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PubMed2002

The application of dynamic field shaping and dynamic dose rate control in conformal rotational treatment of the prostate.

The current philosophy of dose escalation in the treatment of prostate cancer has forced the treatment planner to re-evaluate his/her planning approach. Precise and accurate delivery of dose to the prostate while maintaining the required dose limits to the normal critical structures, such as the rectum, has become increasingly difficult in light of these escalated doses. Conformal treatment techniques allow the treatment planner to precisely shape each individual treatment field so that desired volume coverage and normal tissue sparing can be achieved. In addition to these beam-shaping advantages, adjustment of an individual beam's weighting also helps to create the desired distribution and tissue sparing. Rotational therapy "simulates" treatment with multiple beams and angles, similar to the thought process behind conformal treatment technique. With rotational therapy, however, the treatment planner's inability to provide adequate beam shaping and weighting adjustment has placed limits on its value as a viable planning option. The introduction of computer-controlled treatment machines, which allow dynamic adjustment of the field shape with the rotation of the beam, makes it possible to re-evaluate rotational therapy as a potential option. Similarly, the treatment planner's ability to change field weighting can be accomplished by the application of dynamic dose rate control, allowing a rotational beam to deliver a weighting similar to that possible with conformal fixed-field techniques. Dose-volume histogram data will be used to evaluate doses delivered to the prostate, rectum, and bladder using rotational therapy with dynamic field shape and dynamic dose rate control as a treatment planning option. The dose delivery and normal tissue-sparing potential of this technique compared to coplanar and noncoplanar conformal fixed-field techniques will also be presented.

Femur Head↗
PubMed1997

Dynamic collimator and dose rate control: enabling technology for enhanced dynamic wedge.

The key features that make dynamic dose delivery possible in the Enhanced Dynamic Wedge application are computerized position and control of the independent collimating jaws and computerized dynamic control of the linear accelerator dose rate. These features will be described and related to the current implementation of Enhanced Dynamic Wedge.

Particle Accelerators↗
PubMed2002

Pressurized hot water extraction with on-line fluorescence monitoring: a comparison of the static, dynamic, and static-dynamic modes for the removal of polycyclic aromatic hydrocarbons from environmental solid samples.

A comparison of the feasibility of the three operational modes of pressurized hot solvent extraction (PHSE) (namely, static, where a fixed extractant volume is used; dynamic, where the extractant continually flows through the sample; and static-dynamic mode, which consists of a combination of the two previous modes) for the extraction of polycyclic aromatic hydrocarbons (PAHs) from environmental solid samples (such as soil, sediment, trout, and sardine) has been performed. In all cases, a sodium dodecyl sulfate (SDS) aqueous solution was used as leaching agent. The use of a flow injection manifold between the extractor and a molecular fluorescence detector allowed real-time on-line fluorescence monitoring of the PAHs extracted from the samples, thus working as a screening system and providing qualitative and semiquantitative information on the target analytes extracted from both natural and spiked samples. The on-line monitoring option allowed the extraction kinetics to be monitored and the end of the leaching step to be determined independently of the sample matrix, thereby reducing extraction times. Efficiencies close to 100% have been provided by the three modes, which differ in the extraction time required for total removal of the target compounds. The time needed for the dynamic mode was shorter than that for the static mode. However, the establishment of a static extraction step prior to dynamic extraction was the key to shorten the time required for complete extraction. The method has been applied to a certified reference material (CRM 524, BCR, industrial soil/organics) for quality assurance/validation.

Animals↗
PubMed1995

Structure and dynamics of a DNA.RNA hybrid duplex with a chiral phosphorothioate moiety: NMR and molecular dynamics with conventional and time-averaged restraints.

