RICERCA ITALIANA     

PHYSICAL PROPERTIES OF POLYMER-BASED NANOSTRUCTURED BIOMATRICES

Università degli Studi di Parma

Abstract

The research project aims at improving the knowledge of structural and dynamic properties of matrices based on natural and synthetic polymers. The objectives of this study are twofold:
- to improve our understanding of basic aspects of solvent-solute interactions in chemical and physical gel systems;
- to make use of this detailed picture to optimize the tailoring of polymer- and biopolymer-structures for biomedical applications, namely: nanostructures for modulated drug delivery
Two types of materials will be studied in the project:
i) matrices based on poly (vinyl alcohol) suitably modified in order to obtain hydrogel microspheres with a large surface/volume ratio and therefore with a high capacity of loading scarcely soluble drugs (typically anti-tumor drugs) otherwise difficult to deliver directly.
ii) matrices based on hyaluronic acid, HYA, a biopolymer present in the sinovial fluid of mammals. We will investigate a derivative of HYA with just 4 % of the repeating units grafted with hydrophobic alkyl chains. This modified HYA is able to form, even at very low polymer concentrations (c 10 g/L), stable hydrogels with remarkable viscoelastic properties.
Our aim is to impart to the new systems properties, absent in the starting materials, that make it possible to tune the biomatrix characteristics in response to external thermodynamic parameters that can be relevant in bio-technological applications. Examples are the thermo-sensitivity, and the presence of an internal dimensionally tunable nanostructure in matrices of type (i), the enhanced resistance to enzymatic degradation with respect to the natural polymer for (ii)-type matrices. If these characteristics will be effectively matched, the new device will be able to increase the bioavailability of the drug and therefore its efficacy.
The achievement of such results is based on a detailed knowledge and on a careful control of physical and chemical parameters intervening in determining the relationships connecting the structural and dynamic features of the matrix with its behaviour in vitro at physiological conditions. Moreover in these "composite" biomaterials water-solute interactions, even at low solute concentration, can modify the dynamic properties of both solvent and solute. A detailed understanding of the mechanisms responsible for these modifications has not yet been attained. It is therefore important to study the conformational and dynamic properties of the macromolecular species as well as those of the solvent in different thermodynamic conditions (concentration, temperature, pressure).
We plan to carry out this program by an integrated approach comprising the optimisation of chemical preparation methods, the use of advanced spectroscopic techniques for structural and dynamic characterisation at a microscopic level (including those available at large synchrotron and neutron facilities), and the development of models and computer simulations. To this purpose the project team is made up from groups with complementary chemical and physical expertise and with a precise knowledge of the requirements that originate from technological applications in the fields of drug delivery and of smart carriers.
A key role in the project will be played by equilibrium and non-equilibrium computer simulations. The description, at an atomistic level, of the interactions, without using over-simplified models, will enable us to investigate in detail the dynamics of both macromolecules and solvent. Novel non equilibrium techniques will be used to describe conformational transitions ruled by slow relaxation dynamics like those leading to thegelation processes. The simulation results will also act as a guide to the interpretation of the X-ray and neutron data providing information on space- and time correlations over length- and time-scales accessible to the experiments.
The project will be jointly carried out by three research units (Parma, Roma "Tor Vergata" and Trento); among them collaborations are already active since several years on systems similar to the ones proposed here. This project will then also provide an opportunity for strengthening these collaborations, profiting of already acquired experience, and beginning new ones.
The project will also provide an opportunity for training young scientists (overall we plan to fund four post-docs and one PhD position within the project) in the synthesis methodologies of these new materials, in advanced spectroscopic techniques, in operating at large scale facilities for neutrons and synchrotron radiation, and in using advanced computer simulation methods. <<<

