Dynamics with Advanced Sampling Methods: Supplementary Information Emre Sevgen,, Federico Giberti,, Hythem Sidky, Jonathan K. Whitmer, Giulia Galli,

More information

2014 Ryan Lawn and Tree Overseeding Evaluation. University of Nebraska-Lincoln & Kansas State University. Zac Reicher, Jared Hoyle, and Matt Sousek

2014 Ryan Lawn and Tree Overseeding Evaluation. University of Nebraska-Lincoln & Kansas State University. Zac Reicher, Jared Hoyle, and Matt Sousek 2014 Ryan Lawn and Tree Overseeding Evaluation University of Nebraska-Lincoln & Kansas State University Zac Reicher, Jared Hoyle, and Matt Sousek This study was done at the Rocky Ford Turfgrass Research

More information

Molecular Mechanics. Yohann Moreau. November 26, 2015

Molecular Mechanics. Yohann Moreau. November 26, 2015 Molecular Mechanics Yohann Moreau yohann.moreau@ujf-grenoble.fr November 26, 2015 Yohann Moreau (UJF) Molecular Mechanics, Label RFCT 2015 November 26, 2015 1 / 29 Introduction A so-called Force-Field

More information

Created by T. Madas MIXED SURD QUESTIONS. Created by T. Madas

Created by T. Madas MIXED SURD QUESTIONS. Created by T. Madas MIXED SURD QUESTIONS Question 1 (**) Write each of the following expressions a single simplified surd a) 150 54 b) 21 7 C1A, 2 6, 3 7 Question 2 (**) Write each of the following surd expressions as simple

More information

CHAPTER 5 : THE STRAIGHT LINE

CHAPTER 5 : THE STRAIGHT LINE EXERCISE 1 CHAPTER 5 : THE STRAIGHT LINE 1. In the diagram, PQ is a straight line. P 4 2 4 3 2 1 0 1 2 2 2. Find (a) the -intercept, (b) the gradient, of the straight line. Q (5,18) Q Answer :a).. b) 3

More information

( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r)

( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) Born Oppenheimer Approximation: Ĥ el ( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) For a molecule with N electrons and M nuclei: Ĥ el What is E el (R)? s* potential surface Reaction Barrier Unstable intermediate

More information

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39

NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39 NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4 5 6 7 8 9 10 Total/100 A 80 B 70 C 60 D 50 E 40 U 39 1. Figure 2 y A(1, 7) B(20, 7) D(8, 2) O x C(p, q) The points A(1, 7), B(20, 7) and C(p, q) form

More information

Experimental location Land type Soil type ph. K (meq/100) Jute Agriculture Experimental Station (JAES), Manikgonj, BJRI

Experimental location Land type Soil type ph. K (meq/100) Jute Agriculture Experimental Station (JAES), Manikgonj, BJRI Soil characteristics Nutrient status Experimental location AEZ Land type Soil type ph % OM % N P (ppm) K (meq/100) Jute Agriculture Experimental Station (JAES), Manikgonj, BJRI Active Brahmaputra and Jamuna

More information

5-1 Perpendicular and Angle Bisectors

5-1 Perpendicular and Angle Bisectors 5-1 Perpendicular and Angle Bisectors Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Construct each of the following. 1. A perpendicular bisector. 2. An angle bisector. 3. Find the midpoint and

More information

Protein Modeling Methods. Knowledge. Protein Modeling Methods. Fold Recognition. Knowledge-based methods. Introduction to Bioinformatics

Protein Modeling Methods. Knowledge. Protein Modeling Methods. Fold Recognition. Knowledge-based methods. Introduction to Bioinformatics Protein Modeling Methods Introduction to Bioinformatics Iosif Vaisman Ab initio methods Energy-based methods Knowledge-based methods Email: ivaisman@gmu.edu Protein Modeling Methods Ab initio methods:

More information

Machine learning the Born-Oppenheimer potential energy surface: from molecules to materials. Gábor Csányi Engineering Laboratory