The three-dimensional structure of two thiophosphate-modified DNA.RNA hybrid duplexes d(GCTATAApsTGG).r(CCAUUAUAGC), one with R-thiophosphate chirality and one with S-thiophosphate chirality, have been determined by restrained molecular dynamics simulations (rMD). As the two yielded almost identical results, a description of results can be presented in the singular. The conformational flexibility of this hybrid has been investigated by employing time-averaged constraints during the molecular dynamics simulations (MD-tar). A set of structural restraints, comprising 322 precise interproton distance constraints obtained by a complete relaxation matrix analysis of the 2D NOE intensities as well as J coupling constants obtained from quantitative simulations of DQF-COSY cross-peaks in deoxyriboses, was reported in our previous paper [González, C., Stec, W., Kobylanska, A., Hogrefe, R. I., Reynolds, M., & James, T. L. (1994) Biochemistry 33, 11062-11072]. Multiple conformations of the deoxyribose moieties were evident from the scalar coupling constant analysis. Accurate distance constraints, obtained from complete relaxation matrix analysis, yielded a time-averaged solution structure via conventional restrained molecular dynamics which is not compatible with the experimental J coupling constants (root-mean-square deviation in J value approximately 2 Hz). However, vicinal coupling constant information can be reproduced when time-averaged constraints are used during the molecular dynamics calculations instead of the conventional restraints (Jrms approximately 0.6 Hz). MD-tar simulations also improve the NMR R factors. This improvement is more evident in the DNA than in the RNA strand, where no indication of conformational flexibility had been obtained. Analysis of the MD-tar trajectories confirms that deoxyriboses undergo pucker transitions between the S and N domain, with the major conformer in the S domain. The ribose moieties in the RNA strand, however, remain in the N domain during the entire simulation. Conformations of deoxyriboses in the intermediate domain near O4'-endo are obtained when the average structure is calculated with conventional NMR restraints. Since these conformations cannot account for the experimental J coupling information, and they only appear in a very low population in the MD-tar ensemble, we conclude that intermediate E sugar puckers are artifacts produced by the attempt to fit all the structural constraints simultaneously when in reality more than one conformer is present. Most structural features of the duplex remain the same in the average structure and in the MD-tar ensemble, e.g., the minor groove width, exhibiting an intermediate value compared with those of canonical A- and B-like structures.(ABSTRACT TRUNCATED AT 250 WORDS)

Base Sequence↗
PubMed1982

Protein dynamics in solution and in a crystalline environment: a molecular dynamics study.

The effect of a solvent and a crystalline environment on the dynamics of proteins is investigated by the method of computer simulation. Three 25-ps molecular dynamics simulations at 300 K of the bovine pancreatic trypsin inhibitor (BPTI), consisting of 454 heavy atoms, are compared: one of BPTI in vacuo, one of BPTI in a box with 2647 spherical nonpolar solvent atoms, and one of BPTI surrounded by fixed crystal image atoms. Both average and time-dependent molecular properties are examined to determine the effect of the environment on the behavior of the protein. The dynamics of BPTI in solution or in the crystal environment are found to be very similar to that found in the vacuum calculation. The primary difference in the average properties is that the equilibrium structure in the presence of solvent or the crystal field is significantly closer to the X-ray structure than is the vacuum result; concomitantly, the more realistic environment leads to a number density closer to experiment. The presence of solvent has a negligible effect on the overall magnitude of the positional or dihedral angle fluctuations in the interior of the protein; however, there are changes in the decay times of the fluctuations of interior atoms. For surface residues, both the magnitude and the time course of the motions are significantly altered by the solvent. There tends to be an increase in the displacements of long side chains and the flexible parts of the main chain that protrude into the solvent. Further, these motions tend to have a more diffusive character with longer relaxation times than in vacuo. The crystal environment has a specific effect on a number of side chains which are held in relatively fixed positions through hydrogen-bond and electric interactions with the neighboring protein atoms. Most of the effects of the solution environment seem to be sufficiently nonspecific that it may be possible to model them by applying a mean field and stochastic dynamic methods.

Animals↗
PubMed1998

Solution NMR structure and backbone dynamics of the major cold-shock protein (CspA) from Escherichia coli: evidence for conformational dynamics in the single-stranded RNA-binding site.

