Adhesion forces between functionalized latex microspheres and protein-coated surfaces evaluated using colloid probe atomic force microscopy

Proteins are important in bacterial adhesion, but interactions at molecular-scales between proteins and specific functional groups are not well understood. The adhesion forces between four proteins [bovine serum albumin (BSA), protein A, lysozyme, and poly-d-lysine] and COOH, NH2 and OH-functionalized (latex) colloids were examined using colloid probe atomic force microscopy (AFM) as the function of colloid residence time (T) and solution ionic strength (IS). For three of the proteins, OH-functionalized colloids produced higher adhesion forces to proteins (2.6-30.5 nN; IS=1 mM, T=10s) than COOH- and NH2-functionalized colloids (1.6-6.8 nN). However, protein A produced the largest adhesion force (8.1+/-1.0 nN, T=10 s) with the COOH-functionalized colloid, demonstrating the importance of specific and unanticipated protein-functional group interactions. The NH2-functionalized colloid typically produced the lowest adhesion forces with all proteins, likely due to repulsive electrostatic forces and weak bonds for NH2-NH2 interactions. The adhesion force (F) between functionalized colloids and proteins consistently increased with residence time (T), and data was well fitted by F=ATn. The constant value of n=0.21+/-0.07 for all combinations of proteins and functionalized colloids indicated that water exclusion and protein rearrangement were the primary factors affecting adhesion over time. Adhesion forces decreased inversely with IS for all functional groups interacting with surface proteins, consistent with previous findings. These results demonstrate the importance of specific molecular-scale interactions between functional groups and proteins that will help us to better understand factors colloidal adhesion to surfaces.     

Interfacial phase transition of an environmentally responsive elastin biopolymer adsorbed on functionalized gold nanoparticles studied by colloidal surface plasmon resonance

The change in optical properties of colloidal gold upon aggregation has been used to develop an experimentally convenient colorimetric method to study the interfacial phase transition of an elastin-like polypeptide (ELP), a thermally responsive biopolymer. Gold nanoparticles, functionalized with a self-assembled monolayer (SAM) of mercaptoundecanoic acid onto which an ELP was adsorbed, exhibit a characteristic red color due to the surface plasmon resonance (SPR) of individual colloids. Raising the solution temperature from 10 degrees C to 40 degrees C thermally triggered the hydrophilic-to-hydrophobic phase transition of the adsorbed ELP resulting in formation of large aggregates due to interparticle hydrophobic interaction. Formation of large aggregates caused a change in color of the colloidal suspension from red to violet due to coupling of surface plasmons in aggregated colloids. The surface phase transition of the ELP was reversible, as seen from the reversible change in color upon cooling the suspension to 10 degrees C. The formation of colloidal aggregates due to the interfacial phase transition of adsorbed ELP was independently verified by dynamic light scattering of ELP-modified gold colloids as a function of temperature. Colloidal SPR provides a simple and convenient colorimetric method to study the influence of the solution environment, interfacial properties, and grafting method on the transition properties of ELPs and other environmentally responsive polymers at the solid-water interface.     

Investigation on the interaction between colloidal gold and human complement factor 4 at different pH by spectral methods

The interaction between colloidal gold and human complement factor 4 (human C4) at different pH was investigated by spectral methods, including absorption and resonance light-scattering spectrometry. According to the changes of color and absorption spectra of colloidal gold solution in presence of human C4, the interaction between colloidal gold and human C4 was quantitatively investigated using a semi-empirical "flocculation parameter". At the same time, the changes of resonance light-scattering spectra and transmission electron microscopy (TEM) images indicate that the aggregation of colloidal gold happens by electrostatic interaction in presence of human C4 in the pH range 5-6. However, the colloidal gold solution remains stable at pH >6 and pH <5 due to the repulsive electrostatic interaction between colloidal gold and human C4. The flocculation parameter is directly proportional to the concentration of human C4 in the range from 9.7 to 233.0 microgl(-1). In addition, the interactions between the colloidal gold and bovine serum albumin (BSA) as well as human serum albumin (HSA) were also investigated using the same methods. It was found that there was no aggregation of colloidal gold in presence of BSA and HSA in the pH range 5-6. However, when the pH of solution is 4, the aggregation of colloidal gold happens. Because BSA and HSA have different structure, the intensity of aggregation of colloidal gold in presence of BSA is greater than that in presence of HSA at pH 4.     

