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On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions
Journal Pre-proof On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions
M. Ashoorirad, M. Saviz, A. Fallah PII:
S0167-7322(19)35154-2
DOI:
https://doi.org/10.1016/j.molliq.2019.112344
Reference:
MOLLIQ 112344
To appear in:
Journal of Molecular Liquids
Received date:
14 September 2019
Revised date:
13 December 2019
Accepted date:
17 December 2019
Please cite this article as: M. Ashoorirad, M. Saviz and A. Fallah, On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions, Journal of Molecular Liquids(2018), https://doi.org/10.1016/j.molliq.2019.112344
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© 2018 Published by Elsevier.
Journal Pre-proof
On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions M. Ashoorirad1, M. Saviz1 , A. Fallah1,* 1
Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Abstract
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Collagen is the most abundant protein of the extracellular matrix in connective tissue in the mammalians with potential applications in the coverage of cardiovascular prostheses, regenerative medicine, pharmaceutical industry, controlled drug delivery, and proliferation, migration and cellular differentiation. In this research, the electrical properties (conductivity and permittivity) of type I collagen solution with different concentrations were measured in the frequency range 10KHz - 5MHz and electrical analysis of the measurement results was performed. Analysis shows that special interactions with water molecules have a significant effect on the electrical properties of collagen solutions beyond what is predicted considering the rules of physical composition, such as the Maxwell-Garnet model of mixing rules. Very small variations in the amount of collagen in water, significantly changed solution conductivity and dielectric permittivity. Finally, to simplify the representation of the impedance measurements and to better understanding of the electrical behavior of the solutions, an equivalent electrical circuit model was developed to describe the measured data. The results obtained from the fitted electrical model were in good agreement with the experimental results.
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Keywords: Collagen; Electrical Properties; Bioimpedance Spectroscopy; Electrical Circuit Model. 1. Introduction
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The superiority of collagen as a biomaterial essentially depends on the fact that collagen is a component of the extracellular matrix and therefore is considered as an intrinsic element of the body [1– 5]. Collagen, one of the closest approximation to extracellular matrix [6], is a complex supramolecular structure, with very diverse morphologies across different tissues which give them a wide range of biological functions in the body [3,4]. Collagen is the most important protein in the connective tissues and is the most abundant protein in mammals [7–10]. In the vertebrates, collagen is a major component of the specialized and non-specialized connective tissues, which accounts for about a quarter of the body's total protein, about three-quarters of the human dry skin, more than 90% of the tissues of the tendon and the cornea, and about 80% of organic matter of bones [5]. Up to now, 29 types of collagen have been identified [5]. The difference in collagens is due to the difference in the triple polypeptide chains, the difference in helical length, the different interruptions in the helix and the difference in the helical terminals [5]. Generally, collagen is divided into two types: fibrous and non-fibrous. Collagen types I, II, and III are the most common fibrillar collagens. Collagen type I, is the predominant collagen in most tissues of higher order animals [11] and accounts for 80-85% of collagen in the body [12]. Collagen biopolymer is the most abundant protein in the mammalian body with a molecular weight of 300 kg/mol [13], which consists of amino acid sequences. Collagen contains different amino acids. Amino acids such as Glysine, Prolyne, Hydroxyproline, Glutamine, Arginine, Aspartic acid and Hydroxylysine are present in collagen *
Corresponding Authors: Ali Fallah, Ph.D., Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran, Email: [email protected]
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Journal Pre-proof with more content [14]. Hydroxyproline and Hydroxylysine are not significantly present in proteins other than collagen [14].
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In other words, amino acids with a hydroxyl group are specific to collagen and do not exist in a sufficiently great in other proteins. The presence of these hydroxyl groups in the collagen macromolecule leads to the formation of hydrogen bonds between collagen fibers with each other, and collagen fibers with the water molecule which results in increase of the conductivity of the collagen solution [15]. By linking these amino acids via the peptide bonds, a chain of amino acids is formed. The collagen macromolecule consists of three polypeptide chains that are weaved together with hydrogen bonds and forms a triple helical structure [4,16]. Hydrogen bonds hold amino acids firmly in a mesh of fibers. Each collagen helix consists of approximately 1.5 nm in diameter and 300 nm in length [17,18]. The amino acids in collagen macromolecule have a regular arrangement in each of the three chains. This sequence often follows the pattern of Gly-Pro-X or Gly-X-Hyp, in which Gly is glysine, Pro is hydroxyproline, Hyp is hydroxyproline, and X can be any of different amino acids.
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The Gly-Pro-Hyp chain is the most stable amino acid sequence in collagen. Collagen triple helical structure stabilizes with hydrogen bonds between carbonyl and hydroxyl groups of hydroxyproline [19]. Collagen is a natural protein used as a dielectric gate for organic thin film transistors (OTFTs) in vacuum and air conditions. The high mobility value of the field effect in OTFTs is attributed to the interaction between water molecules and hydroxyl groups in collagen [19] which leads to conductivity enhancement. Hydroxyl groups are found in the hydroxyproline and hydroxylysine amino acids in the collagen structure.
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Generally, polymers are classified as polar and nonpolar depending on their chemical structure. Nonpolar polymers are usually insulating materials with a pseudo-constant permittivity of 2.5 to 3 [20]. The structure of these proteins is made of carbon and hydrogen atoms that are symmetrically arranged along a carbon chain. Polar polymers are composed of molecules including electronegative atoms such as nitrogen, oxygen, chloride and fluoride, and create dipoles within the polymer. The higher dielectric coefficient is a characteristic of these polymers [20]. Proteins are polar biopolymers whose polar index can be weaker or stronger depending on the lateral chain of amino acids present in them [20]. Contrary to complex molecular chains, proteins provide some interesting points, especially their charge content, which results in electrical properties (conductivity and dielectric permittivity) of proteins. The electrical properties of proteins play an important role in evaluating their functions. Many studies have been performed to investigate the electrical, mechanical and structural properties of proteins [20–23]. Electrostatic interactions are important for the overall stability of the protein structure [14], and in total, are considered as the contributions of van der Waals forces, hydrogen bonds, covalent bonds, and hydrophobic interactions [24]. Therefore, these bonds not only stabilize the protein structure, but also contribute to the electrical properties of proteins. Hence, proteins are considered as polarizable materials that can be characterized by their electrical properties [15]. Polarizing the components of a material is due to a change in the redistribution of electrical charges, when the material is exposed to an electric field. Polarization can be due to various effects such as charge accumulation at surfaces of multilayer materials with different dielectric permittivity (interfacial polarization), bipolar orientation or electronic and atomic ( or ionic) polarization [20]. Each of these polarization effects contribute to overall electrical properties. The electrical properties of the materials depend on their chemical composition, in particular the stable dipole moments associated with water molecules. The higher the number of dipoles inside the solution, the higher the total charge transfer and the higher conductivity of the solution [25]. Water molecules enter the amino acids chains of protein and form hydrogen bonds through their hydroxyl group. 2
Journal Pre-proof With the penetration of water into the protein network, the structure and mobility of the protein peptide chains change [20]. Therefore, water molecules can effectively influence the electrical properties of proteins. It has been reported in [26] that the formation of hydrogen bonds between DNA bases enhance conductance. The shorter bond length conforms stronger hydrogen bond and results in more conductance.
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Like other proteins, for collagen, amino acids and hydroxyl groups form hydrogen bonds with water molecules and increase the conductivity of collagen solution. In addition, quasi-ring structures have improved conductivity due to bonds [26]. Some of the amino acids in collagen macromolecules, such as phenylalanine, tyrosine and histidine, have ring structures with bonds, and therefore, can lead to increased conductivity due to free electrons. Since collagen protein consists of polar repeated units of amino acids (-NH-CR-CO) and other polar groups such as COO-, OSO3- and OH- [13], electrical methods can be used to analyze this biomaterial. These methods are used to study the effects of water molecules and frequency of electric field on the electrical properties of collagen. In this study, the electrical properties of type 1 collagen solutions are measured and investigated.