Principal Investigator

Antonio Deriu Università degli Studi di PARMA

Research Objectives

The project aims at investigating the structural and dynamic properties of novel biomatrices (made up from gels and nanogels) suitable for controlled drug delivery. In particular we intend to study:
i) matrices based on poly (vinyl alcohol) suitably modified in order to obtain hydrogel microspheres with a large surface/volume ratio and therefore with a high capacity of loading scarcely soluble drugs (typically anti-tumor drugs) otherwise difficult to deliver directly.
ii) matrices based on hyaluronic acid, HYA, a biopolymer present in the sinovial fluid of mammals. We will investigate a derivative of HYA with just 4 % of the repeating units grafted with hydrophobic alkyl chains. This modified HYA is able to form, even at very low polymer concentrations (c 10 g/L), stable hydrogels with remarkable viscoelastic properties.
Our aim is to obtain and characterize systems providing an appreciable encapsulation of insoluble bioactive molecules, an enhanced bio-availability of the drug, a localized (focal) release with a controlled kinetics, a limited (if any) immunologic response, and an overall acceptability from the patients.
The carriers will be obtained in gel and nanogel form. The accurate design of these materials is crucial as it determines the localization and the efficacy of the release of the carried drug. A further very relevant item that has to be investigated in detail is the water-macromolecule interaction mechanism and its role in determining the structural, dynamic and functional properties of the gels. In the frame of the present project we plan to prepare the above systems, and to characterise in detail their structural and dynamic properties at the molecular level using different complementary techniques. For the structural properties we will use densitometry, static and dynamic light scattering, small angle X-ray scattering and small angle neutron scattering (SANS). For the dynamic properties, we will make use of NMR relaxation spectroscopy, elastic (ENS) quasielastic (QENS) and inelastic (INS) neutron scattering, and the non-resonant (Rayleigh-Thompson) scattering of the Mössbauer radiation (RSMR). These are complementary spectroscopic techniques, that, overall provide access to a very large window of characteristic times: from femtoseconds (INS) up to microseconds (NMR).
Furthermore we plan to investigate the thermodynamic stability and the gelation kinetics using high resolution isothermal microcalorimetry, besides scanning calorimetry both uniform and modulated.
A key role in the project will be played by equilibrium and non-equilibrium computer simulations that will second the experimental measurements The comparison between experimental data and results of the simulations will provide a guide for a deeper understanding of the molecular processes investigated; the MD results will also act as a guide to the interpretation of the X-ray and neutron data providing information on space- and time correlations over length- and time-scales accessible to the experiments. Moreover, they will enable us to extend the analysis to a parameter range that is not accessible to spectroscopic measurements.
The description, at an atomistic level, of the interactions, without using over-simplified models, will enable us to investigate in detail the dynamics of both macromolecules and solvent. Novel non equilibrium techniques will be used to describe conformational transitions ruled by slow relaxation dynamics as those involved in gel formation mechanisms.
As concerns the dynamics of hydration water, MD simulations make it possible to distinguish dynamic phenomena involving molecules with different degree of association to the gel scaffolding.
We expect that the experimental and simulation data will enable us to address several still open problems: - for the structural properties:
- gel formation mechanisms, mapping of hydrophobic and hydrophilic stabilization regions, persistence of H-bonding under different thermodynamic conditions, hydration water arrangements;
- for the dynamic aspects: effect of solvent-solute interactions on the diffusivity properties of the solvent at different degrees of association with the macromolecules, dependence of the kinetic (glass-like) transitions of the polymer chains from the thermodynamic conditions (hydration, temperature, …);
- optimization of the effective interaction potentials for the computer simulations.
The project will also provide an opportunity for training young scientists (we plan to fund four post-doc positions and one PhD position within the project) in advanced spectroscopic techniques, in operating at large scale facilities for neutrons and synchrotron radiation, and in using advanced computer simulation techniques.
Moreover two PhD students, with fellowships funded by the University of Parma, are already available for this project. <<<

First Results

Our aim is to obtain and characterize novel biomatrices suitable for 'smart' drug delivery providing an appreciable encapsulation of insoluble bioactive molecules, an enhanced bio-availability of the drug, a localized (focal) release with a controlled kinetics, a limited (if any) immunologic response, and an overall acceptability from the patients.

The main deliverable will therefore be the optimised preparation protocols for the two classes of biomatrices investigated:
i) matrices based on poly (vinyl alcohol) in form of hydrogel microspheres with a large surface/volume ratio and therefore with a high capacity of loading scarcely soluble drugs.
ii) matrices based on a modified form of hyaluronic acid (with about 4% of the repeating units grafted with hydrophobic alkyl chains) that is able to form, even at very low polymer concentrations (c 10 g/L), stable hydrogels with remarkable viscoelastic properties and enhanced resistance to enzymatic degradation.

The information obtained on PVAMA gels will also be useful as a starting point for further studies on new multifunctional systems obtained from PVA. As an example we may quote recent studies that demonstrated that by incapsulating diethylenetriamine pentaacetic acid (Gd-DTPA) into biodegradable polymeric microparticles it is possible to enable noninvasive monitoring of their local intravesical delivery by magnetic resonance imaging [1]. In a similar context, PVAMA-NiPAAM based microparticles that incapsulate both contrast agents and therapeutic agents could provide a promising approach for image-guided, particle-mediated therapy.

