subtilisin solutions were prepared by mixing and vortexing of 1.25 , 5 , 8 , 12.5 , 15 , 17.5 , 20 , and 25 l of subtilisin stock solution ( sigma aldrich , catalogue number p4860 ; lot 056k1213 ) per ml of 100 mm phosphate buffer ( ph = 8 , filtered with a 0.25 m anotop filter ) , which yielded enzyme solutions at concentrations of 0.05 , 0.2 , 0.3 , 0.5 , 0.6 , 0.7 , 0.8 , and 1 mg ml .
these concentrations correspond to 1.5 , 6 , 9.6 , 15 , 18 , 24 , and 30 u ml , expressed in activity units used in our previous report .
saxs measurements were carried out at beamline 7t - mpw - saxs at bessy ii synchrotron source in berlin , germany , using an x - ray energy of 9650 ev .
enzyme solutions at various concentrations as well as pure buffer ( as background ) were injected in glass capillaries and placed in a capillary holder .
the capillary holder was then mounted on the sample cell chamber , evacuated , and heated to 25 or 55 c .
the individual samples were then exposed to the x - ray beam to record scattering intensity patterns by using a gas detector placed in the vacuum chamber .
the integration and processing of the scattering data was carried out by using the software provided at the beamline .
static and dynamic light scattering measurements were carried out using the 3ddls instrument ( ls instruments , fribourg , switzerland ) using vertically polarized he 
ne laser light ( 25 mw with a wavelength of 632.8 nm ) with an avalanche photodiode detector at angles between 15 and 135 at 55 c . the background scattering intensities ( from pure buffer ) were subtracted from the scattering intensities of the enzyme solutions . at each scattering angle ,
dynamic light scattering measurements were also performed by recording the intensity autocorrelation function g2( ) as a function of lag time . the autocorrelation functions were analyzed by means of the cumulant method in order to determine the initial decay rate and the corresponding average apparent diffusion coefficient dapp .
the decay of the normalized autocorrelation function was modeled as g1( ) = ( g2( ) 
1 ) = exp( ) , where  = dappq is the initial decay rate , q = ( 4n/ )  sin(/2 ) is the scattering vector magnitude , n is the refractive index of the solvent , and  is the wavelength of the laser .
einstein equation , rh = kbt/6dapp , where kb is the boltzmann constant , t is the absolute temperature , and  is the solvent viscosity at the given temperature .
the scattering intensity patterns from static light and x - ray scattering experiments can be described as i(q )  kp(q)s(q ) , where k is an instrument- and sample - dependent constant , p(q ) is the form factor , which depends on the size and shape of the primary particles , and s(q ) is the structure factor giving information about the spatial arrangement of the primary particles at length scales larger than that of the primary particles ( radius of rp ) .
please note that q = ( 4/ )  sin(/2 ) for saxs measurements . in the limit of qrg
< 1 , the mean radius of gyration rg of randomly distributed ( e.g. , freely diffusing ) primary particles or clusters can be determined from the measured scattered intensity i(q ) by using the guinier analysis . in the limit of 1/rg  q  1/rp , where rg is the mean radius of gyration of a sufficiently large cluster composed of primary particles with radius rp , the structure factor for fractal clusters with fractal dimension df scales with q through a power law relation as i(q )  s(q )  q.
 the structural characterization of subtilisin mesoscale clusters , which were previously shown to induce supramolecular order in biocatalytic self - assembly of fmoc  dipeptides , was carried out by synchrotron small - angle x - ray , dynamic , and static light scattering measurements . 
 subtilisin molecules self - assemble to form supramolecular structures in phosphate buffer solutions . 
 structural arrangement of subtilisin clusters at 55 c was found to vary systematically with increasing enzyme concentration . 
 static light scattering measurements showed the cluster structure to be consistent with a fractal - like arrangement , with fractal dimension varying from 1.8 to 2.6 with increasing concentration for low to moderate enzyme concentrations . 
 this was followed by a structural transition around the enzyme concentration of 0.5 mg ml1 to more compact structures with significantly slower relaxation dynamics , as evidenced by dynamic light scattering measurements . 
 these concentration - dependent supramolecular enzyme clusters provide tunable templates for biocatalytic self - assembly . 
Experimental Section