Calculation Of Order Parameters Research Articles

Role of cationic head-group in cytotoxicity of ionic liquids: Probing changes in bilayer architecture using solid-state NMR spectroscopy

The effect of cationic head-group of ionic liquid on the structure and dynamics of phospholipid bilayer was studied to provide insights into the mechanism of ionic liquid-membrane interaction. The effect was observed using six ionic liquids containing benzimidazolium, imidazolium, pyrrolidinium, piperidinium, ammonium, and morpholinium based amphiphilic cations carrying a dodecyl alkyl chain. Unilamellar and multilamellar vesicles composed of zwitterionic 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) were used. Permeability of POPC bilayer was found to have a strong dependence on ionic liquid head-group structure. To probe the structural details of interaction, 31P and 2H based solid-state NMR measurements were performed. The cations differed in terms of their effect on the orientation and disorder in the phosphocholine moiety in lipid head-group as revealed by chemical shift anisotropy of 31P. Cations carrying an unshielded charge like benzimidazolium, imidazolium, and ammonium result in strong reorientation of phosphocholine moiety in lipid head-group. Large sized cations like benzimidazolium and piperidinium result in enhanced lipid chain dynamics as revealed by order parameter calculations of deuterated lipid chains. Relatively polar head-group of morpholinium cation neither impacts the phospholipid head-group nor chain packing. Our results suggest that there exists a direct correlation between ionic liquid head-group induced structural changes in bilayer and their ability to permeabilize/disrupt the membrane and be cytotoxic.

Numerical study about the effect of the size of rectangular Type-II superconductor on the Hc1 and Hc3 values in the case of proximity effect

Numerical study of superconductor has been done by using Time Dependent Ginsburg-Landau (TDGL) to analyze the effect of variation on size of superconductor in the first critical field (Hc1) and the surface critical field values (Hc3) within the proximity effect. The object of this study is rectangular type-II superconductor with its variation on size of extrapolation length values are 3 and 10. The calculation of order parameter in this model used TDGL equation which finished by using ψυ method and proximity effect limit equation at the edge of superconductor. Results shown values of \\ψ′\\2 — Hext for every grid size variation. It also could be used to calculate Hc1 dan Hc3 by variation on size. We also concluded that the bigger size of superconductor made decreasing of Hc1 dan Hc3 values into a certain value until constant.

Study of effective geometry parameter, order parameter, temperature gradients and crossover temperatures of three nematic liquid crystals having highly different clearing temperature

The temperature dependent properties of three liquid crystals (LC) namely effective geometry parameter, order parameter and temperature gradients of refractive indices of two fluorinated isothiocyanato nematic liquid crystal (NLC) compounds 4′-pentylcyclohexyl-3,5-difluoro-4-isothiocyanatobiphenyl, 4'−butylcyclohexyl−3, 5− difluoro− 4− isothiocyanato-biphenyl of high clearing temperature (TC) and low TC LC compound 4 (trans-4/-n-hexycyclohexyl) isothiocyanatobenzene (6CHBT) have been studied. In this paper, the effective geometry parameters of the three LC compounds are calculated. The order parameters of three LC compounds are also calculated from the effective geometry parameter. From the available data, it is found that the two fluorinated NLC compounds exhibit moderately high value of birefringence (∼0.24–0.26) and 6CHBT exhibits a lower value of birefringence (∼0.16). From the study, it is found that the order parameter is found to be higher in higher birefringence and higher TC LC compounds. The values of temperature gradient of ordinary refractive index (dno/dT) are found to be showing negative to positive value while increasing temperature which gives the crossover temperature (TCO). The crossover temperature has been calculated from the temperature gradient at the value (dno/dT) = 0. LC compounds with lower TC are found to have larger TCO value which gives narrower temperature between TCO and TC. The TCO value of compound having larger alkyl group is found to be smaller. The Lorentz field factors for both compound are also reported which can be used for order parameter calculation by different aspects.

Molecular dynamics ensemble refinement of the heterogeneous native state of NCBD using chemical shifts and NOEs.