The structural and dynamic investigations, besides providing information specific to the investigated biomatrix systems, will also enable us to address several still open problems of general interest in the filed of chemical and physical hydrogels.
More specifically, on the structural side we expect to contribute to a better definition of of:
- gel formation mechanisms and kinetics;
- location of hydrophobic and hydrophilic stabilization regions;
- degree of persistence of H-bonding under different thermodynamic conditions;
- structured arrangement of hydration water closely associated to the loose random gel network
The spectroscopic investigations (by NMR, ENS, INS, QENS) will bring new insight in the mechanisms of solvent-solute interaction, an item of general relevance for most of biological systems. In this respect PVA and HYA based networks can be seen as model systems with features similar to those of more complex biopolymer arrangements (as polypeptides and polynucleotides) especially as concerns some generals dynamic processes common to most biopolymers, namely:
- the diffusivity properties of the solvent at different degrees of association with the macromolecules,
- the dependence of the kinetic (glass-like) transitions of the biopolymer chains from the thermodynamic conditions (hydration, temperature, …)

The main deliverables mentioned above (items (i) and (ii)) are of direct relevance for pharmaceutical applications indeed:
- PVA-based systems have already considered in the past years are suitable drug carriers (see for instance [2,3] below and references therein);
- similarly, YHA based are receiving great attention as versatile systems for a veriety of biomedical applications ((see for instance [4,5] below and references therein).

1. HH. Chen, C. Le Visage, B. Qiu, X. Du, R. Ouwerkerk, KW Leong and X. Yang, "MR Imaging of biodegradable polymeric microparticles: a potential method of monitoring local drug delivery", Magn. Res. in Medicine, 53 (2005) 614-620.
2. Kim C-J., Lee P.I., "Composite Poly(vinyl alchol) beads for controlled drug delivery", Pharmaceutical Research, 9 (1992) 10-16.
3. SS. Venkatraman, TO. Murdock, S. Pudjijanto "Pharmaceutical hydrogel formulations, and associated drug delivery devices and methods", US Patent Issued on March 21, 2000.
4. Y-H Liao, SA Jones, B Forbes, GP. Martin and MB. Brown "Hyaluronan: pharmaceutical characterization and drug delivery", Drug Delivery, 12 (2005) 327-342.
5. G. Kogan, L. Soltes, R. Stern, P. Gemeiner "Hyaluronic acid: a natural biopolymer with a broad range of biomedical and industrial applications", Biotechnol. Lett. 29 (2007) 17-25. <<<

Timescale

24 months

National and international background

In recent years pharmaceutical research tackled a range of complex problems in connection with the development of new therapeutic methodologies as for instance: gene- therapies, targeted release of drugs, molecular imaging. The design of novel active pharmaceutical systems requires an integrated approach in order to maximize the effectiveness of the active species by its interaction with a suitable carrier able to eventually release the drug in a controlled way and in a specific region. Usually these drug platforms are hydrogel matrices: multi-component system constituted by an aqueous solution and a polymeric moiety imparting different functions to the matrix, as responsiveness to external stimuli, affinity to receptors, controlled drug release. These systems form nowadays a relevant family of biomaterials and their study will further expand in the next years [1-3]. The aim is to obtain systems able to time tune and to localize the drug release; therefore bio-availability and controlled release should be the benchmarks achievable by using new polymer platforms. In this respect, two types of biomatrices with different physical and chemical characteristics will be investigated in the present project:
(i) injectable micro/nano-hydrogels based on poly (vinyl alcohol);
(ii) macroscopic hydrogels based on hyaluronic acid.
The most important characteristics of systems (i) are:
- Very large surface/volume ratio, a property of major importance for achieving a high loading and release efficiency.
- Overall dimensions allowing parentheral administration (injectability)
- Surface chemical versatility for coupling with suitable molecules allowing the localization of the platforms on receptors of target cells, thus enhancing drug bio-availability.
- Fast response to external gradients as temperatures and pH.
Systems (ii) are macroscopic biomatrices, with typical equilibrium and dynamic properties of hydrogels. Distinctive features of these systems are:
- Injectability due to low shear resistance.
- Possibility of loading the gel with anti-inflammatory drugs.
- An enhanced resistance to enzymatic degradation.
Both classes of biomatrices are obtained by self assembly mechanisms:
Matrixes (i) are made up from chemically cross-linked hydrogel microparticles based on poly (vinyl alcohol-methacrylate), PVAMA (see Scheme 1).


