Rupture of DNA Aptamer: new insights from simulations
aa r X i v : . [ c ond - m a t . s o f t ] O c t Rupture of DNA Aptamer: new insights from simulations
Rakesh Kumar Mishra, Shesh Nath, and Sanjay Kumar Department of Physics, Banaras Hindu University, Varanasi 221 005,India
Base-pockets (non-complementary base-pairs) in a double-stranded DNA play acrucial role in biological processes. Because of thermal fluctuations, it can lowerthe stability of DNA, whereas, in case of DNA aptamer, small molecules e.g.adenosinemonophosphate(AMP), adenosinetriphosphate(ATP) etc, form additionalhydrogen bonds with base-pockets termed as “binding-pockets”, which enhance thestability. Using the Langevin Dynamics simulations of coarse grained model of DNAfollowed by atomistic simulations, we investigated the influence of base-pocket andbinding-pocket on the stability of DNA aptamer. Striking differences have beenreported here for the separation induced by temperature and force, which requirefurther investigation by single molecule experiments.1 . INTRODUCTION
Aptamers are Guanine(G)-rich short oligonucleic acids (DNA, RNA), which can per-form specific function . These have been developed in vitro through SELEX (SystematicEvolution of Ligands by Exponential Enrichment) process for better understanding of thebehavior of antibodies, which are produced in vivo or in living cells . One of the mostextensively characterized examples of aptamer is found in telomerase at the ends of eu-karyotic chromosomes, where it plays an important role in gene regulation . DNA loopsor base-pockets consisting of Guanine can interact with small molecules and proteins andthus enhance their stability, affinity and specificity . For example, adenosinemonophosphate(AMP) binds to DNA loop (termed as binding-pocket) with eight hydrogen bonds, that in-creases the stability of aptamer. It served as the target of drugs for cancer treatment .Their high affinity and selectivity with target proteins make them ideal and powerful probesin biosensors and potent pharmaceuticals . Thus, understanding of the conformationalstability of DNA aptamers before and after the release of drug molecule, and the influenceof the binding of other molecules, are of crucial importance.A double-stranded DNA (dsDNA) can be separated in two single-stranded DNA by in-creasing the temperature and the process is termed as DNA melting. Traditional spectro-scopic techniques used e.g. fluorescence spectroscopy, U V − vis spectroscopy etc. usuallyprovide average responses for molecular interactions . Single molecule force spectroscopy(SMFS) techniques have emerged as valuable tools for measuring the molecular interactionson a single molecule level, and thus unprecedented information about the stability of bio-molecules have been achieved. For example, DNA rupture induced by SMFS techniques havebeen used to understand the strength of hydrogen bonds in nucleic acids, ligands-nucleic in-teraction, protein-DNA interactions etc. . In DNA rupture all intact base-pairs breaksimultaneously and two strands get separated, when a force is applied either at 3 ′ − ′ or5 ′ − ′ ends. This force is identified as rupture force. Motivated by these studies, attemptshave recently been made to understand the enhanced stability of DNA aptamers . For2 a) (b) AMPAMPAMP f f fff ff ffff f FIG. 1. Schematic representations of dsDNA under a shear force applied at the opposite ends withvarying position of (a) binding-pocket (AMP), (b) base-pocket (without AMP). In the constantvelocity simulation, one end marked by blank circle is kept fixed, while in the constant forcesimulation, the force is applied at both ends. The binding-pocket (AMP within circle)Fig. 1(a)corresponds to additional binding of hydrogen bonds with AMP. The circle in Fig. 1(b) representsthe base-pocket consisting of G (say), where base-pairing is absent. example, Nguyen et al. measured the changes in rupture force of a DNA aptamer (thatforms binding-pocket) with AMP (Fig. 1(a)) and without AMP (Fig. 1(b)), and therebydetermined the dissociation constant at single-molecule level. Papamichael et al. used anaptamer-coated probe and an IgE-coated mica surface to identify specific binding areas.Efforts have also been made to determine the rupture force of aptamer binding to proteinsand cells, and it was revealed that the binding-pocket enhances