Development of a kinetic metabolic model: application to Catharanthus roseus hairy root

A kinetic metabolic model describing Catharanthus roseus hairy root growth and nutrition was developed. The metabolic network includes glycolysis, pentose-phosphate pathway, TCA cycle and the catabolic reactions leading to cell building blocks such as amino acids, organic acids, organic phosphates, lipids and structural hexoses. The central primary metabolic network was taken at pseudo-steady state and metabolic flux analysis technique allowed reducing from 31 metabolic fluxes to 20 independent pathways. Hairy root specific growth rate was described as a function of intracellular concentration in cell building blocks. Intracellular transport and accumulation kinetics for major nutrients were included. The model uses intracellular nutrients as well as energy shuttles to describe metabolic regulation. Model calibration was performed using experimental data obtained from batch and medium exchange liquid cultures of C. roseus hairy root using a minimal medium in Petri dish. The model is efficient in estimating the growth rate.
Introduction
In vitro plant biotechnology offers a controlled environment and has been widely studied for phyto-pharmaceuticals and recombinant proteins production. However, the low productivity and the poor reproducibility of the cultures are still limiting the economical feasibility of such in vitro bioprocesses. Moreover, the lack of reproducibility of the cultures significantly complicates process validation and acceptance by the regulatory agencies, and thus the potential to rapidly put a product to market. Different approaches have succeeded in decreasing the technological risk associated with in vitro plant biotechnology. The introduction of elicitors such as chitin [1] and jasmonic acid [2] has shown to enhance significantly the production level for many plant species cultured as cell suspensions and hairy roots. The use of an extractive phase allowed the simplification of harvesting procedures [3, 4]. More recently, cell engineering studies have shown its potential in improving cell catalytic capacity towards the production of secondary metabolites [5–7] and in in vitro molecular farming for recombinant human proteins [8]. However, high variability levels in cell growth and production of biomolecules of interest are still observed. The genetic flexibility of plant cells may partly explain these phenomena [9] and inadequate culture management may also be involved.
A plant cell has the ability to accumulate nutrients and metabolites which are involved in the regulation of its metabolic pathways. The key for improving plant cell culture reproducibility may thus rely on a better understanding of the links that are exerting between a plant cell physiological state and its potential towards growth and production of a biomolecule of interest. This understanding (following that of Bailey [10]) could take the form of a descriptive and predictive metabolic model. Such structured model may then be either useful to enhance our understanding of cell behaviour, in identifying possible regulatory roles [11], as well as being a tool for defining adequate controlled culture conditions. Metabolic modelling has been applied to plant cells for studying specific metabolic sub-networks such as photosynthesis [12, 13], respiration [14], cellulose biosynthesis [15] and lipid biosynthesis [16]. These studies have clearly showed the importance of the energy shuttles on the control of the metabolic pathways. In addition, some nutrients are known to be involved in the regulation of the cell metabolism. Intracellular inorganic phosphate (Pi) plays a central role in the regulation of enzymes activity through phosphorylation/dephosphorylation processes, ATP/ADP concentration ratio, starch synthesis and storage, and in the flux distribution between the glycolysis and the pentose-phosphate pathway (PPP). Intracellular nitrate and ammonium are known to affect amino acid (AA) production.
The large capacity of plant cells for nutrient and metabolite accumulation plays a crucial role in cell growth and biomolecule production, as observed for Daucus carota hairy root [17] and Eschscholtzia californica suspension cells [18]. Recently, we have developed a kinetic model based on intracellular nutrients such as inorganic phosphate, nitrate and sugars which showed to be efficient in simulating carrot hairy root growth for different culture media composition [17]. Therefore, the aim of this work was to include the description of metabolic pathways to the nutritional model in order to describe plant cells behaviour from the estimation of the cells physiological state, including nutritional and metabolic states. Catharanthus roseus was studied as a model biological system. Cell nutritional state in Pi, nitrogen (NO3− and NH4+) and carbohydrates (sucrose, fructose, glucose and starch) is described. The hypothesis of a central primary metabolism at steady state has been proposed based on literature [19, 20]. Using the metabolic flux analysis (MFA) approach, a model reduction [21] was applied on the central primary metabolism network and resulted in independent pathways. A second network includes transient fluxes such as for nutrient uptake and storage, energy shuttles management and root cells growth. Metabolic regulation of the fluxes from energy shuttles and nutrients is included. The hairy root specific growth rate is described as a function of the content in cell building blocks such as amino acids (including proteins), lipids (LIP), organic acids (ORA), organic phosphates (OP) (including nucleic acids) and structural hexoses (STH). Batch and medium exchange cultures of C. roseus hairy root were performed and the experimental data were used for model calibration.