Many proteins display complex dynamical properties that are often intimately linked to their biological functions. As the native state of a protein is best described as an ensemble of conformations, it is important to be able to generate models of native state ensembles with high accuracy. Due to limitations in sampling efficiency and force field accuracy it is, however, challenging to obtain accurate ensembles of protein conformations by the use of molecular simulations alone. Here we show that dynamic ensemble refinement, which combines an accurate atomistic force field with commonly available nuclear magnetic resonance (NMR) chemical shifts and NOEs, can provide a detailed and accurate description of the conformational ensemble of the native state of a highly dynamic protein. As both NOEs and chemical shifts are averaged on timescales up to milliseconds, the resulting ensembles reflect the structural heterogeneity that goes beyond that probed, e.g., by NMR relaxation order parameters. We selected the small protein domain NCBD as object of our study since this protein, which has been characterized experimentally in substantial detail, displays a rich and complex dynamical behaviour. In particular, the protein has been described as having a molten-globule like structure, but with a relatively rigid core. Our approach allowed us to describe the conformational dynamics of NCBD in solution, and to probe the structural heterogeneity resulting from both short- and long-timescale dynamics by the calculation of order parameters on different time scales. These results illustrate the usefulness of our approach since they show that NCBD is rather rigid on the nanosecond timescale, but interconverts within a broader ensemble on longer timescales, thus enabling the derivation of a coherent set of conclusions from various NMR experiments on this protein, which could otherwise appear in contradiction with each other.

Local and nonlocal order parameters in the Kitaev chain

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices we infer the 2D Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

On the Calculation of Acyl Chain Order Parameters from Lipid Simulations.

For molecular dynamics simulations of biological membrane systems to live up to the potential of providing accurate atomic level detail into membrane properties and functions, it is essential that the force fields used to model such systems are as accurate as possible. One membrane property that is often used to assess force field accuracy is the carbon-hydrogen (or carbon-deuterium) order parameters of the lipid tails, which can be accurately measured using experimental NMR techniques. There are a variety of analysis tools available to calculate these order parameters from simulations and it is essential that these computational tools work correctly to ensure the accurate assessment of the simulation force fields. In this work we compare many of these computational tools for calculating the order parameters of POPC membranes. While tools that work on all-atom systems and tools that work on saturated lipid tails in general work extremely well, we demonstrate that the majority of the tested tools that calculate the order parameters for unsaturated united-atom lipid tails do so incorrectly. We identify tools that do perform accurate calculations and include one such program with this work, enabling rapid and accurate calculation of united-atom lipid order parameters. Furthermore, we discuss cases in which it is nontrivial to appropriately predict the unsaturated carbon order parameters in united-atom systems. Finally, we examine order parameter splitting for carbon 2 in sn-2 lipid chains, demonstrating substantial deviations from experimental values in several all-atom and united-atom lipid force fields.

Constructing Landau framework for topological order: quantum chains and ladders

We studied quantum phase transitions in the antiferromagnetic dimerized spin- XY chain and two-leg ladders. From analysis of several spin models we present our main result: the framework to deal with topological orders and hidden symmetries within the Landau paradigm. After mapping of the spin Hamiltonians onto the tight-binding models with Dirac or Majorana fermions and, when necessary, the mean-field approximation, the analysis can be done analytically. By utilizing duality transformations the calculation of nonlocal string order parameters is mapped onto the local order problem in some dual representation and done without further approximations. Calculated phase diagrams, phase boundaries, order parameters and their symmetries for each of the phases provide a comprehensive quantitative Landau description of the quantum critical properties of the models considered. Complementarily, the phases with hidden orders can also be distinguished by the Pontryagin (winding) numbers which we have calculated as well. This unified framework can be straightforwardly applied for various spin chains and ladders, topological insulators and superconductors. Applications to other systems are under way.

Induced liquid-crystalline ordering in solutions of stiff and flexible amphiphilic macromolecules: Effect of mixture composition.

Impact of mixture composition on self-organization in concentrated solutions of stiff helical and flexible macromolecules was studied by means of molecular dynamics simulation. The macromolecules were composed of identical amphiphilic monomer units but a fraction f of macromolecules had stiff helical backbones and the remaining chains were flexible. In poor solvents the compacted flexible macromolecules coexist with bundles or filament clusters from few intertwined stiff helical macromolecules. The increase of relative content f of helical macromolecules leads to increase of the length of helical clusters, to alignment of clusters with each other, and then to liquid-crystalline-like ordering along a single direction. The formation of filament clusters causes segregation of helical and flexible macromolecules and the alignment of the filaments induces effective liquid-like ordering of flexible macromolecules. A visual analysis and calculation of order parameter relaying the anisotropy of diffraction allow concluding that transition from disordered to liquid-crystalline state proceeds sharply at relatively low content of stiff components.

