Analysis on the Network Node of Konjac Glucomannan Molecular Chain①

WENCheng-RongSUNZhong-QiPANGJieMAZhenSHENBen-ShuXIEBing-QingJINGPu

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Analysis on the Network Node of Konjac Glucomannan Molecular Chain①

WEN Cheng-RongaSUN Zhong-QiaPANG JieaMA ZhenaSHEN Ben-Shua②XIE Bing-QingaJING Pub

a(350002)b(200240)

The dynamic changes of the complex network and the material form and function were actuated by the molecular chains. The interaction behavior between molecular chains was difficult to illuminate because the dynamic changes of macromolecules were observed difficultly by normal spectrum method and the methods to test and evaluate the complex network evolution prediction and intervention are rare. The mathematic model of domino offect of molecular chains was established based on the topological structure of molecular chain aggregation of Konjac glucomannan, and the molecular entanglement mechanism of Konjac glucamannan blends was studied through molecular simulation and knot theory analysis combined with experimental verification. The results suggested that two network models (topological entanglement and solid knot) of Konjac glucomannon blends were formed through hydrogen bond nodes. The topological entanglement was strengthened with the increase of concentration and the form of molecular chains was Gaussian chain which could not allow traverse moving owing to the intermolecular cross and entanglement and the shield of intramolecular interaction. Besides, the structures of Konjac glucomannon blends became more stable due to the solid knot. Both of them were verified by the experimental results. This experimental method simplifies the microscopic description of Konjac glucomannon, and there is important guiding significance of the experimental results for the prediction and control of polysaccharides’ structure and function.

knot, Konjac glucomannon, topological entanglement, network node

1 INTRODUCTION

As a typical mathematical method, topology has important applications on the aspect of chain ring formed by polymer, such as nucleic acids, proteins, polysaccharides,[1-3]. The knot theory, one of topologies, is a new research field developed rapidly in recent years. It helps explain how interaction causes change of polymer chain spatial structure and form complex network, then it helps forecast and regulate the polymer’s function[4-5]. Molecular chain is a new research subject in knot theory. The forming of polymer molecular chain model can help form prediction mechanism of the path of chain, which is expected to provide a simple, unified platform andfairer comparison for the evolution of complex net-works. What’s more, it will greatly promote the theory of evolution of complex networks model. The polymer’s physicochemical properties can be pre- dicted by its structure characteristic parameters[6].

How to drive the evolution of a complex network of macromolecules at the molecular level, to explore the interactions between molecules, to find be- havioral effects of macromolecular molecular chains and to provide prediction and regulation of poly- mer’s structure and function have become a hot and difficult issue of studies reference. Now the researches on polymer’s chain are almost focused on the experimental results and test methods, and those on molecular simulation almost focus on the si- mulation system, single mechanism and simulation methods. Owing to the complexity of biological macromolecules, the existing methods are not good to clarify the intermolecular interaction behaviors, or to achieve the target of regulating its structure and function in dose-effect.

Polysaccharide is a kind of macromolecular sub- stances with complex structure and functions[7,8], whose physical and chemical properties and bi- ological activity are affected by their network structure[9,10]. How to characterize and design the molecular structure of polysaccharide and regulate its function has become difficult and hot issue. In some cases, the polysaccharide will show a ring structure of end to end, which is not a simple planar ring structure, but topological structure in different environments[11]. Some of its properties and be- haviors are independent on their chemical com- position and other details, but only on its own topological structure.These properties and behavior of polysaccharide are between micro and macro, which need to be studied from mesoscale. So, it can be studied by approximated research of molecular simulation, without considering the details[12,13]. Although the basis of research is experiment, we need to explore the nature of the phenomenon from theory and calculations, and then calculate the unknown quantity.