Model general structure
The model has been first developed by Tikhomiroff [22]. The cell metabolic network (Fig. 1) is divided into two interlinked sub-networks as the stationary (SPMP) (Fig. 2) and the transient (TPMP) primary metabolic pathways (Fig. 1). The SPMP includes glycolysis, PPP, the TCA cycle and the catabolic reactions leading to the cell building blocks. The cell building blocks are amino acids and peptides which were taken as a unique pool of AA, ORA, OP, LIP and STH. The TPMP network is linked to the SPMP network and describes cells growth and nutrient transport between medium and intracellular volumes. Compartmentalization of nutrients and metabolites among the cytosol, the vacuole and other organelles is not included in the model and a single cell population was considered to describe the hairy root cells pools. This simplification already showed to be efficient to model hairy root growth and nutrition [17]. The secondary metabolism is simplified to fluxes leading to two pools, one accounting for the global pool in secondary metabolites derived from tryptamin (TRYSM), and one accounting for the global pool in secondary metabolites derived from secologanin (SECSM). The model is thus composed of interlinked metabolic networks that are at steady (SPMP) and transient (TPMP) states, and is described by a mass balance using the stoichiometric matrix and the hairy root specific growth rate:
where S is the stoichiometric matrix, Φ is a vector containing reaction fluxes, μ is the hairy root specific growth rate and M is a vector containing the concentration in cellular metabolites and nutrients. Root mass with time can then be estimated both kinetically and from a mass balance on all cell constituents.Fig. 1The metabolic model global structure. Fluxes in the transient primary metabolic pathways (TPMP). Flux numbers refer to the stoichiometric biochemical reactions of Table 3. Kinetic description of the resulting fluxes is presented in Table 4Fig. 2Fluxes in the stationary primary metabolic pathways (SPMP). Flux numbers refer to the stoichiometric biochemical reactions of Table 1
Stationary primary metabolic pathways
The pseudo-steady-state assumption for the central metabolism was based on observations from Rontein et al. [19] and Stitt and Fernie [20] and proposed to simplify the model development. The original SPMP metabolic network has 31 fluxes (Fig. 2; Table 1), which were reduced to 20 independent pathways (Fig. 3; Table 2) using the method proposed by Simpson et al. [21] and Stephanopoulos et al. [23] and the following simplifications. Briefly, the minimal number of independent feasible metabolic pathways is determined with a group of metabolites assumed at steady state: G6P, F6P, R5P, G3P, E4P, CHO, PEP, PYR, A-CoA, OXO and OAA. The “N” matrix (11×31) is first constructed from the 31 biochemical reactions and the 11 metabolites at steady state. The determination of the independent pathways then requires the knowledge of the kernel matrix “K” (31×number of independent pathways), which describe each pathway as a linear combination of the 31 biochemical reactions of the SPMP. This matrix is the non-trivial solution of the equation:
Since this equation has an infinite number of solutions, both “N” and “K” matrices are decomposed each into two matrices:
with “ N1” and “ K2” selected as square invertible matrices. Starting using identity matrix for “K2”, “K1” can then be determined by modifying “K2” such that possible independent pathways can be identified:
Using the complete matrix K, we can build the independent pathways presented in Fig. 3. In this work, the size of this matrix is 31×20. The complete method to obtain the pathways can be found in Ref. [22].Table 1Biochemical reactions of the stationary primary metabolic pathwaysFluxν(1)a–cν(2)a–cν(3)aν(4)aν(5)bν(6)bν(7)a,cν(8)aν(9)aν(10)bν(11)aν(12)bν(13)aν(14)a–cν(15)aν(16)a–cν(17)c,dν(18)a–cν(19)c,dν(20)a–cν(21)eν(22)bν(23)bν(24)aν(25)bν(26)eν(27)ν(28)ν(29)dν(30)aν(31)da[39]b[24]c[40]d[27]e[41]f[26]Fig. 3Reduced independent biochemical pathways from the SPMP. Pathway numbers refer to the stoichiometric biochemical reactions of Table 2. Kinetic description of the resulting fluxes is presented in Table 4. The 20 independent biochemical pathways were obtained from the 31 biochemical reactions of the SPMP described in Fig. 2 and Table 1, using the reduction method of Simpson et al. [21] and Stephanopoulos et al. [23], as described in Sect. 3Table 2Independent fluxes of the SPMPs after pathways reduction using MFA approachFluxaν(r1)ν(r2)ν(r3)ν(r4)ν(r5)ν(r6)ν(r7)ν(r8)ν(r9)ν(r10)ν(r11)ν(r12)ν(r13)ν(r14)ν(r15)ν(r16)ν(r17)ν(r18)ν(r19)ν(r20)aThe biochemical reactions are denoted with an "r" to indicate that they are obtained from pathways reduction
The nutrient concentrations described are glucose (GLC), fructose (FRU), sucrose (SUC), ammonium (NH4) and inorganic phosphate (Pi). The anaplerotic pathways are simplified to the transformation of phosphoenolpyruvate (PEP) into oxaloacetate (OAA). The metabolite pools resulting from the SPMP are starch (STA), STH (cell wall and membrane constituents), OP (nucleotides, phospholipids, nucleic acids), total AA including that of peptides, ORA, pools from tryptamin (TRYSM) and from secologanin (SECSM). Starch biosynthesis (flux v(r14) in Table 2) and catabolism (v(r13)) are included. AA (v(r5)) are assumed to be synthesized from oxoglutarate, since it is the site for ammonium fixation and thus the initiation step in the AA biosynthesis [24], even though there are AA synthesized from other pathways. Tryptamin (TRYSM) biosynthesis (v(r1)) has been explicitly described because this AA is a precursor, with secologanin (SECSM) (v(r2) and v(r10)), to the formation of the secondary metabolites. OP biosynthesis (v(r11)) has been simplified as illustrated in Fig. 3 and is accounting for the four nucleotides. The biosynthesis of STH results from multiple biochemical reactions [25] but it is simplified to the condensation of G6P with R5P (v(r12)). The biosynthesis (v(r7)) and catabolism (v(r15)) of LIP is linked to acetyl-coenzyme A [26] as for ORA biosynthesis (v(r16)) and catabolism (v(r17)). The kinetic expressions of the fluxes are described in the next section.
