The Structure of the Electric Double Layer of Macromolecules Suspended in Human Cerebrospinal Fluid

The cerebrospinal fluid (CSF) is hydrophilic colloidal fluid circulating around the brain and spinal cord [1]. Normal CSF contains up to 5 white blood cells per mm3 and circa 563 different varieties of peptides and 581 proteins suspended all together in the bulk electrolyte solution. According to Ohshima’s theory of electrophoresis we can regard proteins and biological cells as hard particles [2-4]. Both protein molecules and cells occurring in CSF are electronegative macroparticles because of conversion of amino acid side chains to carboxylate anions at physiological pH 7,33 of CSF and negatively charged sialic acid residues on the membrane surface, respectively [5]. At the junction of the particle-electrolyte solution interface there appears the double electrical layer and on the basis of Gouy and Stern models a particle is surrounded by the inner Stern layer of stagnant ions and the external diffuse Gouy layer of mobile counterions [6-9]. The full description of the electrochemical potential phenomena on the surface of biomolecules was demonstrated by Dukhin [10]. Generally, the Stern layer is a thin layer of one molecule diameter whereas the diffuse layer size is up to hundreds nanometers [11].


Introduction
The cerebrospinal fluid (CSF) is hydrophilic colloidal fluid circulating around the brain and spinal cord [1]. Normal CSF contains up to 5 white blood cells per mm 3 and circa 563 different varieties of peptides and 581 proteins suspended all together in the bulk electrolyte solution. According to Ohshima's theory of electrophoresis we can regard proteins and biological cells as hard particles [2][3][4]. Both protein molecules and cells occurring in CSF are electronegative macroparticles because of conversion of amino acid side chains to carboxylate anions at physiological pH 7,33 of CSF and negatively charged sialic acid residues on the membrane surface, respectively [5]. At the junction of the particle-electrolyte solution interface there appears the double electrical layer and on the basis of Gouy and Stern models a particle is surrounded by the inner Stern layer of stagnant ions and the external diffuse Gouy layer of mobile counterions [6][7][8][9]. The full description of the electrochemical potential phenomena on the surface of biomolecules was demonstrated by Dukhin [10]. Generally, the Stern layer is a thin layer of one molecule diameter whereas the diffuse layer size is up to hundreds nanometers [11].
In this work, optical microscopy as a tracking system has been used to determine the properties of individual biomolecules suspended in the CSF. On the basis of experimental and theoretical data we calculated the size of biomolecules suspended in the CSF and then the thickness of the Stern layer. Thus, the structure of EDL around the biomolecules could be presented.
So far, molecular electrokinetic processes such as Brownian movements and Stern layer occurring in CSF have been described by authors on the surface of the human arachnoid membrane [12]. A preliminary report of this work was presented at the SPIE International Optical Conference [13].

Materials and Methods
The investigation is a part of the research project Bioethics Committee of the Regional Medical Council in Szczecin to perform these clinical studies. According to accepted ethical rules in medical researches, we obtained written informed consent in each case in our study. The samples of the cerebrospinal fluid were collected by lumbar puncture during routine diagnostic procedures from 27 patients hospitalized due to suspicion of having normal pressure hydrocephalus. All samples were water-clear and the contents of proteins and cells were in the normal range. In the following step, the sample was placed on the Bürker plate, and then 20 fields of 100 μm x 100 μm each were analyzed to determine the number and diameter of the particles. The optical analyzis was carried out using the Nikon microscope ECLIPSE 600 connected to a digital camera and a computer equipped with software Lucia v.4.6 by Laboratory Imaging company for picture analysis. The thickness of the Stern layer of the macromolecules suspended in the CSF was estimated by relating surrounding ions to these particles.

Results
This chapter deals with numerical results obtained from examination of 540 microscopic fields with CSF samples from 27 neurosurgical patients, 12 women and 15 men (mean age 56 years, age range 20 to 81 years). Demographic and clinical data of the patients are presented in Table 1. The observed microscopic pictures of the macroparticles suspended in the CSF are shown in Figure 1.
Biomolecules suspended in the CSF differ in size. In the optical microscopic pictures we recognized 724 particles, from 7 to 148 per patient. The averaged diameter of all observed particles was 5,1 ± 2,05 μm (mean ± SD), varied from 1,7 μm to 9,5 μm. The data in Figure   occasion we could observe the Brownian movements of the particles suspended in the CSF which are illustrated in Figure 3. Consecutive examples of macroparticles motions in the CSF are shown to reveal the effect of the thermal fluctuations of the electrolyte solvent on the macroparticles.
The large micro-objects observed in the CSF reflect macromolecules, both protein molecules and cells. Therefore, the largest particles with the diameter around 8 μm are most probably leukocytes and the smaller macroparticles are aggregated proteins or fragmented cells. The major protein in CSF is albumin with molecular radius of 36Ǻ and it has a strong negative charge. A negative charge carried on the membrane surface of the leukocytes equals -18 milivolt [5]. Generally, the main CSF macromolecules are electronegative.
The cerebrospinal fluid consists of different ions, both anions (Cl, HCO 3 , PO 4 ) and cations (Na, K, Ca 2 , Mg 2 ), with total ionic strength about 0,176. Among these ions, there is a markedly higher amount of Na + (0,138 mol/L) and Clˉ (0,119 mol/L) than others (about 0,001-0,04 mol/L) [1]. Based on a paper of Li and co-workers, for an electrolyte concentration is below 10 -4 mol/L there is no adsorption on the solid surface [14]. Therefore, only Na + and Clˉ ions concentrations in CSF are sufficient to produce the electric double layer.
Under the conditions described above, the electronegative macroparticles suspended in CSF are surrounded by positive sodium ions which attach firmly and build the Stern layer. This leads then to binding of negative chloride ions and hence to form the diffuse layer. The thickness of the Stern layer of macroparticles suspended in CSF equals the diameter of Na + ion and it is about 0,366 nm [15]. Figure  4 offers a schematic model of the electric double layer around the macroparticles suspended in the cerebrospinal fluid.

Discussion
Owing much to the fundamental concept of Smoluchowski electrokinetic theory, the double layer at the junction of two phases was introduced by Helmholtz in 1879 and extended by Gouy and Stern afterwards [8,16]. Both an aqueous electrolyte solution and the phospholipid cell surface or protein surface are dielectric media. Deriving from the concept of electrostatics theory, an electric field is formed on the membrane/protein surfaces [5]. As a consequence, the surface potential attracts ions of the opposite charge and repels ions   of the same charge. Basing on the standard Stern model, we could present the model of EDL of macromolecules suspended in CSF. In our approach, we excluded the water ions flux into the compact Stern layer, the concept which is now under a great considerations [17,18].
Microscopic examination is the gold standard to analyze biological particles suspended in CSF and this optical method allows for investigating the size of particles with diameter down to 0,4 μm [19]. We could analyze the shape and size of particles and observe the movements of the macroparticles occurring in the CSF. Macroparticles motions reflect the Brownian movements of the solvent nanoparticles invisible to optical microscopy. From the microscopic analyzis of the CSF samples the average diameter of the observed macroparticles is 5,1μm (from 1,7 μm to 9,5 μm).
Numerous biomedical studies have demonstrated that the thickness of the Stern layer is about 0,2-0,5 nm and is in relation to the radius of one molecule [20,21]. We stated that the macroparticles suspended in the CFS are surrounded by positive sodium ions forming the Stern layer which is strongly attached to the particle surface. Our studies proved that the thickness of the Stern layer equals the diameter of the Na + ion, i.e., 0,366 nm.