Machine learning the Born-Oppenheimer potential energy surface: from molecules to materials. Gábor Csányi Engineering Laboratory Machine learning the Born-Oppenheimer potential energy surface: from molecules to materials Gábor Csányi Engineering Laboratory Interatomic potentials for molecular dynamics Transferability biomolecular

More information

Lecture 11: Potential Energy Functions

Lecture 11: Potential Energy Functions Lecture 11: Potential Energy Functions Dr. Ronald M. Levy ronlevy@temple.edu Originally contributed by Lauren Wickstrom (2011) Microscopic/Macroscopic Connection The connection between microscopic interactions

More information

Current address: Department of Chemistry, Hong Kong Baptist University, Kowloon Tong, Hong Kong,

Current address: Department of Chemistry, Hong Kong Baptist University, Kowloon Tong, Hong Kong, Hydrolysis of Cisplatin - A Metadynamics Study Supporting Information Justin Kai-Chi Lau a and Bernd Ensing* b Department of Chemistry and Applied Bioscience, ETH Zurich, USI Campus, Computational Science,

More information

Supporting Information for. DNA elasticity from short DNA to nucleosomal DNA

Supporting Information for. DNA elasticity from short DNA to nucleosomal DNA Supporting Information for DNA elasticity from short DNA to nucleosomal DNA Ashok Garai, 1 Suman Saurabh, 1 Yves Lansac, 2 and Prabal K. Maiti* 1 1 Centre for Condensed Matter Theory, Department of Physics,

More information

All-atom Molecular Mechanics. Trent E. Balius AMS 535 / CHE /27/2010

All-atom Molecular Mechanics. Trent E. Balius AMS 535 / CHE /27/2010 All-atom Molecular Mechanics Trent E. Balius AMS 535 / CHE 535 09/27/2010 Outline Molecular models Molecular mechanics Force Fields Potential energy function functional form parameters and parameterization

More information

Assessing the potential of atomistic molecular dynamics simulations to probe reversible. protein-protein recognition and binding

Assessing the potential of atomistic molecular dynamics simulations to probe reversible. protein-protein recognition and binding Supporting information for Assessing the potential of atomistic molecular dynamics simulations to probe reversible protein-protein recognition and binding Luciano A. Abriata and Matteo Dal Peraro Laboratory

More information

Geometry Semester 1 Exam Released

Geometry Semester 1 Exam Released 1. Use the diagram. 3. In the diagram, mlmn 54. L 5 1 4 3 2 Which best describes the pair of angles 1 and 4? (A) complementary (B) linear pair (C) supplementary (D) vertical 2. Use the diagram. E F A B

More information

Geometry Regents Practice Midterm

Geometry Regents Practice Midterm Class: Date: Geometry Regents Practice Midterm Multiple Choice Identify the choice that best completes the statement or answers the question. 1. ( points) What is the equation of a line that is parallel

More information

Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

More information

Geometry Honors: Midterm Exam Review January 2018

Geometry Honors: Midterm Exam Review January 2018 Name: Period: The midterm will cover Chapters 1-6. Geometry Honors: Midterm Exam Review January 2018 You WILL NOT receive a formula sheet, but you need to know the following formulas Make sure you memorize

More information

: i; ii: i:i: I. : q t:iig l3 [i E. i;issii:i::: r p. ! s:r;e;:e;!f. as Iet5;Fgi. i EiiF;:'+3EI. : :*gsc:li-ii. ; si;;ei:i:g; .

: i; ii: i:i: I. : q t:iig l3 [i E. i;issii:i::: r p. ! s:r;e;:e;!f. as Iet5;Fgi. i EiiF;:'+3EI. : :*gsc:li-ii. ; si;;ei:i:g; . , / - H f ) - $ H A - --" G \/ - - f \f ff P) G T - ), - ) -..R '' (.) f- w (, AA - Нотная библиотека \ S R.- R \?! -! h )! - X* - Y - J. ** " { B e B Rk * f [He 1e [Y!!-- e *J! *Jee.1!.,1g -!. -! >. j.,

More information

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2

4) If ax 2 + bx + c = 0 has equal roots, then c is equal. b) b 2. a) b 2 Karapettai Nadar Boys Hr. Sec. School One Word Test No 1 Standard X Time: 20 Minutes Marks: (15 1 = 15) Answer all the 15 questions. Choose the orrect answer from the given four alternatives and write

More information

Relative binding enthalpies from molecular dynamics simulations. using a direct method

Relative binding enthalpies from molecular dynamics simulations. using a direct method Relative binding enthalpies from molecular dynamics simulations using a direct method Amitava Roy, 1 Duy P. Hua, 1 Joshua M. Ward, 1 and Carol Beth Post* Department of Medicinal Chemistry, Markey Center

More information

0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.

