this is because it can provide site - specific information about protein motions over a large range of time scales . over the past decade , n nmr relaxation experiments employing model - free analysis ( 1,2 ) have become the de facto standard used to characterize protein motions on a picosecond to nanosecond time scale . however , as with any scientific method , this approach has certain limitations ( 3,4 ) . perhaps the most obvious difficulty lies in the fact that n relaxation measurements are inherently time - consuming and tedious , often requiring many hours of data collection , processing and spectral analysis . a second problem is that relaxation measurements are often seriously compromised by peak overlap , poor signal intensity or peak broadening . a third problem is that the precision and accuracy of relaxation - derived measurements tends to deteriorate rapidly as the frequency of internal nanosecond motions approach that of the protein 's overall tumbling rate ( 5,6 ) . this is because n relaxation rates become insensitive to internal fluctuations that are much slower than overall tumbling . since calculations of relaxation rates are based on measuring peak intensities , their accuracy can be severely compromised by low signal - to - noise ratios . this is especially true when dealing with larger ( > 150 residues ) proteins or proteins undergoing s  ms conformational exchange . another complication to the model - free formalism lies in the fact that its proper application often requires information about anisotropy of protein overall diffusion and , as a result , the method can not be used when the 3d structure is not known or when it is largely disordered . these limitations with traditional relaxation measurements prompted us to develop a new , chemical - shift - based technique to characterize protein mobility from nmr data . specifically , we wanted to develop an easy - to - use , robust approach that would not be affected by protein tumbling rates , uncertainties in peak intensities or lack of knowledge about the protein 's 3d structure . this method is called the random coil index or rci ( 7 ) . as described in our previous publications ( 7,19 ) , the rci method exploits the fact that there is a remarkable amount of dynamic information intrinsic to nmr chemical shifts . the connection between chemical shifts , especially random coil chemical shifts , and protein flexibility has been known for quite some time ( 811 ) . random coil chemical shifts can be defined as shifts that result from a fast exchange among energy - weighted populations of all theoretically possible conformations of an unfolded polypeptide chain ( 12,13 ) . the difference between an observed chemical shift for a given amino acid in a given protein , and its corresponding random coil value is called the secondary chemical shift . secondary chemical shifts have been used for many years to qualitatively estimate the level of protein structural disorder ( 1418 ) . however , until recently , no quantitative relationships between secondary chemical shifts and protein dynamic parameters had been derived . the rci is able to combine the chemical shift data from six different nuclei ( c , c , co , n , hn and hor any combinations thereof ) into a single parameter that closely correlates with amplitudes of backbone protein motions such as order parameters ( s ) and root mean square fluctuations ( rmsfs ) of structural ensembles . previous descriptions of the rci method focused on explaining the algorithm , rationalizing its utility and assessing its accuracy . as a result , only a modest effort went into making the rci - based software user - friendly and flexible . in an attempt to make the rci approach more accessible to the nmr community and much more robust , we decided to create an rci web server and to optimize the rci protocol for nmr assignments with different degrees of completeness and mis - referencing . the rci server is a unique server , designed to support rapid ( 510  s ) , residue - specific determination of protein flexibility and protein mobility using only chemical shift assignment data as input . it accepts almost any combination of nmr chemical shift assignments as its input and it outputs the expected values of the rmfs of md and nmr ensembles as well as model - free order parameters ( 1,2 ) . to improve the accuracy and reproducibility of the calculations , assessments of the rci server performance show an agreement between the values it calculates and experimentally obtained amplitudes of motions range from r = 0.770.82 depending on the type of experimental method . the rci server is composed of two parts , a front - end web - interface ( written in python and html ) and a back - end consisting of several programs including rci ( 7 ) , csi ( 11 ) , refcor [ based on ( 19 ) ] , as well as several parsing and conversion utilities for handling different input files . the csi program is written in ansi standard c , while rci , refcor , the input parsing and the conversion utilities are written in python . the rci server accepts protein chemical shift assignments in standard bmrb nmr - star ( 20 ) and shifty ( 21 ) formats as input . users can either upload an input file into the web server ( via a browse button ) or paste the data in a standard text box ( figure 1 ) . users are also offered several options to adjust program operations to suit their specific needs . to begin : ( 1 ) experimental chemical shifts are first uploaded by the user . ( 2 ) the input chemical shifts are then re - referenced ( if necessary ) by refcor . ( 3 ) the protein sequence is extracted from the nmr assignments and used to ( 4 ) determine the appropriate random coil chemical shifts ( 22 ) and ( 5 ) determine the neighboring residue correction factors for the i  1 and i  2 residues ( 23 ) . the correction factors are applied to the random coil chemical shifts to obtain reference chemical shifts . ( 6 ) reference chemical shifts are then subtracted from the corrected experimental chemical shifts to obtain the secondary chemical shifts for the c , c , co , n , hn and h nuclei . ( 7 ) optionally , gaps in the chemical shift assignments , if any , are filled in by averaging the chemical shifts of neighboring residues . ( 9 ) secondary chemical shifts of are scaled to account for differences in their resonance frequencies , and , if below a certain  floor limit ( currently 0.5  p.p.m . ) , replaced with this floor value . ( 10 ) initial rci values are calculated using the following expression . 
