Search results for: dynamical modeling

Authors: Arcady Ponosov

Abstract:

A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Chil-Chyuan Kuo, Chen-Hsuan Tsai

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This study presents a cost-effective approach for rapid fabricating modeling platforms utilized in fused deposition modeling system. A small-batch production of modeling platforms about 20 pieces can be obtained economically through silicone rubber mold using vacuum casting without applying the plastic injection molding. The air venting systems is crucial for fabricating modeling platform using vacuum casting. Modeling platforms fabricated can be used for building rapid prototyping model after sandblasting. This study offers industrial value because it has both time-effectiveness and cost-effectiveness.

Keywords: vacuum casting, fused deposition modeling, modeling platform, sandblasting, surface roughness

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Francesco Morgan Bono, Simone Cinquemani

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This research aims to enhance bridge monitoring by employing innovative techniques that incorporate exogenous factors into the modeling of sensor signals, thereby improving long-term predictability beyond traditional static methods. Using real datasets from two different bridges equipped with Linear Variable Displacement Transducer (LVDT) sensors, the study investigates the fundamental principles governing sensor behavior for more precise long-term forecasts. Additionally, the research evaluates performance on noisy and synthetically damaged data, proposing a residual-based alarm system to detect anomalies in the bridge. In summary, this novel approach combines advanced modeling, exogenous factors, and anomaly detection to extend prediction horizons and improve preemptive damage recognition, significantly advancing structural health monitoring practices.

Keywords: structural health monitoring, dynamic models, sindy, railway bridges

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Authors: Seongsoo Lee

Abstract:

IP reuse is an effective design methodology for modern SoC design to reduce effort and time. However, description and modeling methods of IP interfaces are different due to different IP designers. In this paper, standardized description and modeling methods of IP interfaces are proposed. It consists of 11 items such as IP information, model provision, data type, description level, interface information, port information, signal information, protocol information, modeling level, modeling information, and source file. The proposed description and modeling methods enables easy understanding, simulation, verification, and modification in IP reuse.

Keywords: interface, standardization, description, modeling, semiconductor IP

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Authors: Ayse Ozturk

Abstract:

The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

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Authors: Barenten Suciu

Abstract:

Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.

Keywords: bullet train, creep, cylindrical wheels, damping, dynamical hunting, stability, vibration analysis

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Authors: Amin Behradfar

Abstract:

‎Tourism has a direct impact on the national revenue for all touristic countries. It creates work opportunities‎, ‎industries‎, ‎and several investments to serve and raise nations performance and cultures. ‎This paper is devoted to analyze dynamical behaviour of a four-dimensional non-linear tourism-based social-ecological system by using the codimension two bifurcation theory‎. ‎In fact we investigate the cusp bifurcation of that‎. ‎Implications of our mathematical results to the tourism‎ ‎industry are discussed‎. Moreover, profitability‎, ‎compatibility and sustainability of the tourism system are shown by the aid of cusp bifurcation and numerical techniques‎.

Keywords: tourism-based social-ecological dynamical systems, cusp bifurcation, center manifold theory, profitability, ‎compatibility, sustainability

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Authors: Owolabi Kolade Matthew

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In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species system. We analyze the linear stability of stationary solutions in the one-dimensional multi-system modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyzes to determine the global dynamics of the system. In the presence of diffusion, a viable exponential time differencing method is applied to multi-species nonlinear time-dependent partial differential equation to address the points and queries that may naturally arise. The scheme is described in detail, and justified by a number of computational experiments.

Keywords: asymptotically stable, coexistence, exponential time differencing method, global and local stability, predator-prey model, nonlinear, reaction-diffusion system

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Authors: Sadia Arshad

Abstract:

The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Mohamed Belhorma, Aboubakar S. Bouchikhi, Belkacem Bounab

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This paper addresses modeling a Double A-Arm suspension, a three-dimensional nonlinear model has been developed using the multibody systems formalism. Dynamical study of the different components responses was done, particularly for the wheel assembly. To validate those results, the system was constructed and simulated by RecurDyn, a professional multibody dynamics simulation software. The model has been used as the Objectif function in an optimization algorithm for ride quality improvement.

Keywords: double A-Arm suspension, multibody systems, ride quality optimization, dynamic simulation

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Authors: Chao-Qing Dai

Abstract:

Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: Katalina Grigorova, Kaloyan Mironov

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The paper focuses on the benefits of business process modeling. Although this discipline is developing for many years, there is still necessity of creating new opportunities to meet the ever-increasing users’ needs. Because one of these needs is related to the conversion of business process models from one standard to another, the authors have developed a converter between BPMN and EPC standards using workflow patterns as intermediate tool. Nowadays there are too many systems for business process modeling. The variety of output formats is almost the same as the systems themselves. This diversity additionally hampers the conversion of the models. The presented study is aimed at discussing problems due to differences in the output formats of various modeling environments.

