Mechanism of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase

Thermal denaturation and aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been studied using differential scanning calorimetry (DSC), dynamic light scattering (DLS), and analytical ultracentrifugation. The maximum of the protein thermal transition (T(m)) increased with increasing the protein concentration, suggesting that the denaturation process involves the stage of reversible dissociation of the enzyme tetramer into the oligomeric forms of lesser size. The dissociation of the enzyme tetramer was shown by sedimentation velocity at 45 degrees C. The DLS data support the mechanism of protein aggregation that involves a stage of the formation of the start aggregates followed by their sticking together. The hydrodynamic radius of the start aggregates remained constant in the temperature interval from 37 to 55 degrees C and was independent of the protein concentration (R(h,0) approximately 21 nm; 10 mM sodium phosphate, pH 7.5). A strict correlation between thermal aggregation of GAPDH registered by the increase in the light scattering intensity and protein denaturation characterized by DSC has been proved.     

Mechanism of chaperone-like activity. Suppression of thermal aggregation of betaL-crystallin by alpha-crystallin

Thermal denaturation and aggregation of beta(L)-crystallin from bovine lens have been studied using differential scanning calorimetry (DSC) and dynamic light scattering (DLS). According to the DLS data, the distribution of the beta(L)-crystallin aggregates by their hydrodynamic radius (R(h)) remains monomodal to the point of precipitating aggregates (sodium phosphate, pH 6.8; 100 mM NaCl; 60 degrees C). The size of the start aggregates (R(h,0)) and duration of the latent stage (t(0)) leading to the formation of the start aggregates have been determined from the light scattering intensity versus the hydrodynamic radius plots and the dependences of R(h) on time. The R(h,0) value remains constant at variation of the beta(L)-crystallin concentration, whereas the t(0) value increases with diminishing beta(L)-crystallin concentration. The suppression of beta(L)-crystallin aggregation by alpha-crystallin is connected with the decrease in the R(h,0) value and increase in the t(0) value. In the presence of alpha-crystallin the aggregate population is split into two components. The first component is represented by stable aggregates whose size remains constant in time. The aggregates of the other kind grow until they reach the size characteristic of aggregates prone to precipitation. The DSC data show that alpha-crystallin has no appreciable influence on thermal denaturation of beta(L)-crystallin.     

Kinetics of thermal aggregation of glycogen phosphorylase b from rabbit skeletal muscle: mechanism of protective action of alpha-crystallin

The kinetics of thermal aggregation of glycogen phosphorylase b (Phb) from rabbit skeletal muscle have been studied by dynamic light scattering (0.08M Hepes, pH 6.8, containing 0.1M NaCl; 48 degrees C). The hydrodynamic radius of the start aggregates determined from the initial linear parts of the dependences of the hydrodynamic radius (R(h)) on time was found to be 16.7 +/- 1.0 nm. At rather high values of time, the R(h) value for the protein aggregates becomes proportional to t(1/1.8) = t(0.56) suggesting that the aggregation process proceeds in the regime of diffusion-limited cluster-cluster aggregation. In the presence of alpha-crystallin, a protein possessing the chaperone-like activity, the process of protein aggregation switches to the regime of reaction-limited cluster-cluster aggregation as indicated by the exponential dependence of the R(h) value on time. It was shown that the addition of alpha-crystallin raises the rate of thermal inactivation of Phb. These data in combination with the results of the study of interaction of Phb with alpha-crystallin by analytical ultracentrifugation suggest that alpha-crystallin interacts with the intermediates of unfolding of the Phb molecule.     

The study of amorphous aggregation of tobacco mosaic virus coat protein by dynamic light scattering