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In this paper, the electrical properties of type I collagen (the most abundant collagen type [5]) in soluble phase are investigated and the effect of increasing collagen concentrations on these properties is studied and analyzed. To theoretically confirm the role of water in the electrical properties of collagen protein, Maxwell-Garnet model for the mixing rules of physical composition of materials was implemented in MATLAB environment. Finally, an equivalent electrical circuit model was fitted to measured data at different concentrations. The advantage of this model is that by determining the various parameters of the model for each concentration, better intuition can be obtained of the electrical events occurring in collagen solution under the influence of the electric field. 2. Materials and methods 2.1. Preparation of collagen solutions
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Dry Type 1 Collagen, obtained from calf skin, was purchased from the Pasteur Institute (Tehran). A total of 20 mg of collagen was dissolved in 2 ml of acetic acid 2.5% (v/v in deionized water) using a magnetic stirrer and therefore, 2 ml of collagen solution at a concentration of 10 mg/ml was prepared. Using this solution, collagen solutions with the concentration of 250, 500, 750 and 1000 were prepared by diluting the original collagen solution with deionized water.
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2.2. Biosensor fabrication and impedance measurements To measure the electrical properties of the collagen solutions, flat gold electrodes with size of 1.9 cm × 1 cm were constructed on a FR4 substrate. With the help of two other FR4 plates with dimensions of 1.7cm × 1cm, two other walls of the enclosure measuring the electrical properties of the collagen solution were prepared and carefully sealed. After preparing the compartment containing electrodes, existence of any leakage on it was tested. Then, it was washed well with detergent and rinsed with deionized water. After drying, it was sprayed with 70% ethanol and used for measurements after alcohol evaporation. In order to keep the sensor stable during different measurements, the sensor was fixed on a circular base of Plexiglas material (Figure 1. ). Impedance measurements of collagen solutions were performed at room temperature ( ) and frequency range of 10 KHz to 5 MHz at 200 linearly spaced frequencies using a Hioki IM3570 impedance analyzer and an average of four measurements per frequency. Before data collection the Hioki IM3570 was calibrated using the open/short/load procedure based on its user manual. Further details of this calibration are provided in [27]. Also, as far as possible, the interconnecting wires were twisted pairs to minimize the induction of electromagnetic noise. 3
Journal Pre-proof Using a sampler, 3.5 ml of collagen solution was slowly poured in the sensing enclosure in such a way to prevent bubbles formation inside the solution. Then, a sinusoidal stimulation current of 100 A amplitude was applied to the electrodes at a frequency range of 10KHz to 5MHz. These measurements were performed using 3.5 ml of collagen solution with four concentrations of 250, 500, 750 and 1000μg/mL to study the effects of increasing collagen fibers concentration on the conductivity and permittivity of the solutions. Measurement errors were less than 1%. This means that the difference between the measured impedances among the at least three samples of each concentration has been less than 1%. The measurements errors of impedance magnitude and phase for different concentrations have been indicated using error bars in Figure 2. 2.3. Statistical Analysis
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All the experimental data are presented as the mean of three repetitions. At each repetition, three samples were measured for each concentration. Statistical analysis was done by student’s T-test. Differences were statistically significant at P-values less than 0.01.
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3. Results and discussion 3.1. Electrical properties of proteins
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The response of a material to an electric field is determined with its electrical properties (conductivity and dielectric permittivity). In aqueous media, conductivity is mainly due to the presence of charged ions in the environment. The higher the number of these charged factors, the greater the expected conductivity. The dielectric permittivity is defined as the power of the material in energy storage (electrical capacitor). The greater the dielectric permittivity of a material, the greater the ability of the material to store energy when exposed to an electric field, in other words, its electrical capacity is increased.
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Since proteins are composed of polar repeating units of amino acids and neutral, polar, and charged side chains [13], they can be considered as polarizable materials. In a peptide bond in a protein molecule, the two amino acid residues are linked by removing a water molecule from the carboxyl group from an amino acid and an amino group from another acid through a covalent bond, and charged agents are generated in the protein molecule. Due to this natural charge, proteins are sensitive to electrical excitation and exhibit specific electrical properties under certain conditions. As the electric properties of proteins depend on their composition and chemical structure, environmental parameters and material processing also affect the charge and consequently the electrical properties of protein solutions [20].
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3.2. Measuring electrical properties of type I collagen solution The Nyquist diagram of the measurements is shown in Figure 3. The experimental curves demonstrate a distinguishable electrical sensitivity to even small concentrations of collagen. An elevation of collagen concentration causes a significant change in the real part of the impedance which results in increasing conductivity. For a more accurate comparison of the electrical properties of collagen solution at different concentrations, the electrical properties (conductivity and dielectric permittivity) of collagen solution were obtained at different concentrations by calculating the geometric coefficient of the measuring electrode. Considering the dimensions of the electrode used in the sensor fabrication (section 2.2), the geometric factor of the measuring electrodes was calculated and the electrical complex conductivity was obtained. Specifically [28,29]: (1) (2)
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Journal Pre-proof Collagen Protein Electrical Model
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IM 3570 Impedance Analyzer
Rcol
Rct
Collagen fibers in solution
L2000 4-Terminal Probe
USB Port
𝑃𝑜𝑡
𝐻𝑃𝑜𝑡 𝑢𝑟𝑟𝑒𝑛𝑡
1 cm
1.9 cm
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Figure 1. Measurement setup for measuring electrical properties of type I collagen protein solution.
Figure 2. Measurements errors of (a) impedance magnitude and (b) impedance phase for different concentrations of collagen solution using error bars representation. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
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Journal Pre-proof Where Z is the measured impedance, A is the area of the electrodes, and L is the distance between the electrodes. The
ratio is the geometric factor of the measurement chamber. The
is the vacuum
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permittivity and is the relative permittivity of the collagen solution. is complex conductivity. The resulting conductivity is a complex value, its real part is the conductivity ( ) of collagen solution, and its imaginary part is a factor of the relative dielectric permittivity of collagen solution ( ). Conductivity and relative dielectric permittivity of collagen solutions are presented in Figure 4.
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Figure 3. Nyquist diagram of collagen protein solutions with different concentrations at the frequency range of 10KHz to 5MHz. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
125KHz
(a)
(b)
Figure 4. (a) Conductivity and (b) dielectric permittivity of collagen solution with different concentrations at the frequency range of 10KHz to 5MHz. For frequencies more than 125KHZ, relationship between concentration and dielectric permittivity is inversed. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
As shown in Figure 4, the conductivity of the collagen solutions significantly increases with increasing concentrations. Various factors contribute to the increase in conductivity by increasing the concentration of collagen fibers in the solution. Electrical conduction of collagen fibers in a soluble phase can be due to the electrical interaction between bipolar molecules of water and active chemical groups on 6
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collagen fibers. The intertwined structure of collagen is retained together by electrostatic and hydrophobic bonds trapping large quantities of liquids and allowing the exchange of ions and metabolites with surrounding tissues [5]. Besides, with increasing number of hydroxyl groups in the polymer, mobility increases [30]. Hydroxyl groups are significantly present in the amino acid chains of collagen helical macromolecules. Therefore, the existence of these functional groups increases mobility which leads to an increase in electrical conductivity of collagen solution. On the other hand, O- and H3O + (hydronium ion) groups are produced in the collagen solution using the following reaction:
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Figure 5. Interaction of the hydroxyl group of hydroxyproline amino acid in the peptide chains of collagen fibers with the water molecule and formation of hydronium ion.
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The residue of the hydroxyproline amino acid with the O- group in the collagen macromolecule is immobilized due to its large size [19]. In contrast, H3O + ions are able to move freely and easily inside the solution and therefore, when the electric field is applied to collagen solution, these ions move to the negative pole of the field, resulting in high conductivity. Since the number of these ions increases with increasing collagen fiber content (increasing the concentration of collagen solution), the measured conductivity would be proportional to the concentration of collagen solution and increases (Figure 4(a)).