The major cold-shock protein (CspA) from Escherichia coli is a single-stranded nucleic acid-binding protein that is produced in response to cold stress. We have previously reported its overall chain fold as determined by NMR spectroscopy [Newkirk, K., Feng, W., Jiang, W., Tejero, R., Emerson, S. D., Inouye, M., and Montelione, G. T. (1994) Proc. Natl. Acad. Sci. U.S.A. 91, 5114-5118]. Here we describe the complete analysis of 1H, 13C, and 15N resonance assignments for CspA, together with a refined solution NMR structure based on 699 conformational constraints and an analysis of backbone dynamics based on 15N relaxation rate measurements. An extensive set of triple-resonance NMR experiments for obtaining the backbone and side chain resonance assignments were carried out on uniformly 13C- and 15N-enriched CspA. Using a subset of these triple-resonance experiments, the computer program AUTOASSIGN provided automatic analysis of sequence-specific backbone N, Calpha, C', HN, Halpha, and side chain Cbeta resonance assignments. The remaining 1H, 13C, and 15N resonance assignments for CspA were then obtained by manual analysis of additional NMR spectra. Dihedral angle constraints and stereospecific methylene Hbeta resonance assignments were determined using a new conformational grid search program, HYPER, and used together with longer-range constraints as input for three-dimensional structure calculations. The resulting solution NMR structure of CspA is a well-defined five-stranded beta-barrel with surface-exposed aromatic groups that form a single-stranded nucleic acid-binding site. Backbone dynamics of CspA have also been characterized by 15N T1, T2, and heteronuclear 15N-1H NOE measurements and analyzed using the extended Lipari-Szabo formalism. These dynamic measurements indicate a molecular rotational correlation time taum of 4.88 +/- 0.04 ns and provide evidence for fast time scale (taue < 500 ps) dynamics in surface loops and motions on the microsecond to millisecond time scale within the proposed nucleic acid-binding epitope.

Amides↗
PubMed1998

Barstar has a highly dynamic hydrophobic core: evidence from molecular dynamics simulations and nuclear magnetic resonance relaxation data.

The dynamic behavior of the ribonuclease inhibitor barstar has been investigated by molecular dynamics (MD) simulations in explicit water. Two 2.5 ns MD simulations were performed, and an ensemble of 25 000 structures was generated. This ensemble reproduces the solution structures and is consistent with the experimental structural restraints from NMR spectroscopy. Reorientation of the backbone NH bond vectors and side chain methyl groups was monitored by calculation of autocorrelation functions and the generalized S2 order parameters. Order parameters derived for motion in the approximately 100 ps time scale were compared with those obtained from NMR relaxation measurements. Consistent with experiment, the backbone NH bond vectors were relatively rigid. In contrast, the side chain methyl groups exhibited a wide dynamic range, from restricted motion comparable to that of the backbone to rapid unrestricted motion. The order parameters for the methyl groups correlate well with their spatial separation from the backbone and are residue-type dependent. Smaller S2axis values were observed for leucine methyl groups, in part due to side chain hopping between two predominant rotamers (g+t and tg-). Motions such as the flipping of aromatic rings and the hopping of leucine side chains were prevalent within the hydrophobic core, suggesting that the core is fluid-like with low energy barriers between native conformational substates. Thus, our studies suggest that the entropy of the native state can be significant and should not be discounted in thermodynamic considerations of protein folding. On the basis of our results, the side chain motion represents the primary source of the residual entropy of the native state and entropic considerations based solely on backbone dynamics would be incomplete.

Bacillus↗
PubMed2001

Dynamic structures of horse liver alcohol dehydrogenase (HLADH): results of molecular dynamics simulations of HLADH-NAD(+)-PhCH(2)OH, HLADH-NAD(+)-PhCH(2)O(-), and HLADH-NADH-PhCHO.