0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10. 0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation

More information

5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram.

5-1 Practice Form K. Midsegments of Triangles. Identify three pairs of parallel segments in the diagram. 5-1 Practice Form K Midsegments of Triangles Identify three pairs of parallel segments in the diagram. 1. 2. 3. Name the segment that is parallel to the given segment. 4. MN 5. ON 6. AB 7. CB 8. OM 9.

More information

Supplemental Material: Solute Adsorption at Air-Water Interfaces and Induced. Interface Fluctuations: The Hydrophobic Nature of Ions?

Supplemental Material: Solute Adsorption at Air-Water Interfaces and Induced. Interface Fluctuations: The Hydrophobic Nature of Ions? Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies Supplemental Material: Solute Adsorption at Air-Water Interfaces and Induced Interface

More information

Gauge field localization on brane worlds

Gauge field localization on brane worlds Gauge field localization on brane worlds Rommel Guerrero and R. Omar Rodriguez Universidad Centroccidental Lisandro Alvarado - Venezuela Miami 2013 R. Guerrero UCLA) Gauge field localization December 2013

More information

Enhanced sampling via molecular dynamics II: Unbiased approaches

Enhanced sampling via molecular dynamics II: Unbiased approaches Enhanced sampling via molecular dynamics II: Unbiased approaches Mark E. Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Sciences New York University, 100 Washington Square East, NY

More information

Chapter 2 Practice Test

Chapter 2 Practice Test Name: Class: Date: ID: A Chapter 2 Practice Test 1. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. 2. What is the conclusion of the following

More information

Supplementary Figure 2 FF at concentration of 8 mg/ml dissolved in 100% DMSO. The molecules assemble into plate-like structures. Scale bar is 50 µm.

Supplementary Figure 2 FF at concentration of 8 mg/ml dissolved in 100% DMSO. The molecules assemble into plate-like structures. Scale bar is 50 µm. 1 2 3 4 5 6 7 8 9 10 11 Supplementary Figure 1 Microfluidics device mixing efficiency. Yellow and blue food coloring solutions are introduced to inlets 1 and 2, respectively. After approximately one tenth

More information

High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules

High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules Markus Schneider Fritz Haber Institute of the MPS, Berlin, Germany École Polytechnique Fédérale de Lausanne, Switzerland دانشگاه

More information

Electronic Supplementary Information (ESI)

Electronic Supplementary Information (ESI) Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 2017 Electronic Supplementary Information (ESI) The correspondence between conformational

More information

Homework 10: p.147: 17-41, 45

Homework 10: p.147: 17-41, 45 2-4B: Writing Proofs Homework 10: p.147: 17-41, 45 Learning Objectives: Analyze figures to identify and use postulates about points, lines and planes Analyze and construct viable arguments in several proof

More information

Supporting Information of Carboranes: The Strongest Brønsted Acids in Alcohol Dehydration

Supporting Information of Carboranes: The Strongest Brønsted Acids in Alcohol Dehydration Electronic Supplementary Material (ESI) for Catalysis Science & Technology. This journal is The Royal Society of Chemistry 2017 Supporting Information of Carboranes: The Strongest Brønsted Acids in Alcohol

More information

Homework 3/ Solutions

Homework 3/ Solutions MTH 310-3 Abstract Algebra I and Number Theory S17 Homework 3/ Solutions Exercise 1. Prove the following Theorem: Theorem Let R and S be rings. Define an addition and multiplication on R S by for all r,