Transient primary metabolic pathways
The TPMP network includes the biochemical reactions that cannot satisfy the pseudo-steady-state hypothesis. These include nutrients transport and accumulation, root cells growth and energy shuttles dynamics. The general structure of the TPMP and its interactions with the SPMP are illustrated in Figs. 1 and 2. The stoichiometric mass balances are presented in Table 3 and the kinetic terms used in fluxes’ regulation are described in Table 4. Extracellular nutrients such as sucrose (ESUC), glucose (EGLC), fructose (EFRU), ammonium (ENH4), nitrate (ENO3) and Pi (EPi) are included. Sucrose is hydrolysed into fructose and glucose extracellularly by apoplastic invertases (Table 3, v(28)), or intracellularly as described in the SPMP (Table 2, v(r19)). It should be noted that sucrose biosynthesis (Table 2, v(r20)) is not included into the model because there are no evidence that hairy roots have active chloroplasts. v(r19) then represents the net flux of sucrose hydrolysis. Alternative glycolytic pathways [27] are described and the carbohydrate sources include sucrose, glucose, fructose and starch. However, since all the biosynthesis pathways of the SPMP are defined with glucose as precursor, all available intracellular carbon sources have first to be converted into glucose. Fructose conversion (v(r3)), starch catabolism (v(r13)) and sucrose hydrolysis (v(r19)) processes are thus feeding the intracellular glucose pool. Plant cell adaptation mechanism to Pi deficiency is described with the fluxes for the degradation of pyrophosphate (v(26)) and OP (v(23)) into Pi. The plant cell storage capacity for sugars, NO3−, NH4+, Pi and cell building blocks is described. Respiration is described (v(30)), however, oxygen is assumed to be non-limiting as discussed below. Energy loss associated with maintenance and other reactions that are not included into the SPMP is contained in flux v(29).Table 3Biochemical reactions of the transient primary metabolic pathwaysFluxaν(21)ν(22)ν(23)ν(24)ν(25)ν(26)ν(27)ν(28)ν(29)ν(30)ν(31)aStoichiometric coefficients were taken from Ref. [24]Table 4Kinetic expression of the fluxesFluxa–c is fixed at 0 and no sucrose synthesis is consideredaReaction number refers to pathways of SPMP in Fig. 3, and of TPMP in Fig. 1bNot shown fluxes are related to exchange between the cytoplasm and the vacuole and were not included in this modelcUse of NTP, NDP, NADH, NAD, NADPH and NADP in flux kinetics was taken from Ref. [24]d[42]e[43]f[44]
Metabolic regulation
Metabolic regulation of two kinds is integrated into the model: that associated with the energetic status of the cells and that related to the nutritional state of the cells, variable denoted as “θi” below. Each flux (ν) is regulated as follows, according to a multiplicative kinetic of each mechanism involved.
The order of the regulation kinetics can also be adjusted from the term αi to account for multi-steps mechanisms. Since we established the independent pathways for the SPMP with arbitrary conditions, it is not possible to compare the structure of the resulting kinetics with literature. However, the identified independent pathways have been selected for their feasibility, and their combination is mathematically equivalent to the whole metabolic system (31 fluxes), given that the pseudo-steady-state hypothesis is acceptable.
Furthermore, a sigmoid function is used for nutrients acting like switches to avoid large discontinuities when solving the differential equations, which would have been the case using a simple on/off switch type. Continuous functions are also more representative of biological behaviour [28]. The sigmoid function is also used for imposing maximum accumulation levels (see Table 4):
The parameter “a” defines the steepness of the function, “Mi” is the concentration of the nutrient involved in the regulation of a flux and “Mi,t” is the nutrient concentration threshold.
The role of energy shuttles in the regulatory mechanisms is described in Table 4. NADH, NADPH and NTP (the sum of ATP, GTP, CTP and UTP) as well as their reduced forms (NAD, NADP and NDP) are used. The sum in energy shuttles per g DW of roots in both oxidized and reduced forms (NADH + NAD; NDP + NTP; NADPH + NADP) are taken constant with time. However, the energetic status of the cells [NADH/(NADH + NAD); NTP/(NDP + NTP); NADPH/(NADPH + NADP)] was not assumed constant. ATPase proton pumps that are linked to H+/nutrient co-transport and involved in the control of intracellular pH are thus included. ATP consumption for transmembrane transport of glucose (v(21)), fructose (v(22)), sucrose (v(24)), nitrate (v(27)) and Pi (v(31)) is thus included. A unique value for the affinity constant for NTP (KmNTP) is used. The same strategy of using unique affinity constants for NAD, NADH, NADP and NADPH is also applied.
Root cells nutritional state in Pi, NH4 and in sugars are involved in metabolic flux regulation. Intracellular Pi is involved in enzyme activation/deactivation processes through dephosphorylation/phosphorylation, in the biosynthesis of NTP (v(30)) and of many other metabolites as described below. Intracellular NH4 is involved in AA biosynthesis (v(r5)) (Fig. 3; Table 4). Michaelis–Menten kinetics with NH4 and Pi are at power two since a second-order mechanism is involved. NH4 has first to be transformed into NH2 radical, then into an AA which is finally integrated into a protein structure. Management of carbon source is crucial for plant cells since glucose, fructose, sucrose and starch can be used. However, since the model is based only on glucose, biochemical reactions converting other sugars into glucose are described (Fig. 3; Table 4). Starch biosynthesis (v(r14)) is controlled by the total intracellular available sugar concentration, and the sum in intracellular GLC, FRU and SUC has to be above 0.2 mmol/g DW for the STA biosynthesis to occur. A maximal STA storage capacity of 1.5 mmol/g DW was observed experimentally (see Sect. 7). Starch is degraded (v(r13)) when the GLC concentration is below 0.2 mmol/g DW. PPP (v(r4)) is regulated by NADP/(NADP+NAPH) ratio, which has to be above 0.5 for the pathway to be active. Pyruvate kinase regulation (v(r6)) is under the control of intracellular Pi concentration with a flux increase at 1 mmol Pi/g DW and below. G3P conversion into PEP (v(r8)) is regulated by Pi concentration with a flux increase at 1 mmol Pi/g DW and below. TCA cycle (v(r9)) is regulated by the NAD/(NAD+NADH) ratio, and a ratio that is above 0.5 will induce a flux increase. GLC (v(21)) and FRU (v(22)) uptake require a STA concentration that is below 0.07 and 0.02 mmol/g DW, respectively. OP synthesis (v(r11)) is regulated by intracellular Pi concentration with a flux increase at above 0.1 mmol Pi/g DW. OP degradation (v(23)) is controlled by intracellular Pi concentration with a flux increase at below 0.045 mmol Pi/g DW. LIP (v(r15)) and ORA (v(r17)) degradation into A-CoA is controlled by NADH concentration with fluxes increase at below 1 mmol NADH/g DW. Phosphofructokinase regulation (v(r18)) is controlled by intracellular Pi with a flux increase below 1 mmol Pi/g DW. Respiration rate (v(30)) is controlled by NDP/(NTP+NDP) ratio with a flux increase below a ratio of 0.5. Finally, regulation of root cells growth rate (v(32) is controlled by the intracellular concentration in the cell building blocks such as OP, LIP, amino acids and peptides (AA), ORA and STH. Monod model was used for LIP, AA and ORA. A hybrid Moser–Monod model was used for OP and STH with each kinetic term at power 4 and 1.25, respectively (Table 4). Since OP and STH are crucial to cell growth, the steepness of the affinity for both cell building blocks was increased.
