oxdna Workshop Reem Mokhtar & Tong Niu September 8, 2015 Duke University

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1 oxdna Workshop Reem Mokhtar & Tong Niu Duke University September 8, / 34

2 Overview 1 Coarse-graining DNA for simulations of DNA nanotechnology., Introducing improved structural properties and salt dependence into a coarse-grained model of DNA., Usage 2 / 34

3 Coarse-graining DNA for simulations of DNA nanotechnology., Coarse-graining DNA for simulations of DNA nanotechnology.,2013 What can oxdna do? oxdna Model Features 2 Introducing improved structural properties and salt dependence into a coarse-grained model of DNA.,2015 Differences between oxdna2 and oxdna 3 Usage Input Files Output: Energy File Layout Usage Input File Energy File Example: Hairpin Formation 3 / 34

4 Capture biophysical processes 1 Structural 2 Thermodynamic 3 Mechanical 4 Can be simulated on diffusive time-scales Insight into dynamic processes 1 hybridization 2 strand exchange 3 hairpin formation What can oxdna do? Quantitative reproduction of phenomena not fitted 1 Kinetics of toehold mediated strand exchange 2 Overstretching force of duplex DNA Response to mechanical stress 1 stretching 2 twisting 3 bending 4 / 34

5 oxdna Model The model treats DNA as: 1 A string of rigid nucleotides 2 Which interact through potentials 3 Which depend on the position and orientation of the nucleotides 5 / 34

6 oxdna Model The interactions are: 1 Sugar-phosphate backbone connectivity, 2 Excluded volume, 3 Hydrogen bonding, 4 Nearest-neighbour stacking, 5 Cross-stacking between base-pair steps in a duplex, 6 Coaxial stacking. 6 / 34

7 pic orientational dependence allows the model to represent the nd by e is opy ick her ntind the ase hat TheFig. form 1 (a) ofainternucleotide representation the potential: rigid nucleotides that are the basic unit of the de oxdna coarse-grained model. The bases are represented by an ellipsoid to reflect The the orientational V oxdna dependence = of the interactions. (b) Three strands in an 11-basepair double helix with stabilising interactions indicated in the inset. All nucleo- ith (V b. b. + V stack + V exc ) + on tides also interact through short-ranged excluded-volume repulsions. <ij> (V HB + V cr.st. + V exc + V cx.st. ) i,j / <ij> oxdna Model This journal is c the Owner Societies / 34