Strategies for the anchoring of metal complexes, clusters, and colloids inside nanoporous alumina membranes

Two complementary strategies are presented for the anchoring of molecular palladium complexes, of cobalt or platinum clusters or of gold colloids inside the nanopores of alumina membranes. The first consists in the one step condensation of an alkoxysilyl functional group carried by the metal complex with the hydroxy groups covering the surface of the membrane pores. Thus, using the short-bite alkoxysilyl-functionalized diphosphane ligands (Ph2P)2N(CH2)3Si(OMe)3 (1) and (Ph2P)2N(CH2)4SiMe2(OMe)] (2) derived from (Ph2P)2NH (dppa) (dppa bis(diphenylphosphanyl)amine), the palladium complexes [Pd(dmba)(kappa2-P,P-(Ph2P)2N(CH2)3Si(OMe)3)] Cl (3) and [Pd(dmba)[kappa2-P,P-(Ph2P)2N(CH2)4SiMe2(OMe)]]Cl (4) (dmba-H = dimethylbenzylamine). respectively, were tethered to the pore walls. After controlled thermal treatment. confined and highly dispersed palladium nanoparticles were formed and characterized by transmission electron microscopy (TEM). This method could not be applied to the cobalt cluster [Co4(CO)8(mu-dppa)[mu-P,P-(Ph2P)2N(CH2)4SiMe2(OMe)]] (7) owing to its too limited solubility. However, its anchoring was achieved by using the second method which consisted of first derivatizing the pore walls with 1 or 2. The covalent attachment of the diphosphane ligands provides a molecular anchor that allows subsequent reaction with the cluster [Co4(CO)10(mu-dppa)] 6 to generate anchored 7 and this step was monitored by UV/Vis spectroscopy. In addition, the presence of carbonyl ligands in the cluster provides for the first time a very sensitive spectroscopic probe in the IR region which confirms both cluster incorporation and the retaining of its molecular nature inside the membrane. The presence of the bridging dppa ligand in 6 provides additional stabilization and accounts for the selectivity of the procedure. Using this method, platinum clusters (diameter ca. 2 nm) and gold colloids (diameter ca. 13 nm) were immobilized after passing their solution through the functionalized membrane pores. The resulting membranes were characterized by TEM which demonstrated the efficiency of the complexation and showed the high dispersion of the metal loading. The successful application of these methods has demonstrated that nanoporous alumina membranes are not only unique supports to incorporate metal complexes, clusters, or colloids but can also be regarded as functional matrices or microreactors, thus opening new fields for applications.     

Internal and free energy in a pair of like-charged colloids: Monte Carlo simulations

The effective interaction between two colloidal particles in a bath of monovalent co- and counterions is studied by means of lattice Monte Carlo simulations with the primitive model. The internal electrostatic energy as a function of the colloid distance is studied fixing the position of the colloids. The free energy of the whole system is obtained introducing a bias parabolic potential, that allows us to sample efficiently small separations between the colloidal particles. For small charges, both the internal and free energy increase when the colloids approach each other, resulting in an effective repulsion driven by the electrostatic repulsion. When the colloidal charge is large enough, on the other hand, the colloid-ion coupling is strong enough to form double layers. The internal energy in this case decreases upon approaching the colloids because more ions enter the double layer. This attractive contribution to the interaction between the colloids is stronger for larger charges and larger ionic concentrations. However, the total free energy increases due to the loss of ionic entropy, and resulting finally in a repulsive interaction potential driven by the entropic contributions. The loss of ionic entropy can be almost quantitatively reproduced with the ideal contribution, the same level of approximation as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The overall behavior is captured by the DLVO theory qualitatively, and a comparison is made with the functional form predicted by the theory, showing moderate agreement.     