Molecular dynamics simulations of the oxidation of benzyl alcohol by horse liver alcohol dehydrogenase (HLADH) have been carried out. The following three states have been studied: HLADH.PhCH(2)OH.NAD(+) (MD1), HLADH.PhCH(2)O(-).NAD(+) (MD2), and HLADH.PhCHO.NADH (MD3). MD1, MD2, and MD3 simulations were carried out on one of the subunits of the dimeric enzyme covered in a 32-A-radius sphere of TIP3P water centered on the active site. The proton produced on ionization of the alcohol when HLADH.PhCH(2)OH.NAD(+) --> HLADH.PhCH(2)O(-).NAD(+) is transferred from the active site to solvent water via a hydrogen bonding network consisting of serine48 hydroxyl, ribose 2'- and 3'-hydroxyl groups, and Hist51. Hydrogen bonding of the 3'OH of ribose to Ile269 carbonyl maintains this proton in position to be transferred to water. Molecular dynamic simulations have been employed to track water1287 from the TIP3 water pool to the active site, thus exhibiting the mode of entrance of water to the active site. With time the water1287 accumulates in two different positions in order to accept the proton from the ribose 3'-OH and from His51. There can be identified two structural substates for proton passage. In the first substate the imidazole Ne2 of His51 is adjacent to the nicotinamide ribose C2'-OH and hydrogen bonding distances for proton transfer through the hydrogen bonded relay series PhCH(2)OH...Ser48-OH...Ribose2'-OH...His51...OH(2) (path 1) average 2.0, 2.0, and 2.1 A and (for His51...OH(2)) minimal distances less or equal to 2.5 A. The structure for path 1 is present 20% of the time span. And in the second substate, there are two possible proton passages: path 1 as before and path 2. Path 2 involves the hydrogen-bonded relay series PhCH(2)OH...Ser48-OH...Ribose2'-OH...Ribose3'-OH...His51.OH(2) with the average bonding distances being 2.0, 2.0, 2.1, and 2.0 A and (for His51...OH(2)) minimal distances less or equal to 2.5 A (20% probability of the time span), respectively. During the molecular dynamics simulation the NAD(+) ribose conformations have stabilized at the C2'-endo-C3'-exo or the C2'-endo conformations. With the C2'-endo conformation the first and second substates are able to persist for different time spans, while with the C2'-endo-C3'-exo conformation the only possible pathway involves the first substate. For both first and second substates the fluctuation of the distances between the ribose-OH protons and N epsilon 2 of His51 imidazole ring is partially contributed by the "windshield wiper" motion of the His51 imidazole ring. Since the imidazole of His-51 contributes only about 10-fold to activity, as estimated from the decrease in activity upon substitution with a Gln, there must be an alternate route for the proton to pass to solvent without going through this histidine. A third pathway involves ribose C3'-OH and Ile-269. In MD2, near attack conformers (NACs) for hydride transfer from PhCH(2)O(-) to NAD(+) represent approximately 60% of E.S conformers. The molecular dynamic study of MD3 at mildly basic pH reveals that reactive ground state conformers (NACs) for hydride transfer from NADH to PhCHO amount to 12 mol % of conformers. In MD3, anisotropic bending of the dihydronicotinamide ring of NADH (average value of alpha(c) = 4.0 degrees and alpha(n) = 0.5 degrees, respectively) is observed.

Alcohol Dehydrogenase↗
PubMed2005

The influence of aqueous versus glassy solvents on protein dynamics: vibrational echo experiments and molecular dynamics simulations.

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.

Computer Simulation↗
PubMed2006

On the role of tetramethylammonium cation and effects of solvent dynamics on the stability of the cage-like silicates Si6O156- and Si8O208- in aqueous solution. A molecular dynamics study.

We have undertaken explicit solvent molecular dynamics simulations to investigate the preferential stabilization of the silicate octamer Si(8)O(20)(8-) over the hexamer Si(6)O(15)(6-) in relation with the ability of tetramethylammonium (TMA) to form an adsorption layer around these cage-like polyions. We have found that the hexamer cannot support such a layer and as a result is vulnerable to hydrolysis. The dynamics of TMA desorption off the surface of the hexamer is investigated in connection with the solvent dynamics. We have studied the energetics of this preferential stabilization by calculating the relative change in the free energies of formation between the complexes Si(8)O(20)(8-).8TMA and Si(6)O(15)(6-).6TMA and found the former to be more stable by 70 kcal/mol. We also find that the energetics are consistent with experimental data, suggesting that the hexamer is a long-lived metastable species. Furthermore, we have studied the solvent structure and dynamics in the vicinity of both the bare polyions and their complexes with TMA. We have found that, as anticipated, both the octamer and the hexamer participate in hydrogen bonds with the water molecules, regardless of whether a TMA adsorption layer exists or not. In fact, we find that the presence of a TMA adsorption layer has a rather profound effect on the stability of these hydrogen bonds-it increases their lifetime by at least a factor of 2 relative to that of the hydrogen bonds between water and the bare polyions.