8 are constructed The radialfrom part the of the functions stacking given andbelow: hydrogen-bonding potentials: 8 term tends to have only a small role for correctly formed base pairs, but is im FENE spring (used VMorse(r, to connect,r 0,a) backbones): VMorse(r c,,r 0,a)) if r low <r<r high, Backbone base vector approximately 3.4 Å) >< Vsmooth(r, and one unit b Base normal oxdna low of,r c,low energy ) is equal to E = if r Model c,low 1 <r<r 20 J low (or, equivalently, minimizing hydrogenf1(r) bonding = between bases that are not opposite each other (2.7) Vsmooth(r, in >: VFENE(r, b high,r,r 0 c,high, )= ) kt at T =300Kcorrespondsto0.1E). if r high <r<r c,high, 0 2 ln (r r 1 0 ) 2. (2.1) 2 V HB = f 1 ( r HB, NB,a HB, rhb 0, rc,low HB, otherwise. 2.4 rc,high HB, rlow HB, rhigh HB ) The Morse The radial potential part potential of (used the for cross-stacking stacking f 4 ( 1,a HB,1, HB,1 0, and and? H-bonding): coaxial HB,1 ) f stacking potentials: 8 4( 2,a HB,2, HB,2 0,? HB,2 ) Vharm(r, δr stack f 4 ( 3,a HB,3, 0 k, r 0 ) HB,3, Vharm(r c? HB,3 ),k,r f 4( 0 ) if r 4,a low <r<r HB,4, HB,4 0 high,, Functional>< forms VMorse(r,? HB,4 ) kvsmooth(r, δrhb f 4 ( 7,a HB,7, HB,7 0,rb 0 low,a)=,,r c,low 1)? HB,7 ) exp f ( (rif rr 4( 8,a c,low 0 )a) <r<r 2. HB,8, HB,8 0 low,, (2.2) f2(r) =? (2.8) HB,8 ). The potential used to model kvsmooth(r, >: DNA consists b high,rof c,high a sum ) of terms if rdesigned high <r<r to represent c,high, physical The Harmonic radial potential part of the (used 0 stacking for cross-stacking and hydrogen-bonding and coaxial otherwise. potentials: stacking): interactions, such as excluded volume, base-stacking and hydrogen bonding. Cross-stacking approximately 3.4 Å) 8 and one unit of energy is equal The radial part VMorse(r, of the excluded,r 0,a) volume VMorse(r potential: c,,r 0,a)) if r low <r<r high, 0.74 units >< Vharm(r, 8 k, r 0 )= k to E = These terms J (or equivalently, are Vsmooth(r, b low,r c,low ) if r c,low <r<r low, f1(r) = >< VLJ(r,, ) 2 r r0 2. (2.3) kt constructed at T =300Kcorrespondsto0.1E). from the functions given below: if r<r?, (2.7) 0.80 units V cross stack represents cross-stacking Vsmooth(r, interactions b between a base in a base pair an θ FENE spring 5 >: (used to f3(r) connect = high,r Vsmooth(r, backbones): c,high ) b, r if r high <r<r c,high, 0 >: c ) if r? <r<r c, (2.9) Lennard - Jones (used for soft repulsion): 2.4 The potential 0 otherwise. otherwise. neighbour bases on the opposite strand, providing additional 12 stabilization of the du θ radial part of thevfene(r, cross-stacking,r 6 and coaxial stacking potentials: The angular Functional modulation forms factor VLJ(r, used, 0, )= )=4 in stacking, 2 ln (r r 1 0 ) 2. (2.1) hydrogen-bonding, 2. cross-stacking(2.4) and θ 3 8 r r 134]. Here it is incorporated coaxial stacking: through Vharm(r, ak, potential r 0 ) Vharm(rwhich c,k,r 0 ) is if ra low function <r<r high of, the distanc The >< potential Morse potential Quadratic used terms to8 (used model (used kvsmooth(r, for for DNA stacking modulation): consists b low,r and c,low ofh-bonding): a) sum terms if designed r c,low <r<r to represent low, physical θ 2 θ f2(r) = Vmod(, a, 0 ) if 0? < < 0 +?, (2.8) 6 interactions, such as excluded >< kvsmooth(r, volume, b >: high,r c,high ) if r high <r<r c,high, Vsmooth(,b, 0 base-stacking c ) if 0 and c hydrogen < < 0 bonding.? These terms θ f4( ) = 0 VMorse(r,, Vmod(,,r 0,a)= otherwise. 4 Vsmooth(,b, 29 >: 0 a, 0 + c )=1 1 exp ) if 0 a( ( (r +? 0 ) 2. r 0 )a) 2. (2.10) < < 0 + c (2.5) (2.2) are constructed from the functions given below:, The radial part of the 0 excluded volume potential: otherwise. Quadratic Harmonic smoothing potential (used terms for for 8cross-stacking truncation: and coaxial stacking): FENE spring (used to connect backbones): Another modulating term which >< VLJ(r, is used, to ) impose if right-handedness r<r?, (e ectively a onesided modulation): VFENE(r, Vsmooth(x,,r 0, )= b, x c )=b(x f3(r) = Vsmooth(r, b, r >: c ) if r? <r<r c, (2.9) Vharm(r, k, r 1 0 )= k c x) 2. (2.6) 0 otherwise. 8 2 ln (r r 0 ) 2 2 r r0 2. (2.3). (2.1) 2 θ r backbone 8 δ 1 if x>0, These The Lennard functional angular - Jones modulation forms potential are factor combined (used >< used forin stacking, hydrogen-bonding, cross-stacking and Vmod(x, to soft give repulsion): Morse potential (used for stacking anda, H-bonding): 0) the following if x? <x<0, truncated, smooth and di erentiable functions: 12 if x c f5( )= (2.11) coaxial stacking: θ Vsmooth(x, b, x 7 8 >: c ) <x<x 6?, VLJ(r,, δr base back Vmod(, VMorse(r, a, 0,r ) 0 0 )=4,a)= 1 if 0 exp otherwise. ( (r? < r < 0. )a) 2 (2.4) r r 0 +.?, (2.2) >< Vsmooth(,b, 0 24 c ) if 0 c < < 0?, Interactions f4( ) = (2.10) Quadratic Harmonic potential terms (used Vsmooth(,b, (used for for modulation): cross-stacking >: 0 + c ) if and 0 + coaxial? < stacking): < 0 + c, δr back base The functional forms of Section are combined otherwise. Vmod(, to produce a potential for model DNA: δr base Vharm(r, X a, k, 0 r )=1 0 )= k a( Another modulating V = term which isvbackbone used to impose + 2 r 0 Vstack right-handedness + r0 2 ). 2. (2.3) (2.5) Vexc 0 (e ectively a onesided modulation): (2.12) X nn igure 2.3: Illustration 1 Thomas of the variables E Ouldridge used to parameterize (2012). the Coarse-grained potential. Not shown in modelling this diagram Quadratic Lennard are - Jones smoothing + potential terms (used for truncation: of DNA and DNA VHB for + self-assembly. Vcross soft stack repulsion): + Vcoaxial 8 In: stack + url: Vexc. e chirality inducing terms cos( 1), cos( 2), cos( 3) and cos( 4), which are discussed in detail in Sections other pairs 1 if x>0,.4.2 and It is convenient to define each pairwise interaction as if one nucleotide (coloured Herered thein sum this over nn runs overvlj(r, consecutive Vsmooth(x, >< Vmod(x,, )=4 b, a, bases x c )=b(x 0) within c if x icture) is being influenced by the other (coloured black): this allows each angle to be well-defined when? strands. x) 2. <x<0,. For illustrations of(2.4) (2.6) the f5( )= r r 8 (2.11) / 34 alculating forces and torques. When calculating the energy, of course, the final result does not depend on > V (x, b, x c ) if x c <x<x?,