Sterically stabilized silica colloids: Radical grafting of poly(methyl methacrylate) and hydrosilylative grafting of silicones to functionalized silica

Colloidal silica sols having a narrow dispersity, prepared by the ammonia-catalyzed hydrolysis of Si(OEt)₄, were functionalized by reaction with vinyltrimethoxysilane (H₂C?CHSi(OMe)₃) or methacryloxypropyltri-methoxysilane (H₂C?CMeCO₂(CH₂)₃Si(OMe)₃. The electrostatically stabilized colloids were stable in acetone and dimethylformamide. Radical polymerization of methyl methacrylate in the presence of either type of functionalized particle led to particles with surfacegrafted poly(methyl methacrylate) (PMMA). The efficiency of polymer grafting was shown to be related to the nature of the functional groups. The PMMA-modified, sterically stabilized particles were colloidally stable in solvents ranging from acetone to toluene but unstable in water or hexane. The vinyl functionalized silica was alternatively reacted with HSiMe₂-terminated silicones in a platinum-catalyzed hydrosilylation. The resultant sterically stabilized particles were stable in hexane. It was thus possible to convert the unmodified silica to organo-functionalized silica and finally to polymer-grafted silica while maintaining colloidal stability. During the course of these modifications, the mechanism for colloidal stability changed from electrostatic to steric stabilization.     

Preparation of Amino-functionalized Multiwall Carbon Nanotube/Gold Nanoparticle Composites

Multiwall carbon nanotubes (MWNT) were modified orderly with carboxyl groups and amino groups. The MWNT/gold nanoparticle composites were formed when the amino‐functionalized MWNT was interacted with gold colloids. The functionalized MWNT was characterized using Fourier transform infrared spectroscopy and X‐ray photoelectron spectroscopy. The amino‐functionalized MWNT allows further attaching gold nanoparticles through electrostatic interaction between the negatively charged gold nanoparticles and amino groups on the surface of the MWNT. The composite of gold nanoprticles and amino‐functionalized MWNT was characterized by transmission electron microscopy. This method decorating carbon nanotubes can be used to identify the location of functional groups, i.e. defect sites on carbon nanotubes.     

Photochemical formation of silver-gold (Ag?Au) composite colloids in solutions containing sodium alginate

Photochemical formation of colloidal silver, colloidal gold and silver-gold (Ag-Au) composite colloids under mild conditions has been studied. Irradiation of either aqueous AgCIO₄ or HAuCI₄ solution in the presence of sodium alginate (SA) with 253.7 nm light yielded colloidal silver or gold, whose particle diamter was 10-30 nm or 40-60 nm, respectively. The Ag-Au composite colloids consisting of mixtures of silver and gold domains (particle diameter 30-150 nm) have been prepared and their extinction spectra have been examined on the basis of a conventional Mie theory in combination with an effective medium theory to estimate the optical constants of these colloids. It has been shown that the extinction spectra of the Ag-Au composite colloids are completely different from those of Ag-Au alloy colloids, in that the former have two extinction maxima close to the colloidal extinction bands of pure silver and gold, in contrast to a single extinction maximum of the latter. The importance of natural, high-molecular carboxylic acids such as alginic acid in the photochemical formation of metal colloids and thin films has been stressed.     

Probing BSA binding to citrate-coated gold nanoparticles and surfaces

The interaction of bovine serum albumin (BSA) with gold colloids and surfaces was studied using zeta-potential and quartz crystal microbalance (QCM) measurements, respectively, to determine the surface charge and coverage. The combination of these two measurements suggests that BSA binding to gold nanoparticles and gold surfaces occurs by an electrostatic mechanism when citrate is present. The binding of BSA to bare gold is nearly two times greater than the binding of BSA to a citrate-coated gold surface, suggesting that protein spreading (denaturation) on the surface may occur followed by secondary protein binding. On the other hand, binding to citrate-coated gold surfaces can be fit to a Langmuir isotherm model to obtain a maximum surface coverage of (3.7 +/- 0.2) x 10(12) molecules/cm(2) and a binding constant of 1.0 +/- 0.3 microM(-1). The zeta-potential measurements show that the stabilization of colloids by BSA has a significant contribution from a steric mechanism because the colloids are stable, even at their isoelectric point (pI approximately 4.6). To be consistent with the observed phenomena, the electrostatic interactions between BSA and citrate must consist of salt-bridges, for example, of the carboxylate-ammonium type, between the citrate and the lysine on the protein surface. The data support the role of strong electrostatic binding but do not exclude contributions from steric or hydrophobic interactions with the surface adlayer.     

