New tools make possible physics-based analytics in an embedded environment. By computing locally – performing predictive and prescriptive analytics at the edge of the IoT – significantly less data must be directed to the cloud. Further, the data sent are more informative and they are available in server-less situations. This improves reliability, speeds computation time and reduces power consumption. In addition, physics-based models have the ability to assess the internal state of an observed system. This makes their predictions more accurate. By enabling physics-based models to operate in real time in small footprint embedded devices, the resultant robust predictive ability can lead to a reduction of needed, and often expensive, system monitoring sensors. To illustrate how embedded model-driven analytics can be implemented, two real world examples will be demonstrated: an electric motor health monitor and a high voltage safety system. Each step in the implementation process will be shown, from model design to the utilization of embedded scientific computing tools, final real-time model optimization, and system predictions.
Communication between distantly spaced genomic regions is one of the key features of gene regulation in eukaryotes. Chromatin per se can stimulate efficient enhancer-promoter communication (EPC); however, the role of chromatin structure and dynamics in this process remains poorly understood. Here we show that nucleosome spacing and the presence of nucleosome-free DNA regions can modulate chromatin structure/dynamics and, in turn, affect the rate of EPC in vitro and in silico. Increasing the length of internucleosomal linker DNA from 25 to 60 bp results in more efficient EPC. The presence of longer nucleosome-free DNA regions can positively or negatively affect the rate of EPC, depending upon the length and location of the DNA region within the chromatin fiber. Thus the presence of histone-free DNA regions can differentially affect the efficiency of EPC, suggesting that gene regulation over a distance could be modulated by changes in the length of internucleosomal DNA spacers.
One of the critical unanswered questions in genome biophysics is how the primary sequence of DNA bases influences the global properties of very-long-chain molecules. The local sequence-dependent features of DNA found in high-resolution structures introduce irregularities in the disposition of adjacent residues that facilitate the specific binding of proteins and modulate the global folding and interactions of double helices with hundreds of basepairs. These features also determine the positions of nucleosomes on DNA and the lengths of the interspersed DNA linkers. Like the patterns of basepair association within DNA, the arrangements of nucleosomes in chromatin modulate the properties of longer polymers. The intrachromosomal loops detected in genomic studies contain hundreds of nucleosomes, and given that the simulated configurations of chromatin depend on the lengths of linker DNA, the formation of these loops may reflect sequence-dependent information encoded within the positioning of the nucleosomes. With knowledge of the positions of nucleosomes on a given genome, methods are now at hand to estimate the looping propensities of chromatin in terms of the spacing of nucleosomes and to make a direct connection between the DNA base sequence and larger-scale chromatin folding
Multi-stranded helices are widespread in nature. The interplay of polymeric properties with biological function is seldom discussed. This study probes analogies between structural and mechanical properties of collagen and DNA. We modeled collagen with Eulerian rotational and translational parameters of adjacent rungs in the triple-helix ladder and developed statistical potentials by extracting the dispersion of the parameters from a database of atomic-resolution structures. The resulting elastic model provides a common quantitative way to describe collagen deformations upon interacting with integrins or matrix metalloproteinase and DNA deformations upon protein binding. On a larger scale, deformations in Type I collagen vary with a periodicity consistent with the D-periodic banding of higher-order fibers assemblies. This indicates that morphologies of natural higher-order collagen packing might be rooted in the characteristic deformation patterns.
Battery cell and pack simulation has become an important field for complex vehicle and energy systems simulations, as well as for model based control of such systems. The quality and performance of simulation, besides the quality of the model itself, is greatly determined by the characteristics of the model solver. Speed, accuracy, ability for quick computation of sensitivities and low memory footprint are some of the solver characteristics required for successful deployment. Different simulation time steps among the system components as well as different simulation concepts, such as continuous time or discrete event time, as is the case for power supplies simulation, favor a simulation environment where the battery subsystem is implemented “in-the-loop”, running as a co-simulation slave process. General purpose model solvers, by their own nature, impose too much overhead or lack essential functions. In this paper we will present “dtSolve”, a model solver written for physics based battery model simulations and we will demonstrate its performance in “real-time” complex battery pack multi-physics simulations. dtSolve implements Automatic Differentiation (AD), adaptive time steps, Differential Algebraic Equation (DAE) formulation for transient solutions, sparse matrix techniques, a space optimized DAE solver and an optimization code, all of them tightly coupled into an object oriented design platform.
The looping of DNA provides a means of communication between sequentially distant genomic sites that operate in tandem to express, copy, and repair the information encoded in the DNA base sequence. The short loops implicated in the expression of bacterial genes suggest that molecular factors other than the naturally stiff double helix are involved in bringing the interacting sites into close spatial proximity. New computational techniques that take direct account of the three-dimensional structures and fluctuations of protein and DNA allow us to examine the likely means of enhancing such communication. Here, we describe the application of these approaches to the looping of a 92 base-pair DNA segment between the headpieces of the tetrameric Escherichia coli Lac repressor protein. The distortions of the double helix induced by a second protein—the nonspecific nucleoid protein HU—increase the computed likelihood of looping by several orders of magnitude over that of DNA alone. Large-scale deformations of the repressor, sequence-dependent features in the DNA loop, and deformability of the DNA operators also enhance looping, although to lesser degrees. The correspondence between the predicted looping propensities and the ease of looping derived from gene-expression and single-molecule measurements lends credence to the derived structural picture.