Konjac glucomannan (KGM) is one of the natural polysaccharides in which glucose and mannose at the molar ratio of 1:1.6～1.7 are connected via-1,4 glycosidic bonds[14]. KGM has been widely applied in the fields of food, biomedical, materials,. as water conservation materials, cartilage, drug and nutrient carriers, and so on[6,14]. Owing to the limi- tations of experimental studies, the conformation of KGM molecular chain and its stable formation mechanism, especially the interaction of other poly- mer and inorganic small molecule compounds, have not been studied in depth[15]. Based on the topology of KGM, combined with molecular simulation and mathematical model establishment, the molecular links of KGM, KGM compounds, and KGM blends are analyzed. The processes of changing from trivial knot to the topology entanglement and topological knot and building molecular chain network mathe- matical model to predict the formation of a link mechanism are studied. And the mathematical model of molecular chain network and prediction me- chanism of chain path are established as well. In order to achieve predicting results, the verification of experimental research is adopted, too. This study fuses so many multidisciplinary advantages that it provides a new thought of the functional regulation of poly- saccharides and other macromolecules.

2 MATERIALS AND METHODS

2.1 Materials

Konjac refined powder was obtained from San Ai Organic Konjac Development Co., Ltd., Zhaotong, Yunnan, China; Curdlan (CUD) was purchased from Japanese Takeda kirin food co., LTD., Japan; Other chemical reagents (analytical grade) were obtained from Sinopharm Chemical Reagent Co. Ltd.

2.2 Main instruments and equipments

EquipmentTypeOrigin Circular dichroism, CDBioLogic MOS 450Thermo Electron Corporation, USA Magnetic stirring85-2Changzhou sino instrument co., LTD Digital thermostat water bathHH-2Jiangyin Poly Scientific Instruments Co. Ltd. Electronic analytical balancePL402-CMETTLER TOLEDO Instruments Co., Ltd.

2.3 Experimental methods

2.3.1 Preparation of KGM/borax blend

1.0 g KGM was dispersed in 100 mL distilled deionized water to obtain 0.01 g/mL solutions, and stirred by a magnetic stirrer for 2 h at 45 ℃, then vacuum filtrated by a 200 mesh filter cloth. 5 mL 0.6% borax solution was added to 95 mL KGM solution which was stored at 4 ℃ for 1 d, then stirred for 20 min and kept at room temperature for 40 min[16].

2.3.2 Circular dichroism (CD) spectra

The same volume of 80mol/L congo dye solution and KGM/ borax blend solution were mixed. After being stored for 24 h, bioLogic MOS 450 circular dichroism spectrometer was used. Deter- mination conditions: temperature: 25 ℃, radius of color dish: 0.2 cm, wavelength: 180～400 nm, distinguishability: 0.5 nm, scanning speed: 30 nm/ min.

2.3.3 Molecular model optimization

The molecular dynamic simulation of the solution of KGM and its blends in water (4 ℃) in addition to individual aqueous solutions was carried out on O2working station (American HP) using Hyper- Chem7.0 release soft ware (American Hypercube Corporation). Force-field function included bond, angle and non-bonding; the Langevin temperature regulation method was used to adjust the tempera- ture; the ensemble was canonical ensemble; the step size of calculation was 0.001 ps and the relaxation time 0.1 ps; the system was run for 100 ns; and the interval of data collection was 2 ps. In order to understand the law of molecular conformation change in optimizing procession intuitively, the H atoms were concealed.

2.3.4 Molecular chain model building of KGM

The kink theory was analyzed by simplifying the complex structure of KGM to flat topological structure combined with molecular chain folding, based on the topology analysis of P. C. Burns[17]. Then the mathematic model was established and the knot was found. The results were verified by experi- mental research at last.

We assumed that the zero chain knot coincided with the negative half shaft of theaxis in the three-dimensional rectangular coordinate system, whose terminal point is the origin of coordinate. So, the terminal point of the ithchain knot was marked as Mi= (xi, yi, zi), i = 0, 1, 2, …, n, which means M0= (0, 0, 0). And we also assumed that QiMi= { cosφi, cosψi, cosθi}, because the following chain knot is relative to the prior’s free rotatability, of which free rotation angle Φ is a uniformly distributed random number in the range of [0, 2π)[18].