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Except for hydroxyl groups of amino acids in collagen macromolecules that form hydrogen bonds with water molecules and increase the conductivity of collagen solution, another feature of the chemical structure of amino acids of the collagen macromolecule also improves conductivity. Ring structures lead to improved conductivity due to their -bonds [26]. Some of the amino acids in collagen macromolecule, such as phenylalanine, tyrosine and histidine, have a benzene ring with -bonds and, due to free electron, increase the conductivity of the collagen solution. The higher the concentration of collagen solution, the higher the number of these amino acids inside the solution, resulting in greater conductivity. However, in our measurements on the dry collage (see supplementary data) there was observed no difference between bare electrodes and electrodes with the same mass of collagen related to the different concentrations. Meanwhile, for the same amount of dry collagen dissolved in acetic acid and diluted with deionized water, very significant changes in electrical properties were observed. Thus, we think that this factor may have no important effect on the electrical properties of the collagen solution. On the other hand, the formation of bipolar moments in the solution, essentially contributes to the reduction of the total impedance of the solution [25]. Since the hydroxyproline residues with the O- group (Figure 5) and other charged groups in collagen fibers form local electric dipoles inside the solution, the collagen solution would present dielectric property when exposed to an electric field. Since the number of dipoles in the solution is proportional to the collagen concentration, changing the concentration of collagen changes the dielectric behavior of the solution. In the low-frequency range (f < 125KHz), the dielectric coefficient increases with increasing concentration of collagen solution. In the higher frequency range (f > 125KHz), dielectric permittivity of the collagen solution decreases with
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Journal Pre-proof increasing the concentration of collagen solution. A more detailed study of the effect of frequency on the electrical properties of collagen solution is given in section 3.4. 3.3. Maxwell-Garnet mixing model To theoretically demonstrate that the measured electrical properties for collagen solutions are due to the presence of water and the formation of hydrogen bonds and other chemical interactions between the charged agents present in the collagen amino acid chains with the water molecules, the electrical properties of collagen with different fractional volumes were obtained using the Maxwell-Garnet mixing model. In the Maxwell-Garnet model, only physical interactions between the various components of a mixture are considered.
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Dielectric mixing rules are algebraic formulas that can be used to calculate the effective permittivity of a mixture as a function of constituent permittivities, their fractional volumes, and some other possible parameters that characterize the microstructure of the mixture. The mixture can be discrete, meaning that the homogeneous inclusions are embedded in another homogeneous environment. The size of the inclusions in the mixture needs to be much smaller than the wavelength [31].
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In practice, the inclusions can take many different shapes. The only shape for which simple analytical solutions are available is the ellipsoid shape that fortunately covers many practical situations [31]. In the case of collagen molecule, which is an inclusion in the 2.5% acetic acid medium, it is properly approximated as an ellipsoid shape.
(3)
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The properties of a dilute mixture with a fractional volume less than 0.1 can be correctly calculated using the Maxwell-Garnet mixing law [31]:
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Where is a dimensionless quantity, the volume fraction of the inclusions in the mixture and subscripts e and i refer to the environment and inclusion, respectively. This formula is widely used in various fields. If f → 0 then the inclusion phase is vanished and and if f → 1 then the environment phase is vanished and . To calculate the effective permittivity of the mixture of collagen inclusions in 2.5% acid acetic medium using mixing rules, given that the collagen fibers are 1.5 nm in diameter and 300 nm in length, the collagen molecules approximately form randomly oriented ellipsoid inclusions with axial dimensions of 0.75 nm, 0.75 nm and 150 nm. In this calculation, the permittivity of solid collagen fibers is assumed to be 2.5 [20] respectively at room temperature. The permittivity of 2.5% acetic acid as the base material (medium) was considered as 59 (see supplementary data). To calculate the fractional volume of collagen inclusions in acetic acid medium, assuming the protein density is 1.35 gr/mL [32], for the collagen solution at a concentration of 250 g/mL fractional volume would be: (4) To obtain the fractional volumes for concentrations of 500, 750 and 1000 , this value is multiplied by 2, 3, and 4, respectively. The corresponding permittivity was calculated and plotted in MATLAB environment using the mixing rules ( Figure 6 ). As can be seen from these graphs, for different fractional volumes corresponding to different concentrations of collagen solution, the 8
Journal Pre-proof permittivity variation is negligible respect to medium permittivity. Thus, in terms of mixing rules and only considering physical interactions without regard to chemical interactions, there is no significant difference between the electrical properties of dry collagen with different fractional volumes. However, in the measured data for collagen solutions, although the mass of collagen varies similarly, the electrical properties change significantly. This fact is due to the presence of water and the chemical interactions between the water molecules and the charged agents present in the structure of collagen fibers, which significantly increases the conductivity and permittivity.
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Furthermore, in our measurements on dry collagen, no significant relations were observed between recorded impedance characteristics of bare electrodes and electrodes coated by different amount of dry collagen corresponding with different concentrations of the collagen solutions (see supplementary data).
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Figure 6: Permittivity of solid state collagen fibers at different fractional volumes corresponding to the collagen solutions at different concentrations calculated by the Maxwell-Garnet mixing rule in MATLAB environment at frequency range of 10KHz to 5MHz.
3.4. The effect of frequency on the electrical properties of collagen solution Frequency is an important factor that influences the electrical behavior of different materials, including proteins. As the frequency increases, the dipoles in the protein are not able to follow faster changes in the electric field polarity, and as a result, the effect of these dipoles decreases with increasing frequency, and the dielectric permittivity of the protein decreases [20]. In performed measurements on collagen protein with different concentrations, this decreasing trend of the dielectric permittivity respect to the frequency is clearly seen (Figure 4). As shown in Figure 4 (b), the dielectric behavior of collagen solution in low and high frequencies is quite different. For frequencies below 125 KHz, with increasing collagen concentration, the relative dielectric permittivity is increased, while for frequencies higher than 125 KHz, with increasing the concentration of collagen solution, the dielectric permittivity decreases. At low frequencies (<125KHz), electrical dipole in collagen macromolecules have the opportunity to be aligned with the electric field before changing the direction of the field, and their overall results create a larger capacitor, but at higher frequencies (>125 KHz) because of the rapid changes in the electric field, the electrical dipoles in the 9
Journal Pre-proof structure of collagen fibers do not have the opportunity to rotate and align with the electric field and results in decreasing dielectric permittivity of collagen solution respect to its concentration. As the concentration of collagen fibers in the solution is increased, due to the greater number of fibers and their more intertwining, a smaller number of dipoles in the solution are capable of aligning to the electric field and exhibiting their capacitive (dielectric permittivity) properties. This leads to a decrease in the dielectric permittivity (capacitance) at higher frequencies (> 125KHz) respect to collagen concentration increasing. Due to the large size of charged residues in the collagen fibers, they immobilize in the solution at higher frequencies and result in a further reduction in the dielectric permittivity by increasing the concentration. By increasing the concentration of collagen solution, the number of large residues would increase and the dielectric permittivity of the solution further decreases.
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On the other hand, as shown in Figure 4(a), as the frequency increases, the conductivity increases with respect to collagen solutions concentration. This is due to the decrease in dielectric properties (capacitance) of collagen solution respect to frequency increment. By decreasing the capacitance, the overall impedance is reduced and the conductivity is increased.