The kinetics of heat-induced and cetyltrimethylammonium bromide induced amorphous aggregation of tobacco mosaic virus coat protein in Na(+)/Na(+) phosphate buffer, pH 8.0, have been studied using dynamic light scattering. In the case of thermal aggregation (52 degrees C) the character of the dependence of the hydrodynamic radius (R(h)) on time indicates that at certain instant the population of aggregates is split into two components. The size of the aggregates of one kind remains practically constant in time, whereas the size of aggregates of other kind increases monotonously in time reaching the values characteristic of aggregates prone to precipitation (R(h)=900-1500 nm). The construction of the light scattering intensity versus R(h) plots shows that the large aggregates (the start aggregates) exist in the system at the instant the initial increase in the light scattering intensity is observed. For thermal aggregation the R(h) value for the start aggregates is independent of the protein concentration and equal to 21.6 nm. In the case of the surfactant-induced aggregation (at 25 degrees C) no splitting of the aggregates into two components is observed and the size of the start aggregates turns out to be much larger (107 nm) than on the thermal aggregation. The dependence of R(h) on time for both heat-induced aggregation and surfactant-induced aggregation after a lapse of time follows the power law indicating that the aggregation process proceeds in the kinetic regime of diffusion-limited cluster-cluster aggregation. Fractal dimension is close to 1.8. The molecular chaperone alpha-crystallin does not affect the kinetics of tobacco mosaic virus coat protein thermal aggregation.     

Effect of α-crystallin on thermal aggregation of glycogen phosphorylase <Emphasis Type="Italic">b</Emphasis> from rabbit skeletal muscle

Thermal aggregation of rabbit skeletal muscle glycogen phosphorylase b (Phb) has been investigated using dynamic light scattering under conditions of a constant rate of temperature increase (1 K/min). The linear behavior of the dependence of the hydrodynamic radius on temperature for Phb aggregation is consistent with the idea that thermal aggregation of proteins proceeds in the kinetic regime wherein the rate of aggregation is limited by diffusion of the interacting particles (the regime of "diffusion-limited cluster-cluster aggregation"). In the presence of alpha-crystallin, a protein exhibiting chaperone-like activity, the dependence of the hydrodynamic radius on temperature follows the exponential law; this suggests that the aggregation process proceeds in the kinetic regime where the sticking probability for colliding particles becomes lower than unity (the regime of "reaction-limited cluster-cluster aggregation"). Based on analysis of the ratio between the light scattering intensity and the hydrodynamic radius of Phb aggregates, it has been concluded that the addition of alpha-crystallin results in formation of smaller size starting aggregates. The data on differential scanning calorimetry indicate that alpha-crystallin interacts with the intermediates of the unfolding process of the Phb molecule. The proposed scheme of thermal denaturation and aggregation of Phb includes the stage of reversible dissociation of dimers of Phb into monomers, the stage of the formation of the starting aggregates from the denatured monomers of Phb, and the stage of the sticking of the starting aggregates and higher order aggregates. Dissociation of Phb dimer into monomers at elevated temperatures has been confirmed by analytical ultracentrifugation.     

Comparative Analysis of the Effects of α-Crystallin and GroEL on the Kinetics of Thermal Aggregation of Rabbit Muscle Glyceraldehyde-3-Phosphate Dehydrogenase

Effects of α-crystallin and GroEL on the kinetics of thermal aggregation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been studied using dynamic light scattering and analytical ultracentrifugation. The analysis of the initial parts of the dependences of the hydrodynamic radius of protein aggregates on time shows that in the presence of α-crystallin or GroEL the kinetic regime of GAPDH aggregation is changed from the regime of diffusion-limited cluster–cluster aggregation to the regime of reaction-limited cluster–cluster aggregation, wherein the sticking probability for the colliding particles becomes lower the unity. In contrast to α-crystallin, GroEL does not interfere with formation of the start aggregates which include denatured GAPDH molecules. On the basis of the analytical ultracentrifugation data the conclusion has been made that the products of dissociation of GAPDH and α-crystallin or GroEL play an important role in the interactions of GAPDH and chaperones at elevated temperatures.     

Evidence for the formation of start aggregates as an initial stage of protein aggregation

The kinetics of thermal aggregation of glycogen phosphorylase b and glyceraldehyde 3-phosphate dehydrogenase from rabbit skeletal muscles were studied using dynamic light scattering. Use of high concentrations of the enzymes (1-3 mg/ml) provided a simultaneous registration of the native enzyme forms and protein aggregates. It was shown that initially registered aggregates (start aggregates) were large-sized particles. The hydrodynamic radius of the start aggregates was about 100 nm. The intermediate states between the native enzyme forms and start aggregates were not detected. The initial increase in the light scattering intensity is connected with accumulation of the start aggregates, the size of the latter remaining unchanged. From a certain moment in time aggregates of higher order, formed as a result of sticking of the start aggregates, make a major contribution to the enhancement of the light scattering intensity.     