Materials and methods
Culture conditions
Liquid cultures of hairy roots were performed in Petri dish as described in Jolicoeur et al. [17]. The major problem in culturing hairy roots is the difficulty to obtain a representative sample of the root network since the roots develop a highly dense interlinked bed. Petri dish culture allowed distributing the roots inoculum in a series of dishes with each dish taken as a single sample. Root growth was also limited by the use of a low salt medium, thus preventing the occurrence of dense root network. Previous results in Petri dish [17] and in bioreactor [3] suggest that there was no oxygen limitation in the cultures of this work.
Hairy roots of C. roseus L. G. Don were established as described by Bhadra et al. [29], with Agrobacterium rhizogenes strain A4. Hairy roots were transferred every month in Petri dishes in 25 mL of minimum medium [30] supplemented with 3% (w/v) sucrose and with a threefold KH2PO4 (0.352 mM). In the batch culture experiments, approximately 0.125 g fresh weight (FW) of hairy roots was inoculated in each Petri dish containing 25 mL of minimum medium. In the medium exchange cultures, approximately 0.125 g FW of hairy roots was inoculated in Petri dish containing 25 mL of minimum medium. The medium was renewed at 3- or 2-day intervals to avoid depletion of Pi in the medium. Whole Petri dishes were harvested in triplicates (n=3) periodically and taken as distinct samples. Liquid from each dish was filtered at 0.45 μm (Millipore, Billerica, Massachusetts) and stored at −20°C for further analysis. Roots were filtered under vacuum on a glass fiber filter (47 mm diameter Glass Microfiber filters GF/D, Whatman, #1823 047) and rinsed three times with 20 mL of de-ionized water. The filtered roots were removed from the filter and weighed for FW in a disposable aluminum dish (Fisher Scientific, # 08–732) on a precision balance (Sartorius). Fresh roots were immediately frozen into liquid N2 and stored in liquid N2 for further analysis. Root samples were then freeze dried (Duratop and Duradry, FTS Systems Inc., Stone Ridge, NY, USA), weighted for DW measurement and grinded (mortar and pestle) for further analysis. All further analyses were performed using freeze-dried roots.
Amino acids analysis
Approximately 2 mg of freeze-dried roots were extracted in 1 mL of 2% w/v 5-sulfosalicylic acid. The samples were sonicated for 15 min and then centrifuged at 12,000g for 5 min. The supernatant was analysed for AA by HPLC using a modified method from Gombert et al. [31] as described in Benslimane et al. [32]. The column is a high-efficiency Nova-Pak TM (C18, 4 μm). Precolumn derivatization of the AA was performed using AccQ.Fluor (6-aminoquinolyl-N-hydroxysuccinimidyl carbamate, or AQC), which is an N-hydroxysuccinimide-activated heterocyclic carbamate, and the derivatized AA were quantified via a fluorescence detector. α-Aminobutyric acid was used as an internal standard. The standard error of measurement using this method was routinely below 5%. AA concentration was then calculated since the peak for each individual AA accounted for the combination of free and that from peptides and proteins.
Extraction of sugars
Approximately 10 mg of freeze-dried roots was washed with 80% ethanol and then centrifuged at 16,000g for 5 min. This wash was done three times and each time the supernatant was kept for glucose, fructose and sucrose analyses. After the third wash the pellet was kept for starch analysis.
Analysis of sugars
Glucose, fructose and sucrose analysis was performed with a Beckman Coulter HPLC (Beckman Coulter Canada Inc, Mississauga, Canada; Pump model 126, automatic injector model 508) equipped with a Gilson model 132 refractive index detector. A Prevail Carbohydrate ES column 4.6 mm×250 mm (Alltech Canada, Guelph, Ontario, Canada), coupled with a Prevail Carbohydrate ES All-Guard 4.6 mm×7.5 mm guard column (Alltech Canada, Guelph, Ontario, Canada), was used at a column temperature of 35°C. The injection volume was 20 μL. The mobile phase consisted of acetonitrile and water 75:25 (v/v) at 1.0 mL/min. The cell pellet obtained from the soluble sugars extraction was re-suspended in 1 mL de-ionized water and sterilized at 121°C for 15 min together with a 1 mL 6 g/L starch solution in de-ionized water. Samples were allowed to reach room temperature and their volume was readjusted to 1 mL with de-ionized water if necessary. Starch calibration standards from 0 to 6 g/L were prepared by serial dilutions of the starch solution in de-ionized water. Calibration standards and samples were diluted 1:1 with an amyloglucosidase solution (Sigma, St. Louis, Missouri, USA, Cat. #S9144) and incubated for 15 min in an ultrasound bath at 60°C. Samples and standards were centrifuged for 10 min at 16,000g. A 10 μL aliquot of the supernatant was directly transferred into a spectrometric cuvette with 500 μL of “Glucose Infinity” reagent (Sigma, Cat. #17-25). After incubation (15 min) at room temperature, 500 μL of 100 mM KH2PO4 buffer pH 7.5 was added followed by spectrophotometric reading at 340 nm.