 1 
 where |c| , |co| , |c| , |n| , |nh| and |h| are the absolute values of the secondary chemical shifts ( in p.p.m . ) of c , co , c , a , b , c , d , e and f are weighting coefficients ( table 1 in the rci online help ) . left angle and right angle brackets ( <  > ) indicate that the average is being calculated . ( 12 ) if the rci values are above a certain  ceiling limit ( currently 0.6 ) , they are replaced with this ceiling value . ( 13 ) the final rci values are obtained after a second smoothing by three - point averaging . ( 14 ) finally , in the last step the expected values of model - free order parameters ( s ) , rmfs of md and nmr ensembles are calculated using the following empirical expressions . 
 2 
 3 
 4 a more detailed description of the aforementioned steps has been published elsewhere ( 19 ) . figure 2.a flow chart describing the rci protocol . a flow chart describing the rci protocol . by default , the rci web server uses random coil reference chemical shifts and neighboring residue correction values originally published by schwarzinger and co - authors ( 22,23 ) . this is the only set of random coil values and neighboring residue correction for residues i  1 and i  2 that were obtained under similar experimental conditions and , therefore , are expected to be quite consistent with each other . however , users can also select different sets of random coil chemical shifts , including those values published by wang and jardetzky ( 24 ) , wishart et al . users are also offered an option to select i  1 neighboring residue correction values published by wang and jardetzky ( 24 ) instead of the default values . while these options do affect rci - based flexibility profiles , the differences in mean correlation coefficients for different combinations of random coil values and neighboring residue corrections ( table 2 of the rci online help ) are relatively small and may be considered statistically insignificant . by default , however , if unassigned residues are located in the middle of a well - defined secondary structure region ( e.g. -helix , -sheet ) , it is not unreasonable to expect that their flexibility will be similar to that of neighboring assigned resides . in these cases , the rci web server allows users to predict the flexibility of unassigned residues based dynamic properties of adjacent regions . the rci web server also has a somewhat similar option to fill small gaps in the per - residue distributions of secondary chemical shifts . such gaps happen more often than a lack of assignments for all the six nuclei and should be dealt with separately . the use of incomplete assignments generally reduces the quality of rci - based flexibility predictions ( see table 1 of the rci online help ) . by default , the rci web server fills small gaps in per - residue distributions of secondary chemical shifts by averaging secondary chemical shifts of residues i + 1 and i  1 , and , if not available , residues i + 2 and i  2 . end effects. these are poorly understood phenomena that alter the chemical shifts of the n- and c - termini of proteins in unpredictable ways . the rci web server offers an option to apply an end - effect correction to the rci values . this end - effect correction is turned on by default . a detailed protocol describing how the end - effect correction is handled was published elsewhere ( 27 ) . users should be aware that the improvement of rci predictions due to the end - effect correction is not related to the dynamic averaging of chemical shifts . rather , it originates from the indirect correlation between the severity of the end effects and protein flexibility due to their shared dependence on the proximity to a terminal residue . therefore , if the correction is applied , the rci profile at the terminal regions should be interpreted as a commonly observed trend of protein flexibility at termini of proteins . the rci server offers users the option to disable the end effect correction or to exclude the first and the last three residues from predictions . a particularly useful and important feature of the rci web server is its capacity to correct mis - referenced chemical shifts . this automated reference correction is done using a local implementation of the refcor program . about 20% of newly deposited assignments in the bmrb database were found mis - referenced by a recent survey ( 28 ) . given the relatively high level of mis - referencing in biomolecular nmr and given the fact that mis - referenced shifts can substantially reduce the performance of chemical - shift - based methods such as rci ( 7 ) , we believed that implementing this reference correction protocol was absolutely vital to maintaining the server 's performance . the refcor reference correction protocol is based on the secondary structure predictions from the chemical shift index ( csi ) ( 29 ) and was published elsewhere ( 27 ) . briefly , refcor uses csi - based predictions of secondary structure along with typical chemical shift values observed in different secondary structures are used to calculate the necessary reference correction for each nucleus . since csi predictions are also affected by shift mis - referencing , the protocol is repeated several