Such systems have been already synthesized and characterized in the laboratories of the Roma "Tor Vergata" Research Unit [4,5]. They have been studied as potential "humor vitreous" substitutes offering the background for a new class of thermoresponsive microgels potentially exploitable as microdevices for drug loading and release in physiologic conditions.
Matrixes (ii) are macroscopic hydrogels stabilized by non-covalent interactions and based on hyaluronic acid (HYA) partially hydrophobized by grafting the polymer chain with alkyl side groups, these matrices are indicated in the following as HYADD. HYA is a polysaccharide with a relevant number of functionalities in Nature, (see Scheme 2) [3].


Till the seventies, HYA has been considered a molecule able to control the viscosity of the sinovial fluid where it is usually found. In recent years it has been understood that this biopolymer takes part in building the cartilages, constituting the coating of chondrocytes. In the presence of proteins regulating the aggregation processes in the cartilage, HYA organizes itself in large aggregates with high charge density that able to attract osmotically huge amount of water in tissues. Other functions of HYA are the hydrodynamic regulation of the fluids of the extracellular matrix and of cell proliferation and mobility. Moreover HYA takes part in several cell interactions as receptor of CD44, a protein regulating the adhesion process in tumor cells. In biomedicine, HYA has been employed as cell scaffold in tissue engineering and it is used in the treatment of osteoarticular pathologies of the knee and in general as supplement of the sinovial fluid residing in the joints. The focus of academic and industrial laboratories is nowadays addressed onto a derivative of HYA where just 4 % of the repeating units has been grafted with alkyl side chains containing 16 carbon atoms. This modified HYA is able to form a hydrogel at very low concentrations, probably due to the clustering of the hydrophobic side chains.
A detailed knowledge of the scaffolding of the polymer- and biopolymer-networks is a necessary pre-requisite to optimize the release capabilities of gel-carrier for specific drugs and environments. A further very important requirement is to obtain a detailed description of the water-macromolecule interaction and of their role in determining the structural, dynamic and functional properties of the gels. In hydrated polymer- and biopolymer-systems, hydrogen bonds are formed among water molecules, between water and the macromolecule, and within the macromolecule. The first hydration shell (d &lt; 5Å) is quite closely associated to the random gel network: it determines its mobility, enables hydrogen-bonding and proton transfer, and facilitates a plethora of biochemical processes [7,8]. Macromolecule-water interactions are short-range, however their integrated effects propagate to relatively large-scale lengths modifying appreciably, even at very low biopolymer concentration, the translational and rotational diffusion properties of large volumes of interstitial water [9].
In polysaccharides, for instance, a variety of complex structures from ordered fiber packing at moderate hydration level, up to dilute gels, can be formed depending on hydration and therefore on the degree of water-macromolecule association. Polysaccharides based hydrogels are relatively stable even at very low saccharide concentration (down to 1% and less). Water may act also as a ‘plasticiser’ inducing some degree of alignment of the saccharidic units and affecting thus not only the conformation but also the dynamical properties at a molecular level [10,11].
The investigation of the microscopic and mesoscopic structural and dynamic properties of polymer- and biopolymer-based gels and nanogels and of the effects connected with their interaction with the solvent has to be tackled using a variety of complementary spectroscopic techniques. On the side of the structural properties we recall static and dynamic light scattering, X-ray small angle scattering, a technique that can take advantage nowadays from the availability of high brilliance synchrotron radiation sources, and neutron small angle scattering. These techniques are highly complementary as:
i. their combined use makes it possible to span a wide range of characteristic lengths, from the atomic scale up to microns;
ii. the different sensitivity of X rays and neutrons to light elements (hydrogen and deuterium) and to the heavier ones (carbon, nitrogen, oxygen) enables one to distinguish, in the diffraction profile, the contributions from different molecular species according to their different 'contrast'; in a similar way it is also possible to locate hydrated and anhydrous regions within the polymer scaffolding.
On the side of the microscopic dynamic properties, one has to mention, among others, NMR relaxation spectroscopy [12], the measure of chemical potentials [13], dielectric relaxation and microwave spectroscopy measurements [14]. The experimental results, together with data from computer simulations, confirmed that water bound to hydrophilic sites has relaxation times lengthened compared to bulk water, and this can be interpreted in terms of an increased hydrogen bond connectivity in the vicinity of a hydrophilic surface [15].