Journal Article↗
PubMed2006

Influence of substrate dynamics on CO-MgO(001) bonding--using molecular dynamics snapshots in quantum-chemical calculations.

Combined molecular dynamics (MD) and quantum mechanics (QM) calculations have been performed for CO adsorbed on MgO(001) at 50 K. The changes in the adsorption energy caused by the surface dynamics have been analyzed, and a clear correlation was found between the dynamic variation of the adsorption energy and the electrostatic field above the adsorption site. By separating the electrostatic contributions arising from the local structure at the adsorption site from those originating from the rest of the slab, a linear expression of these contributions could be fitted which closely reproduces the dynamic changes in the adsorption energy. Using this simple linear expression, the distribution of adsorption energies for CO above the Mg(2+) sites on the MgO(001) surface at 50, 80, and 150 K have been predicted.

Journal Article↗
PubMed2006

Tribochemical reaction dynamics of phosphoric ester lubricant additive by using a hybrid tight-binding quantum chemical molecular dynamics method.

To study the atomistic behavior of the phosphoric ester molecule on the nascent Fe surface under boundary lubrication conditions, we adopted a hybrid tight-binding quantum chemical molecular dynamics method. First, we investigated chemical interactions between phosphoric ester and the nascent Fe surface. Phosphoric ester was shown to interact with the nascent Fe surface, forming both covalent and ionic bonds. Formation and dissociation dynamics of covalent bonds during tribochemical reaction was clearly observed during the simulation. The effect of friction condition on the tribochemical reaction dynamics was then studied, and it was indicated that friction would influence the formation and the dissociation of covalent bonds. By using a hybrid tight-binding quantum chemical molecular dynamics method, we obtained insights on initial tribochemical reaction processes for the formation of tribofilm from the phosphoric ester molecule on the nascent Fe surface.

Journal Article↗
PubMed2006

A molecular dynamics investigation of the influence of hydration and temperature on structural and dynamical properties of a dimyristoylphosphatidylcholine bilayer.

A series of molecular dynamics simulations of dimyristoylphosphatidylcholine bilayers, with different levels of hydration and temperature, were performed to examine the influence of hydration on properties of lipid membranes. Structural and dynamical properties such as area per lipid, electron densities, order parameters for all CH bonds and water, diffusion, and reorientation autocorrelation functions were determined and were all found to be affected by changes in the hydration level. The simulations give an overall picture of the bilayer going to a more ordered state when the hydration level is reduced. Lipid headgroups were found to adopt an orientation more parallel to the membrane plane when the water content was decreased. Dynamical properties such as lipid diffusion and relaxation of reorientation time correlation functions were found to become slower with the removal of water. Our simulation results generally agree with experimental data in cases where such data are available. One important conclusion drawn is that while structural properties are affected only moderately dynamical properties are affected very strongly by a decrease of water content.

Computer Simulation↗
PubMed2007

Structural and dynamic properties of concentrated alkali halide solutions: a molecular dynamics simulation study.