Elastic Energy Partitioning in DNA Deformation and Binding to Proteins.

We study the elasticity of DNA based on local principal axes of bending identified from over 0.9-μs all-atom molecular dynamics simulations of DNA oligos. The calculated order parameters describe motion of DNA as an elastic rod. In 10 possible dinucleotide steps, bending about the two principal axes is anisotropic yet linearly elastic. Twist about the centroid axis is largely decoupled from bending, but DNA tends to overtwist for unbending beyond the typical range of thermal motion, which is consistent with experimentally observed twist-stretch coupling. The calculated elastic stiffness of dinucleotide steps yield sequence-dependent persistence lengths consistent with previous single-molecule experiments, which is further analyzed by performing coarse-grained simulations of DNA. Flexibility maps of oligos constructed from simulation also match with those from the precalculated stiffness of dinucleotide steps. These support the premise that base pair interaction at the dinucleotide-level is mainly responsible for the elasticity of DNA. Furthermore, we analyze 1381 crystal structures of protein-DNA complexes. In most structures, DNAs are mildly deformed and twist takes the highest portion of the total elastic energy. By contrast, in structures with the elastic energy per dinucleotide step greater than about 4.16 kBT (kBT: thermal energy), the major bending becomes dominant. The extensional energy of dinucleotide steps takes at most 35% of the total elastic energy except for structures containing highly deformed DNAs where linear elasticity breaks down. Such partitioning between different deformational modes provides quantitative insights into the conformational dynamics of DNA as well as its interaction with other molecules and surfaces.

Dynamic behavior of photo-induced orientation of poly(methyl methacrylate) – Solvent Red 23 thin films

We investigate the effect of the photo-orientation and stability of the Solvent Red 23 dye incorporated in poly(methyl methacrylate) thin films as a guest–host system. A probe–pump optical system was used to investigate the dichroic behavior of the samples. Orthogonally polarized laser lights induce a smaller increase in the transmitted beam intensity. A stronger polar order was induced using a parallel probe–pump laser light compared to that of the perpendicular state. It was found that the dichroic ratio value of the poly(methyl methacrylate) – Solvent Red 23 thin film increased by 0.174 at the photostationary state, indicating that the net orientation of Solvent Red 23 molecules has increased 17.4% in the direction perpendicular to the applied beam field. The dynamic evolution of the dichroic ratio showed that the relaxation is rather slow, and it deteriorates in a slow exponential fashion, which may take a very long time to reach the isotropic state. The contrast ratios were 0.449 and 0.267 in parallel and orthogonal probe–pump configurations, respectively. The order parameter calculations reveal that about 70% of photo-induced anisotropy remains after relaxation for a long time.

Effects of different self-assembled monolayers on thin-film morphology: a combined DFT/MD simulation protocol.

Organic thin film transistors (OTFTs) are multilayer field-effect transistors that employ an organic conjugated material as semiconductor. Several experimental groups have recently demonstrated that the insertion of an organic self-assembled monolayer (SAM) between the dielectric and the semiconductive layer is responsible for a sensible improvement of the OTFT performances in terms of an increased charge carrier mobility caused by a higher degree of order in the organic semiconductor layer. Here, we describe a combined periodic density functional theory (DFT) and classical molecular dynamics (MD) protocol applied to four different SAMs and a pentacene monolayer deposited onto their surfaces. In particular, we investigate the morphology and the surface of the four SAMs and the translational, orientational, and nematic order of the monolayer through the calculation of several distribution functions and order parameters pointing out the differences among the systems and relating them to known experimental results. Our calculations also suggest that small differences in the SAM molecular design will produce remarkable differences in the SAM surface and monolayer order. In particular, our simulations explain how a SAM with a bulky terminal group results in an irregular and rough surface that determines the deposition of a disordered semiconductive monolayer. On the contrary, SAMs with a small terminal group generate smooth surfaces with uninterrupted periodicity, thus favoring the formation of an ordered pentacene monolayer that increases the mobility of charge carriers and improves the overall performances of the OTFT devices. Our results clearly point out that the in silico procedure presented here might be of help in tuning the design of SAMs in order to improve the quality of OTFT devices.

Accurately modeling nanosecond protein dynamics requires at least microseconds of simulation.