Self-similarity properties of alpha-crystallin supramolecular aggregates.

The supramolecular aggregation of alpha-crystallin, the major protein of the eye lens, was investigated by means of static and dynamic light scattering. The aggregation was induced by generating heat-modified alpha-crystallin forms and by stabilizing the clusters with calcium ions. The kinetic pattern of the aggregation and the structural features of the clusters can be described according to the reaction limited cluster-cluster aggregation theory previously adopted for the study of colloidal particles aggregation systems. Accordingly, the average mass and the hydrodynamic radius of alpha-crystallin supramolecular aggregates grow exponentially in time. The structure factor of the clusters is typical of fractal aggregates. A fractal dimension df approximately 2.15 was determined, indicating a low probability of sticking together of the primitive aggregating particles. As a consequence, the slow-forming clusters assemble a rather compact structure. The basic units forming the fractal aggregates were found to have a radius about twice (approximately 17 nm) that of the native protein and 5.3 times its size, which is consistent with an intermediate molecular assembly corresponding to the already known high molecular weight forms of alpha-crystallin.     

Thermo- and photoinduced aggregation of alpha-crystallin

Some properties of bovine alpha-crystallin, in particular its thermo- and photoaggregation, were studied by fluorescent spectroscopy of tryptophan residues and the probe 8-anilino-1-naphthalenesulfonate and light scattering. The effective diameter of a globule of native alpha-crystallin was 90 A, as estimated from the data on the polarization and lifetime of 8-anilino-1-naphthalenesulfonate using the Levshin-Perren equation, and increases at an aggregation of no less than 140 A. The increase in the intensity of tryptophan fluorescence of alpha-crystallin during its thermo- and photodenaturation with the formation of aggregates is due to local conformational changes in the surroundings of tryptophan residues and light scattering. Tryptophan residues are buried in the interior of the aggregates. The thermoaggregation of the protein occurs not only at high temperatures. By approximating the experimental time dependence of slow spontaneous aggregation to the range of large times, the time of denaturation aggregation t(e) was found. For alpha-crystallin (at a concentration of 0.8 mg/ml in phosphate buffer at pH 8.4), t(e) at 70 degrees C is 100 h. This approach can be used in finding t(e) for any protein during its thermal treatment or long-term storage.     

Self-assembly of melanin studied by laser light scattering

The unknown molecular weight and chemical structure of melanin place the study of these pigments outside the range of the classical biochemical techniques; thus in this paper the problem of characterizing these heterogeneous biopolymers was approached by means of light scattering techniques, static and dynamic. The static technique allowed us to identify the macromolecular properties (MW and R(g)(2)(1/2)) of melanin extracted from sepia inksac and of two synthetic analogues: L-Dopa melanin obtained by autooxidation and by enzymatic oxidation by Tyrosinase. By dynamic light scattering (DLS), the hydrodynamic radius R(h) was measured to monitor the temporal behaviour of the polymerization and aggregation processes and R(h) variation by changing the chemical constraints of the polymerization medium, such as pH and ionic strength. The fractal dimension d of the aggregates of melanin, both natural and synthetic, in the past only recognized during the aggregation of the synthetic one by lowering the pH of the medium, was a useful parameter to further investigate and compare the structure of melanin granules of differing origins, revealing for the natural sample, a structure with clusters that are spherical, not largely hydrated and self-assembled, following a reaction limited aggregation kinetics (d=2.38).     

Mechanism of thermal aggregation of yeast alcohol dehydrogenase I: role of intramolecular chaperone

Kinetics of thermal aggregation of yeast alcohol dehydrogenase I (yADH) have been studied using dynamic light scattering at a fixed temperature (56 degrees C) and under the conditions where the temperature was elevated at a constant rate (1 K/min). The initial parts of the dependences of the hydrodynamic radius on time (or temperature) follow the exponential law. At rather high values of time splitting of the population of aggregates into two components occurs. It is assumed that such peculiarities of the kinetics of thermal aggregation of yADH are due to the presence of a sequence -YSGVCHTDLHAWHGDWPLPVK- in the polypeptide chain possessing chaperone-like activity. Thermodynamic parameters for thermal denaturation of yADH have been calculated from the differential scanning calorimetry data.     