More information

Molecular Simulation II. Classical Mechanical Treatment

Molecular Simulation II. Classical Mechanical Treatment Molecular Simulation II Quantum Chemistry Classical Mechanics E = Ψ H Ψ ΨΨ U = E bond +E angle +E torsion +E non-bond Jeffry D. Madura Department of Chemistry & Biochemistry Center for Computational Sciences

More information

A matrix over a field F is a rectangular array of elements from F. The symbol

A matrix over a field F is a rectangular array of elements from F. The symbol Chapter MATRICES Matrix arithmetic A matrix over a field F is a rectangular array of elements from F The symbol M m n (F ) denotes the collection of all m n matrices over F Matrices will usually be denoted

More information

Aspects of nonautonomous molecular dynamics

Aspects of nonautonomous molecular dynamics Aspects of nonautonomous molecular dynamics IMA, University of Minnesota, Minneapolis January 28, 2007 Michel Cuendet Swiss Institute of Bioinformatics, Lausanne, Switzerland Introduction to the Jarzynski

More information

Narayana IIT Academy INDIA

Narayana IIT Academy INDIA Narayana II Academy INDIA Sec: Sr. II_IZ (Incoming) CU- Date:-5-8 ime: 7: AM to : AM 6_P Max.Marks: 86 KEY SHEE PHYSICS C A C 4 D 5 A 6 AC 7 AD 8 AD 9 ACD AC ACD ACD C 4 5 5 5 6 7 6 8 CHEMISRY 9 C A D

More information

Section 2.3: Particle Motion

Section 2.3: Particle Motion : Particle Motion Particle Motion Particle motion describes the physics of an object (a point) that moves along a line; usually horizontal There are three different functions that model this action Position!

More information

Millimeter and submillimeter wave spectra of N-methyl formamide and propionamide

Millimeter and submillimeter wave spectra of N-methyl formamide and propionamide Millimeter and submillimeter wave spectra of N-methyl formamide and propionamide A.A. Mescheryakov, E.A. Alekseev, V.V. Ilyushin Institute of Radio Astronomy, NASU, Kharkov, Ukraine R.A. Motiyenko, L.

More information

Algebraic Expressions

Algebraic Expressions Algebraic Expressions 1. Expressions are formed from variables and constants. 2. Terms are added to form expressions. Terms themselves are formed as product of factors. 3. Expressions that contain exactly

More information

Adaptive Tracking and Estimation for Nonlinear Control Systems

Adaptive Tracking and Estimation for Nonlinear Control Systems Adaptive Tracking and Estimation for Nonlinear Control Systems Michael Malisoff, Louisiana State University Joint with Frédéric Mazenc and Marcio de Queiroz Sponsored by NSF/DMS Grant 0708084 AMS-SIAM

More information

Name: Class: Date: B. The twentieth term is A. D. There is not enough information.

Name: Class: Date: B. The twentieth term is A. D. There is not enough information. Class: Date: Chapter 2 Review 1. Based on the pattern, what are the next two terms of the sequence? 9, 15, 21, 27,... A. 33, 972 B. 39, 45 C. 162, 972 D. 33, 39 2. What conjecture can you make about the

More information

b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem

b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals Converse d) Opposite sides Parallel and Congruent Theorem Chapter 7 1. State which theorem you can use to show that the quadrilateral is a parallelogram. a) Parallelogram Opposite Angles Converse b) Parallelogram Opposite Sides Converse c) Parallelogram Diagonals

More information

BOARD ANSWER PAPER : MARCH 2014

BOARD ANSWER PAPER : MARCH 2014 BOARD ANSWER PAPER : MARCH 014 ALGEBRA 1 Algebra 1. Attempt any five subquestions from the following: i. Given, t, t 4 1 d t 4 t 1 4 ii. (x + 5) (x ) 0 x + 5 0 or x 0 x 5 or x iii. Since, θ Valueof thecomponent

More information

The Erdos-Mordell inequality

The Erdos-Mordell inequality The Erdos-Mordell inequality George Tsintsifas, Thessaloniki, Greece. Let ABC be a triangle and an interior point M. We denote by AM =, BM = x 2, CM = x 3. The distances of the point M from BC, CA, AB