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3.5. Fitting an electrical equivalent circuit to measured bio-impedance data
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Bioimpedance or electrical impedance of biological samples describes the electrical properties of these materials. The purpose of collecting these measurements is to provide details of electrochemical structures and electrical processes within a tissue or material being studied [33]. The bioimpedance spectrum is a safe, noninvasive, and inexpensive way to measure the electrical responses of living tissues and other biomaterials that can reflect the physiological and pathological status of the tissue or biomaterial being measured. To measure bioimpedance, a sinusoidal current (or voltage) is applied through the stimulation electrodes to the measured biomaterial sample, and its response is measured as voltage (or current) through the recording electrodes. By dividing the recorded response to the stimulation applied to the measured sample, a complex quantity is obtained called bioimpedance.
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To simplify the representation of the impedance spectrum measurements and to better understand the electrical behavior of the samples being measured, an equivalent electrical circuit schematic is desirable; electrical circuits models are regularly used to fit and interpret bioimpedance data [33–36]. In this method the measured spectrum is fitted on to an equivalent electrical circuit model which is constructed based on resemblances between the electrical circuit model and the measured physical phenomena (e.g. double layers). Thus, the spectral behavior is confined to several descriptive parameters of the model reducing a bioimpedance dataset from the potentially hundreds of data points to several parameters (dependent on the number of circuit components in the model). In this study, an equivalent circuit model is fitted to measured bioimpedance data and can be used to describe and analyze the electrical behavior of collagen protein solution. Due to the measured electrical properties of the collagen protein solution mentioned in the previous sections, this protein solution has both ohmic and capacitive components. Therefore, a conventional parallel RC circuit could model its electrical behavior. The analyzed collagen protein solutions are electrolytes, and they tend to induce a specific interfacial layer near to the sensor electrodes that is named a double layer ( ). The sensor electrode becomes polarized with regard to the collagen solution that attracts the ions of contrary charge. This effect can be illustrated by a double layer capacitor and a faradic resistance at the electrodeelectrolyte interface. The double layers of the electrode-solution interface are also conventionally modeled as parallel RC sections in series with the solution. As shown in Figure 1. the electrical equivalent 10
Journal Pre-proof circuit is symmetrically modeled on the basis of the electrodes structure and electrical behavior of collagen protein solution. The parameters , , ، , , and stand for double layer capacity, charge transfer resistance, bulk solution resistance, ionic conduction and dielectric behavior of collagen protein solution, respectively. Since the equivalent electrical circuit models for both electrodes (paired parallel ) are similar and in series, they can be considered equivalent to a single combined parallel circuit for modeling the electrode-solution behavior. Therefore, the equivalent circuit that was considered to fit the measured bioimpedance data is simplified as shown in Figure 7. The equivalent impedance of the circuit is described in Eq. (5).
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Collagen Protein Electrical Model
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Figure 7. Equivalent electrical circuit model fitted to measured bioimpedance data to analyze impedance characteristics of collagen protein solutions.
3.5.1 Fitting algorithm for determination of electrical circuit model parameters
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A complex nonlinear least square algorithm in MATLAB software was used to find model parameters that cause best agreement between measured impedance spectrum and model (estimated) spectrum. This algorithm attempts to minimize the distance between the measured bioimpedance spectrum and the estimated impedance with the model by solving an optimization problem: 𝑛∑
(6)
𝑡
Where is the vector of bioimpedance parameters ( ، ، ، ، ), is the estimated impedance (Figure 7) calculated using , 𝑡 is the measured bioimpedance, and 𝑡 are the calculated and measured dataset at frequency , and is the total number of data points in the measured dataset. The Eq.(6) is simultaneously applied on real and imaginary parts of impedance dataset. The optimization algorithm aims find bioimpedance parameters in a way to ideally reduce the least square error to zero or realistically to the level of error within the dataset [35]. Several factors such as an incorrect model for the dataset being fitted, poor estimation for the initial values, and noise may cause the algorithm to fail on converging to a useful fit. The measured and fitted impedance spectroscopy of type 1 collagen solution at concentration range of 250-1000 g/mL were plotted as a Nyquist curve in Figure 8. The values of equivalent electrical circuit 11
Journal Pre-proof model parameters for different concentrations are given in Table 1. Fitting quality is indicated by sum of squared errors (SSE) at the final row of the table. SSE is the sum of squared differences between real and imaginary parts of the measured and fitted impedances. It is a measure of the discrepancy between the measured data and an estimation model. SSE is defined as below:
SSE=∑
(7)
Where, , , , , and N are the real part of the measured impedance, real part of the estimated impedance using the proposed electrical model, imaginary part of the measured impedance, imaginary part of the estimated impedance using the proposed electrical model, and N is the number of frequencies in which the measurements have been performed, respectively.
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As it can be seen in Figure 3, the elevation of the collagen concentration decreases the semicircle diameter of the Nyquist diagram. From the point of the electrochemical impedance spectroscopy, this observation can be explained as a reduction of charge transfer resistance ( ) in electrical model proposed in Figure 7 and is consistent with the fitted values. From experimental data (Figure 4), the collagen solutions with various concentrations have specific electrical properties (conductivity and dielectric permittivity) which can be modeled by a RC circuit ( ) in series with bulk solution resistance ( ). As it can be seen from the values of the model parameters in Table 1, with increasing collagen protein concentration, the value of decreases which means that with elevation in collagen concentration the conductivity improves which is consistent with the measured results presented in Figure 4(a). The value of is increased respect to collagen concentration which is again consistent with our understanding of the measured data (Figure 4(b)). is bulk solution resistance which is affected by both ohmic and capacitive components.
750 g/mL
1000 g/mL
1227
1274
1193
1039
1785
752.3
294.2
94.13
22.46
47.32
142.5
733
98.25
86.35
56.64
42.12
𝑛
235.07
206.99
305.63
366.67
SSE
0.001
0.003
0.004
0.009
𝑝
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Parameters of Fitted Electrical Circuit Model
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Table 1: Calculated parameters for the electrical circuit model fitted to the measured impedance data for different concentrations of collagen protein.
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Figure 8. Nyquist diagram of measured and fitted data using electrical equivalent circuit presented in Figure 7 for collagen solution with concentrations of (a) 250μg/mL, (b) 500μg/mL, (c) 750μg/mL, and (d) 1000μg/mL.
4. Conclusion
In this paper, the electrical properties of collagen protein were investigated in soluble phase at the frequency range of 10KHz to 5MHz and an equivalent electrical circuit was fitted to the measured data using the least squares algorithm. Proteins are sensitive to electrostatic methods due to their polarization, and exhibit special electrical properties when subjected to an electric field. Because of this polarization property, impedance spectroscopy can be used as an effective method for protein analysis. Simulations results using the Maxwell-Garnet model of mixing rules for physical composition of materials, showed that only with respect to the rules of physical composition there is no difference between the different fractional volumes of collagen. However, the same weight of collagen in soluble state, significantly changed its conductivity and dielectric permittivity. Hence, the main cause of the variation in electrical properties of collagen solution appears to be the formation of hydronium ions due to the interaction of water molecules with the collagen macromolecule. The number of dipoles in the solution is proportional to the collagen concentration. Hence, changing the concentration of collagen changes the dielectric behavior of the solution. 13
Journal Pre-proof Conflict of interest statement We, Masoomeh Ashoorirad, Mehrdad Saviz, and Ali Fallah certify that there is no conflict of interest. Acknowledgment This work was supported by Iran National Science Foundation (INSF) through the financial agreement number 97015120.
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CRediT author statement
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[31]
Masoomeh Ashoorirad: Investigation, Conceptualization, Methodology, Writing-Original Draft Preparation, Visualization, Software, Validation, Formal Analysis.
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Mehrdad Saviz: Supervision, Writing-Reviewing and Editing, Formal Analysis, Conceptualization.
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Ali Fallah: Supervision, Writing-Reviewing and Editing, Project Administration, Funding Acquisition.