Glycation by ascorbic acid oxidation products leads to the aggregation of lens proteins

Previous studies from this laboratory have shown that there are striking similarities between the yellow chromophores, fluorophores and modified amino acids released by proteolytic digestion from calf lens proteins ascorbylated in vitro and their counterparts isolated from aged and cataractous lens proteins. The studies reported in this communication were conducted to further investigate whether ascorbic acid-mediated modification of lens proteins could lead to the formation of lens protein aggregates capable of scattering visible light, similar to the high molecular aggregates found in aged human lenses. Ascorbic acid, but not glucose, fructose, ribose or erythrulose, caused the aggregation of calf lens proteins to proteins ranging from 2.2 x 10(6) up to 3.0 x 10(8 )Da. This compared to proteins ranging from 1.8 x 10(6) up to 3.6 x 10(8 )Da for the water-soluble (WS) proteins isolated from aged human lenses. This aggregation was likely due to the glycation of lens crystallins because [U-(14)C] ascorbate was incorporated into the aggregate fraction and because NaCNBH(3), which reduces the initial Schiff base, prevented any protein aggregation. Reactions of ascorbate with purified crystallin fractions showed little or no aggregation of alpha-crystallin, significant aggregation of beta(H)-crystallin, but rapid precipitation of purified beta(L)- and gamma-crystallin. The aggregation of lens proteins can be prevented by the binding of damaged crystallins to alpha-crystallin due to its chaperone activity. Depending upon the ratios between the components of the incubation mixtures, alpha-crystallin prevented the precipitation of the purified beta(L)- and gamma-crystallin fractions during ascorbylation. The addition of at least 20% of alpha-crystallin by weight into glycation mixtures with beta(L)-, or gamma-crystallins completely inhibited protein precipitation, and increased the amount of the high molecular weight aggregates in solution. Static and dynamic light scattering measurements of the supernatants from the ascorbic acid-modified mixtures of alpha- and beta(L)-, or gamma-crystallins showed similar molar masses (up to 10(8 )Da) and hydrodynamic diameter (up to 80( )nm). These data support the hypothesis, that if the lens reducing environment is compromised, the ascorbylation of lens crystallins can significantly change the short range interactions between different classes of crystallins leading to protein aggregation, light scattering and eventually to senile cataract formation.     

How α-crystallin prevents the aggregation of insulin

Using steady-state, polarized, and phase-modulation fluorometry, the dithiothreitol-induced denaturation of insulin and formation of its complex with alpha-crystallin in solution were studied. Prevention of the aggregation of insulin by alpha-crystallin is due to formation of chaperone complexes, i.e. interaction of chains of the denatured insulin with alpha-crystallin. The conformational changes in alpha-crystallin that occur during complex formation are rather small. It is unlikely that N-termini are directly involved in the complex formation. The 8-anilino-1-naphthalenesulfonate (ANS) is not sensitive to the complex formation. ANS emits mainly from alpha-crystallin monomers, dimers, and tetramers, but not from oligomers or aggregates. The possibility of highly sensitive detection of aggregates by light scattering using a spectrofluorometer with crossed monochromators is demonstrated.     

Kinetics of Thermal Denaturation and Aggregation of Bovine Serum Albumin

Thermal aggregation of bovine serum albumin (BSA) has been studied using dynamic light scattering, asymmetric flow field-flow fractionation and analytical ultracentrifugation. The studies were carried out at fixed temperatures (60°C, 65°C, 70°C and 80°C) in 0.1 M phosphate buffer, pH 7.0, at BSA concentration of 1 mg/ml. Thermal denaturation of the protein was studied by differential scanning calorimetry. Analysis of the experimental data shows that at 65°C the stage of protein unfolding and individual stages of protein aggregation are markedly separated in time. This circumstance allowed us to propose the following mechanism of thermal aggregation of BSA. Protein unfolding results in the formation of two forms of the non-native protein with different propensity to aggregation. One of the forms (highly reactive unfolded form, U_hr) is characterized by a high rate of aggregation. Aggregation of U_hr leads to the formation of primary aggregates with the hydrodynamic radius (R_h,1) of 10.3 nm. The second form (low reactive unfolded form, U_lr) participates in the aggregation process by its attachment to the primary aggregates produced by the U_hr form and possesses ability for self-aggregation with formation of stable small-sized aggregates (A_st). At complete exhaustion of U_lr, secondary aggregates with the hydrodynamic radius (R_h,2) of 12.8 nm are formed. At 60°C the rates of unfolding and aggregation are commensurate, at 70°C the rates of formation of the primary and secondary aggregates are commensurate, at 80°C the registration of the initial stages of aggregation is complicated by formation of large-sized aggregates.     