(1) When i = 1, the uniformly distributed random number in the range of [0, 2π) is Φ1, andcosφ1is confirmed.

Then we get a formula as follows: cosψ1= ±√ (1-cos2φ1- cos2θ1)= ±√ (1-cosφ1),(θ1=π/2). It is “+” as 0 ≤ φ1≤ π, while it is “-” as π ≤ φ1≤ 2π.

And we get the following formulas, x1= l*sin70°32*cosφ1, y1= l*sin70°32*cosψ1, z1= l*sin70°32*cosθ1, which means the point of M1is confirmed.

Popularly, if the point of Mi= (xi, yi, zi) is confirmed, we can count the results of cosines in the direction of Mi-1Mias below: cosα1= (xi-xi-1)/l, cosβ1= (yi-yi-1)/l, cosγ1= (zi-zi-1)/l.

Then the coordinate values of planar circle (Qi+1) are as follows:

ui+1= xi+1*cosα1, vi+1= yi+1*cosβ1, wi+1= zi+1*cosγ1.

And the plane equation is perpendicular to the direction of Mi-1Miand crosses the point of Qi+1as below: cosαi*(x-ui+1)+cosβi*(y-vi+1)+cosγi*(z-wi+1)= 0.

For instance, if i = 1 and φ1= π/4, we get the following results: cosφi=√2/2, cosψi=√2/2, cosθi=0;

x1= 0.6717* l, y1= 0.6717* l, z1= 0;

cosα1= 0.6717, cosβ1= 0.6717, cosγ1= 0;

u2= 0.67172* l, v2= 0.67172* l, w2= 0;

0.6717*(x- 0.67172* l) + 0.6717*(y- 0.67172* l) = 0, which can be simplified to x+y = 0.67172* l.

(2) If we get the uniformly distributed random number (Φi+1) in the range of [0, 2π), we can work out

cosθi+1= (-cosαi* cosφi+1* cosγi±| cosβi|*√ (|cos2βi+ cos2γi- cos2φi+1|))/( cos2βi+ cos2γi) (The probability of "+" and "-" is the same) and cosψi+1= ±√ (1-cos2φi+1- cos2θi+1), (It is “+” as 0 ≤ φi+1≤ π, but “–” as π ≤ φi+1≤ 2π) from the simultaneous equations as follows: cosαi* cosφi+1+ cosβi* cosψi+1+ cosγi* cosθi+1= 0 and cos2φi+1+ cos2ψi+1+cos2θi+1= 0.

Then the point values of Mi+1= (xi+1, yi+1, zi+1) are worked out as below:

xi+1= ui+1+r* cosφi+1, yi+1= vi+1+r* cosψi+1, zi+1= wi+1+r* cosθi+1.

3 RESULTS AND ANALYSIS

3.1 Establishment of the KGM molecularchain model

The force of intermolecular chains is hydrogen bonds of KGM-KGM and KGM-water when KGM is dissolved in water. The stable conformation and topological structure of KGM in water are shown in Figs. 1 and 2, respectively.

The knot is a closed curve which never crosses itself in three-dimensional space. When a knot is equivalent with the planar circumference, we call it a trivial knot which plays a role of zero[19]. KGM is composed of-(1→4) linked D-mannose and D-glucose in a molar ratio of 1.6:1 or 1.4:1, with about 1 in 19 units being acetylated. KGM may contain short side branches at the C-3 position of mannoses, and acetyl groups are randomly present at the C-6 position of sugar units[20]. The C and O atoms are represented by salient points and end- points, respectively. The bonds between C and C or O are represented by straight line, while those between H and O or C are ignored. The molecular chain of KGM in water solution is approximately circular from overlooking (shown as Fig. 1), and its helix chain is a trivial knot (shown as Fig. 2).