Highlights: Measuring electrical properties of collagen solution with different concentrations Relations between electrical properties and the mass of collagen in the solution Water role on the electrical properties of the collagen solution Fitting an electrical model on to the measured data of the collagen solution 16
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M. Ashoorirad, M. Saviz, A. Fallah PII:
S0167-7322(19)35154-2
DOI:
https://doi.org/10.1016/j.molliq.2019.112344
Reference:
MOLLIQ 112344
To appear in:
Journal of Molecular Liquids
Received date:
14 September 2019
Revised date:
13 December 2019
Accepted date:
17 December 2019
Please cite this article as: M. Ashoorirad, M. Saviz and A. Fallah, On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions, Journal of Molecular Liquids(2018), https://doi.org/10.1016/j.molliq.2019.112344
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© 2018 Published by Elsevier.
Journal Pre-proof
On the electrical properties of collagen macromolecule solutions: Role of collagen-water interactions M. Ashoorirad1, M. Saviz1 , A. Fallah1,* 1
Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
Abstract
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Collagen is the most abundant protein of the extracellular matrix in connective tissue in the mammalians with potential applications in the coverage of cardiovascular prostheses, regenerative medicine, pharmaceutical industry, controlled drug delivery, and proliferation, migration and cellular differentiation. In this research, the electrical properties (conductivity and permittivity) of type I collagen solution with different concentrations were measured in the frequency range 10KHz - 5MHz and electrical analysis of the measurement results was performed. Analysis shows that special interactions with water molecules have a significant effect on the electrical properties of collagen solutions beyond what is predicted considering the rules of physical composition, such as the Maxwell-Garnet model of mixing rules. Very small variations in the amount of collagen in water, significantly changed solution conductivity and dielectric permittivity. Finally, to simplify the representation of the impedance measurements and to better understanding of the electrical behavior of the solutions, an equivalent electrical circuit model was developed to describe the measured data. The results obtained from the fitted electrical model were in good agreement with the experimental results.
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Keywords: Collagen; Electrical Properties; Bioimpedance Spectroscopy; Electrical Circuit Model. 1. Introduction
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The superiority of collagen as a biomaterial essentially depends on the fact that collagen is a component of the extracellular matrix and therefore is considered as an intrinsic element of the body [1– 5]. Collagen, one of the closest approximation to extracellular matrix [6], is a complex supramolecular structure, with very diverse morphologies across different tissues which give them a wide range of biological functions in the body [3,4]. Collagen is the most important protein in the connective tissues and is the most abundant protein in mammals [7–10]. In the vertebrates, collagen is a major component of the specialized and non-specialized connective tissues, which accounts for about a quarter of the body's total protein, about three-quarters of the human dry skin, more than 90% of the tissues of the tendon and the cornea, and about 80% of organic matter of bones [5]. Up to now, 29 types of collagen have been identified [5]. The difference in collagens is due to the difference in the triple polypeptide chains, the difference in helical length, the different interruptions in the helix and the difference in the helical terminals [5]. Generally, collagen is divided into two types: fibrous and non-fibrous. Collagen types I, II, and III are the most common fibrillar collagens. Collagen type I, is the predominant collagen in most tissues of higher order animals [11] and accounts for 80-85% of collagen in the body [12]. Collagen biopolymer is the most abundant protein in the mammalian body with a molecular weight of 300 kg/mol [13], which consists of amino acid sequences. Collagen contains different amino acids. Amino acids such as Glysine, Prolyne, Hydroxyproline, Glutamine, Arginine, Aspartic acid and Hydroxylysine are present in collagen *
Corresponding Authors: Ali Fallah, Ph.D., Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran, Email: [email protected]
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Journal Pre-proof with more content [14]. Hydroxyproline and Hydroxylysine are not significantly present in proteins other than collagen [14].
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In other words, amino acids with a hydroxyl group are specific to collagen and do not exist in a sufficiently great in other proteins. The presence of these hydroxyl groups in the collagen macromolecule leads to the formation of hydrogen bonds between collagen fibers with each other, and collagen fibers with the water molecule which results in increase of the conductivity of the collagen solution [15]. By linking these amino acids via the peptide bonds, a chain of amino acids is formed. The collagen macromolecule consists of three polypeptide chains that are weaved together with hydrogen bonds and forms a triple helical structure [4,16]. Hydrogen bonds hold amino acids firmly in a mesh of fibers. Each collagen helix consists of approximately 1.5 nm in diameter and 300 nm in length [17,18]. The amino acids in collagen macromolecule have a regular arrangement in each of the three chains. This sequence often follows the pattern of Gly-Pro-X or Gly-X-Hyp, in which Gly is glysine, Pro is hydroxyproline, Hyp is hydroxyproline, and X can be any of different amino acids.
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The Gly-Pro-Hyp chain is the most stable amino acid sequence in collagen. Collagen triple helical structure stabilizes with hydrogen bonds between carbonyl and hydroxyl groups of hydroxyproline [19]. Collagen is a natural protein used as a dielectric gate for organic thin film transistors (OTFTs) in vacuum and air conditions. The high mobility value of the field effect in OTFTs is attributed to the interaction between water molecules and hydroxyl groups in collagen [19] which leads to conductivity enhancement. Hydroxyl groups are found in the hydroxyproline and hydroxylysine amino acids in the collagen structure.
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Generally, polymers are classified as polar and nonpolar depending on their chemical structure. Nonpolar polymers are usually insulating materials with a pseudo-constant permittivity of 2.5 to 3 [20]. The structure of these proteins is made of carbon and hydrogen atoms that are symmetrically arranged along a carbon chain. Polar polymers are composed of molecules including electronegative atoms such as nitrogen, oxygen, chloride and fluoride, and create dipoles within the polymer. The higher dielectric coefficient is a characteristic of these polymers [20]. Proteins are polar biopolymers whose polar index can be weaker or stronger depending on the lateral chain of amino acids present in them [20]. Contrary to complex molecular chains, proteins provide some interesting points, especially their charge content, which results in electrical properties (conductivity and dielectric permittivity) of proteins. The electrical properties of proteins play an important role in evaluating their functions. Many studies have been performed to investigate the electrical, mechanical and structural properties of proteins [20–23]. Electrostatic interactions are important for the overall stability of the protein structure [14], and in total, are considered as the contributions of van der Waals forces, hydrogen bonds, covalent bonds, and hydrophobic interactions [24]. Therefore, these bonds not only stabilize the protein structure, but also contribute to the electrical properties of proteins. Hence, proteins are considered as polarizable materials that can be characterized by their electrical properties [15]. Polarizing the components of a material is due to a change in the redistribution of electrical charges, when the material is exposed to an electric field. Polarization can be due to various effects such as charge accumulation at surfaces of multilayer materials with different dielectric permittivity (interfacial polarization), bipolar orientation or electronic and atomic ( or ionic) polarization [20]. Each of these polarization effects contribute to overall electrical properties. The electrical properties of the materials depend on their chemical composition, in particular the stable dipole moments associated with water molecules. The higher the number of dipoles inside the solution, the higher the total charge transfer and the higher conductivity of the solution [25]. Water molecules enter the amino acids chains of protein and form hydrogen bonds through their hydroxyl group. 2
Journal Pre-proof With the penetration of water into the protein network, the structure and mobility of the protein peptide chains change [20]. Therefore, water molecules can effectively influence the electrical properties of proteins. It has been reported in [26] that the formation of hydrogen bonds between DNA bases enhance conductance. The shorter bond length conforms stronger hydrogen bond and results in more conductance.
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Like other proteins, for collagen, amino acids and hydroxyl groups form hydrogen bonds with water molecules and increase the conductivity of collagen solution. In addition, quasi-ring structures have improved conductivity due to bonds [26]. Some of the amino acids in collagen macromolecules, such as phenylalanine, tyrosine and histidine, have ring structures with bonds, and therefore, can lead to increased conductivity due to free electrons. Since collagen protein consists of polar repeated units of amino acids (-NH-CR-CO) and other polar groups such as COO-, OSO3- and OH- [13], electrical methods can be used to analyze this biomaterial. These methods are used to study the effects of water molecules and frequency of electric field on the electrical properties of collagen. In this study, the electrical properties of type 1 collagen solutions are measured and investigated.