Ions extraction
Ions were extracted from approximately 10 mg of freeze-dried roots in 1.5 mL of 5% (w/v) trichloroacetic acid. This mixture was sonicated at 40°C for 30 min and then centrifuged at 16,000g for 10 min. The supernatant was filtered at 0.45 μm and analysed by HPLC.
Ions analysis
Culture medium and intracellular contents in majors ions (Cl−, NO3−, H2PO4−, SO42−, NH4+, K+, Na+, Ca2+) were analysed using a Dionex HPLC system (Dionex Canada Ltd., Oakville, Canada) equipped with an isocratic pump, an automated sampler AS-3500 and a pulsed electrochemical detector in the conductivity mode, controlled by the Dionex A1-450 software for cations and the Dionex Peaknet software for anions. Anions were separated using a 4×250 mm IONPAC AS14A-SC analytical column, an IONPACAG14A-SC guard column and a ASRS-1 anion self-regeneration suppressor to improve the signal-to-noise ratio. The mobile phase consisted of an aqueous buffer of 2 mM Na2CO3/1 mM NaHCO3 solution flowing at a rate of 1.0 mL/min. Cations were separated using a 4×250 IONPAC CS-12 analytical column, a IONPAC CG-12 guard column and a CSRS-1 cation self-regenerating suppressor. The mobile phase was an aqueous 20 mM methanesulphonic acid solution flowing at a rate of 0.9 mL/min.
Model simulations
The model simulations were done using the Matlab software (The MathWorks Inc., Natick, MA, USA). The differential equations system was integrated through the Ordinary Differential Equation solver ode15s.m. The model error minimization was performed by means of manual and algorithm-based methods. The former was done to find good initial estimates based on literature (when available). The latter was then used to reduce the global error between the estimates and the experimental data. The algorithm used was the lsqcurvefit.m subroutine (Optimisation toolbox, Matlab) based on the Levenberg–Marquardt algorithm [33].
Results and discussion
Model calibration and determination of the kinetic parameters
Model calibration was performed using experimental data from C. roseus hairy root batch and medium exchange cultures. Each experiment (one batch and one medium exchange) was performed in triplicate. A total of 14 samples were taken during the batch experiment and 17 during the medium exchange. Parameter values were obtained from experimental data (maximum uptake rates, maximum growth rate, sucrose maximum hydrolysis rate and some of the maximal accumulation levels) and from literature, taking values from other plant species when unavailable for C. roseus (Tables 5, 6, 7). Adjustment of the unknown parameters as well the values taken from literature was performed manually in parallel using a non-linear least-square algorithm (lsqcurvefit) from Matlab software. The least-squares criterion was applied on all the data points (triplicates taken as mean in (Mi)exp). The sum of squares were weighted as described below.
whereTable 5Affinity constants (Km)ComponentValueLiteratureSpeciesUnitsReferencesAA0.0136Catharanthus roseusmmol/g DWModel calibrationFRU0.120C. roseusmmol/g DWModel calibrationGLC0.120C. roseusmmol/g DWModel calibrationLIP0.00254C. roseusmmol/g DWModel calibrationNAD0.00023C. roseusmmol/g DWModel calibrationNADH0.00030C. roseusmmol/g DWModel calibrationNADP0.000585C. roseusmmol/g DWModel calibrationNADPH0.00037C. roseusmmol/g DWModel calibrationNDP0.010C. roseusmmol/g DWModel calibrationNH40.2279C. roseusmmol/g DWModel calibrationNTP0.00625C. roseusmmol/g DWModel calibrationORA0.00807C. roseusmmol/g DWModel calibrationPi0.1997C. roseusmmol/g DWModel calibrationPPi0.0737C. roseusmmol/g DWModel calibrationSUC1.00C. roseusmmol/g DWModel calibrationSTA1.00C. roseusmmol/g DWModel calibrationSTH0.2C. roseusmmol/g DWModel calibrationOP0.0206C. roseusmmol/g DWModel calibrationEFRU0.04616Daucus carotamM[17]EGLC0.05356D. carotamM[17]ENO3_HA0.06770.281Citrus reticulatamM[45]0.005–0.2Arabidopsis thaliana[46]0.006–0.02Zea mays[43]ENO3_LA1.430.5A. thalianamM[46]0.02–0.1Z. mays[43]0.16D. carota[17]EPI_HA0.00260.007C. roseusmM[47]0.0056C. roseus[48]0.0035C. roseus[49]0.003C. roseus[49]0.0025Nicotinana tabacum[50]0.0079Lemma gibba[51]0.00049Z. mays[52]0.0018Z. mays[52]0.007Chara corallina[37]0.004C. corallina[37]0.025Nitella translucens[53]0.0024Neurospora crassa[54]0.0029N. crassa[54]0.0026D. carota[17]EPI_LA0.0800.900C. roseusmM[49]0.0463C. roseus[49]0.058Nicotinana glutinosa[55]0.076L. gibba[51]0.190C. corallina[37]0.220C. corallina[37]0.370N. crassa[54]1.029N. crassa[54]0.47D. carota[17]ESUC26.69C. roseusmMModel calibrationNO30.5181C. roseusmmol/g DWModel calibrationTable 6Maximum reaction rates (Vmax)Reaction in TPMPCurrent value (mmol/g DW/d)Literature (mmol/g DW/d)SpeciesReferencer174.9934C. roseusModel calibrationr22C. roseusModel calibrationr30.764C. roseusModel calibrationr410,000C. roseusModel calibrationr5150C. roseusModel calibrationr61C. roseusModel calibrationr70.1C. roseusModel calibrationr83.0C. roseusModel calibrationr930.0C. roseusModel calibrationr102.00C. roseusModel calibrationr116.00C. roseusModel calibrationr120.05C. roseusModel calibrationr1315.0C. roseusModel calibrationr142.00C. roseusModel calibrationr165C. roseusModel calibrationr180.764C. roseusModel calibrationr190.1C. roseusModel calibrationr200.01C. roseusModel calibration2115.1C. roseusModel calibration224.6929C. roseusModel calibration230.4986C. roseusModel calibration240.100C. roseusModel calibration251.1377C. roseusModel calibration2633.5326C. roseusModel calibration27 HA0.00150.1555C. reticulata[45]0.072–0.1968Z. mays[43]27 