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Some Planar Isospectral Domains. Peter Buser, John Conway, Peter Doyle, and Klaus-Dieter Semmler. 1 Introduction

Some Planar Isospectral Domains. Peter Buser, John Conway, Peter Doyle, and Klaus-Dieter Semmler. 1 Introduction IMRN International Mathematics Research Notices 1994, No. 9 Some Planar Isospectral Domains Peter Buser, John Conway, Peter Doyle, and Klaus-Dieter Semmler 1 Introduction In 1965, Mark Kac [6] asked, Can

More information

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure.

Examples: Identify three pairs of parallel segments in the diagram. 1. AB 2. BC 3. AC. Write an equation to model this theorem based on the figure. 5.1: Midsegments of Triangles NOTE: Midsegments are also to the third side in the triangle. Example: Identify the 3 midsegments in the diagram. Examples: Identify three pairs of parallel segments in the

More information

Scuola di Chimica Computazionale

Scuola di Chimica Computazionale Societa Chimica Italiana Gruppo Interdivisionale di Chimica Computazionale Scuola di Chimica Computazionale Introduzione, per Esercizi, all Uso del Calcolatore in Chimica Organica e Biologica Modellistica

More information

Supplementary Fig. 1. Progress of the surface mediated Ullmann coupling reaction using STM at 5 K. Precursor molecules

Supplementary Fig. 1. Progress of the surface mediated Ullmann coupling reaction using STM at 5 K. Precursor molecules Supplementary Fig. 1. Progress of the surface mediated Ullmann coupling reaction using STM at 5 K. Precursor molecules (4-bromo-1-ethyl-2-fluorobenzene) are dosed on a Cu(111) surface and annealed to 80

More information

F. Bianchini, H. Fjeelvåg and P. Vajeeston Department of Chemistry University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway.

F. Bianchini, H. Fjeelvåg and P. Vajeeston Department of Chemistry University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway. Electronic Supplementary Material (ESI) for Physical Chemistry Chemical Physics. This journal is the Owner Societies 17 First-principles study of structural stability and electro-chemical properties of

More information

1. SETS AND FUNCTIONS

1. SETS AND FUNCTIONS . SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,

More information

Paper: 03 Class-X-Math: Summative Assessment - I

Paper: 03 Class-X-Math: Summative Assessment - I 1 P a g e Paper: 03 Class-X-Math: Summative Assessment - I Total marks of the paper: 90 Total time of the paper: 3.5 hrs Questions: 1] Triangle ABC is similar to triangle DEF and their areas are 64 cm

More information

Algorithmic Challenges in Photodynamics Simulations

Algorithmic Challenges in Photodynamics Simulations Algorithmic Challenges in Photodynamics Simulations Felix Plasser González Research Group Institute for Theoretical Chemistry, University of Vienna, Austria Grundlsee, 24 th February 2016 Photodynamics

More information

Supplementary information Silver (I) as DNA glue: Ag + - mediated guanine pairing revealed by removing Watson- Crick constraints

Supplementary information Silver (I) as DNA glue: Ag + - mediated guanine pairing revealed by removing Watson- Crick constraints Supplementary information Silver (I) as DNA glue: Ag + - mediated guanine pairing revealed by removing Watson- Crick constraints Steven M. Swasey [b], Leonardo Espinosa Leal [c], Olga Lopez- Acevedo [c],

More information

Session 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education

Session 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools

More information

Structural Bioinformatics (C3210) Molecular Mechanics

Structural Bioinformatics (C3210) Molecular Mechanics Structural Bioinformatics (C3210) Molecular Mechanics How to Calculate Energies Calculation of molecular energies is of key importance in protein folding, molecular modelling etc. There are two main computational

More information

Free Radical-Initiated Unfolding of Peptide Secondary Structure Elements

Free Radical-Initiated Unfolding of Peptide Secondary Structure Elements Free Radical-Initiated Unfolding of Peptide Secondary Structure Elements Thesis of the Ph.D. Dissertation by Michael C. Owen, M.Sc. Department of Chemical Informatics Faculty of Education University of

