DNA electrophoresis studied with the cage model

The cage model for polymer reptation, proposed by Evans and Edwards, and its recent extension to model DNA electrophoresis, are studied by numerically exact computation of the drift velocities for polymers with a length L of up to 15 monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by a regime where the velocity decreases exponentially with the applied electric field strength. In agreement with de Gennes' reptation arguments, we find that asymptotically for large polymers the diffusion coefficient D decreases quadratically with polymer length; for the cage model, the proportionality coefficient is DL^2=0.175(2). Additionally we find that the leading correction term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of kink representation approac

Programming DNA-Based Systems through Effective Molarity Enforced by Biomolecular Confinement

The fundamental concept of effective molarity is observed in a variety of biological processes, such as protein compartmentalization within organelles, membrane localization and signaling paths. To control molecular encountering and promote effective interactions, nature places biomolecules in specific sites inside the cell in order to generate a high, localized concentration different from the bulk concentration. Inspired by this mechanism, scientists have artificially recreated in the lab the same strategy to actuate and control artificial DNA-based functional systems. Here, it is discussed how harnessing effective molarity has led to the development of a number of proximity-induced strategies, with applications ranging from DNA-templated organic chemistry and catalysis, to biosensing and protein-supported DNA assembly

Computational Complexity of Atomic Chemical Reaction Networks

Informally, a chemical reaction network is "atomic" if each reaction may be interpreted as the rearrangement of indivisible units of matter. There are several reasonable definitions formalizing this idea. We investigate the computational complexity of deciding whether a given network is atomic according to each of these definitions. Our first definition, primitive atomic, which requires each reaction to preserve the total number of atoms, is to shown to be equivalent to mass conservation. Since it is known that it can be decided in polynomial time whether a given chemical reaction network is mass-conserving, the equivalence gives an efficient algorithm to decide primitive atomicity. Another definition, subset atomic, further requires that all atoms are species. We show that deciding whether a given network is subset atomic is in $\textsf{NP}$, and the problem "is a network subset atomic with respect to a given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$. A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et al., further requires that each species has a sequence of reactions splitting it into its constituent atoms. We show that there is a $\textbf{polynomial-time algorithm}$ to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We show that the reachability problem for reachably atomic networks is $\textsf{Pspace}$-$\textsf{Complete}$. Finally, we demonstrate equivalence relationships between our definitions and some special cases of another existing definition of atomicity due to Gnacadja

Conformational analysis of nucleic acids revisited: Curves+

We describe Curves+, a new nucleic acid conformational analysis program which is applicable to a wide range of nucleic acid structures, including those with up to four strands and with either canonical or modified bases and backbones. The program is algorithmically simpler and computationally much faster than the earlier Curves approach, although it still provides both helical and backbone parameters, including a curvilinear axis and parameters relating the position of the bases to this axis. It additionally provides a full analysis of groove widths and depths. Curves+ can also be used to analyse molecular dynamics trajectories. With the help of the accompanying program Canal, it is possible to produce a variety of graphical output including parameter variations along a given structure and time series or histograms of parameter variations during dynamic

Configurable and Up-Scalable Microfluidic Life Science Platform for Cell Based Assays by Gravity Driven Sequential Perfusion and Diffusion