The Effect of Solute Concentration on Equilibrium Partitioning in Polymeric Gels

The effect of solute concentration on the equilibrium partitioning of sphere-like, colloidal solutes in stiff polymer hydrogels is examined theoretically and experimentally. The theoretical development is a statistical mechanics approach, and allows quantitative calculations to be performed to determine the concentration-dependent partition coefficient correct to first order in solute concentration at specific surface charge densities. The theory predicts that repulsive steric and/or electrostatic solute-fiber interactions exclude solute from the gel phase, but that repulsive solute-solute interactions cause partitioning into the gel to increase with increasing solute concentration. These trends are enhanced for larger solutes, increased fiber volume fractions, or stronger electrostatic repulsion. Partition coefficients have also been measured for two proteins, bovine serum albumin (BSA) and alpha-lactalbumin (ALA), in a system consisting of a salt solution and cubes of agarose hydrogel. To investigate the effect of electrostatic interactions, the experiments were performed at 0.15 M KCl and 0.01 M KCl. The theory underpredicts the strong electrostatic repulsion between BSA macromolecules at the lower ionic strength. The experimental results for ALA show the influence of an attractive interaction between the protein macromolecules, in addition to hard-sphere repulsive and electrostatic interactions. Copyright 2001 Academic Press.     

DNA-mediated phase behavior of microsphere suspensions

We have constructed a phase diagram for DNA-modified microsphere suspensions based on experimental and theoretical studies. The system is comprised of 1 microm red fluorescent colloids functionalized with strands of an identical oligonucleotide sequence and 1 microm green fluorescent colloids functionalized with the complementary sequence. Keeping the suspension composition and temperature fixed, the phase behavior of colloidal mixtures was studied as a function of salt and oligonucleotide concentration. We observed a colloidal fluid phase of dispersed, single particles at low salt concentrations and low DNA densities. We attribute this colloidal fluid phase to unfavorable hybridization conditions. With increasing salt or hybridizing oligonucleotide concentrations, we observed phase transitions of fluid --> fluid + aggregates --> aggregates due to an increase in duplex affinity, duplex number, or both. Computational analysis assigns a 4 kBT attraction between pairs of complementary microspheres at the destabilizing fluid --> fluid + aggregates transition.     

Protein-resistant self-assembled monolayers on gold with latent aldehyde functions

In the present study, oligo(ethylene glycol) (OEG)-linked alkanethiols were synthesized which carry a vicinal diol on one end of the OEG chain. After self-assembled monolayer (SAM) formation on gold, the vicinal diols were converted into aldehyde functions by exposure to aqueous NaIO4, as previously used for SAMs with OEG chains buried in the center of the SAM [Jang et al. Nano Lett. 2003, 3, 691-694]. Mixed SAMs with latent aldehydes on 5% of the OEG termini showed high protein resistance, which greatly slowed the kinetics of protein coupling on the time scale of minutes. Small bioligands (such as biocytin hydrazide) or small heterobifunctional crosslinkers (maleimidopropionyl hydrazide, pyridyldithiopropionyl hydrazide) with hydrazide functions were efficiently bound to the aldehyde functions on the SAM, providing for specific capture of streptavidin or for fast covalent binding of proteins with free thiols or maleimide functions, respectively. In conclusion, OEG-terminated SAMs with latent aldehydes serve as protein-resistant sensor surfaces which are easily functionalized with small ligands or with heterobifunctional crosslinkers to which the bait molecule is attached in a subsequent step.     

Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.     