More information

Chem 1140; Molecular Modeling

Chem 1140; Molecular Modeling P. Wipf 1 Chem 1140 $E = -! (q a + q b )" ab S ab + ab!k

More information

Parts Manual. EPIC II Critical Care Bed REF 2031

Parts Manual. EPIC II Critical Care Bed REF 2031 EPIC II Critical Care Bed REF 2031 Parts Manual For parts or technical assistance call: USA: 1-800-327-0770 2013/05 B.0 2031-109-006 REV B www.stryker.com Table of Contents English Product Labels... 4

More information

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''?

Which statement is true about parallelogram FGHJ and parallelogram F ''G''H''J ''? Unit 2 Review 1. Parallelogram FGHJ was translated 3 units down to form parallelogram F 'G'H'J '. Parallelogram F 'G'H'J ' was then rotated 90 counterclockwise about point G' to obtain parallelogram F

More information

f(x + y) + f(x y) = 10.

f(x + y) + f(x y) = 10. Math Field Day 202 Mad Hatter A A Suppose that for all real numbers x and y, Then f(y x) =? f(x + y) + f(x y) = 0. A2 Find the sum + 2 + 4 + 5 + 7 + 8 + 0 + + +49 + 50 + 52 + 53 + 55 + 56 + 58 + 59. A3

More information

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES

STRAND J: TRANSFORMATIONS, VECTORS and MATRICES Mathematics SKE, Strand J STRAND J: TRANSFORMATIONS, VECTORS and MATRICES J4 Matrices Text Contents * * * * Section J4. Matrices: Addition and Subtraction J4.2 Matrices: Multiplication J4.3 Inverse Matrices:

More information

Supporting information to: Time-resolved observation of protein allosteric communication. Sebastian Buchenberg, Florian Sittel and Gerhard Stock 1

Supporting information to: Time-resolved observation of protein allosteric communication. Sebastian Buchenberg, Florian Sittel and Gerhard Stock 1 Supporting information to: Time-resolved observation of protein allosteric communication Sebastian Buchenberg, Florian Sittel and Gerhard Stock Biomolecular Dynamics, Institute of Physics, Albert Ludwigs

More information

Counting, symbols, positions, powers, choice, arithmetic, binary, translation, hex, addresses, and gates.

Counting, symbols, positions, powers, choice, arithmetic, binary, translation, hex, addresses, and gates. Counting, symbols, positions, powers, choice, arithmetic, binary, translation, he, addresses, and gates. Counting. Suppose the concern is a collection of objects. As an eample, let the objects be denoted

More information

Maharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution

Maharashtra State Board Class X Mathematics - Geometry Board Paper 2016 Solution Maharashtra State Board Class X Mathematics - Geometry Board Paper 016 Solution 1. i. ΔDEF ΔMNK (given) A( DEF) DE A( MNK) MN A( DEF) 5 5 A( MNK) 6 6...(Areas of similar triangles) ii. ΔABC is 0-60 -90

More information

Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation

Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation Polypeptide Folding Using Monte Carlo Sampling, Concerted Rotation, and Continuum Solvation Jakob P. Ulmschneider and William L. Jorgensen J.A.C.S. 2004, 126, 1849-1857 Presented by Laura L. Thomas and

More information

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain.

2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 1) Explain what it means to bisect a segment. Why is it impossible to bisect a line? 2) Are all linear pairs supplementary angles? Are all supplementary angles linear pairs? Explain. 3) Explain why a four-legged

More information

Introduction to Classical Molecular Dynamics. Giovanni Chillemi HPC department, CINECA

Introduction to Classical Molecular Dynamics. Giovanni Chillemi HPC department, CINECA Introduction to Classical Molecular Dynamics Giovanni Chillemi g.chillemi@cineca.it HPC department, CINECA MD ingredients Coordinates Velocities Force field Topology MD Trajectories Input parameters Analysis