the rupture force by manyfolds .Despite the progress made, there are noticeable lack of investigations. For example, themelting of DNA aptamer in presence and absence of AMP and its dependence on the positionin a DNA strand need to be measured and understood correctly. The aim of this paper is todevelop a theoretical model to understand the role of a base-pocket and a binding-pocket onthe rupture of a DNA aptamer. For this, a coarse grained model of DNA is developed. Here,dsDNA is made up of two segments. One of the segments consists of a DNA loop or the base-3ocket of eight G type nucleotides. The other segment is stem, which is made up of twelveG-C base-pairs. We vary the position of the binding-pocket (Fig. 1 (a)) and the base-pocket(Fig. 1(b)) along the chain, and measure the rupture force and melting temperature forboth cases (with and without AMP). For the first time, we report the profile as a functionof base/binding-pocket position. We find that even though the melting profile has oneminima (U-shape), there are two minima (W-shape) for rupture. This reflects that thereare two symmetric positions, where the system can be more unstable. Extensive atomisticsimulations have been performed to validate these findings, which helped us to delineate thecorrect understanding of the role of base-pockets in the stability of DNA aptamer. In Sec.II, we briefly describe the model and the Langevin dynamics simulation to study the ruptureof DNA aptamer . The discussion on the melting and rupture profile of DNA aptamer asa function of base/binding-pocket position has also been made in this section. In Sec. III,we briefly explain the atomistic simulation and discuss the model independency of theresults. Finally in Sec. IV, we conclude with a discussion on some future perspectives. II. MODEL AND METHOD
We first adopt a minimal model introduced in Ref. for a homo-sequence of dsDNAconsisting of N base-pairs, where covalent bonds and base-pairing interactions are modelledby harmonic springs and Lennard-Jones (LJ) potentials, respectively. By using Langevindynamics simulation, it was shown that the rupture force and the melting temperatureremain qualitatively similar to the experiments . Energy of the model system isgiven by. E = X l =1 N X j =1 k ( r ( l ) j +1 ,j − d ) + X l =1 N − X i =1 N X j>i +1 C r ( l ) i,j + N X i =1 N X j =1 ǫ C ( | r (1) i − r (2) j | ) − A ( | r (1) i − r (2) j | ) δ ij ! , (1)4 -4 -3 -2 -1 Loading Rate6121824 f c f P (f) (a) With AMPWithout AMP (b)
FIG. 2. (a) Probability distribution of rupture force of DNA aptamer with AMP(solid line) andwithout AMP(dashed line) for the same loading rate(0.0205). (b) Variation of rupture force withloading rate. where N is the number of beads in each strand. Here, r ( l ) j represents the position of bead j on strand l . In the present case, l = 1(2) corresponds to first (complementary) strand ofdsDNA. The distance between intra-strand beads, r ( l ) i,j , is defined as | r ( l ) i − r ( l ) j | . The harmonic(first) term with spring constant k = 100 couples the adjacent beads along each strand. Theparameter d (= 1 .
12) corresponds to the equilibrium distance in the harmonic potential,which is close to the equilibrium position of the LJ potential. The second term takes careof excluded volume effects i.e. , two beads can not occupy the same space . The thirdterm, described by the Lennard-Jones (LJ) potential, takes care of the mutual interactionbetween the two strands. The first term of LJ potential (same as second term of Eq.1) willnot allow the overlap of two strands. The second term of the LJ potential corresponds to thebase-pairing between two strands. The base-pairing interaction is restricted to the nativecontacts ( δ ij = 1) only i.e. , the i th base of the 1 st strand forms pair with the i th base of the2 nd strand only. It is to be noted here that ǫ represents the strength of the LJ potential.In Eq. 1, we use dimensionless distances and energy parameters and set ǫ = 1, C = 1 and A = 1, which corresponds to a homosequence dsDNA. The binding-pocket and base-pocketcan be modelled by substituting A = 1 & ǫ = 2 (Fig. 1(a)) and A = 0 & ǫ = 1 (Fig. 1(b)),respectively, among the bases inside the circle. The equation of motion is obtained from thefollowing Langevin equation: 5 d r dt = − ζ d r dt + F c ( t ) + Γ ( t ) , (2)where m (= 1) and ζ (= 0 .