Aggregation of a multidomain protein: A coagulation mechanism governs aggregation of a model IgG1 antibody under weak thermal stress

Using an IgG1 antibody as a model system, we have studied the mechanisms by which multidomain proteins aggregate at physiological pH when incubated at temperatures just below their lowest thermal transition. In this temperature interval, only minor changes to the protein conformation are observed. Light scattering consistently showed two coupled phases: an initial fast phase followed by several hours of exponential growth of the scattered intensity. This is the exact opposite of the lag‐time behavior typically observed in protein fibrillation. Dynamic light scattering showed the rapid formation of an aggregate species with a hydrodynamic radius of about 25 nm, which then increased in size throughout the experiment. Theoretical analysis of our light scattering data showed that the aggregate number density goes through a maximum in time providing compelling evidence for a coagulation mechanism in which aggregates fuse together. Both the analysis as well as size‐exclusion chromatography of incubated samples showed the actual increase in aggregate mass to be linear and reach saturation long before all molecules had been converted to aggregates. The CH2 domain is the only domain partly unfolded in the temperature interval studied, suggesting a pivotal role of this least stable domain in the aggregation process. Our results show that for multidomain proteins at temperatures below their thermal denaturation, transient unfolding of a single domain can prime the molecule for aggregation, and that the formation of large aggregates is driven by coagulation.     

Detection of monodisperse aggregates of a recombinant amelogenin by dynamic light scattering

Recombinant murine amelogenins M179 and M166 were expressed in Escherichia coli and purified. The aggregation properties of these amelogenins have been investigated in aqueous solutions as well as acetonitrile-containing solutions using dynamic light scattering. Dynamic light scattering provides direct measurement of the translational diffusion coefficient and hydrodynamic radius, and of an estimate of the molecular weight. Polydispersity and statistical parameters of how to interpret the analysis are also provided. Amelogenin aggregation was examined in solutions of a range of pH, ionic strengths, and protein concentrations. It was shown that at pH 7.8–8 and ionic strength of 0.02–0.05M the M179 molecules form monodispersed aggregates with hydrodynamic radii ranging from 15 to 19 nm. Analysis of hydrodynamic radii and size distribution of M179 aggregates in acetonitrile-containing solvents compared to that in aqueous solutions indicated a primary role for hydrophobic interactions in the association process of amelogenin molecules to form aggregates. Comparison between the aggregates formed by M179 and M166, which lacks the hydrophilic carboxy-terminal 13 residue sequence of M179, suggested that the self-assembly of amelogenin molecules to form stable and monodisperse aggregates requires the presence of the hydrophilic carboxy-terminal sequence of M179. © 1994 John Wiley & Sons, Inc.     

Complete protection by alpha-crystallin of lens sorbitol dehydrogenase undergoing thermal stress

Sorbitol dehydrogenase (l-iditol:NAD(+) 2-oxidoreductase, E.C. 1.1.1. 14) (SDH) was significantly protected from thermally induced inactivation and aggregation by bovine lens alpha-crystallin. An alpha-crystallin/SDH ratio as low as 1:2 in weight was sufficient to preserve the transparency of the enzyme solution kept for at least 2 h at 55 degrees C. Moreover, an alpha-crystallin/SDH ratio of 5:1 (w/w) was sufficient to preserve the enzyme activity fully at 55 degrees C for at least 40 min. The protection by alpha-crystallin of SDH activity was essentially unaffected by high ionic strength (i.e. 0.5 m NaCl). On the other hand, the transparency of the protein solution was lost at a high salt concentration because of the precipitation of the alpha-crystallin/SDH adduct. Magnesium and calcium ions present at millimolar concentrations antagonized the protective action exerted by alpha-crystallin against the thermally induced inactivation and aggregation of SDH. The lack of protection of alpha-crystallin against the inactivation of SDH induced at 55 degrees C by thiol blocking agents or EDTA together with the additive effect of NADH in stabilizing the enzyme in the presence of alpha-crystallin suggest that functional groups involved in catalysis are freely accessible in SDH while interacting with alpha-crystallin. Two different adducts between alpha-crystallin and SDH were isolated by gel filtration chromatography. One adduct was characterized by a high M(r) of approximately 800,000 and carried exclusively inactive SDH. A second adduct, carrying active SDH, had a size consistent with an interaction of the enzyme with monomers or low M(r) aggregates of alpha-crystallin. Even though it had a reduced efficiency with respect to alpha-crystallin, bovine serum albumin was shown to mimic the chaperone-like activity of alpha-crystallin in protecting SDH from thermal denaturation. These findings suggest that the multimeric structural organization of alpha-crystallin may not be a necessary requirement for the stabilization of the enzyme activity.     