LA0.1670.72–1.92Z. mays[43]281.001.69D. carota[17]290.382C. roseusModel calibration30900C. roseusModel calibration31 HA0.001753.80C. roseus[47]0.415C. roseus[48]0.127C. roseus[49]0.196C. roseus[49]1.96N. tabacum[50]0.0369N. tabacum[50]0.1728L. gibba[51]0.13824Z. mays[52]0.0092C. corallina[37]0.0576N. translucens[53]3.80N. crassa[54]0.0030D. carota[17]31 LA0.0401.268C. roseus[49]0.090C. roseus[49]0.046N. glutinosa[55]0.265L. gibba[51]0.023L. gibba[51]0.104C. corallina[37]0.0576C. corallina[37]10.4N. crassa[54]5.64N. crassa[54]0.045D. carota[17]GLC0.764C. roseusModel calibration320.1400.27D. carota[17]Table 7State variables and initial values (t=0) used for model simulationsComponentValuesUnitsSpeciesReferencesAA0.818/0.779mmol/g DWC. roseusBatch/medium exchangeFRU0.0336/0.0556mmol/g DWC. roseusBatch/medium exchangeGLC0.1625/0.1744mmol/g DWC. roseusBatch/medium exchangeSEC0.00515mmol/g DWC. roseusUnpublished resultsLIP0.1mmol/g DWN. tabacum suspension cells[34]NAD7×10−5mmol/g DWYoung photosynthetic tissue[56]NADH1.25×10−5mmol/g DWYoung photosynthetic tissue[56]NADP8×10−6mmol/g DWYoung photosynthetic tissue[56]NADPH1.12×10−4mmol/g DWYoung photosynthetic tissue[56]NDP2×10−3mmol/g DWYoung photosynthetic tissue[56]NH40.053/0.041mmol/g DWC. roseusBatch/medium exchangeNTP6.8×10−3mmol/g DWYoung photosynthetic tissue[56]ORA0.16mmol/g DWN. tabacum suspension cells[34]Pi0.117/0.100mmol/g DWC. roseusBatch/medium exchangePPi0.0015mmol/g DWPotato tubers[34]SUC0.403/0.330mmol/g DWC. roseusBatch/medium exchangeSTA1.705/1.137mmol/g DWC. roseusBatch/medium exchangeSTH0.081mmol/g DWN. tabacum suspension cells[34]TRY0.001428mmol/g DWC. roseusUnpublished resultsOP0.01mmol/g DWC. roseusModel calibrationEFRU8.33/29.6mMC. roseusBatch/medium exchangeEGLC7.22/23.0mMC. roseusBatch/medium exchangeENH40mMC. roseusCulture mediumENO33.27/3.27mMC. roseusBatch/medium exchangeEPi0.100/0.100mMC. roseusBatch/medium exchangeESUC114.0/149.0mMC. roseusBatch/medium exchangeNO30.385/0.345mmol/g DWC. roseusBatchX0.0197/0.0180gDWC. roseusBatch/medium exchange
Error terms were weighted using the maximum (max(Mi)exp) and the minimum (min(Mi)exp) experimental values (exp) from either batch or medium exchange cultures. This method was preferred to a method using experimental error because the experimental error was very high for some data points and varied with experimental data (Table 8). This method has also showed previously to perform adequately to calibrate a nutritional model on hairy root data [17]. All the experimental data points from batch and medium exchange culture were used for the non-linear least-square regression. The total number of experimental data was then of 411 with 13 different measurements for each of the 31 samples plus eight measurements for intracellular AA. Many set of parameters were tested as initial guesses to improve the fitting. A combination of parameter values (Tables 5, 6) showed to minimize the global error for combined data from batch and from medium exchange cultures, using a convergence criterion of 1×10−6 on the variation of the global error. From the calculation of R2 values (Table 8) for each of the 28 state variables that were fitted (14 state variables in two experiments), it seems that the best fit is obtained for cells growth and nutrient transport and storage (NO3, Pi, NH4). However, the sensitivity analysis also suggests that some parameters can still be optimized (Fig. 4). A critical problem with such a descriptive model is a high number of parameters. The model has 35 maximum reaction rates and 26 affinity constants and the least-square regression was only performed on only 14 of the 31 state variables of the model. It is then possible that the identified solution corresponds to a local minimum. More measurements on metabolite concentration are thus necessary to improve the performance of the model and for being able to perform an adequate identifiability analysis on the parameters. In this context, the proposed model is probably over-parameterized. However, the goal of this work was not to establish a minimal model but a descriptive model that can be used as a tool useful at improving our understanding of plant cell culture.Table 8Mean standard deviations on measured variables and correlation coefficients (R2)ComponentMean SD (%) (batch)Mean SD (%) (medium exchange)R2 (batch)R2 (medium exchange)AA11.8813.830.05210.0413FRU9.9234.960.00120.0415GLC10.8148.290.00580.1059NH49.8626.100.60500.8628Pi35.8512.010.75680.8303SUC25.7945.750.00320.0781STA9.0112.440.00100.0013EFRU15.0618.620.09130.0612EGLC13.2613.910.08380.0785ENO340.766.050.94560.9459EPi26.2743.200.98950.7737ESUC11.2610.830.91230.9461NO313.2624.960.65410.4103X14.7820.460.97500.9708Fig. 4Sensitivity analysis on model parameters for batch (solid bar) and medium exchange (empty bar) cultures. Relative change in error is calculated as described in Sect. 7.1. Parameter adjustment of +50% (a). Parameter adjustment of −50% (b). Parameters not shown have absolute relative error changes that are below 0.05
Simulation of the cells physiological state
Hairy root growth