4) are the mass of a bead and the friction coefficient, respectively.Here, F c is defined as − dEd r and the random force Γ is a white noise , i.e., < Γ ( t ) Γ ( t ′ ) > =6 ζ T δ ( t − t ′ ). The 6 th order predictor-corrector algorithm with time step δt =0.025 has beenused to integrate the equation of motion. The results are averaged over many trajectories.First, we have calculated the rupture force of a dsDNA of two different lengths . Wehave inserted a base-pocket in the interior of the chain (circle in Fig. 1(b) and calculated therequired force for the rupture at temperature T = 0 .
12. In order to obtain the rupture forcefor the DNA aptamer, we switched on the interaction among the base-pocket nucleotideswith AMP (Fig. 1(a)): each of these extra interaction strength is double of the base-pairing interactions. Following the experimental protocol , we performed constant velocitysimulation by fixing one end of a DNA strand marked by a blank circle in Fig. 1. Force f = K ( vt − x ) is applied on the other end of the strand marked by filled circle in Fig.1. Here, x is the displacement of the pulled monomer from its original position, v is thevelocity, t is the time and K (= 0 .
8) is the spring constant . The rupture force is identifiedas the maximum force, at which two strands separate suddenly. A selection of rupture forcedistribution of 500 events have been shown in Fig. 2(a). For a given loading rate, themost probable rupture force f c is obtained by the Gaussian fit of the distribution of ruptureforce . In Fig. 2(b), we have shown the variation of f c (with and without AMP) with theloading rate ( Kv ). It is apparent from the plots that the rupture force required for theDNA aptamer is larger than the DNA (without AMP) with base-pocket, and the qualitativenature remains same as seen in the experiment .For the better understanding of the role of base-pocket and binding-pocket, we varied itsposition along the chain continuously from one end to the other, and calculated the meltingtemperature ( T m ) and rupture force ( f c ) for each position in the constant force ensemble(CFE) . The melting temperature is obtained here by monitoring the energy fluctuation6 i m i m i f c i f c (b) Without AMP (d) Without AMP(c) With AMP(a) With AMP FIG. 3. (a) Variation of T m with binding-pocket positions and (b) with base-pocket positions. (c)Variation of f c with binding-pocket positions and (d) with base-pocket positions. (∆ E ) or the specific heat ( C ) with temperature, which are given by the following relations < ∆ E > = < E > − < E > (3) C = < ∆ E >T . (4)The peak in the specific heat curve gives the melting temperature. Since this simulation isin the equilibrium, we have used 10 realizations with different seeds and reported the meanvalue of the rupture force. In Fig.3 (a) − (d), we have plotted the variation of T m (at f = 0)and f c ( T = 0 .