The physicochemical properties of alkali halide solutions have long been attributed to the collective interactions between ions and water molecules in the solution, yet the structure of water in these systems and its effect on the equilibrium and dynamic properties of these systems are not clearly understood. Here, we present a systematic view of water structure in concentrated alkali halide solutions using molecular dynamics simulations. The results of the simulations show that the size of univalent ions in the solution has a significant effect on the dynamics of ions and other transport properties such as the viscosity that are correlated with the structural properties of water in aqueous ionic solution. Small cations (e.g., Li+) form electrostatically stabilized hydrophilic hydration shells that are different from the hydration shells of large ions (e.g., Cs+) which behave more like neutral hydrophobic particles, encapsulated by hydrogen-bonded hydration cages. The properties of solutions with different types of ion solvation change in different ways as the ion concentration increases. Examples of this are the diffusion coefficients of the ions and the viscosities of solutions. In this paper we use molecular dynamics (MD) simulations to study the changes in the equilibrium and transport properties of LiCl, RbCl, and CsI solutions at concentrations from 0.22 to 3.97 M.

Journal Article↗
PubMed2005

Spreading dynamics of chain-like monolayers: a molecular dynamics study.

Using large-scale molecular dynamics simulations, we have shown previously that the spreading dynamics of sessile drops on solid surfaces can be described in detail using the molecular-kinetic theory of dynamic wetting. Here we present our first steps in extending this approach to investigate the spreading dynamics of Langmuir-Blodgett monolayers. We make use of a monolayer model originally developed by Karaborni and Toxvaerd, but somewhat simplified to facilitate large-scale simulations. Our preliminary results are in good agreement with recent experimental observations and also support a molecular-kinetic interpretation in which the driving force for spreading is the lateral pressure in the monolayer. Away from equilibrium, initial spreading rates are constant and logarithmically dependent on pressure. However, near equilibrium, spreading is pseudo-diffusive and follows the square root of time. In both regimes the controlling factor is the equilibrium frequency of molecular displacements within the monolayer.

Journal Article↗
PubMed2005

Time series analysis of ion dynamics in glassy ionic conductors obtained by a molecular dynamics simulation.

We present several characteristics of ionic motion in glassy ionic conductors brought out by time series analysis of molecular dynamics (MD) simulation data. Time series analysis of data obtained by MD simulation can provide crucial information to describe, understand and predict the dynamics in many systems. The data have been treated by the singular spectrum analysis (SSA), which is a method to extract information from noisy short time series and thus provide insight into the unknown or partially unknown dynamics of the underlying system that generated the time series. Phase-space plot reconstructed using the principal components of SSA exhibited complex but clear structures, suggesting the deterministic nature of the dynamics.

Journal Article↗
PubMed2005

Dissipative quantum phase space dynamics on dynamically adapting grids.

A moving grid approach to a dynamical study of dissipative systems is described. The dynamics are studied in phase space for the Caldeira-Leggett master equation. The grid movement is based on the principle of equidistribution and, by using a grid smoothing technique, the grid points trace a path that continuously adapts to reflect the dynamics of a phase-space distribution function. The technique is robust and allows accurate computations to be obtained for long propagation times. The effects of dissipation on the dynamics are studied and results are presented for systems subject to both periodic and nonperiodic multiminimum potential functions.

Journal Article↗
PubMed2005

Structure and ultrafast dynamics of liquid water: a quantum mechanics/molecular mechanics molecular dynamics simulations study.

A quantum mechanics/molecular mechanics molecular dynamics simulation was performed for liquid water to investigate structural and dynamical properties of this peculiar liquid. The most important region containing a central reference molecule and all nearest surrounding molecules (first coordination shell) was treated by Hartree-Fock (HF), post-Hartree-Fock [second-order Moller-Plesset perturbation theory (MP2)], and hybrid density functional B3LYP [Becke's three parameter functional (B3) with the correlation functional of Lee, Yang, and Parr (LYP)] methods. In addition, another HF-level simulation (2HF) included the full second coordination shell. Site to site interactions between oxygen-oxygen, oxygen-hydrogen, and hydrogen-hydrogen atoms of all ab initio methods were compared to experimental data. The absence of a second peak and the appearance of a shoulder instead in the gO-O graph obtained from the 2HF simulation is notable, as this feature has been observed so far only for pressurized or heated water. Dynamical data show that the 2HF procedure compensates some of the deficiency of the HF one-shell simulation, reducing the difference between correlated (MP2) and HF results. B3LYP apparently leads to too rigid structures and thus to an artificial slow down of the dynamics.

Journal Article↗