The model allows estimating root growth from flux ν(32) as well as from the total estimated mass of the root cells constituents per dish (Σ Mi on a mass basis), taking average molecular weights for the cell building blocks (Fig. 5). However, the total mass calculated at initial condition (t=0) was 25% lower than that of the inoculum with 0.0148 g DW per dish as compared to 0.0197 g DW per dish, respectively. The difference of −0.0049 g DW per dish can be explained from the molecular species that are present in the cells but which are not included in the model. Therefore, the estimation of root mass with time obtained from ν(32) was compared with that calculated from total cell mass, but adding a constant correction factor of +25%. Model simulations then describe hairy root growth for both batch and medium exchange cultures. Both root mass estimates from ν(32) and ΣMi are superimposed (Fig. 5). However, the sum of the molecular species is overestimating measured biomass at the end of batch culture because of cell accumulation in diverse compounds while growth slowed down. Surprisingly, both batch and medium exchange cultures behaved similarly with a maximum specific growth rate of 0.035 d−1 and a growth cessation at around 40 d. Periodic medium renewal has avoided nutrient depletion in macronutrients and sugars (Fig. 6). However, the plateau observed for the medium exchange culture may have resulted from a limitation in micronutrients, which were not measured. Therefore, only experimental data obtained before the occurrence of the plateau for the medium exchange culture were used for model calibration and other analyses. The strategy of describing cell growth as a function of intracellular content in building blocks thus showed to perform adequately. This result may support the global model structure as well as the hypothesis of pseudo-steady state for the SPMP. The central primary metabolic network, described here as SPMP, was observed at pseudo-steady state by Rontein et al. [19] for most of in vitro culture duration for tomato suspension cells [20]. However, this hypothesis has to be further investigated.Fig. 5Model simulation for Catharanthus roseus hairy root batch (filled square) and medium exchange (triangle) liquid cultures in Petri dish. a–e. Intracellular concentration in cell building blocks with time. Batch (f) and medium exchange (g) cultures. The specific growth rate is described from ν(32) as a function of intracellular concentration in cell building blocks. Model simulations for batch (solid lines) and medium exchange (dashed lines) cultures, and total mass for the molecular species accounted in the model increased of 0.0049 g DW accounting for non-estimated molecular species (dashed line). Root mass was calculated using average MW for STA (180.15, based on glucose units); SEC (400); TRY (187); NAD/NADH (712/713); NADP/NADPH (744.4/745.4); NDP/NTP (476/507); ORA (809.75); STH (180.15, based on glucose units); OP (average of 305 from nucleotides); LIP (810, based on that of A-CoA); IPP (246) and AA (average of 136.75)Fig. 6Extracellular concentration in nutrients with time. Experimental data for C. roseus hairy root batch (filled square) and medium exchange (triangle) liquid cultures. Concentration in sugars (a–c), inorganic phosphate (d) and nitrate (e) in the culture media with time. Model simulations for batch (solid lines) and medium exchange (dashed lines) cultures
The cells building blocks
The measured total AA concentration decreased with time for the batch culture and reached a plateau for the medium exchange culture (Fig. 5a). Simulated AA concentrations seem to follow the trend for experimental data but were overestimated for both batch and medium exchange cultures. The deviations cannot be explained, however, by exuded AA and proteins since no AA were detected in the used culture media. Values of 0.63±0.10 to 0.82±0.10 mmol AA/g DW were measured for the batch culture which corresponds to 0.088±0.014 and 0.12±0.014 g AA/g DW, respectively (taking an average amino acid MW of 140 g/mol). Higher values were measured in the medium exchange culture with 0.63±0.15 to 1.1±0.14 mmol AA/g DW, which represents 0.12±0.021 and 0.16±0.020 g AA/g DW, respectively. Free AA content of 0.21 mmol AA/g DW (estimated at 0.029 g AA/g DW) is reported in literature for tobacco suspension cells using B5 medium [34] and 0.15 mmol AA/g DW (estimated at 0.021 g AA/g DW) in potato tuber [35, 36]. In tomato cell culture, the total protein content was of 0.1–0.4 g proteins/g DW [19]. The total AA mass per root dry weight that have been measured, which represents the sum of free AA and that of peptides and proteins, is thus within the range reported in literature. The use of a minimal medium may explain a low value for total AA. The other cell building blocks were not measured but the model estimations were close to literature data. Total ORA concentration was estimated at 0.15 mmol/g DW as compared to 0.42 mmol/g DW reported by Farré et al. [35]. Total STH were estimated at 0.14 mmol/g DW as compared to a range of 0.3–1.6 mmol/g DW (on the basis of glucose units). Maximal simulated rates of biosynthesis were compared with that from literature. The rate of AA biosynthesis (v(r5)) was estimated at 0.12 mmol/g DW/d, which was within the range of 0.094–0.36 mmol/g DW/d reported by Rontein et al. [19] for tomato suspension cells. STH biosynthesis (v(r12)) was slow with 0.009 mmol/g DW/d as compared to 0.36 mmol/g DW/d [19]. Maximal net rate of starch (STA) biosynthesis (v(r14)) was 0.20 mmol/g DW/d as compared to 0.15 mmol/g DW/d [19]. Differences in metabolic fluxes may be explained from the differences in the specific growth rate. Rontein et al. [19] have reported a specific growth rate of 0.4 d−1 for tomato suspension cells in B5 medium as compared to 0.035 d−1 in this study for C. roseus using a minimal medium. The same minimal medium has been reported previously to induce lower growth rate as compared to standard media for carrot hairy root [17].