9 pic nd by e is opy ick her ntind the ase hat de The ith on orientational dependence allows the model to represent the oxdna Model Structural Fig. 1 (a) Properties A representation of the rigid nucleotides that are the basic unit of the pitch, oxdna base-pair coarse-grained rise and model. radius, The bases propeller are represented twist, byand ellipsoid distinction to reflect between the orientational major and dependence minor of grooves the interactions. (new! (b) see Three example strands in inan oxdna 11-basepair double helix with stabilising interactions indicated in the inset. All nucleo- folder MAJOR MINOR GROOVING) tides also interact through short-ranged excluded-volume repulsions. This journal is c the Owner Societies / 34

10 Features 1 Molecular and Brownian dynamics 2 Monte Carlo simulations 3 Regular Metropolis Monte Carlo simulations 4 Additional interactions: oxdna can be extended to simulate additional pairwise potentials. 5 External forces: In order to favor motif formation or to mimic different external environments, different kind of forces can be applied to nucleotides or points in space. 6 Standalone single- and double-strand generator 7 Output converter 8 Cadnano converter 10 / 34

11 Introducing improved structural properties and salt dependence into a coarse-grained model of DNA., Coarse-graining DNA for simulations of DNA nanotechnology., Introducing improved structural properties and salt dependence into a coarse-grained model of DNA.,2015 Differences between oxdna2 and oxdna 3 Usage 11 / 34

12 oxdna Differences between oxdna2 and oxdna 1 The interactions for the different bases are identical except for the hydrogen-bonding term (only Watson-Crick base pairs). 2 For thermodynamics, uses SantaLucia 2 for melting of short duplexes oxdna2 1 Different widths for major and minor grooves. 2 Including term for salt-dependent interaction 3 Differentiating between AA and TT stacking interaction (instead of fitting using SantaLucia). Evidence that contiguous AA are much stiffer than TT. 2 John SantaLucia and Donald Hicks (2004). The thermodynamics of DNA structural motifs. In: Annual Review of Biophysics and Biomolecular Structure 33.1, pp doi: /annurev.biophys url: 12 / 34