The dynamic organization of chromatin plays an essential role in the regulation of gene expression and in other fundamental cellular processes. The underlying physical basis of these activities lies in the sequential positioning, chemical composition, and intermolecular interactions of the nucleosomes—the familiar assemblies of ~150 DNA base pairs and eight histone proteins—found on chromatin fibers. Here we introduce a mesoscale model of short nucleosomal arrays and a computational framework that make it possible to incorporate detailed structural features of DNA and histones in simulations of short chromatin constructs. We explore the effects of nucleosome positioning and the presence or absence of cationic N-terminal histone tails on the 'local' inter-nucleosomal interactions and the global deformations of the simulated chains. The correspondence between the predicted and observed effects of nucleosome composition and numbers on the long-range communication between the ends of designed nucleosome arrays lends credence to the model and to the molecular insights gleaned from the simulated structures. We also extract effective nucleosome-nucleosome potentials from the simulations and implement the potentials in a larger-scale computational treatment of regularly repeating chromatin fibers. Our results reveal a remarkable effect of nucleosome spacing on chromatin flexibility, with small changes in DNA linker length significantly altering the interactions of nucleosomes and the dimensions of the fiber as a whole. In addition, we find that these changes in nucleosome positioning influence the statistical properties of long chromatin constructs. That is, simulated chromatin fibers with the same number of nucleosomes exhibit polymeric behaviors ranging from Gaussian to worm-like, depending upon nucleosome spacing. These findings suggest that the physical and mechanical properties of chromatin can span a wide range of behaviors, depending on nucleosome positioning, and that care must be taken in the choice of models used to interpret the experimental properties of long chromatin fibers.
The binding of proteins onto DNA contributes to the shaping and packaging of genome as well as to the expression of specific genetic messages. With a view to understanding the interplay between the presence of proteins and the deformation of DNA involved in such processes, we developed a new method to minimize the elastic energy of DNA fragments at the mesoscale level. Our method makes it possible to obtain the optimal pathways of protein-decorated DNA molecules for which the terminal base pairs are spatially constrained. We focus in this work on the deformations induced by selected architectural proteins on circular DNA. We report the energy landscapes of DNA minicircles subjected to different levels of torsional stress and containing one or two proteins as functions of the chain length and spacing between the proteins. Our results reveal cooperation between the elasticity of the double helix and the structural distortions of DNA induced by bound proteins. We find that the imposed mechanical stress influences the placement of proteins on DNA and that, the proteins, in turn, modulate the mechanical stress and thereby broadcast their presence along DNA.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerlineʼs tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.
The 50th anniversary of Biopolymers coincides closely with the like celebration of the discovery of the Escherichia coli (lac) lactose operon, a classic genetic system long used to illustrate the influence of biomolecular structure on function. The looping of DNA induced by the binding of the Lac repressor protein to sequentially distant operator sites on DNA continues to serve as a paradigm for understanding long-range genomic communication. Advances in analyses of DNA structures and in incorporation of proteins in computer simulations of DNA looping allow us to address long-standing questions about the role of protein-mediated DNA loop formation in transcriptional control. Here we report insights gained from studies of the sequence-dependent contributions of the natural lac operators to Lac repressor-mediated DNA looping. Novel superposition of the ensembles of protein-bound operator structures derived from NMR measurements reveals variations in DNA folding missed in conventional structural alignments. The changes in folding affect the predicted ease with which the repressor induces loop formation and the ways that DNA closes between the protein headpieces. The peeling of the auxiliary operators away from the repressor enhances the formation of loops with the 92-bp wildtype spacing and hints of a structural reason behind their weak binding.
We present the small-amplitude vibrations of a circular elastic ring with periodic and clamped boundary conditions. We model the rod as an inextensible, isotropic, naturally straight Kirchhoff elastic rod and obtain the vibrational modes of the ring analytically for periodic boundary conditions and numerically for clamped boundary conditions. Of particular interest are the dependence of the vibrational modes on the torsional stress in the ring and the influence of the rotational inertia of the rod on the mode frequencies and amplitudes. In rescaling the Kirchhoff equations, we introduce a parameter inversely proportional to the aspect ratio of the rod. This parameter makes it possible to capture the influence of the rotational inertia of the rod. We find that the rotational inertia has a minor influence on the vibrational modes with the exception of a specific category of modes corresponding to high-frequency twisting deformations in the ring. Moreover, some of the vibrational modes over or undertwist the elastic rod depending on the imposed torsional stress in the ring.