06) much below T m as a function of pocket position ( D i ). It is interesting tonote that for thermal melting, the variation looks like “ ∩ shape” for the DNA aptamer (withAMP) shown in Fig.3(a), and for without AMP, profile has “U- shape” having one minima(Fig. 3(b). The rupture force remains invariant with binding-pocket positions for AMP(Fig.3(c)), which is consistent with experiment . Interestingly, in the absence of AMP, theprofile has “W-shape”, i.e. , with two minima (Fig.3(d)). Although, one may intuitivelyexpect the shape of profiles to be symmetric for the homosequence. But it is not apparent,why does the profile has one minimum for the thermal melting and two minima for the DNArupture in the absence of AMP. 7e now confine ourselves to understand these issues. In case of DNA aptamer melting,one would expect naively that the aptamer is more stable, when the binding-pocket is inthe interior of the chain. Thus, T m should be high (Fig. 3(a)) compare to the bindingpocket at the end resulting in a “ ∩ shape” profile. In absence of AMP, the profile lookslike “U-shape”. For a short chain, DNA melting is well described by the two state model with ∆ G = ∆ H − T ∆ S , where H and S are the enthalapy and entropy, respectively. Themelting temperature T m = ∆ H ∆ S corresponds to the state with ∆ G = 0 indicating that thesystem goes from the bound-state to the open-state and change in the free energy of thesystem is zero. It is often practically easier to identify T m as the temperature where 50%hydrogen bonds are broken.For a homo-sequence chain (without base-pocket), it was shown that the chain opens fromthe end rather than the interior of the chain . In such a case, the major contribution tothe entropy comes from the opening of base-pairs near the end of the chain, and decreasesto zero, when one approaches to the interior of the chain. In this case, there are twocontributions to the entropy: entropy associated with opening of the end base-pairs ( S E )and the base-pocket entropy ( S BP ). When a base-pocket is inserted at the end of DNAchain, there is an additional contribution to the entropy, which is greater than ∆ S E or(∆ S BP ), but less than the sum of two. Thus, T m decreases to ∼ .
171 from ∼ . . Asthe base-pocket moves along the chain, entropy of interior base-pairs increases. Combinedeffect of both entropies reduces the melting temperature further. Once the base-pocket isdeep inside, the total entropy of the system becomes equal to the sum of end-entropy andbase-pocket entropy. As a result, T m remains constant( ∼ . in vitro .Understanding the decrease in T m with base-pocket position does not explain, why therupture profile of DNA has two minima. It is clear from the Fig. 3 (b) & (d) that thebase-pocket entropy alone is not responsible for this ( W ) shape. Based on the ladder8
10 20 30 D i f c N=8N=10N=12N=16N=20N=24N=32
FIG. 4. Variation of f c with base-pocket positions for different lengths. model of DNA (homo-sequence), de Gennes proposed that the rupture force f c is equalto 2 f ( χ − tanh( χ N )) . Here, f is the force required to separate a single base-pair and χ − is the de Gennes length, which is defined as q Q R . Q and R are the spring constants charac-teristic of stretching of the backbone and hydrogen bonds , respectively. de Gennes lengthis the length over which differential force is distributed. Above this length, the differentialforce approaches to zero and there is no extension in hydrogen bonds due to the appliedforce . When the base-pocket is at the end, four bases of one strand is under the tension,whereas the complementary four bases are free, thereby increasing the entropy of the system.The four bases act like a tethered length and a force is required to keep it stretched so thatrupture can take place. It is nearly equal to the ruptured force of a 12 base-pair dsDNAwith no defect. As the base-pocket moves towards the center, the entropy of base-pocketdecreases as the ends of the base-pocket is now not free. Since, the de Gennes length forthe base-pocket is infinite ( R = 0), it implies that the differential force remains constantinside the base-pocket, thereby decreases the stability of DNA, and as a result, rupture forcedecreases further. The force acting at ends penetrates only up to the de Gennes length andwithin this, the rupture force keeps on decreasing as base-pocket moves and approaches toits minimum. Above a certain length, the rupture force starts increasing, which can be seenin Fig.3 (d) and approaches to the maximum at the middle of the chain. By symmetry, weget profile of two minima of “W-shape”.It should be pointed here, that the de Gennes length in the present model is about ten ,9ut for a DNA of length 16 base-pairs (12 complementary and 4 non complementary), theminima is around D i = 4. Note that the penetration depth for the two ends (say 5 ′ − ′ )is different because of the asymmetry arising due to the presence of base-pocket, and hencethe minima shifts. If we increase the length of DNA, keeping the base-pocket size constant,one would then expect that the minima will shift towards 10 (above the de Gennes length,the end-effect vanishes). This indeed we see in Fig. 4, where the variation of f c with base-pocket position for different chain lengths ( N = 8 , , , , ,