13 0.925 avg), which is not too dissimilar to the preliminary value suggested in Ref. 60. We note that this value gives satisfactory predictions for F for a wide range of salt concentrations down to 0.05M. Differences between oxdna2 and oxdna The interactions are: 1 Sugar-phosphate backbone connectivity, 2 Excluded volume, 3 Hydrogen bonding, 4 Nearest-neighbour stacking, 5 Cross-stacking between base-pair steps in a duplex, 6 Coaxial stacking. 7 Electrostatic interactions via Debye-Huckel-like term (DH) VII. THE oxdna2 MODEL V oxdna2 = In summary, the oxdna2 potential can be written as X nearest neighbours X + (VHB other pairs (V backbone + V stack + V 0 exc) + Vcross stack + Vexc + V coax stack + V DH ), This article is copyrighted as indicated in the article. Reuse of AIP content is subject to 13 the / 34 terms (12) where a Vx indicates that the term is either modified for oxdna2 or, in the case of VDH, new in oxdna2. The modified parameters for oxdna2 are compared with those for oxdna in Table S1, and a full account of the changes is given in Sec. I of the supplementary material. 69 All other parameters remain the same as in the original model. We emphasise that, after all the relevant changes to the potential were made, the hydrogen bonding and stacking parameters were modified to ensure that the close agreement to experimental duplex melting temperatures achieved for the original model was retained with oxdna2 (this was done immediately after the changes to V backbone, as described at the end of Sec. V). VIII. PHYSICAL PROPERTIES OF oxdna2 The structural, mechanical, and thermodynamic properties of DNA for the new version of oxdna presented in this paper, which we call oxdna2, are slightly di erent from the properties for the original oxdna model. We briefly highlight details of the given briefly the suppleme The stru the pitch and Fig. 6. As mi ing salt conc backbone site consistent wi crease in neig as salt conce approximatel mental eviden that the pitc tions (0.162M is chosen (b backbone inte tures agrees we set the b bundle desig in the mode roughly bp/turn around in the presenc The ther Fig. 7. The t duplex at 0.5 the original o if at all on duplex forma of forming th presumably d two single str between back of the bound

14 Files 1 Configuration 1 general information (timestep, energy, box size) 2 orientation, positions of each nucleotide Input Files 2 Topology: backbone-backbone bonds between nucleotides in the same strand 14 / 34

15 Files 1 Configuration 1 general information (timestep, energy, box side) 2 orientation, positions of each nucleotide Input Files 2 Topology: backbone-backbone bonds between nucleotides in the same strand File relaxed.conf under oxdna/examples/cadnano INTERFACE/TILE t = T b = Lz Ly Lz E = Etot U K 15 / 34

16 Files 1 Configuration 1 general information (timestep, energy, box size) 2 orientation, positions of each nucleotide Input Files 2 Topology: backbone-backbone bonds between nucleotides in the same strand File topology.dat under oxdna/examples/cadnano INTERFACE/TILE N Ns S# B 3 bond 5 bond 16 / 34

17 MD Simulations 1 time (steps * dt) 2 potential energy 3 kinetic energy 4 total energy Output: Energy File Layout Note Potential, kinetic and total energies are divided by the total number of particles. Example MD / 34

18 Output: Energy File Layout MC simulations 1 time (steps) 2 potential energy 3 acceptance ratio for translational moves 4 acceptance ratio for rotational moves 5 acceptance ratio for volume moves Example MC / 34

19 VMMC simulations 1 time (steps) 2 potential energy Output: Energy File Layout 3 acceptance ratio for translational moves 4 acceptance ratio for rotational moves 5 acceptance ratio for volume moves 6 if umbrella sampling enabled: [order parameter coordinate 1] [order parameter coordinate 1]... [order parameter coordinate n] [current weight] Example VMMC / 34