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In this paper, the electrical properties of type I collagen (the most abundant collagen type [5]) in soluble phase are investigated and the effect of increasing collagen concentrations on these properties is studied and analyzed. To theoretically confirm the role of water in the electrical properties of collagen protein, Maxwell-Garnet model for the mixing rules of physical composition of materials was implemented in MATLAB environment. Finally, an equivalent electrical circuit model was fitted to measured data at different concentrations. The advantage of this model is that by determining the various parameters of the model for each concentration, better intuition can be obtained of the electrical events occurring in collagen solution under the influence of the electric field. 2. Materials and methods 2.1. Preparation of collagen solutions
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Dry Type 1 Collagen, obtained from calf skin, was purchased from the Pasteur Institute (Tehran). A total of 20 mg of collagen was dissolved in 2 ml of acetic acid 2.5% (v/v in deionized water) using a magnetic stirrer and therefore, 2 ml of collagen solution at a concentration of 10 mg/ml was prepared. Using this solution, collagen solutions with the concentration of 250, 500, 750 and 1000 were prepared by diluting the original collagen solution with deionized water.
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2.2. Biosensor fabrication and impedance measurements To measure the electrical properties of the collagen solutions, flat gold electrodes with size of 1.9 cm × 1 cm were constructed on a FR4 substrate. With the help of two other FR4 plates with dimensions of 1.7cm × 1cm, two other walls of the enclosure measuring the electrical properties of the collagen solution were prepared and carefully sealed. After preparing the compartment containing electrodes, existence of any leakage on it was tested. Then, it was washed well with detergent and rinsed with deionized water. After drying, it was sprayed with 70% ethanol and used for measurements after alcohol evaporation. In order to keep the sensor stable during different measurements, the sensor was fixed on a circular base of Plexiglas material (Figure 1. ). Impedance measurements of collagen solutions were performed at room temperature ( ) and frequency range of 10 KHz to 5 MHz at 200 linearly spaced frequencies using a Hioki IM3570 impedance analyzer and an average of four measurements per frequency. Before data collection the Hioki IM3570 was calibrated using the open/short/load procedure based on its user manual. Further details of this calibration are provided in [27]. Also, as far as possible, the interconnecting wires were twisted pairs to minimize the induction of electromagnetic noise. 3
Journal Pre-proof Using a sampler, 3.5 ml of collagen solution was slowly poured in the sensing enclosure in such a way to prevent bubbles formation inside the solution. Then, a sinusoidal stimulation current of 100 A amplitude was applied to the electrodes at a frequency range of 10KHz to 5MHz. These measurements were performed using 3.5 ml of collagen solution with four concentrations of 250, 500, 750 and 1000μg/mL to study the effects of increasing collagen fibers concentration on the conductivity and permittivity of the solutions. Measurement errors were less than 1%. This means that the difference between the measured impedances among the at least three samples of each concentration has been less than 1%. The measurements errors of impedance magnitude and phase for different concentrations have been indicated using error bars in Figure 2. 2.3. Statistical Analysis
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All the experimental data are presented as the mean of three repetitions. At each repetition, three samples were measured for each concentration. Statistical analysis was done by student’s T-test. Differences were statistically significant at P-values less than 0.01.
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3. Results and discussion 3.1. Electrical properties of proteins
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The response of a material to an electric field is determined with its electrical properties (conductivity and dielectric permittivity). In aqueous media, conductivity is mainly due to the presence of charged ions in the environment. The higher the number of these charged factors, the greater the expected conductivity. The dielectric permittivity is defined as the power of the material in energy storage (electrical capacitor). The greater the dielectric permittivity of a material, the greater the ability of the material to store energy when exposed to an electric field, in other words, its electrical capacity is increased.
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Since proteins are composed of polar repeating units of amino acids and neutral, polar, and charged side chains [13], they can be considered as polarizable materials. In a peptide bond in a protein molecule, the two amino acid residues are linked by removing a water molecule from the carboxyl group from an amino acid and an amino group from another acid through a covalent bond, and charged agents are generated in the protein molecule. Due to this natural charge, proteins are sensitive to electrical excitation and exhibit specific electrical properties under certain conditions. As the electric properties of proteins depend on their composition and chemical structure, environmental parameters and material processing also affect the charge and consequently the electrical properties of protein solutions [20].
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3.2. Measuring electrical properties of type I collagen solution The Nyquist diagram of the measurements is shown in Figure 3. The experimental curves demonstrate a distinguishable electrical sensitivity to even small concentrations of collagen. An elevation of collagen concentration causes a significant change in the real part of the impedance which results in increasing conductivity. For a more accurate comparison of the electrical properties of collagen solution at different concentrations, the electrical properties (conductivity and dielectric permittivity) of collagen solution were obtained at different concentrations by calculating the geometric coefficient of the measuring electrode. Considering the dimensions of the electrode used in the sensor fabrication (section 2.2), the geometric factor of the measuring electrodes was calculated and the electrical complex conductivity was obtained. Specifically [28,29]: (1) (2)
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Journal Pre-proof Collagen Protein Electrical Model
Cdl
Ccol
Cdl
Rs Rct
IM 3570 Impedance Analyzer
Rcol
Rct
Collagen fibers in solution
L2000 4-Terminal Probe
USB Port
𝑃𝑜𝑡
𝐻𝑃𝑜𝑡 𝑢𝑟𝑟𝑒𝑛𝑡
1 cm
1.9 cm
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Figure 1. Measurement setup for measuring electrical properties of type I collagen protein solution.
Figure 2. Measurements errors of (a) impedance magnitude and (b) impedance phase for different concentrations of collagen solution using error bars representation. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
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Journal Pre-proof Where Z is the measured impedance, A is the area of the electrodes, and L is the distance between the electrodes. The
ratio is the geometric factor of the measurement chamber. The
is the vacuum
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permittivity and is the relative permittivity of the collagen solution. is complex conductivity. The resulting conductivity is a complex value, its real part is the conductivity ( ) of collagen solution, and its imaginary part is a factor of the relative dielectric permittivity of collagen solution ( ). Conductivity and relative dielectric permittivity of collagen solutions are presented in Figure 4.
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Figure 3. Nyquist diagram of collagen protein solutions with different concentrations at the frequency range of 10KHz to 5MHz. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
125KHz
(a)
(b)
Figure 4. (a) Conductivity and (b) dielectric permittivity of collagen solution with different concentrations at the frequency range of 10KHz to 5MHz. For frequencies more than 125KHZ, relationship between concentration and dielectric permittivity is inversed. Differences were statistically significant at P-values less than 0.01 and measurements error was less than 1%.
As shown in Figure 4, the conductivity of the collagen solutions significantly increases with increasing concentrations. Various factors contribute to the increase in conductivity by increasing the concentration of collagen fibers in the solution. Electrical conduction of collagen fibers in a soluble phase can be due to the electrical interaction between bipolar molecules of water and active chemical groups on 6
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collagen fibers. The intertwined structure of collagen is retained together by electrostatic and hydrophobic bonds trapping large quantities of liquids and allowing the exchange of ions and metabolites with surrounding tissues [5]. Besides, with increasing number of hydroxyl groups in the polymer, mobility increases [30]. Hydroxyl groups are significantly present in the amino acid chains of collagen helical macromolecules. Therefore, the existence of these functional groups increases mobility which leads to an increase in electrical conductivity of collagen solution. On the other hand, O- and H3O + (hydronium ion) groups are produced in the collagen solution using the following reaction:
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Figure 5. Interaction of the hydroxyl group of hydroxyproline amino acid in the peptide chains of collagen fibers with the water molecule and formation of hydronium ion.