Keywords: business process modeling, business process modeling standards, workflow patterns, converting models

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi

Abstract:

In this paper a real-time obstacle avoidance approach for both autonomous and non-autonomous dynamical systems (DS) is presented. In this approach the original dynamics of the controller which allow us to determine safety margin can be modulated. Different common types of DS increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle especially when robot moves very fast in changeable complex environments. The method is validated by simulation and influence of different autonomous and non-autonomous DS such as important characteristics of limit cycles and unstable DS. Furthermore, the position of different obstacles in complex environment is explained. Finally, the verification of avoidance trajectories is described through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, safety margin

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Authors: Vramori Mitra, Bornali Sarma, Arun K. Sarma

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Recurrence is a ubiquitous feature of any real dynamical system. The states in phase space trajectory of a system have an inherent tendency to return to the same state or its close state after certain time laps. Recurrence quantification analysis technique, based on this fundamental feature of a dynamical system, detects evaluation of state under variation of control parameter of the system. The paper presents the investigation of nonlinear dynamical behavior of plasma floating potential fluctuations obtained by using a Langmuir probe in different magnetic field under the variation of discharge voltages. The main measures of recurrence quantification analysis are considered as determinism, linemax and entropy. The increment of the DET and linemax variables asserts that the predictability and periodicity of the system is increasing. The variable linemax indicates that the chaoticity is being diminished with the slump of magnetic field while increase of magnetic field enhancing the chaotic behavior. Fractal property of the plasma time series estimated by DFA technique (Detrended fluctuation analysis) reflects that long-range correlation of plasma fluctuations is decreasing while fractal dimension is increasing with the enhancement of magnetic field which corroborates the RQA analysis.

Keywords: detrended fluctuation analysis, chaos, phase space, recurrence

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Authors: Jairo Aparecido Martins, Estaner Claro Romão

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This paper presents the static and cyclic stresses in combination with fatigue analysis resultant of loads applied on the friction discs usually utilized on industrial clutches. The material chosen to simulate the friction discs under load is aluminum. The numerical simulation was done by software COMSOL^TM Multiphysics. The results obtained for static loads showed enough stiffness for both geometries and the material utilized. On the other hand, in the fatigue standpoint, failure is clearly verified, what demonstrates the importance of both approaches, mainly dynamical analysis. The results and the conclusion are based on the stresses on disc, counted stress cycles, and fatigue usage factor.

Keywords: aluminum, industrial clutch, static and dynamic loading, numerical simulation

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Authors: Mohammad Reza Zamani Kouhpanji

Abstract:

Characterizing the fatigue and fracture properties of nanostructures is one of the most challenging tasks in nanoscience and nanotechnology due to lack of a MEMS/NEMS device for generating uniform cyclic loadings at high frequencies. Here, the dynamic response of a recently proposed MEMS/NEMS device under different inputs signals is completely investigated. This MEMS/NEMS device is designed and modeled based on the electromagnetic force induced between paired parallel wires carrying electrical currents, known as Ampere’s Force Law (AFL). Since this MEMS/NEMS device only uses two paired wires for actuation part and sensing part, it represents highly sensitive and linear response for nanostructures with any stiffness and shapes (single or arrays of nanowires, nanotubes, nanosheets or nanowalls). In addition to studying the maximum gains at different resonance frequencies of the MEMS/NEMS device, its dynamical responses are investigated for different inputs and nanostructure properties to demonstrate the capability, usability, and reliability of the device for wide range of nanostructures. This MEMS/NEMS device can be readily integrated into SEM/TEM instruments to provide real time study of the fatigue and fracture properties of nanostructures as well as their softening or hardening behaviors, and initiation and/or propagation of nanocracks in them.

Keywords: MEMS/NEMS devices, paired wire actuators and sensors, dynamical response, fatigue and fracture characterization, Ampere’s force law

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Authors: Jay Xiong, Li Lin

Abstract:

Existing software modeling and visualization approaches using UML are outdated, which are outcomes of reductionism and the superposition principle that the whole of a system is the sum of its parts, so that with them all tasks of software modeling and visualization are performed linearly, partially, and locally. This paper introduces revolutionary solutions for modeling and visualization of complex software systems, which make complex software systems much easy to understand, test, and maintain. The solutions are based on complexity science, offering holistic, automatic, dynamic, virtual, and executable approaches about thousand times more efficient than the traditional ones.