20 Usage To generate the topology and configuration files from a specific sequence, we use generate-sa.py under oxdna/utils/: 1 Box side (ensuring no change in number of particles) 2 Input sequence Example Sequence File DOUBLE AGGGCT CCTGTA Generate generate-sa.py 3 sequence file 20 / 34

21 Usage To generate the topology and configuration files from a specific sequence, we use generate-sa.py under oxdna/utils/: 1 Box side 2 Input sequence Example Sequence File AAAAAAAAAAAAAAAAAAAAAAAAAAAAAA Generate generate-sa.py 20. sequence file 21 / 34

22 Usage Input File topology = generated.top conf_file = generated.conf trajectory_file = trajectory.dat #log_file = log.dat print_conf_interval = time_scale = linear external_forces=0 Generate Trajectory oxdna inputfile 22 / 34

23 Usage Visualization Under UTILS: traj2vis xyz trajectory file topology file Analyze bonds Under UTILS: output_bonds input file trajectory file [count] 23 / 34

24 Input File Syntax 1 case-sensitive 2 options in the documentation are in form of key = value 3 arbitrary spaces 4 leading # for comments 5 pipe sign between values separates alternative values 6 default value is right after equal sign 24 / 34

25 Input File Generic Options interaction_type = DNA DNA2 RNA patchy LJ Simulation model 25 / 34

26 Input File Generic Options sim_type = MD MC VMMC Molecular Dynamics, Monte Carlo, or Virtual Move Monte Carlo 26 / 34

27 Input File Generic Options backend = CPU CUDA CUDA backend is only supported by sim type=md. 27 / 34

28 Energy File Energy File Layout The energy file layout for MD simulations is [time (steps * dt)] [potential energy] [kinetic energy] [total energy] Note Potential, kinetic and total energies are divided by the total number of particles. 28 / 34

29 Example: Hairpin Formation VMMC simulations 1 Sequence-averaged (SA) model. 2 Sequence-dependent (SD) model. 3 SA model in which two base pairs are connected by mutual traps Monte Carlo Repeatedly randomly sample a volume in d-dimensional space to obtain an estimate of an integral at the price of a statistical error. 29 / 34

30 MC Monte Carlo methods Repeated random sampling of a volume in d-dimensional space to obtain an estimate of an integral at the price of a statistical error. General pattern for pseudocode 1 Define a domain of possible inputs. 2 Generate inputs randomly from a probability distribution over the domain. 3 Perform a deterministic computation on the inputs. 4 Aggregate the results. 30 / 34

31 VMMC Problem: sequential updates of particles (which leads to low acceptance rates when attractions are strong, leading to strong suppression of collective motion). Algorithm avoids this problem by proposing simultaneous moves of collections clusters of particles according to gradients of interaction energies. 31 / 34

32 Sequence-averaged (SA) model Stacking Parameters For stacking energies in ssdna, uses the thermodynamic results in Jill A Holbrook et al.,1999, with the exception of AA and TT stacking not distinguished (in oxdna) Files Input: inputmd HB energy: hb energy.dat Energy: energy.dat Trajectory: trajectory.dat Last Trajectory File: last conf.dat Log file: log.dat 32 / 34

33 Sequence-dependent (SD) model Files Input: inputmd seq dep HB energy: hb energy seq dep. Energy: energy seq dep.dat Trajectory: trajectory seq dep.d Last Trajectory File: last conf seq dep.d Log file: log seq dep.dat 33 / 34

34 SA model in which two base pairs are connected by mutual traps Files Input: inputtrap HB energy: hb energy trap.dat Energy: energy trap.dat Trajectory: trajectory trap.dat Last Trajectory File: last conf trap.dat Log file: log trap.dat 34 / 34

arxiv: v3 [q-bio.bm] 19 May 2015

arxiv: v3 [q-bio.bm] 19 May 2015 arxiv:1504.00821v3 [q-bio.bm] 19 May 2015 Introducing Improved Structural Properties and Salt Dependence into a Coarse-Grained Model of DNA Benedict E. K. Snodin, 1, a) Ferdinando Randisi, 2, 3 Majid Mosayebi,