times using newly generated re - referenced shifts until the csi predictions become stable . the reference correction option is always turned on by default although it can be switched off , if necessary . an average rci run takes between 5 cpu s ( without chemical shift reference correction ) and 20  s ( with reference correction ) . as might be expected , the rci web server displays the name of the input file , the options selected and a plot of the per - residue rci distribution . users may download per - residue distributions of the rci , predicted model - free order parameters , predicted rmsfs of md and nmr ensembles as both text files and graphical images . these files may also be obtained individually or as a single linked file containing all the results . re - referenced chemical shifts and csi - based predictions of secondary structure are also available for download or direct viewing on the website . in addition to its extensive data output , the rci web server also offers a comprehensive list of help pages to assist users in preparing their input files , in understanding the rci method and in interpreting the web server output . this information is provided to make the rci protocol as transparent as possible and to facilitate protocol troubleshooting if required . the rci web server was optimized and evaluated on a set of 18 proteins ranging in length from 56 to 283 residues ( 1585 residues in total ) , for which complete or nearly complete h , c and n chemical shifts were known ( table 3 of the rci online help ) . a subset of 14 proteins was used to generate molecular dynamic ( md ) ensembles and optimize weighting coefficients in the rci expression [ equation ( 1 ) ] . this was done by using a simple grid search to maximize rci correlation with rmsf values determined by molecular dynamics . the weighting coefficients were obtained for all 63 possible assignment scenarios ( table 1 of the rci online help ) . to evaluate the performance of the algorithm for the training set , we used a leave - one - out procedure by removing the query protein from rci training set prior to running the program . the average correlation coefficients for the full training set and for all leave - one - out runs were identical ( r = 0.82 ) . to ensure that the rci algorithm had not been over - trained , four additional proteins , which were not previously included in the training set , were tested . the average correlation coefficient between the rci determined md rmsf and the calculated md rmsf for these proteins was identical ( r = 0.82 ) to that of the training set ( see table 3 of the rci online help for information about the tested proteins ) . to validate the relationship between rci predictions and the amplitudes of protein motions , the correlation of rci with model - free order parameters [ observed and predicted from the structure ( 30 ) ] and per - residue rmsf values of nmr ensembles were calculated . the average correlation coefficients for the eighteen sets of order parameters and sixteen sets of nmr rmsfs were 0.77 and 0.81 , respectively . the performance of the conversion expressions shown in equations ( 24 ) were assessed by calculating the average error between rci - predicted motional amplitudes and the corresponding experimentally and theoretically obtained parameters . the average errors for the order parameters ( 18 proteins ) , the nmr rmsfs ( 16 proteins ) and the md rmsfs ( 18 proteins ) were 0.05 , 0.44   and 0.50   , respectively . figure 1 in the rci online help shows examples of the good correlations obtained between rci and other measures of protein motional amplitudes ( e.g. nmr rmsf , md rmsf , s ) for such pharmaceutically important proteins as interleukin-4 and the hiv-1 gag protein . additional information about optimizing and testing the rci method ( i.e. details of md simulations , pdb ids and bmrb codes of proteins , etc . ) can be found in the original papers on the rci method ( 7 ) as well as on the rci online help pages . in summary , we have described a web server that is capable of rapidly and accurately predicting protein flexibility using only chemical shift assignments as the input . comparisons suggest that these predictions correlate well with other measures of protein mobility , such as model - free order parameters and root - mean square fluctuations ( rmsfs ) of nmr and md ensembles . the approach is generally applicable to proteins of any size for which h , c and n shift assignments are available . the web server is unique in its ability to extract dynamic information from nmr data without the prior knowledge of tertiary structure , without the need for favorable rates of rotational diffusion and without the need for exceptionally good spectral sensitivity . we have already used the rci approach to monitor a number of interesting dynamic processes in proteins , such as the ph - induced conversion of the prion protein ( prp ) into its scrapie form ( prp ) and the dynamic response of picornaviral protease active sites to inhibitor binding ( manuscripts in preparation ) . we believe the rci method may lead to important changes in the ways backbone protein flexibility is measured and reported by the scientific community .