In the last decade contributions from more sophisticated computer molecular dynamics simulations (MD) and from high energy resolution scattering experiments have appeared. Cold and thermal neutron techniques (quasielastic, (QENS), and inelastic (INS) neutron scattering), and gamma-radiation scattering techniques (Rayleigh Scattering of Mössbauer Radiation, RSMR), have been used to study the dynamic properties at the molecular level of biological water and the time course of the hydration mechanisms.
In particular RSMR experiments performed by the Parma Research Unit on some saccharide systems similar to the ones of interest for this project indicated that water of hydration is highly ordered and it gives rise to Bragg-like peaks in the diffraction profile. The ordering of these waters is not only structural but also dynamic and we have observed propagation of acoustic phonon-like modes along these ordered water structures [16-19]. QENS and INS experiments on last generation neutron spectrometers [20-24] altogether provided interesting data on the dynamic structure factor, S(Q,w), over a large momentum transfer (hQ) and energy transfer (hw) intervals. These correspond to lengths in the 1 to 100 Å region, and to times ranging from those of localized high frequency vibrations (10^(-12)-10^(-13) s) to the slowest random-walk time-scales associated with molecular diffusion (ns region). It is also worth remarking that RSMR and neutron scattering are a good combination of complementary techniques to probe the microscopic atomic dynamics. Indeed RSMR is sensitive only to heavier atoms (oxygen in the case of water), while hydrogens are almost invisible for gamma-rays; this technique therefore probes essentially the dynamics of the center of mass of the molecule. Neutrons scattering on the other hand is dominated by hydrogens (cross-section(H) ~ 20 x cross-section(O)) and therefore the two data altogether give a comprehensive picture of the various dynamic feature of the molecular motions.
On the side of computer simulations, nowadays the ever growing power of modern computers makes it possible to study more and more complex macromolecular systems, in particular with classical molecular dynamics methods. At the same time new methods for solving the Fokker-Planck equation based on the Path-Integral and on the instantons method have emerged, which in the future will allow us to understand the details of conformational transformations occurring on a long time scale and developing as a sequence of rare events.
In the Trento Research Unit there is a specific know-how in both methods.
As concerns molecular dynamics simulations, a considerable experience was gathered in the past in the study of glyco-lipidic molecules, and in the related development of force-fields at the atomistic level [25]. The results have been successfully compared with the experimental ones obtained by X-ray and neutron scattering, both at large (SAXS) and small (WAXS) angle, reaching a very good coincidence between the simulated and the real system [26-28].
It is generally understood that the formation of polymer based matrices is a cooperative phenomenon, involving conformational transitions occurring as a sequence of rare events. Such conformational transitions can be described in terms of several reaction coordinates, which can be analitically expressed as geometrical properties of the single molecules. For the analysis of this and other processes it is possible to use a new variational method developed in Trento, and originally applied to the study of protein folding [29, 30]. Such method allows for investigating the transition process between assigned initial and a final states, using a generalized version of the Onsager-Machlup action [31] in the Hamilton-Jacobi formulation. The method, which does not require approximations other than those implied by the use of the underlying Langevin dynamics, allows to obtain the most probable path in the configuration space without the need to identifying an a-priori reaction coordinate, as it is needed in other methods for the analysis of rare events (e.g. [32]). Compared to standard molecular dynamics, this approach makes it possible to avoid investing computational time when the system is not evolving, therefore solving the problem of the existence of very different time scales in a process involving rare events.
As concerns the definition of the force-field to be used in the simulations, recently a version of GROMOS was developed, which is applicable to mono- and di-saccharide systems [33,34]. This potential can be extended to the description of HYA. Recently the GROMOS force field was also used by the Rome "Tor Vergata" group to describe PVA hydrogels [35], without the MA inclusions. Such force fields are the necessary starting point both for the molecular dynamics simulations, and, in the future, for the DFP simulations.