3.2 Establishment of the KGM/CUD molecular model

3.2.1 Entanglement of KGM/CUD blends

The mesoscopic molecular chain of KGM/CUD blends in water solution is shown in Fig. 3, from which we can observe the mesoscopic morphology of KGM/CUD blend. Fig. 3 tells us that the KGM chains are entangled and intertwined with the CUD chains tightly, existing in a form of random coil state. The overlapping effect of the molecular chain has formed a strong interaction entanglement between the molecular chains that are conducive to enhancing the interaction of intermolecular chain and the pro- perties of KGM/CUD blend.

Fig. 1. Stable conformation of KGM in water solution

Fig. 2. Knot structure of KGM in water solution

Fig. 3. Mesoscopic molecular chain form of KGM-CUD blends (Red is CUD; pink, blue and green are KGM)

3.2.2 Topology entanglement model of the KGM/CUD blends

Entanglement is one of the most important charac- ters of polymer’s condensed state. It is a network structure constituted with physical junction points between the polymer chains, and the movement of the molecular chain is fettered and restricted by the surrounding molecules. According to Flory’s deduc- tion[21], the intermolecular chain’s entanglement is more stable due to its orientation when the entangled molecular chains form a network structure. But the orientation will take time, and the hindering of entanglement between the molecular chains makes it longer. If the entanglement of molecular chains has a synergistic effect, it is beneficial to the stability of structure; otherwise it is harmful.

When KGM and CUD are blended in the external force, the entanglement processes of molecular chains are hindered with each other, and the time of forming a network structure is prolonged. Otherwise, the entanglement of molecular chains is affected by the concentration. When in low concentration, the entanglement tends to be folded by itself; when the concentration is increased, the polymer chains are throughout entangled with each other to form an entanglement network, as shown in Fig. 3; when in extreme high concentration, the polymer chains penetrate fully with each other, which are Gaussian chains, so that intramolecular interaction is replaced by intermolecular interaction and completely shiel- ded. The entanglement and penetration of molecular chains are respectively shown as the box and circle parts in Fig. 4, because of which the traverse move- ment of molecular chains is restricted. Therefore, the molecular structure is stable.

3.3 Establishment of the KGM/borax molecular model

3.3.1 Molecular simulation of the KGM/borax molecule

The conformation and hydrogen bonding sites of KGM/borax blends are shown in Fig. 5. The mole- cular dynamics simulations of KGM/boric blends were taken out under periodic boundary conditions in different temperature. It shows that the molecular chains were helical structures under the effect of hydrogen bonds in low and normal temperature. But, as the temperature increased, the hydrogen bonding sites between the KGM molecule and boric acid ions changed slightly. Although the hydrogen bonds of boric acid ions with acetyl were broken, those of the boric acid ions with -OH of Man and Glu glycone remained stable. It suggests that the helical struc- tures of KGM/borax blends were stable with less influence of temperature.

3.3.2 Solid knot of KGM/borax blends

There is some difference between the mechanism of molecular chain entanglement between KGM/ borax blends with KGM/other polymer blends. The KGM molecular chain forms helix rings through self winding, knots through weak bonds and supra- molecular force such as hydrogen bond, and solid knots through coordination reaction between boric acid ions and glycosyl, in KGM/borax blends. The molecular conformation is stable because of the acetyl on the helix structure, which owns interspace in the structure. The mathematic modelof KGM/ borax blends is a torus knot ring, as shown in Fig. 6.

3.3.3 Circular dichroism spectrum of KGM/borax blends

The circular dichroism spectrum is an important method to research the conformation of polymer molecule including the discipline of conformation change. As shown in Fig. 7, the variation tendencies of the circular dichroism spectrum of KGM/borax blends are almost the same at 30 and 60 ℃ from 180 to 400 nm wavelength. Both of them have positive cotton domino offect near 190, 210, 250, and 320 nm, and negative cotton domino offect around 200, 220, 300, and 345 nm. The difference lies in that the positive cotton domino offect of KGM/borax blends at 60℃ is weaker than that at 30℃, while it is on the contrary for the negative, especially in the 200 nm wavelength. Overall, the effect of temperature on the conformation of KGM/borax blends is slight, suggesting that the helical structures of KGM/borax blends were stable and the analysis of solid knot was feasible.