Microfluidics has the potential to significantly change the way modern biology is performed, but for this potential to be realized several on-chip integration and operation challenges have to be addressed. Critical issues are addressed in this work by first demonstrating an integrated microfluidic tmRNA purification and real time nucleic acid sequence based amplification (NASBA) device. The device is manufactured using soft lithography and a unique silica bead immobilization method for the nucleic acid micro purification column. The integrated device produced a pathogen-specific response in < 3 min from the chip-purified RNA. Further enhancements in the device design and operation that allow the on-chip integration of mammalian cell handling and culturing produced a novel integrated NASBA array. This system demonstrated for the first time that it is possible to combine on a single micro-device cell culture and real time NASBA. In order to expand the cell based assay capabilities of the integrated NASBA array and simplify the device operation novel hydrodynamics and cell sedimentation within trench structures and gravity driven sequential perfusion and diffusion mechanisms were developed. These mechanisms were characterized and implemented within an iCell array device. iCell array can completely integrate cell based assays with bio-analytical read-out. The device is highly scalable and can enable the configurable on-chip integration of procedures such as adherent and non-adherent cell-culture, cellstimulation, cell-lysis, cell-fixing, protein-immunoassays, bright field and fluorescent microscopic monitoring, and real time detection of nucleic acid amplification. The device uses on-board gravity driven flow control which makes it simple and economical to operate with dilute samples (down to 5 cells per reaction), low reagent volumes (50 nL per reaction), highly efficient cell capture (100% capture rates) and single cell protein and gene expression sensitivity. The key results from this work demonstrate a novel technology for versatile, fully integrated microfluidic array platforms. By multiplexing this integrated functionality, the device can be used from routine applications in a biology laboratory to high content screenings