References:
1. K. Akiyoshi, J. Sunamoto; Supramolecular Science (1996) 3, 157 - 163
2. 2) J. Sunamoto, T. Sato, T. Taguchi, H. Hamazaki; Macromolecules (1992) 25, 5665 - 5670
3. 3) K. Akiyoshi, S. Deguchi, N. Moriguchi, S. Yamaguchi, J. Sunamoto; Macromolecules (1993) 26, 3062 - 3068.
4. F. Cavalieri, F. Miano, P. D’Antona, G. Paradossi; Biomacromolecules, 2004, 5, 2439-2446.
5. G. Paradossi, F. Cavalieri, E. Chiessi, C. Spagnoli, M. K.Cowman; Journal of Materials Science: Materials in Medicine, 2003,14,687 – 691.
6. M. Morra, Biomacromolecules, 2005, 6, 1205-1223.
7. G.A. Jeffrey, and W. Saenger Springer Verlag, N.Y., (1991).
8. S.B. Zimmerman, and A.P. Minton, Ann. Rev. Biophys. Biomol. Struct., 22 (1993) 27.
9. H.D. Middendorf, .D. Di Cola, F. Cavatorta, A. Deriu, C.J. Carlile, Biophys. Chem. 53 (1994) 145.
10. D. French, D. 1998. in “Starch:Chemistry and Technology, 2nd ed.” (R.L. Whistler, J.N. BeMiller, E.D. Paschall, Eds.) Academic press, New York, 1998 pp. 183.
11. M. Di Bari, F. Cavatorta, A. Deriu, G. Albanese, Biophysical J. 81, 1190 (2001).
12. H. Hauser, M.C. Phillips, Prog. Surf. Membr. Sci., 13 (1979) 297.
13. J.L. Lis, M. MacAlister, N. Fuller, R.P. Rand, V.A. Parsegian, Biophys. J. 37 (1982) 657.
14. M. Marquandt, G. Nimtz, Phys. Rev. Lett. 57 (1986) 1036; G. Nimtz, and W. Weiss, Z. Phys. B 67 (1987) 483.
15. W. Weiss, J. Phys. 48 (1987) 877.
16. G. Albanese, A. Deriu, F. Cavatorta, Biopolymers 33, 633 (1993).
17. G. Albanese, A. Deriu, F. Cavatorta, A. Rupprecht, Hyperfine Interactions, 95, 97 (1995).
18. F. Cavatorta, G. Albanese, A. Deriu, A. Rupprecht, A., Il Nuovo Cimento D 18, 371 (1996).
19. Deriu, A, Cavatorta, F., Albanese, G., Hyperfine Int. 141-142, 261 (2002).
20. A. Deriu, Physica B 182 (1992) 349; H.D. Middendorf, D. Di Cola, F. Cavatorta, A. Deriu, C.J. Carlile, Biophys. Chem. 53 (1994) 145.
21. M.-C. Bellisent-Funel, J.M. Zanotti, S.H. Chen, Faraday Discuss. 103 (1996).
22. M. Settles and W. Doster, Faraday Discuss., 103 (1996) 269.
23. F. Demmel, W. Doster, W. Petry, A. Schulte, Eur. Biophys. J 26 (1997) 327.
24. W. Doster and M. Settles, in Hydration Processes in Biology:Theoretical and Experimental Approaches Vol. 305, (ed. M.-C. Bellissent-Funel), IOP Press, Amsterdam, 1999.
25. H.J.C. Berendsen, D. van der Spool, R. van Drunen, Comp. Phys. Commun. 1995, 91 42-56.
26. M. Sega, R. Vallauri, P. Brocca and S. Melchionna. J.Phys.Chem B 2004, 108, 20322-20330.
27. M. Sega, R. Vallauri, P. Brocca, S. Melchionna, and L. Cantù, J. Phys. Chem B 111, 10965(2007).
28. M. Sega, R. Vallauri and S. Melchionna. Phys. Rev. E 72, 2005 41201-4.
29. P. Faccioli, M. Sega, F. Pederiva, H. Orland, Phys. Rev. Lett. 97, 108101 (2006).
30. M. Sega, P. Faccioli, F. Pederiva, G. Garberoglio, H. Orland, Phys. Rev. Lett. 99, 118102 (2007).
31. L. Onsager and S. Machlup Phys. Rev. 1953, 91 1505-1512.
32. A. Laio and M. Parrinello PNAS, 2002, 20 12562-12566.
33. R.D. Lins, P.H. Huenenberger, J. Comp. Chem. 26, 1400, 2005.
34. C.S. Pereira, D. Kony, R. Baron, M. Mueller, W.F. van Gunsteren, P.H. Huenenberger, Biophys. J. 90, 4337, 2006.
35. E. Chiessi, F. Cavalieri, G. Paradossi, J. Phys. Chem. B, 111, 2820-2827 (2007).
36. T. Maeda, T. KAnda, Y. Yonekura, K. Yamamoto, T. Aoyagi; Biomacromolecules, 2006, 7, 545 -549. <<<