Keywords: complex systems, software maintenance, software modeling, software visualization

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Authors: Akaash Tawade, Manan Khattar, Lucas Spangher, Costas J. Spanos

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Many grids are increasing the share of renewable energy in their generation mix, which is causing the energy generation to become less controllable. Buildings, which consume nearly 33% of all energy, are a key target for demand response: i.e., mechanisms for demand to meet supply. Understanding the behavior of office workers is a start towards developing demand response for one sector of building technology. The literature notes that dynamic computational modeling can be predictive of individual action, especially given that occupant behavior is traditionally abstracted from demand forecasting. Recent work founded on Social Cognitive Theory (SCT) has provided a promising conceptual basis for modeling behavior, personal states, and environment using control theoretic principles. Here, an adapted linear dynamical system of latent states and exogenous inputs is proposed to simulate energy demand amongst office workers engaged in a social energy shifting game. The energy shifting competition is implemented in an office in Singapore that is connected to a minigrid of buildings with a consistent 'price signal.' This signal is translated into a 'points signal' by a reinforcement learning (RL) algorithm to influence participant energy use. The dynamic model functions at the intersection of the points signals, baseline energy consumption trends, and SCT behavioral inputs to simulate future outcomes. This study endeavors to analyze how the dynamic model trains an RL agent and, subsequently, the degree of accuracy to which load deferability can be simulated. The results offer a generalizable behavioral model for energy competitions that provides the framework for further research on transfer learning for RL, and more broadly— transactive control.

Keywords: energy demand forecasting, social cognitive behavioral modeling, social game, transfer learning

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Authors: Sakiru Badmos, David R. Cole, Alberto Striolo

Abstract:

It is known that confinement in nm-size pores affects many structural and transport properties of water and co-existing volatile species. Of particular interest for fluids in sub-surface systems, in catalysis, and in separations are reports that confinement can enhance the solubility of gases in water. Equilibrium molecular dynamics simulations were performed for aqueous H₂S confined in slit-shaped silica pores at 313K. The effect of pore width on the H₂S solubility in water was investigated. Other properties of interest include the molecular distribution of the various fluid molecules within the pores, the hydration structure for solvated H₂S molecules, and the dynamical properties of the confined fluids. The simulation results demonstrate that confinement reduces the H₂S solubility in water and that the solubility increases with pore size. Analysis of spatial distribution functions suggests that these results are due to perturbations on the coordination of water molecules around H₂S due to confinement. Confinement is found to dampen the dynamical properties of aqueous H₂S as well. Comparing the results obtained for aqueous H₂S to those reported elsewhere for aqueous CH₄, it can be concluded that H₂S permeates hydrated slit-shaped silica nano-pores faster than CH₄. In addition to contributing to better understanding the behavior of fluids in subsurface formations, these observations could also have important implications for developing new natural gas sweetening technologies.

Keywords: confinement, interfacial properties, molecular dynamic simulation, sub-surface formations

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Authors: S. A. Che Osmi, W. M. F. W. Ishak, S. F. Che Osmi

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Nowadays the issues of water quality and water pollution have been a major problem across the country. A lot of management attempt to develop their own TMDL database in order to control the river pollution. Over the past decade, the mathematical modeling has been used as the tool for the development of TMDL. This paper presents the application of water quality modeling to develop the total maximum daily load (TMDL) information. To obtain the reliable database of TMDL, the appropriate water quality modeling should choose based on the available data provided. This paper will discuss on the use of several water quality modeling such as QUAL2E, QUAL2K, and EFDC to develop TMDL. The attempts to integrate several modeling are also being discussed in this paper. Based on this paper, the differences in the application of water quality modeling based on their properties such as one, two or three dimensional are showing their ability to develop the modeling of TMDL database.