Aggregation kinetics of bovine serum albumin studied by FTIR spectroscopy and light scattering

To investigate which type of structural and conformational changes is involved in the aggregation processes of bovine serum albumin (BSA), we have performed thermal aggregation kinetics in D(2)O solutions of this protein. The tertiary conformational changes are followed by Amide II band, the secondary structural changes and the formation of beta-aggregates by the Amide I' band and, finally, the hydrodynamic radius of aggregates by dynamic light scattering. The results show, as a function of pD, that: tertiary conformational changes are more rapid as pD increases; the aggregation proceeds through formation of ordered aggregates (oligomers) at pD far from the isoelectric point of the protein; disordered structures add as the pD decreases. Moreover, beta-aggregates seem to contribute only to oligomers formation, as showed by the good correlation between kinetics of scattering intensity and IR absorption intensity. These results indicate for BSA a general mechanism of aggregation composed by partial unfolding of the tertiary structure and by the decrease of alpha-helix and random coil contents in favor of beta-sheet aggregates. This mechanism strictly depends on pD and gives rise to almost two distinct types of macromolecular aggregates.     

Jack bean urease (EC 3.5.1.5) aggregation monitored by dynamic and static light scattering

Aggregation of jack bean urease (JBU) is involved in many alterations of its biological properties, notably the ureolytic and entomotoxic activities. In order to investigate this phenomenon, protein aggregates were characterized by dynamic (DLS) and static light scattering (SLS) spectroscopies through determination of apparent hydrodynamic radii, the average molecular masses, radii of gyration and second virial coefficients. No effect of disulfide reducing agents on protein association was observed contrasting with previous reports implicating their function in the prevention of JBU aggregation. The influence of freeze-thawing cycles on protein aggregation was also investigated. Our results showed that after freeze-thawing cycles the native form of JBU with apparent hydrodynamic radius of 7 nm and radius of gyration of 12 nm is replaced by high-order oligomers and this aggregation is not reverted neither by dithiothreitol (DTT) treatment nor by high concentration of salts. Altogether the data help to understand the complex behavior of JBU in solution and may correlate with the diversity of biological properties of this enzyme.     

Adsorption of DNA onto positively charged amidine colloidal spheres and the resultant bridging interaction

The complexation behaviour of duplex linear DNA (negatively charged) with amidine functionalised sub-micron latex spheres (positively charged) was studied using dynamic light scattering (DLS) and a PALS interferrometric zeta potential sizer. Four types of DNA-sphere complex were investigated as a function of component concentration by combining amidine functionalised polystyrene microspheres with radii of 10.5 nm and 60 nm, and herring DNA of lengths of 35 nm and 85 nm. At low DNA concentrations (c(DNA)), the undercharged complexes showed a small increase in measured hydrodynamic radius (R(h)) and a decrease in zeta potential with increasing c(DNA). Within a critical DNA concentration range R(h) was seen to peak sharply, and the zeta potentials were approximately 0 mV, corresponding to the formation of unstable neutral complexes. Immediately above this concentration region the measured R(h) values became comparable with those at low c(DNA), and the zeta potential became negative, indicating the formation of stable overcharged complexes. The small and large spheres formed multi-sphere and single sphere overcharged aggregates respectively, which is thought to be determined by the relative magnitude of the chain persistence length (approximately 50 nm) and the sphere radius, switching on or off the DNA bridging interaction.