DNA 나노구조체의 염기서열에 따른 형상 및 역학적 특성을 예측하는 멀티스케일 모델링 방법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 기계항공공학부, 2020. 8. 김도년.DNA nanotechnology is a rising field that designs, manufactures, and analyzes DNA nanostructures using the self-assembly principle, creating various related applications. DNA nanostructures are based on the connection between sequences (A, T, G, and C), and its mechanical properties are derived from interactions between atoms. Therefore, to completely understand the mechanical characteristics of DNA nanostructures, all-atomic simulation is required. However, in general, a DNA nanostructure is composed of connections between thousands of sequences in a salt solution, and in order to simulate it on an atomic scale, the atomic system containing billions of degrees of freedom should be solved numerically, which is almost impossible. Accordingly, coarse-grained models have been developed to analyze DNA nanostructures by reducing the degree of freedom, but there are still difficulties to achieve both high efficiency and accuracy of the analysis. Here, this study presents a method to rapidly predict DNA nanostructures at the nanoscale accuracy through multiscale modeling. First, the connections between sequences were classified, and molecular dynamics simulations of a reduced system including them were performed to quantify the sequence-dependent mechanical properties. Next, a finite element model was developed to embody the unique properties, and electrostatic repulsion inside the structure due to the negative charge of DNA in the solution. The assembled finite elements incorporate all the mechanical properties at the sequence-level. Through numerical procedure and normal mode analysis, the equilibrium shape and dynamic properties are rapidly and accurately predicted. The proposed approach can be applied to the analysis of nucleic-acid-based structures and extended to multiscale modeling methods of biomaterials.DNA 나노기술은 DNA의 자가조립원리를 이용해 나노 해상도의 정밀한 구조체를 설계 및 제작, 해석하는 분야로, DNA 나노구조체를 이용한 수많은 응용 연구가 지속적으로 제시되고 있다. DNA 나노구조체는 기본 염기(A, T, G, C) 간의 연결체로서, 이에 따른 국소적인 역학적 물성은 염기를 구성하는 원자 간의 상호작용에 의해 발현된다. 따라서 DNA 나노구조체의 역학적 거동을 온전히 이해하기 위해서는 나노 스케일의 전원자 시뮬레이션이 필요하다. 그러나 일반적으로 DNA 나노구조체는 염이 포함된 수용액 환경에서 수천 개의 염기가 연결되어 구성되므로, 이를 원자 스케일에서 해석하기 위해서는 억 단위의 원자 자유도 문제를 수치적으로 해결해야 하여, 시스템 전체의 전원자 시뮬레이션은 거의 불가능하다. 이에 자유도를 줄여 DNA 나노구조체를 해석하기 위한 여러 축소모델이 개발되고 있으나, 해석의 높은 효율성과 정확성을 모두 달성하려면 여전히 난제가 많다. 이에 본 연구에서는 멀티스케일 모델링을 통해 염기 스케일의 정확도로 DNA 나노구조체를 효율적으로 해석하는 방법을 제시한다. 먼저 염기 간의 다양한 연결 방식을 분류하고, 이를 포함한 작은 시스템의 분자동역학 시뮬레이션을 통해, 염기에 따른 역학적 특성을 정량화하고 물성 라이브러리를 구축하였다. 다음으로 염기 간의 연결에 따른 고유한 역학적 물성과 수용액 환경에서 DNA의 음전하로 인해 발생하는 구조체 내부의 정전기적 반발력을 완전히 반영하는 유한요소 모델을 개발하여, DNA 나노구조체를 구성하는 모든 염기 간의 연결과 구조체 내부의 상호작용을 유한요소 연결체로 변환하였다. 구성된 유한요소 연결체는 염기 스케일의 해상도로 DNA 나노구조체의 역학적 특성을 모두 내포하고 있어, 비선형 수치해석과 고유모드 분석을 통해 DNA 나노구조체의 염기서열에 따른 평형 형상과 동적 특성을 정확하고 빠르게 예측할 수 있다. 본 연구에서 제시하는 기법은 핵산 기반의 구조체 해석에 쉽게 적용할 수 있으며, 다양한 바이오 재료의 멀티스케일 모델링 기술로 확장될 수 있다.1. Introduction 28 1.1. Background and objectives 28 1.2. Research outline 30 1.3. Overview of the multiscale modeling approach 32 2. Investigation of the mechanical properties of DNA 37 2.1. Abstract 37 2.2. Methods 38 2.2.1. Generation of DNA oligomers 38 2.2.2. Molecular dynamics simulations of DNA oligomers 41 2.2.3. Overview of characterizing mechanical properties 43 2.2.4. Mechanical properties of a base-pair step 57 2.2.5. Elastic theory for the base-pair step 60 2.2.6. Equivalent isotropic rigidities in bending and shearing 64 2.3. Mechanical rigidities of base-pair steps 66 2.4. Mechanical coupling coefficients of base-pair steps 72 2.5. Effects of simulation parameters and neighboring sequence 75 3. Multiscale modeling of DNA nanostructures 90 3.1. Abstract 90 3.2. Finite element framework for structural motifs 91 3.2.1. Operators 92 3.2.2. The co-rotational formulation of the two-node beam element 93 3.2.3. Internal force vector in the global coordinate 96 3.2.4. Stiffness matrix in the global coordinate 99 3.3. Local stiffness matrix and internal force vector 101 3.3.1. Net displacement in the local coordinate 102 3.3.2. Displacement field 103 3.3.3. Strain field 104 3.3.4. Strain energy 107 3.3.5. Stiffness matrix in the local coordinate 109 3.3.6. Internal force vector in the local coordinate 110 3.4. Intrinsic properties of the base-pair step 111 3.4.1. Relative geometric parameters in the 3DNA definition 111 3.4.2. Relative geometry and mechanical properties 115 3.4.3. Modification of triad axes for