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The residue of the hydroxyproline amino acid with the O- group in the collagen macromolecule is immobilized due to its large size [19]. In contrast, H3O + ions are able to move freely and easily inside the solution and therefore, when the electric field is applied to collagen solution, these ions move to the negative pole of the field, resulting in high conductivity. Since the number of these ions increases with increasing collagen fiber content (increasing the concentration of collagen solution), the measured conductivity would be proportional to the concentration of collagen solution and increases (Figure 4(a)).
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Except for hydroxyl groups of amino acids in collagen macromolecules that form hydrogen bonds with water molecules and increase the conductivity of collagen solution, another feature of the chemical structure of amino acids of the collagen macromolecule also improves conductivity. Ring structures lead to improved conductivity due to their -bonds [26]. Some of the amino acids in collagen macromolecule, such as phenylalanine, tyrosine and histidine, have a benzene ring with -bonds and, due to free electron, increase the conductivity of the collagen solution. The higher the concentration of collagen solution, the higher the number of these amino acids inside the solution, resulting in greater conductivity. However, in our measurements on the dry collage (see supplementary data) there was observed no difference between bare electrodes and electrodes with the same mass of collagen related to the different concentrations. Meanwhile, for the same amount of dry collagen dissolved in acetic acid and diluted with deionized water, very significant changes in electrical properties were observed. Thus, we think that this factor may have no important effect on the electrical properties of the collagen solution. On the other hand, the formation of bipolar moments in the solution, essentially contributes to the reduction of the total impedance of the solution [25]. Since the hydroxyproline residues with the O- group (Figure 5) and other charged groups in collagen fibers form local electric dipoles inside the solution, the collagen solution would present dielectric property when exposed to an electric field. Since the number of dipoles in the solution is proportional to the collagen concentration, changing the concentration of collagen changes the dielectric behavior of the solution. In the low-frequency range (f < 125KHz), the dielectric coefficient increases with increasing concentration of collagen solution. In the higher frequency range (f > 125KHz), dielectric permittivity of the collagen solution decreases with
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Journal Pre-proof increasing the concentration of collagen solution. A more detailed study of the effect of frequency on the electrical properties of collagen solution is given in section 3.4. 3.3. Maxwell-Garnet mixing model To theoretically demonstrate that the measured electrical properties for collagen solutions are due to the presence of water and the formation of hydrogen bonds and other chemical interactions between the charged agents present in the collagen amino acid chains with the water molecules, the electrical properties of collagen with different fractional volumes were obtained using the Maxwell-Garnet mixing model. In the Maxwell-Garnet model, only physical interactions between the various components of a mixture are considered.
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Dielectric mixing rules are algebraic formulas that can be used to calculate the effective permittivity of a mixture as a function of constituent permittivities, their fractional volumes, and some other possible parameters that characterize the microstructure of the mixture. The mixture can be discrete, meaning that the homogeneous inclusions are embedded in another homogeneous environment. The size of the inclusions in the mixture needs to be much smaller than the wavelength [31].
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In practice, the inclusions can take many different shapes. The only shape for which simple analytical solutions are available is the ellipsoid shape that fortunately covers many practical situations [31]. In the case of collagen molecule, which is an inclusion in the 2.5% acetic acid medium, it is properly approximated as an ellipsoid shape.
(3)
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The properties of a dilute mixture with a fractional volume less than 0.1 can be correctly calculated using the Maxwell-Garnet mixing law [31]:
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Where is a dimensionless quantity, the volume fraction of the inclusions in the mixture and subscripts e and i refer to the environment and inclusion, respectively. This formula is widely used in various fields. If f → 0 then the inclusion phase is vanished and and if f → 1 then the environment phase is vanished and . To calculate the effective permittivity of the mixture of collagen inclusions in 2.5% acid acetic medium using mixing rules, given that the collagen fibers are 1.5 nm in diameter and 300 nm in length, the collagen molecules approximately form randomly oriented ellipsoid inclusions with axial dimensions of 0.75 nm, 0.75 nm and 150 nm. In this calculation, the permittivity of solid collagen fibers is assumed to be 2.5 [20] respectively at room temperature. The permittivity of 2.5% acetic acid as the base material (medium) was considered as 59 (see supplementary data). To calculate the fractional volume of collagen inclusions in acetic acid medium, assuming the protein density is 1.35 gr/mL [32], for the collagen solution at a concentration of 250 g/mL fractional volume would be: (4) To obtain the fractional volumes for concentrations of 500, 750 and 1000 , this value is multiplied by 2, 3, and 4, respectively. The corresponding permittivity was calculated and plotted in MATLAB environment using the mixing rules ( Figure 6 ). As can be seen from these graphs, for different fractional volumes corresponding to different concentrations of collagen solution, the 8
Journal Pre-proof permittivity variation is negligible respect to medium permittivity. Thus, in terms of mixing rules and only considering physical interactions without regard to chemical interactions, there is no significant difference between the electrical properties of dry collagen with different fractional volumes. However, in the measured data for collagen solutions, although the mass of collagen varies similarly, the electrical properties change significantly. This fact is due to the presence of water and the chemical interactions between the water molecules and the charged agents present in the structure of collagen fibers, which significantly increases the conductivity and permittivity.
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Furthermore, in our measurements on dry collagen, no significant relations were observed between recorded impedance characteristics of bare electrodes and electrodes coated by different amount of dry collagen corresponding with different concentrations of the collagen solutions (see supplementary data).
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Figure 6: Permittivity of solid state collagen fibers at different fractional volumes corresponding to the collagen solutions at different concentrations calculated by the Maxwell-Garnet mixing rule in MATLAB environment at frequency range of 10KHz to 5MHz.
3.4. The effect of frequency on the electrical properties of collagen solution Frequency is an important factor that influences the electrical behavior of different materials, including proteins. As the frequency increases, the dipoles in the protein are not able to follow faster changes in the electric field polarity, and as a result, the effect of these dipoles decreases with increasing frequency, and the dielectric permittivity of the protein decreases [20]. In performed measurements on collagen protein with different concentrations, this decreasing trend of the dielectric permittivity respect to the frequency is clearly seen (Figure 4). As shown in Figure 4 (b), the dielectric behavior of collagen solution in low and high frequencies is quite different. For frequencies below 125 KHz, with increasing collagen concentration, the relative dielectric permittivity is increased, while for frequencies higher than 125 KHz, with increasing the concentration of collagen solution, the dielectric permittivity decreases. At low frequencies (<125KHz), electrical dipole in collagen macromolecules have the opportunity to be aligned with the electric field before changing the direction of the field, and their overall results create a larger capacitor, but at higher frequencies (>125 KHz) because of the rapid changes in the electric field, the electrical dipoles in the 9
Journal Pre-proof structure of collagen fibers do not have the opportunity to rotate and align with the electric field and results in decreasing dielectric permittivity of collagen solution respect to its concentration. As the concentration of collagen fibers in the solution is increased, due to the greater number of fibers and their more intertwining, a smaller number of dipoles in the solution are capable of aligning to the electric field and exhibiting their capacitive (dielectric permittivity) properties. This leads to a decrease in the dielectric permittivity (capacitance) at higher frequencies (> 125KHz) respect to collagen concentration increasing. Due to the large size of charged residues in the collagen fibers, they immobilize in the solution at higher frequencies and result in a further reduction in the dielectric permittivity by increasing the concentration. By increasing the concentration of collagen solution, the number of large residues would increase and the dielectric permittivity of the solution further decreases.
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On the other hand, as shown in Figure 4(a), as the frequency increases, the conductivity increases with respect to collagen solutions concentration. This is due to the decrease in dielectric properties (capacitance) of collagen solution respect to frequency increment. By decreasing the capacitance, the overall impedance is reduced and the conductivity is increased.