Keywords: TMDL, water quality modeling, QUAL2E, EFDC

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: h-infinity fuzzy control, an LMI approach, Takagi-Sugano (TS) fuzzy system, the photovoltaic systems

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Authors: Pedro F. D. Oliveira, Rangel S. Maia, Aline S. Paula

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As the electric energy consumption grows, the necessity of energy transmission lines increases. One of the problems caused by an oscillatory response to dynamical loads (such as wind effects) in transmission lines is the cable fatigue. Thus, the dynamical behavior of transmission cables understanding and its control is extremely important. The socioeconomic damage caused by a failure in these cables can be quite significant, from large economic losses to energy supply interruption in large regions. Dynamic Vibration Absorbers (DVA) are oscillatory elements used to mitigate the vibration of a primary system subjected to harmonic excitation. The positioning of Stockbridge (DVA for overhead transmission lines) plays an important role in mitigating oscillations of transmission lines caused by airflows. Nowadays, the positioning is defined by technical standards or commercial software. The aim of this paper is to conduct an analysis of multiple DVAs performances in cable conductors of overhead transmission lines. The cable is analyzed by a finite element method and the model is calibrated by experimental results. DVAs performance is analyzed by evaluating total cable energy, and a study of multiple DVAs positioning is conducted. The results are compared to the existing regulations showing situations where proper positioning, different from the standard, can lead to better performance of the DVA. Results also show situations where the use of multiple DVAs is appropriate.

Keywords: dynamical vibration absorber, finite element method, overhead transmission lines, structural dynamics

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Authors: Jixiang Zhang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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Authors: Ch. Surawut, D. Sukawat

Abstract:

In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Saeed Mahjoub Moghadas, Farhad Asadi, Shahed Torkamandi, Hassan Moradi, Mahmood Purgamshidian

Abstract:

In this paper, we present real-time obstacle avoidance approach for both autonomous and non-autonomous DS-based controllers and also based on dynamical systems (DS) method. In this approach, we can modulate the original dynamics of the controller and it allows us to determine safety margin and different types of DS to increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle and especially when robot moves very fast in changeable complex environments. The method is validated in simulation and influence of different autonomous and non-autonomous DS such as limit cycles, and unstable DS on this algorithm and also the position of different obstacles in complex environment is explained. Finally, we describe how the avoidance trajectories can be verified through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, DS-based controllers

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Authors: Zoltan Theisz, Gergely Mezei

Abstract:

Modern industrial automation relies on service oriented concepts of Internet of Things (IoT) device modeling in order to provide a flexible and extendable environment for service meta-repository. However, state-of-the-art meta-modeling techniques prefer design-time modeling, which results in a heavy usage of class sometimes unnecessary static subtyping. Although this approach benefits from clear-cut object-oriented design principles, it also seals the model repository for further dynamic extensions. In this paper, a dynamic multi-level modeling approach is introduced that enables dynamic subtyping through a more relaxed partial instantiation mechanism. The approach is demonstrated on a simple sensor network example.

Keywords: meta-modeling, dynamic subtyping, DMLA, industrial automation, arrowhead

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Authors: Jixiang Zhang, Yanhua Wang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

Abstract:

The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Titus A. Beu

Abstract:

Many modern gene-delivery protocols rely on condensed complexes of DNA with polycations to introduce the genetic payload into cells by endocytosis. In particular, polyethyleneimine (PEI) stands out by a high buffering capacity (enabling the efficient condensation of DNA) and relatively simple fabrication. Realistic computational studies can offer essential insights into the formation process of DNA-PEI polyplexes, providing hints on efficient designs and engineering routes. We present comprehensive computational investigations of solvated PEI and DNA-PEI polyplexes involving calculations at three levels: ab initio, all-atom (AA), and coarse-grained (CG) molecular mechanics. In the first stage, we developed a rigorous AA CHARMM (Chemistry at Harvard Macromolecular Mechanics) force field (FF) for PEI on the basis of accurate ab initio calculations on protonated model pentamers. We validated this atomistic FF by matching the results of extensive molecular dynamics (MD) simulations of structural and dynamical properties of PEI with experimental data. In a second stage, we developed a CG MARTINI FF for PEI by Boltzmann inversion techniques from bead-based probability distributions obtained from AA simulations and ensuring an optimal match between the AA and CG structural and dynamical properties. In a third stage, we combined the developed CG FF for PEI with the standard MARTINI FF for DNA and performed comprehensive CG simulations of DNA-PEI complex formation and condensation. Various technical aspects which are crucial for the realistic modeling of DNA-PEI polyplexes, such as options of treating electrostatics and the relevance of polarizable water models, are discussed in detail. Massive CG simulations (with up to 500 000 beads) shed light on the mechanism and provide time scales for DNA polyplex formation independence of PEI chain size and protonation pattern. The DNA-PEI condensation mechanism is shown to primarily rely on the formation of DNA bundles, rather than by changes of the DNA-strand curvature. The gained insights are expected to be of significant help for designing effective gene-delivery applications.

Keywords: DNA condensation, gene-delivery, polyethylene-imine, molecular dynamics.

Procedia PDF Downloads 101