beam element 117 3.4.4. Intrinsic properties of the BP step 118 3.5. Intrinsic properties of the crossover step 130 3.5.1. Modification of triad axes in the crossover step 130 3.5.2. Triad angle correction 131 3.5.3. Intrinsic properties of the crossover step 132 3.6. Characterization and modeling of single-stranded DNA 142 3.6.1. Intrinsic end-to-end length 142 3.6.2. Single-stranded DNA properties 145 3.7. Finite element framework for electrostatic interaction 147 3.7.1. Electrostatic interaction model 147 3.7.2. Finite element model of electrostatic interaction 148 3.8. Estimation of characteristic values on the electrostatic interaction 152 3.9. Construction of initial configuration 154 3.9.1. General description 154 3.9.2. Initial BP triads for the 2-helix-bundle structure 155 3.9.3. Initial configuration of structural elements for base-pair steps 158 3.9.4. Initial configuration of structural elements for crossover steps 160 3.9.5. Generation of electrostatic elements 161 3.10. Nonlinear solution procedure 162 3.10.1. Overview of the solution procedure 162 3.10.2. Element properties in the initial and final configuration 164 3.10.3. Boundary condition 165 3.10.4. Control of properties in structural elements 166 3.10.5. Control of the number of electrostatic elements 167 3.10.6. Iterative solution methods 168 3.10.7. Subdivision of time interval 170 3.10.8. Condition number of stiffness matrix 172 3.11. Molecular dynamics simulation of DNA nanostructures 173 4. Structural analysis of DNA nanostructures 183 4.1. Abstract 183 4.2. Shape prediction of monomeric structures 184 4.2.1. Electrostatic effects on the structural shape 184 4.2.2. Control of included angle in hinge structures 187 4.2.3. Structural distortion by the mean helicity 189 4.2.4. Bending and twist control by inserting or deleting base-pairs 193 4.3. Shape prediction of hierarchical assemblies 200 4.3.1. Control of opening angle in geometrically-constrained V brick 200 4.3.2. Assessment of the twist-correction effect in the tube structure 204 4.3.3. Prediction of hierarchically assembled polyhedral structures 206 4.4. Structural details at the base-pair level 212 4.4.1. The dimension of the pointer structure 212 4.4.2. Prediction of the base-pair and crossover configuration 216 5. Twist control of DNA nanostructures through sequence design 218 5.1. Abstract 218 5.2. Methods 219 5.2.1. Mechanical analysis of DNA structures with base-pair insertion 219 5.2.2. Design and simulation of twisted DNA origami structures 223 5.2.3. Molecular dynamics simulation of 6-helix-bundle blocks 228 5.2.4. Measurement of the twist angle of 6-helix-bundle structures 229 5.2.5. CanDo simulation based on finite element method 231 5.2.6. Relation of the trans ratio with the global twist angle 233 5.2.7. Preparation of DNA origami structures 239 5.2.8. Image analysis using atomic force microscopy 240 5.2.9. Agarose gel electrophoresis 249 5.2.10. Comparison of Bio-RP and PAGE in the purification of staples 250 5.3. Twist control of DNA nanostructures by programming nick sequences 253 5.3.1. Sequences design to control the twist of DNA nanostructure 254 5.3.2. Prediction and experimental validation of the global twist angle 257 6. Dynamic characteristics of DNA nanostructures 260 6.1. Abstract 260 6.2. Methods 261 6.2.1. Normal mode analysis 261 6.2.2. Root-mean-square fluctuation and correlation coefficients 263 6.3. Prediction of structural fluctuation 267 6.4. Prediction of correlation coefficients 270 7. Global mechanical rigidities of DNA nanostructures 272 7.1. Abstract 272 7.2. Methods 273 7.2.1. Estimation of persistence length from normal mode analysis 273 7.2.2. Theoretical estimation of persistence lengths 278 7.3. Prediction of bending and torsional persistence length 281 8. Conclusion 291 A. SNUPI (Structured NUcleic acids Programming Interface) 292 A.1. System requirement 292 A.2. Preparation for the analysis 293 A.3. General procedure 294 A.4. Examples 295 A.4.1. Example 1: Simple structural analysis using the default option 295 A.4.2. Example 2: Prediction of structural and dynamic properties 299 A.5. Analysis options 304 A.5.1. Finite element analysis option 304 A.5.2. Base-pair and crossover steps options 305 A.5.3. Single-stranded DNA options 306 A.5.4. Electrostatic interaction options 308 A.5.5. Normal mode analysis options 311 A.5.6. RMSF and correlation options 312 A.5.7. Configuration plot options 314 A.5.8. Output file options 315 Bibliography 317 Abstract in Korean 325Docto