Fast protein detection using absorption properties of gold nanoparticles

In this study we describe the use of gold nanoparticles as a fast detection system for the sensitive analysis of proteins. The immunological method allows for protein analysis at the nanogram level, as required for clinical diagnosis. Initially a test protein is used for the development of the assay. The system is subsequently adopted for alpha-fetoprotein, which is a relevant tumor marker. This work demonstrates that antibody functionalized gold nanoparticles can be used for the detection of proteins by forming gold nanoparticle aggregates. The influence of the size of the gold nanoparticles on the sensitivity of the assay is investigated in the range from 20-60 nm particles; the larger particles show here the highest relative changes. The formation of antigen-gold nanoparticle aggregates is detected by an increase in hydrodynamic diameter by dynamic light scattering (DLS). UV/Vis spectroscopy also allows assay monitoring by quantifying the red shift of the plasmon resonance wavelength. Alpha-fetoprotein can be analysed in the concentration range of 0.1-0.4 μg ml(-1). The influence of pH, ionic strength and ratio of sample to Au-NP solution is studied. With this method, the protein AFP can be rapidly detected as demanded for clinical diagnosis.     

Control of gold nanoparticle aggregates by manipulation of interparticle interaction

The size of gold nanoparticle aggregates was controlled by manipulating the interparticle interaction. To manipulate the interparticle interaction of gold nanoparticles prepared by citrate reduction, we applied the substitutive adsorption of benzyl mercaptan on the particle surface in the absence of the cross-linking effect. Various experimental techniques such as UV-vis absorption spectroscopy, surface-enhanced Raman scattering, quasi-elastic light scattering, and zeta-potential measurement were used to characterize the nanoparticle aggregates. Our results suggest that the replacement of the trivalent citrate ions adsorbed on the nanoparticle surface with monovalent benzyl mercaptan ions should destabilize the particles, causing aggregation and hence the increase in the size of nanoparticle aggregates. These experimental results were successfully rationalized by the classical DLVO (Derjaguin-Landau-Vervey-Overbeek) theory that describes the interparticle interaction and colloidal stability in solution. Our findings suggest that the control of surface potential is crucial in the design of stable gold nanoparticle aggregates.     

The nanoscale description of acid penetration to the gold colloids encapsulated in silica sol–gel matrix

Various sizes of gold nano colloidal particles ranging from 5 nm to 100 nm of size were encapsulated in a silica based sol–gel, and these surfaces were exposed to a pH 1 acid solution. This enabled us to observe the process of solvent intrusion and interaction with gold colloids by the absorption spectrum as a function of time. The rate was analyzed by a single exponential analytical function, and the maximum rate was found for gold colloid of 15 nm size. The least acid interaction and colour change was observed for the size of 60 nm. It was speculated that the surface of these gold colloids were homogeneously covered by the sodium tetra-borate buffer which insulated silica gel layer, thus avoiding direct contact of the acid with the surface of the gold colloid. This study confirmed that the nano scale dopant size affects the rate of solvent penetration into a sol–gel cavity.     

Dense aqueous colloidal gold nanoparticles prepared from highly concentrated precursor solution

Gold nanoparticles were fabricated by reduction of highly concentrated Au(III) ions (200 mM) with casein proteins from milk. The gold nanoparticles were converted to nanoparticle-powders after washing and subsequent vacuum drying without aggregation. The nanoparticle-powders completely re-dispersed in aqueous solution, and stable colloidal gold nanoparticles were obtained. UV-vis extinction spectra and dynamic light scattering (DLS) measurements revealed that large assemblies (size, ca. 3 μm) and subaggregates (size, <0.5 μm) composed of gold nanoparticle-casein protein chain-Au(III) ion were dynamically formed and disintegrated over the course of the growth of the gold nanoparticles. Fourier transform infrared (FT-IR) spectra indicated conformational changes of casein proteins induced by the interaction of casein protein-Au(III) ion and -gold nanoparticle. Finally, rapid, one-pot, and highly concentrated synthetic procedures of gold and silver nanoparticle powders protected by casein (mean diameters below 10 nm) were successfully developed using 3-amino-1-propanol aqueous solutions as reaction media. Dense colloidal gold (40 g L(-1)) and silver (22 g L(-1)) nanoparticle aqueous solutions were obtained by re-dispersing the metal nanoparticle powders.     