Advances in hardware and algorithms have greatly extended the timescales accessible to molecular simulation. This article assesses whether such long timescale simulations improve our ability to calculate order parameters that describe conformational heterogeneity on ps-ns timescales or if force fields are now a limiting factor. Order parameters from experiment are compared with order parameters calculated in three different ways from simulations ranging from 10 ns to 100 μs in length. Importantly, bootstrapping is employed to assess the variability in results for each simulation length. The results of 10-100 ns timescale simulations are highly variable, possibly explaining the variation in levels of agreement between simulation and experiment in published works examining different proteins. Fortunately, microsecond timescale simulations improve both the accuracy and precision of calculated order parameters, at least so long as the full exponential fit or truncated average approximation is used instead of the common long-time limit approximation. The improved precision of these long timescale simulations allows a statistically sound comparison of a number of modern force fields, such as Amber03, Amber99sb-ILDN, and Charmm27. While there is some variation between these force fields, they generally give very similar results for sufficiently long simulations. The fact that so much simulation is required to precisely capture ps-ns timescale processes suggests that extremely extensive simulations are required for slower processes. Advanced sampling techniques could aid greatly, however, such methods will need to maintain accurate kinetics if they are to be of value for calculating dynamical properties like order parameters. © 2015 Wiley Periodicals, Inc.

Microscopic Model and Analytic Derivation of Area Per Molecule for DPPC-Cholesterol Bilayers

An area per molecule dependence on components concentration for DPPC-Cholesterol bilayers is calculated analytically using a microscopic model in a biologically relevant concentration range. DPPC lipid is modeled as flexible string with finite bending rigidity [1,2]. Cholesterol molecule is modeled as rigid rod of finite thickness [3]. Surface tension at hydrophobic interface is linear combination of “partial tensions” of bilayer components. The model's three important parameters are: surface tension at hydrophobic interface for pure DPPC membrane, bending rigidity of DPPC lipid, extrapolated surface tension at hydrophobic interface for cholesterol membrane. These parameters are chosen by nearly perfect fitting agreement of our theoretical curve with molecular dynamics simulations data [4] for these two-component bilayers. The molecular chains order parameter dependence on coordinate for 40% cholesterol - 60% DPPC membrane, measurable in NMR experiments, is calculated analytically and compared with molecular dynamics simulation data [5]. The order parameter calculation allows for DPPC tilt angle. The model parameters found by fitting the MD data are used further to calculate lateral pressure distribution and coefficient of thermal area expansion. The microscopic model allows one to study other thermodynamic coefficients and diffusion phenomena in multi-component bilayers. 1.Mukhin S.I., S. Baoukina, Analytical derivation of thermodynamic characteristics of lipid bilayer from a flexible string model. Phys. Rev. E. 71: 061918 (2005). 2.Mukhin S.I., B.B. Kheyfets, Analytical approach to thermodynamics of bolalipid membranes. Phys. Rev. E. 82: 051901 (2010). 3.Mukhin S.I., B.B. Kheyfets, Pore formation phase diagrams for lipid membranes. JETP Lett. 99: 358-362 (2014). 4. Edholm O., J.F. Nagle. Areas of Molecules in Membranes Consisting of Mixtures. Biophys. J. 89: 1827-1832 (2005). 5. Hofsass C., Lindahl E., and Edholm O. Molecular Dynamics Simulations of Phospholipid Bilayers with Cholesterol. Biophys. J. 84: 2192-2206 (2003).

Molecular dynamics simulations of DPPC/CTAB monolayers at the air/water interface.

An atomistic-level understanding of cationic lipid monolayers is essential for development of gene delivery agents based on cationic micelle-like structures. We employ molecular dynamics (MD) simulations for a detailed atomistic study of lipid monolayers composed of both pure zwitterionic dipalmitoylphosphatidylcholine (DPPC) and a mixture of DPPC and cationic cetyltrimethylammonium bromide (CTAB) at the air/water interface. We aim to investigate how the composition of the DPPC/CTAB monolayers affects their structural and electrostatic properties in the liquid-expanded phase. By varying the molar fraction of CTAB, we found the cationic CTAB lipids have significant condensing effect on the DPPC/CTAB monolayers, i.e., at the same surface tension or surface pressure, monolayers with higher CTAB molar fraction have smaller area per lipid. The DPPC/CTAB monolayers are also able to achieve negative surface tension without introducing buckling into the monolayer structure. We also found the condensing effect is caused by the interplay between the cationic CTAB headgroups and the zwitterionic phosphatidylcholine (PC) headgroups which has electrostatic origin. With CTAB in its vicinity, the P-N vector of PC headgroups reorients from being parallel to the monolayer plane to a more vertical orientation. Moreover, detailed analysis of the structural properties of the monolayers, such as the density profile analysis, hydrogen bonding analysis, chain order parameter calculations, and radial distribution function calculations were also performed for better understanding of cationic DPPC/CTAB monolayers.