Fig. 4. Topological entanglement of the KGM/CUD blends (Red is CUD, black is KGM; circle part is penetration, and box part is entanglement)

Fig. 5. Conformation and hydrogen bonding sites of the KGM/borax blends(dotted line is hydrogen bond)

Fig. 6. Torus knot ring of the KGM/borax blends

Fig. 7. Effect of temperature on the circular dichroismspectrum of KGM/borax blends

4 DISCUSSION AND CONCLUTION

Nowadays, there is a further deep research on the prediction of complex networks through topological entanglement and path of chain, as a promotion of molecular dynamics method[22,23]. There are a lot of advantages on using computer simulation to research the network of polymers as well as using the concept of system or entirety to study some complex phenomena, which make the prediction results more accurate because more factors could be considered. It is absolutely a good method to research the complex network structure combined with computer simulation with knot analysis, which has a certain guiding role in predicting and controlling the structure and function of polysaccharides. This means not only makes up for some deficiency of the experimental results which are difficult to observe with the existing experimental methods, but also makes up for the difficulties of complex systems which can not be solved analytically in theory. However, it helps us observe polymer structures and functions more in-depth[24-26].

The complex networks of KGM and CUD were divided into solid molecule through conbining topological entanglement and path of chain together. It can disassemble polysaccharide movement to a lot of single movements and then superposed, describe the structure of natural polysaccharide as a dynamic and elastic network structure, and simplify a polysaccharide to a line and a micromolecule to a dot. Harmonic potential with a same elastic coefficient was used in the interaction between the molecular chains of polysaccharide. We have found that KGM’s helix chain is a trivial knot and proposed and validated the mathematical model of KGM blends molecule chain network (topology entanglement and topological knot model). This is benefit on understanding the complex network of molecular chains in theory, and this also provides network evolution mechanism for the same class or network. The conformation and molecular chain of KGM blends are representated and designed very well and reasonable models of this chain are esta- blished to guide experiment and control its function.

Knot theory and mathematic model simplify the microscopic description of KGM molecular chain, and the predicted results have guiding effect on the structure and function prediction and regulation of polysaccharides. It can also achieve rational reconstruction in this process and the optimization of molecular chain network. Finally, it makes the achievement of full dose regulation possible. It provides a theoretical reference of regulating and controlling the fold, entanglement and properties of polysaccharide molecular chain by using the net- work evolution to simulate the molecular chain of optimal physical and chemical state, but it also provides reference effect of methods on the research of interaction between polysaccharides and rational reconstruction and inorganic micromolecule. The topological entanglement is proved objectively to be existence by experimental facts. But, there should be a new breakthrough in the observations and mole- cular dynamics simulations of microscopic images of polymer topological entanglements. And there should be more databases to solve the problem of complex network control through the prediction theory of path of chain so as to predict the in- formation of structure, which will be the focus of future research directions.

(1) Duan, J. W.; Zheng, Z.; Zhou, P. P.; Qiu, W. Y. The architecture of Sierpinski knots.. 2012, 68, 595-610.

(2) Redner, S. Teasing out the missing links.2008, 453, 47.

(3) Li, H.; Helling, R.; Tang, C.; Wingreen, N. S. Emergence of preferred structures in a simple model of protein folding.1996, 273, 666-669.

(4) Darcy, I. K. Biological distances on DNA knots and links, applications to XER recombination.2001, 10, 269-294.

(5) Vazquez, M.; Colloms, S. D.; Sumners, D. W. Tangle analysis of Xer recombination reveals only three solutions, all consistent with a single three-dimensional topological pathway.2005, 346, 493-504.

(6) Haliloglu, T.; Bahar, I.; Erman, B. Gaussian dynamics of folded proteins.1997, 79, 3090-3093.