Action across long distances on chromatin is a hallmark of eukaryotic transcriptional regulation. Although chromatin structure per se can support long-range interactions, the mechanisms of efficient communication between widely spaced DNA modules in chromatin remain a mystery. The molecular simulations described herein suggest that transient binary internucleosomal interactions can mediate distant communication in chromatin. Electrostatic interactions between the N-terminal tails of the core histones and DNA enhance the computed probability of juxtaposition of sites that lie far apart along the DNA sequence. Experimental analysis of the rates of communication in chromatin constructs confirms that long-distance communication occurs efficiently and independently of distance on tail-containing, but not on tailless, chromatin. Taken together, our data suggest that internucleosomal interactions involving the histone tails are essential for highly efficient, long-range communication between regulatory elements and their targets in eukaryotic genomes.
Within the nucleus of each cell lies DNA—an unfathomably long, twisted, and intricately coiled molecule—segments of which make up the genes that provide the instructions that a cell needs to operate. As we near the 60th anniversary of the discovery of the DNA double helix, crucial questions remain about how the physical arrangement of the DNA in cells affects how genes work. For example, how a cell stores the genetic information inside the nucleus is complicated by the necessity of maintaining accessibility to DNA for genetic processing. In order to gain insight into the roles played by various proteins in reading and compacting the genome, we have developed new methodologies to simulate the dynamic, three-dimensional structures of long, fluctuating, protein-decorated strands of DNA. Our a priori approach to the problem allows us to determine the effects of individual proteins and their chemical modifications on overall DNA structure and function. Here, we present our recent treatment of the communication between regulatory proteins attached to precisely constructed stretches of chromatin. Our simulations account for the enhancement in communication detected experimentally on chromatin compared to protein-free DNA of the same chain length, as well as the critical roles played by the cationic ‘tails’ of the histone proteins in this signaling. The states of chromatin captured in the simulations offer new insights into the ways that the DNA, histones, and regulatory proteins contribute to long-range communication along the genome.
The structural and physical properties of DNA are closely related to its geometry and topology. The classical mathematical treatment of DNA geometry and topology in terms of ideal smooth space curves was not designed to characterize the spatial arrangements of atoms found in high-resolution and simulated double-helical structures. We present here new and rigorous numerical methods for the rapid and accurate assessment of the geometry and topology of double-helical DNA structures in terms of the constituent atoms. These methods are well designed for large DNA data sets obtained in detailed numerical simulations or determined experimentally at high resolution. We illustrate the usefulness of our methodology by applying it to the analysis of three canonical double-helical DNA chains, a 65 bp minicircle obtained in recent molecular dynamics simulations, and a crystallographic array of protein-bound DNA duplexes. Although we focus on fully base-paired DNA structures, our methods can be extended to treat the geometry and topology of melted DNA structures as well as to characterize the folding of arbitrary molecules, such as RNA and cyclic peptides.
We present a self-contained theory for the mechanical response of DNA in single molecule experiments. Our model is based on a one-dimensional continuum description of the DNA molecule and accounts both for its elasticity and for DNA-DNA electrostatic interactions. We consider the classical loading geometry used in experiments where one end of the molecule is attached to a substrate and the other one is pulled by a tensile force and twisted by a given number of turns. We focus on configurations relevant to the limit of a large number of turns, which are made up of two phases, one with linear DNA and the other one with superhelical DNA. The model takes into account thermal fluctuations in the linear phase and electrostatic interactions in the superhelical phase. The values of the torsional stress, of the supercoiling radius and angle, and key features of the experimental extension-rotation curves, namely the slope of the linear region and thermal buckling threshold, are predicted. They are found in good agreement with experimental data.
We derive solutions of the Kirchhoff equations for a knot tied on an infinitely long elastic rod subjected to combined tension and twist, and held at both endpoints at infinity. We consider the case of simple (trefoil) and double (cinquefoil) knots; other knot topologies can be investigated similarly. The rod model is based on Hookean elasticity but is geometrically nonlinear. The problem is formulated as a nonlinear self-contact problem with unknown contact regions. It is solved by means of matched asymptotic expansions in the limit of a loose knot. We obtain a family of equilibrium solutions depending on a single loading parameter (proportional to applied twisting moment divided by square root of pulling force), which are asymptotically valid in the limit of a loose knot. Without any a priori assumption, we derive the topology of the contact set, which consists of an interval of contact flanked by two isolated points of contacts. We study the influence of the applied twist on the equilibrium.
We consider an elastic rod model for twisted DNA in the plectonemic regime. The molecule is treated as an impenetrable tube with an effective, adjustable radius. The model is solved analytically, and we derive formulas for the contact pressure, twisting moment, and geometrical parameters of the supercoiled region. We apply our model to magnetic tweezer experiments of a DNA molecule subjected to a tensile force and a torque and extract mechanical and geometrical quantities from the linear part of the experimental response curve. These reconstructed values are derived in a self-contained manner and are found to be consistent with those available in the literature.
The DNA molecule is modeled as an elastic rod with bending and twisting rigidities, subjected to external tension and twist applied at one end, the other end being clamped. We study the plectonemic equilibrium of such a rod, taking into account the impenetrability constraint. Numerical solutions of this boundary value problem have previously shown that purely elastic models can reproduce the supercoiling response of the DNA molecule. Using a variational approach, we derive analytical formulae for the elastic response of the filament, and extend former numerical results.
We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equilibrium are compared to experiments. The extension of the theory to tight knots is discussed.