More information

St Andrew s Academy Mathematics Department Higher Mathematics VECTORS

St Andrew s Academy Mathematics Department Higher Mathematics VECTORS St Andrew s Academy Mathematics Department Higher Mathematics VECTORS hsn.uk.net Higher Mathematics Vectors Contents Vectors 1 1 Vectors and Scalars EF 1 Components EF 1 Magnitude EF 4 Equal Vectors EF

More information

Objective Mathematics

Objective Mathematics Chapter No - ( Area Bounded by Curves ). Normal at (, ) is given by : y y. f ( ) or f ( ). Area d ()() 7 Square units. Area (8)() 6 dy. ( ) d y c or f ( ) c f () c f ( ) As shown in figure, point P is

More information

SUPPORTING INFORMATION. Control of the hierarchical assembly of π-conjugated. optoelectronic peptides by ph and flow

SUPPORTING INFORMATION. Control of the hierarchical assembly of π-conjugated. optoelectronic peptides by ph and flow Electronic Supplementary Material (ESI) for Organic & Biomolecular Chemistry. This journal is The Royal Society of Chemistry 2017 SUPPORTING INFORMATION Control of the hierarchical assembly of π-conjugated

More information

Supporting Online Material for

Supporting Online Material for www.sciencemag.org/cgi/content/full/314/586/1757/dc1 Supporting Online Material for Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells B. Andrei Bernevig, Taylor L. Hughes,

More information

Chemistry 334 Part 2: Computational Quantum Chemistry

Chemistry 334 Part 2: Computational Quantum Chemistry Chemistry 334 Part 2: Computational Quantum Chemistry 1. Definition Louis Scudiero, Ben Shepler and Kirk Peterson Washington State University January 2006 Computational chemistry is an area of theoretical

More information

Follow this and additional works at: Part of the Biomedical Engineering and Bioengineering Commons

Follow this and additional works at:   Part of the Biomedical Engineering and Bioengineering Commons Clemson University TigerPrints All Dissertations Dissertations 5-2011 Methods Development and Force Field Evaluation for Molecular Simulations of Iinteractions Between Structured Peptides and Functionalized

More information

Math 2201 Chapter 3 Review. 1. Solve for the unknown side length. Round your answer to one decimal place.

Math 2201 Chapter 3 Review. 1. Solve for the unknown side length. Round your answer to one decimal place. Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Solve for the unknown side length. Round your answer to one decimal place. a. 4.1 b. 5.1 c. 4.7 d. 5.6

More information

for article to be Published in J. CHEM. PHYS.

for article to be Published in J. CHEM. PHYS. January 6, 2017 S-1 SUPPLEMENTARY MATERIAL for article to be Published in J. CHEM. PHYS. Full-dimensional ground- and excited-state potential energy surfaces and state couplings for photodissociation of

More information

2-5 Algebraic Proof. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry

2-5 Algebraic Proof. Warm Up Lesson Presentation Lesson Quiz. Holt McDougal Geometry 2-5 Algebraic Proof Warm Up Lesson Presentation Lesson Quiz Geometry Warm Up Solve each equation. 1. 3x + 5 = 17 4. x = 4 2. r 3.5 = 8.7 r = 12.2 3. 4t 7 = 8t + 3 t = 5 2 n = 38 5. 2(y 5) 20 = 0 y = 15

More information

Page 1 of 11 Name: 1) Which figure always has exactly four lines of reflection that map the figure onto itself? A) rectangle B) square C) regular octagon D) equilateral triangle ee4caab3 - Page 1 2) In

More information

MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra

MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra MTH 411 Lecture Notes Based on Hungerford, Abstract Algebra Ulrich Meierfrankenfeld Department of Mathematics Michigan State University East Lansing MI 48824 meier@math.msu.edu August 28, 2014 2 Contents

More information

Development and Application of Combined Quantum Mechanical and Molecular Mechanical Methods

Development and Application of Combined Quantum Mechanical and Molecular Mechanical Methods University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Student Research Projects, Dissertations, and Theses - Chemistry Department Chemistry, Department of Fall 12-2014 Development

More information

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?

0809ge. Geometry Regents Exam Based on the diagram below, which statement is true? 0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100

More information