(7) Dumitriu, S. Eds.. CRC Press 2010.

(8) Stephen, A. M.; Phillips, G. O.; Williams, P. A. Eds.CRC Press 2010.

(9) Zhang, B. B.; Su, H. Q.; Gu, X. J.; Huang, X. L.; Wang, H. M. Effect of structure and charge of polysaccharide flocculants on their flocculation performance for bentonite suspensions.2013, 436, 443-449.

(10) Tzianabos, A. O. Polysaccharide immunomodulators as therapeutic agents, structural aspects and biologic 33.

(11) Orellana, A. Biosynthesis of non-cellulosic polysaccharides in the Golgi apparatus. Topological considerations.2005, 139, 42-45.

(12) Lyman, E.; Cui, H. S.; Voth, G. A. Reconstructing protein remodeled membranes in molecular detail from mesoscopic models.2011, 13, 10430-10436.

(13) Draviam, V. M.; Funahashi, A.; Hiroi, N.; Kimura, A.; Kobayashi, T. J.Meeting report of the international workshop on quantitative biology 2012, mesoscopic and microscopic worlds meet.2012, 3.

(14) Jian, W. J.; Zeng, Y.; Xiong, H. J.; Pang, J. Molecular simulation of the complex of konjac glucomannan–borate in water.2011, 85, 452-456.

(15) Melinda, C.; Timothy, C.; Baldwin, T. J.; Hocking, K. C. Traditional uses and potential health benefits of Amorphophallus konjac K. Koch ex N.E.Br.2010, 128, 268-278.

(16) Forget, A.; Christensen, J.; Lüdeke, S.; Kohler, E.; Tobias, S.; Matloubi, M.; Shastri, V. P. Polysaccharide hydrogels with tunable stiffness and provasculogenic properties via-helix to-sheet switch in secondary structure.2013, 110, 12887-12892.

(17) Jian, W. J.Fujian Agriculture and Forestry University2011.

(18) Burns, P. C.; Deely, K. M.; Skanthakumar, S. Neptunium incorporation into uranyl compounds that form as alteration products of spent nuclear fuel, implications for geologic repository performance.2004, 92, 151-160.

(20) Kinoshita, S.; Terasaka, H. On unions of knots.1957, 9, 131-153.

(21) Katsuraya, K.; Okuyama, K.; Hatanaka, K.; Oshima, R.; Sato, T.; Matsuzaki, K. Constitution of konjac glucomannan, chemical analysis and13C NMR spectroscopy. Carbohydrate Polymers2003, 53, 183-189.

(22) Flory, P. J.; Rehner, J. Statistical mechanics of cross-linked polymer networks II. welling.2004, 11, 521-526.

(23) Walker, D. M.; Tordesillas, A. Topological evolution in dense granular materials, a complex networks perspective.2010, 47, 624-639.

(24) Tuszynska, I.; Bujnicki, J. M. Predicting atomic details of the unfolding pathway for YibK, a knotted protein from the SPOUT superfamily.2010, 27, 511-520.

(25) Lee, J. Y.; Chun, M. S.; Jung, H. W.; Hyun, J. C. Conformational dynamics of sub-micron sized wormlike polyelectrolyte polymer in flow fields.2012, 20, 1163-1172.

(26) Perkyns, J. S.; Lynch, G. C.; Howard, J. J.; Pettitt, B. M. Protein solvation from theory and simulation, exact treatment of Coulomb interactions in three-dimensional theories.2010, 132, 064106.

21 April 2014;

16 July 2014

① This project was supported by the National Natural Science Foundation of China (31271837), Specialized Research Fund for the Doctoral Program of Higher Education jointly funded by Ministry of Education (20113515110010), Special Research Funds from Ministry of Science and Technology (2012GA7200022), Major projects of industries, universities and research in Fujian Province (2013N5003), and Natural Science Foundation of Fujian Province (2011J0101)

. Pang Jie, professor, majoring in food chemistry and nutrition. E-mail: pang3721941@163.com