Reversible Assembly of Microgels by Metallo‐Supramolecular Chemistry

The combination of supramolecular chemistry and soft colloids as microgels represents an ambitious way to develop multi‐versatile colloidal assemblies. Hereafter, terpyridine‐functionalized poly(N‐isopropylacrylamide) (PNiPAM) microgel building blocks are shown to undergo an assemble–freeze–disassemble process. The microgel assemblies, which are controlled by monitoring the attractive and repulsive potentials between the soft colloidal particles, are then frozen by forming inter‐particle metal–terpyridine bis‐complexes upon addition of the metallic cation (such as Fe^II, Co^II). By oxidation of the metal–terpyridine bis‐complex links, the aggregates open up, which is due to the complex dissociation releasing the connected particles in the form of single microgels. We extended our work to the development of 1D filaments and 2D membranes materials made of soft particles connected via supramolecular chemistry.     

Functionalized multiwall carbon nanotube/gold nanoparticle composites

Multiwall carbon nanotubes (MWCNTs) were chemically oxidized in a mixture of sulfuric acid and nitric acid (3:1) while being ultrasonicated. The effect of oxidative ultrasonication at room temperature on development of functional groups on the carbon nanotubes was investigated. The dispersability and the carboxylic acid group concentration of functionalized MWCNTs (fMWNTs) varied with reaction time. The concentration of carboxylic acid groups on fMWNTs increased from 4 x 10(-4) mol/g of fMWNTs to 1.1 x 10(-3) mol/g by doubling the treatment period from 4 to 8 h. The colloidal stability of aqueous fMWCNTs dispersions was enhanced through elongated oxidation. fMWCNTs that were reacted longer than 4 h did not precipitate in aqueous media for at least 24 h. The layer-by-layer self-assembly of polyelectrolytes on fMWCNTs was characterized by zeta potential measurements. The zeta potential of fMWCNTs changed from negative charge to positive charge when cationic polyelectrolytes were self-assembled on their surface. With addition of anionic polyelectrolytes, cationic polyelectrolyte coated fMWCNTs showed the expected charge reversal as expected for multilayer self-assembly. Complex formation of positively charged gold nanoparticles and negatively charged fMWCNTs was achieved with and without polyelectrolyte coatings by electrostatic interaction. The complex formation was characterized by high-resolution transmission electron microscopy and energy-dispersive X-ray spectroscopy. The here found complex formation of positively charged colloidal gold and defect sites on fMWNTs indicates the location of functional groups on carbon nanotubes. It is suggested that positively charged colloids such as gold nanoparticles could be used for detection of defect sites on carbon nanotubes.     

Versatile application of indirect Fourier transformation to structure factor analysis: from X-ray diffraction of molecular liquids to small angle scattering of protein solutions

We highlight versatile applicability of a structure-factor indirect Fourier transformation (IFT) technique, hereafter called SQ-IFT. The original IFT aims at the pair distance distribution function, p(r), of colloidal particles from small angle scattering of X-rays (SAXS) and neutrons (SANS), allowing the conversion of the experimental form factor, P(q), into a more intuitive real-space spatial autocorrelation function. Instead, SQ-IFT is an interaction potential model-free approach to the 'effective' or 'experimental' structure factor to yield the pair correlation functions (PCFs), g(r), of colloidal dispersions like globular protein solutions for small-angle scattering data as well as the radial distribution functions (RDFs) of molecular liquids in liquid diffraction (LD) experiments. We show that SQ-IFT yields accurate RDFs of liquid H(2)O and monohydric alcohol reflecting their local intermolecular structures, in which q-weighted structure function, qH(q), conventionally utilized in many LD studies out of necessity of performing direct Fourier transformation, is no longer required. We also show that SQ-IFT applied to theoretically calculated structure factors for uncharged and charged colloidal dispersions almost perfectly reproduces g(r) obtained as a solution of the Ornstein-Zernike (OZ) equation. We further demonstrate the relevance of SQ-IFT in its practical applications, using SANS effective structure factors of lysozyme solutions reported in recent literatures which revealed the equilibrium cluster formation due to coexisting long range electrostatic repulsion and short range attraction between the proteins. Finally, we present SAXS experiments on human serum albumin (HSA) at different ionic strength and protein concentration, in which we discuss the real space picture of spatial distributions of the proteins via the interaction potential model-free route.