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3.5. Fitting an electrical equivalent circuit to measured bio-impedance data
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Bioimpedance or electrical impedance of biological samples describes the electrical properties of these materials. The purpose of collecting these measurements is to provide details of electrochemical structures and electrical processes within a tissue or material being studied [33]. The bioimpedance spectrum is a safe, noninvasive, and inexpensive way to measure the electrical responses of living tissues and other biomaterials that can reflect the physiological and pathological status of the tissue or biomaterial being measured. To measure bioimpedance, a sinusoidal current (or voltage) is applied through the stimulation electrodes to the measured biomaterial sample, and its response is measured as voltage (or current) through the recording electrodes. By dividing the recorded response to the stimulation applied to the measured sample, a complex quantity is obtained called bioimpedance.
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To simplify the representation of the impedance spectrum measurements and to better understand the electrical behavior of the samples being measured, an equivalent electrical circuit schematic is desirable; electrical circuits models are regularly used to fit and interpret bioimpedance data [33–36]. In this method the measured spectrum is fitted on to an equivalent electrical circuit model which is constructed based on resemblances between the electrical circuit model and the measured physical phenomena (e.g. double layers). Thus, the spectral behavior is confined to several descriptive parameters of the model reducing a bioimpedance dataset from the potentially hundreds of data points to several parameters (dependent on the number of circuit components in the model). In this study, an equivalent circuit model is fitted to measured bioimpedance data and can be used to describe and analyze the electrical behavior of collagen protein solution. Due to the measured electrical properties of the collagen protein solution mentioned in the previous sections, this protein solution has both ohmic and capacitive components. Therefore, a conventional parallel RC circuit could model its electrical behavior. The analyzed collagen protein solutions are electrolytes, and they tend to induce a specific interfacial layer near to the sensor electrodes that is named a double layer ( ). The sensor electrode becomes polarized with regard to the collagen solution that attracts the ions of contrary charge. This effect can be illustrated by a double layer capacitor and a faradic resistance at the electrodeelectrolyte interface. The double layers of the electrode-solution interface are also conventionally modeled as parallel RC sections in series with the solution. As shown in Figure 1. the electrical equivalent 10
Journal Pre-proof circuit is symmetrically modeled on the basis of the electrodes structure and electrical behavior of collagen protein solution. The parameters , , ، , , and stand for double layer capacity, charge transfer resistance, bulk solution resistance, ionic conduction and dielectric behavior of collagen protein solution, respectively. Since the equivalent electrical circuit models for both electrodes (paired parallel ) are similar and in series, they can be considered equivalent to a single combined parallel circuit for modeling the electrode-solution behavior. Therefore, the equivalent circuit that was considered to fit the measured bioimpedance data is simplified as shown in Figure 7. The equivalent impedance of the circuit is described in Eq. (5).
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Collagen Protein Electrical Model
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Figure 7. Equivalent electrical circuit model fitted to measured bioimpedance data to analyze impedance characteristics of collagen protein solutions.
3.5.1 Fitting algorithm for determination of electrical circuit model parameters
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A complex nonlinear least square algorithm in MATLAB software was used to find model parameters that cause best agreement between measured impedance spectrum and model (estimated) spectrum. This algorithm attempts to minimize the distance between the measured bioimpedance spectrum and the estimated impedance with the model by solving an optimization problem: 𝑛∑
(6)
𝑡
Where is the vector of bioimpedance parameters ( ، ، ، ، ), is the estimated impedance (Figure 7) calculated using , 𝑡 is the measured bioimpedance, and 𝑡 are the calculated and measured dataset at frequency , and is the total number of data points in the measured dataset. The Eq.(6) is simultaneously applied on real and imaginary parts of impedance dataset. The optimization algorithm aims find bioimpedance parameters in a way to ideally reduce the least square error to zero or realistically to the level of error within the dataset [35]. Several factors such as an incorrect model for the dataset being fitted, poor estimation for the initial values, and noise may cause the algorithm to fail on converging to a useful fit. The measured and fitted impedance spectroscopy of type 1 collagen solution at concentration range of 250-1000 g/mL were plotted as a Nyquist curve in Figure 8. The values of equivalent electrical circuit 11
Journal Pre-proof model parameters for different concentrations are given in Table 1. Fitting quality is indicated by sum of squared errors (SSE) at the final row of the table. SSE is the sum of squared differences between real and imaginary parts of the measured and fitted impedances. It is a measure of the discrepancy between the measured data and an estimation model. SSE is defined as below:
SSE=∑
(7)
Where, , , , , and N are the real part of the measured impedance, real part of the estimated impedance using the proposed electrical model, imaginary part of the measured impedance, imaginary part of the estimated impedance using the proposed electrical model, and N is the number of frequencies in which the measurements have been performed, respectively.
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As it can be seen in Figure 3, the elevation of the collagen concentration decreases the semicircle diameter of the Nyquist diagram. From the point of the electrochemical impedance spectroscopy, this observation can be explained as a reduction of charge transfer resistance ( ) in electrical model proposed in Figure 7 and is consistent with the fitted values. From experimental data (Figure 4), the collagen solutions with various concentrations have specific electrical properties (conductivity and dielectric permittivity) which can be modeled by a RC circuit ( ) in series with bulk solution resistance ( ). As it can be seen from the values of the model parameters in Table 1, with increasing collagen protein concentration, the value of decreases which means that with elevation in collagen concentration the conductivity improves which is consistent with the measured results presented in Figure 4(a). The value of is increased respect to collagen concentration which is again consistent with our understanding of the measured data (Figure 4(b)). is bulk solution resistance which is affected by both ohmic and capacitive components.
750 g/mL
1000 g/mL
1227
1274
1193
1039
1785
752.3
294.2
94.13
22.46
47.32
142.5
733
98.25
86.35
56.64
42.12
𝑛
235.07
206.99
305.63
366.67
SSE
0.001
0.003
0.004
0.009
𝑝
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500 g/mL
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Parameters of Fitted Electrical Circuit Model
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Table 1: Calculated parameters for the electrical circuit model fitted to the measured impedance data for different concentrations of collagen protein.
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Figure 8. Nyquist diagram of measured and fitted data using electrical equivalent circuit presented in Figure 7 for collagen solution with concentrations of (a) 250μg/mL, (b) 500μg/mL, (c) 750μg/mL, and (d) 1000μg/mL.
4. Conclusion
In this paper, the electrical properties of collagen protein were investigated in soluble phase at the frequency range of 10KHz to 5MHz and an equivalent electrical circuit was fitted to the measured data using the least squares algorithm. Proteins are sensitive to electrostatic methods due to their polarization, and exhibit special electrical properties when subjected to an electric field. Because of this polarization property, impedance spectroscopy can be used as an effective method for protein analysis. Simulations results using the Maxwell-Garnet model of mixing rules for physical composition of materials, showed that only with respect to the rules of physical composition there is no difference between the different fractional volumes of collagen. However, the same weight of collagen in soluble state, significantly changed its conductivity and dielectric permittivity. Hence, the main cause of the variation in electrical properties of collagen solution appears to be the formation of hydronium ions due to the interaction of water molecules with the collagen macromolecule. The number of dipoles in the solution is proportional to the collagen concentration. Hence, changing the concentration of collagen changes the dielectric behavior of the solution. 13
Journal Pre-proof Conflict of interest statement We, Masoomeh Ashoorirad, Mehrdad Saviz, and Ali Fallah certify that there is no conflict of interest. Acknowledgment This work was supported by Iran National Science Foundation (INSF) through the financial agreement number 97015120.
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CRediT author statement
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Masoomeh Ashoorirad: Investigation, Conceptualization, Methodology, Writing-Original Draft Preparation, Visualization, Software, Validation, Formal Analysis.
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Mehrdad Saviz: Supervision, Writing-Reviewing and Editing, Formal Analysis, Conceptualization.
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Ali Fallah: Supervision, Writing-Reviewing and Editing, Project Administration, Funding Acquisition.
Highlights: Measuring electrical properties of collagen solution with different concentrations Relations between electrical properties and the mass of collagen in the solution Water role on the electrical properties of the collagen solution Fitting an electrical model on to the measured data of the collagen solution 16
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