Membrane-associated proteins and peptides.

This chapter discusses the practical aspects of setting up molecular dynamics simulations of membrane-associated proteins and peptides, and the analysis thereof. Topology files for selected lipids are provided and selected analysis tools presented. These include tools for the creation of lipid bilayers of mixed lipid content (DOPE) and easy extraction of lipid coordinates (g_zcoor, g_xycoor), the calculation of helical axes (g_helixaxis) and aromatic order parameters (g_arom), the determination of peptide- or protein-interacting lipids (g_under), and the investigation of lipid-specific interactions through the calculation of lipid-bridged residue-residue contacts (g_prolip).

Elucidating the Relation between Internal Motions and Dihedral Angles in an RNA Hairpin Using Molecular Dynamics.

Molecular dynamics simulations were performed to characterize the internal motions of the ribonucleic acid apical stem loop of human hepatitis B virus. The NMR relaxation rates calculated directly from the trajectory are in good agreement with the experiment. Calculated order parameters follow the experimental pattern. Order parameters lower than 0.8 are observed for nucleotides that are weakly hydrogen bonded to their base pair partner, unpaired, or part of the loop. These residues show slow decay of the internal correlation functions of their base and sugar C-H vectors. Concerted motions around backbone dihedral angles influence the amplitude of motion of the sugar and base C-H vectors. The order parameters for base C-H vectors are also affected by the fluctuation of the glycosidic dihedral angle.

Structure, energetic and phase transition of small nickel-palladium heterogeneous clusters

Molecular dynamics simulation (MD) with Sutton-Chen potential for palladium-palladium, nickel-nickel and palladium-nickel interactions has been used to generate the minimum energy structures and to study the thermodynamic and dynamic properties of mixed transition metal cluster motifs of NinPd(13−n) for n ≤ 13. Thirteen particle icosahedral clusters of neat palladium and nickel atoms were first reproduced accordingly with the results in literature. Then in the palladium icosahedra, each palladium atom has been successively replaced by nickel atom. Calculation is repeated for both palladium-centered and nickel-centered clusters. It is found that the nickel-centered clusters are more stable than the palladium-centered clusters and cohesive energy increases along the palladium end to nickel end. Phase transition of each cluster from one end-species to the other end-species is studied by means of caloric curve, root mean square bond fluctuation and heat capacity. Trend in variation of melting temperature is opposite to the energy trend. Palladium-centered cluster shows a premelting at low temperature due to the solid-solid structural transition. Species-centric order parameters developed by Hewage and Amar is used to understand the dynamic behavior in the solid-solid transition of palladium-centered cluster to more stable nickel-centered cluster (premelting). This species-centric order parameter calculation further confirmed the stability of nickel-centered species over those of palladium-centered species and solid-solid structural transition at low temperature.

Functional implications of large backbone amplitude motions of the glycoprotein 130‐binding epitope of interleukin‐6

Human interleukin (IL)-6 plays a pivotal role in the immune response, hematopoiesis, the acute-phase response, and inflammation. IL-6 has three distinct receptor epitopes, termed sites I, II, and III, that facilitate the formation of a signaling complex. IL-6 signals via a homodimer of glycoprotein 130 (gp130) after initially forming a heterodimer with the nonsignaling α-receptor [IL-6 α-receptor (IL-6R)] via site I. Here, we present the backbone dynamics of apo-IL-6 as determined by analysis of NMR relaxation data with the extended model-free formalism of Lipari and Szabo. To alleviate significant resonance overlap in the HSQC-type spectra, cell-free protein synthesis was used to selectively (15) N-label residues, thereby ensuring a complete set of residue-specific dynamics. The calculated order parameters [square of the generalized model-free order parameter (S(2))] showed significant conformational heterogeneity among clusters of residues in IL-6. In particular, the N-terminal region of the long AB-loop, which corresponds spatially to one of the gp130 receptor binding epitopes (i.e. site III), experiences substantial fluctuations along the conformation of the main chain (S(2) = 0.3-0.8) that are not observed at the other two epitopes or in other cytokines. Thus, we postulate that dynamic properties of the AB-loop are responsible for inhibiting the interaction of IL-6 with gp130 in the absence of the IL-6R, and that binding of IL-6R at site I shifts the dynamic equilibrium to favor interaction with gp130 at site III. In addition, molecular dynamics simulations corroborated the NMR-derived dynamics, and showed that the BC-loop adopts different substates that possibly play a role in facilitating receptor assembly.