24 and 32) has been plotted.In all cases, profiles have two minima, whereas minima shifts towards 10 as N increases.de Gennes equation predicts that f c increases linearly with length for small values of N ,and saturates at the higher values of N , which is consistent with recent experiment andsimulations . Surprisingly, right side of the profile also appears to follow the de Gennesequation. This implies that, the base-pocket can reduce the effective length of the chain, sothat the rupture force is less compare to the bulk value and approaches to a minimum valueat a certain position. As the end-effect decreases, f c starts increasing and approaches to itsbulk value. III. ATOMISTIC SIMULATION
In order to rule out the possibility that the above effect may be a consequence of theadopted model, we performed the atomistic simulations with explicit solvent. Here, wehave taken homo-sequence DNA consisting of 12 G-C bps and a varying base-pocket of 8G-nucleotides . The starting structure of the DNA duplex sequence having the base-pocket is built using make-na server . We used AMBER10 software package with allatom (ff99SB) force field to carry the simulation. Using the LEaP module in AMBER, weadd the AMP molecule (Fig. 5(a)) in the base-pocket and then the N a + (counterions) toneutralize the negative charges on phosphate backbone group of DNA structure (Fig. 5(b)).This neutralized DNA aptamer structure is immersed in water box using TIP3P model forwater . We have chosen the box dimension in such a way that the ruptured DNA aptamer10 a) (b) FIG. 5. (Color online) (a) Structure of AMP molecule, which has been inserted in the base-pocket.(b) Snapshots of binding of AMP molecule at three different positions ( D i =1, 4 and 7) in the DNA. structure remains fully inside the water box. We have taken the box size of 57 × ×
183 ˚ A which contains 15674 water molecules and 30 N a + (counterions). A force routine has beenadded in AMBER10 to do simulation at constant force . In this case, the force has beenapplied at 5 ′ − ′ ends . The electrostatic interactions have been calculated with ParticleMesh Ewald (PME) method using a cubic B-spline interpolation of order 4 and a 10 − tolerance is set for the direct space sum cut off. A real space cut off of 10 ˚ A is used for boththe van der Waal and the electrostatic interactions. The system is equilibrated at F = 0for 100 ps under a protocol described in Ref. and it has been ensured that AMP hasbound with the base-pocket. We carried out simulations in the isothermal-isobaric (NPT)ensemble using a time step of 1 fs for 10 different realizations. We maintain the constantpressure by isotropic position scaling with a reference pressure of 1 atm and a relaxationtime of 2 ps. The constant temperature was maintained at 300 K using Langevin thermostatwith a collision frequency of 1 ps − . We have used 3 D periodic boundary conditions duringthe simulation.Because of extensive time involved in the computation, we restricted ourselves at threedifferent (extremum) base-pocket positions D i =1, 4 and 7 (Fig. 5(b)) and calculated therupture force with 10 realization of different seeds as a mean force. The required ruptureforces for these positions are 840 pN ±
20 pN, 720 pN ±
20 pN and 830 pN ±
20 pN,11ndicating that the complete profile contains two minima . In presence of AMP, whichinteracts with the base-pocket, we find f c =925pN ± IV. CONCLUSIONS
Our numerical studies clearly demonstrate that the force induced rupture and thermalmelting of DNA aptamer will vary quite significantly. In melting, all the nucleotides getalmost equal thermal knock from the solvent molecules, whereas in DNA rupture, force isapplied at the ends and the differential force acts only up to the de Gennes length . As aresult, the stability of DNA in presence of base-pocket is strikingly different (single minima vs double minima). This may have biological/pharmaceutical significance because after therelease of drug molecule, the stability of carrier DNA depends on the position from whichit is released. Hence, at this stage our studies warrant further investigations most likely bynew experiments to explore the role of base-pockets and its position, which will significantlyenhance our understanding about the stability of DNA aptamer and its suitability in thedevelopment and designing of drugs. V. ACKNOWLEDGEMENTS
We thank G. Mishra, D. Giri and D. Dhar for many helpful discussions on the subject.We acknowledge financial supports from the DST, UGC and CSIR, New Delhi, India.
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