Exploring the influence of EGCG on the β-sheet-rich oligomers of human islet amyloid polypeptide (hIAPP1-37) and identifying its possible binding sites from molecular dynamics simulation.

EGCG possesses the ability of disaggregating the existing amyloid fibrils which were associated with many age-related degenerative diseases. However, the molecular mechanism of EGCG to disaggregate these fibrils is poorly known. In this work, to study the influence of EGCG on the full-length human islet amyloid polypeptide 1–37 (hIAPP1–37) oligomers, molecular dynamics simulations of hIAPP1–37 pentamer and decamer with EGCG were performed, respectively. The obtained results indicate that EGCG indeed destabilized the hIAPP1–37 oligomers. The nematic order parameter and secondary structure calculations coupled with the free-energy landscape indicate that EGCG broke the initial ordered pattern of two polymers, greatly reduced their β-sheet content and enlarged their conformational space. On this basis, three possible target sites were identified with the binding capacity order of S1>S2>S3. After a deeper analysis of each site, we found that S1 was the most possible site on which residues B-Ile26/Ala25, A-Phe23, B/C-Leu27 and E-Tyr37 played an important role for their binding. The proposal of this molecular mechanism can not only provide a prospective interaction figure between EGCG and β-sheet-rich fibrils of hIAPP1–37, but also is useful for further discovering other potential inhibitors.

Creatividad y emergencia espontánea de habilidades de danza (Creativity and dance skills emergency)

La creatividad motriz se ha estudiado desde puntos de vista muy diferentes, pero la mayoría de ellos están basados en teorías cognitivistas. No obstante, diversos estudios relacionados con el deporte ya han demostrado la emergencia de comportamiento creativo fruto de la capacidad de todo sistema complejo para autoorganizarse en formas de complejidad crecientes. Mediante el ejemplo del Contact improvisation, en este artículo se pretende demostrar que la creatividad emerge durante la improvisación siguiendo una dinámica no lineal, y se presenta un modelo para estudiar la amplitud exploratoria de cualquier modalidad de danza. Se grabó a una pareja de bailarines que improvisó durante 480 segundos y la danza se analizó con un instrumento de observación compuesto por 49 categorías. Los datos obtenidos se analizaron teniendo en cuenta el modelo de la jerarquía soft-assembled a partir de tres tipos de análisis estadísticos conectados entre ellos: El de Principal Components Jerárquico, el cálculo de distancias de Hamming y el de la amplitud exploratoria o superposición dinámica de parámetros de orden q. Los resultados mostraron que determinadas acciones atraían al sistema, mientras que otras se daban con una probabilidad muy pequeña. La amplitud de la exploración q fue de 0,45, lo que muestra que los bailarines exploran pero que suelen transitar por muchas acciones similares o repetidas. Este modelo puede aplicarse para estudiar como la manipulación de la tarea mediante la variación de la consigna o mediante la imposición de determinados constreñimientos afecta a la creatividad motriz del bailarín.Palabras clave: Sistemas complejos, creatividad motriz, emergencia, contact improvisation, constreñimientos.Abstract: Much research in recent years has focused on motor creativity from different points of view, mostly of them based on cognitive theories. Nevertheless, few sport researchers have studied the creative behavior emergence by means of the complex systems capacity to self-organize in complex patterns. Using the example of Contact improvisation, the aim of this paper is to show how creativity emerges during the improvisation following non linear dynamical principles. Moreover, a model for studying the exploratory dynamics of any dance is presented. A couple of dancers were video-recorded while dancing 480 seconds duet. Dance was analyzed using an observational instrument with 49 categories. The data obtained were then analyzed using a soft-assembled hierarchical model analysis by means of three mutually connected statistical analyses: a Hierarchical Principal Components Analysis, calculation of Hamming Distances and the calculation of dynamic overlap order parameter q. Results revealed that some actions attracted the system, while others were rare. The value of the plateau q was of 0,45, what shows that dancers explore the movement possibilities but use to reproduce some similar actions. This model can be applied in order to study how the manipulation of the task or the use of different constraints can affect the dancers’ motor creativity. Key words: Complex systems, motor creativity, emergence, contact improvisation, constraints.