The cells nutritional state
Extracellular sucrose (ESUC) concentration profile was simulated by the model for both the batch and the medium exchange cultures (Fig. 6), thus suggesting that the sucrose hydrolysis modelling strategy was adequate. In the case of glucose (EGLC) and fructose (EFRU), simulations for the batch culture followed the trend of experimental data but before growth cessation. Then, estimated glucose and fructose levels stayed high as compared to experimental data. This may suggest that the model is underestimating glucose and fructose uptake at reduced growth. However, simulated concentrations in intracellular sucrose (SUC) and glucose (GLC) were following similar trends than experimental data (Fig. 7). However, model simulated constant starch (STA) concentration and overestimated fructose (FRU) concentration. In the case of the medium exchange culture the model simulated adequately experimental data on extracellular and intracellular sucrose and intracellular glucose. Extracellular glucose and fructose concentrations were underestimated and starch and fructose concentrations were overestimated. A maximal sucrose rate of hydrolysis (v(28)) of 0.72 mmol/g DW/d was estimated as compared to 1.7 mmol/g DW/d for D. carota hairy root using same minimal medium [17]. Contents of 0.25 mmol SUC/g DW (batch) and 0.7 mmol SUC/g DW (medium exchange) were obtained as compared to 0.05 mmol SUC/g DW [19], 0.26 mmol SUC/g DW [36] and 0.4 mmol SUC/g DW [34]. For free glucose, cell contents of 0.3–0.05 mmol GLC/g DW were obtained as compared to 0.6 mmol GLC/g DW [19], 0.24 mmol GLC/g DW [36] and 0.18 mmol GLC/g DW [34]. For fructose, cell contents of 0.1–0.25 mmol FRU/g DW were observed as compared to 0.009 mmol FRU/g DW [35], 0.21 mmol GLC/g DW [34] and 0.5 mmol GLC/g DW [19]. Starch accumulation reached 1.25 mmol STA (based on glucose)/g DW as compared to 0.055 [34] and 0.1–0.6 mmol STA (based on glucose)/g DW [19].Fig. 7Intracellular concentration in nutrients and metabolites with time. Experimental data for C. roseus hairy root batch (filled square) and medium exchange (triangle) liquid cultures. Intracellular concentration in sugars (a–d), inorganic phosphate (e), nitrate (f), ammonium (g), and in secondary metabolites issued from tryptamin (h) and secologanin (i) with time. Model simulations for batch (solid lines) and medium exchange (dashed lines) cultures
Model simulations of extracellular Pi and NO3− (ENO3) concentrations followed experimental data for the complete duration of the batch and the medium exchange cultures (Fig. 6). Hairy root growth (simulated and experimental) has ceased concurrently to ENO3 depletion suggesting this ion to be limiting in the batch culture. Intracellular Pi and NH4 were simulated (Fig. 7). It is interesting to note that the final intracellular Pi concentration in the batch culture seemed to reach a plateau at 0.05 mmol/g DW which was simulated. This plateau may be close to the Pi level that is essential to maintain the endogeneous metabolism [37]. A maximum Pi accumulation plateau was also observed for the medium exchange culture around 0.2 mmol/g DW. This value is close to the maximum value of 0.23 mmol/g DW measured for carrot hairy root [17, and references therein]. Maximum intracellular nitrate of 0.6 mmol NO3/g DW was measured for both cultures. Intracellular nitrate was kept constant for the medium exchange and decreased to its initial value for the batch. Intracellular ammonium reached a value of 0.12 mmol NH4/g DW for the medium exchange culture and decreased to 0.09 mmol NH4/g DW after 30 d. For the batch culture, intracellular ammonium reached a maximum value (0.08 mmol NH4/g DW) at day 5 and then decreased closely to its value at inoculation. The model overestimated intracellular NO3 concentration and simulated experimental intracellular concentrations in NH4 for both the batch and medium exchange cultures. A more precise description of the secondary metabolism and of the AA biosynthesis may be required to improve model simulation of nitrogenous compounds.
The cells energetic state
Model has simulated energy rich cells with high levels in NTP and NADH at exponential growth (Fig. 8). However, estimated cell content in NADPH showed an opposite trend with lower values at exponential growth. This result is interesting since NADPH is produced through the pentose-phosphate pathway, which is mostly active at secondary metabolism. The simulated cell energetic level decreased after 20 d at the initial value (inoculation) in batch culture and was constant for the medium exchange culture. Since the medium was renewed every 3 days for the medium exchange experiment, a pseudo-steady state was expected. NTP/(NTP+NDP) and NADH/(NAD+NADH) ratios of ∼75% have been reported for tobacco suspension cells [34]. Farré et al. [35] measured ratios of ∼73% for NTP/(NTP+NDP) in potato tubers. These authors have measured an NTP level of 0.00013 mmol/g DW as compared to 0.00143 and 0.00074 mmol/g DW that was obtained from simulations at exponential growth and stationary growth, respectively. We have recently measured by in vivo NMR ATP levels of 0.009 mmol/g DW at day 1 and 5, and of 0.0065 mmol/g DW at day 10 for suspension cells of E. californica cultured using B5 medium [38]. Energetic levels simulated by the model were then similar to that found in literature. However, variation of energy shuttles concentration has to be further investigated.Fig. 8Energetic level of the cells with time. Intracellular NTP (a), NADH (b) and NADPH (c) relative levels with time. Model simulations for C. roseus hairy root batch (solid lines) and medium exchange (dashed lines) liquid cultures
Conclusion
A metabolic model capable of describing hairy root growth from the estimation of the cells physiological state was developed. The model includes the central metabolism, the primary metabolic pathways (SPMP) assumed at steady state and a network for the TPMP. At this point, the model is simplified and intracellular compartmentalization processes into the different cell compartments and organelles are not included. Nevertheless, the metabolic model showed to perform efficiently in simulating hairy root growth and nutrition. The use of intracellular concentrations in nutrients and co-substrates as well as the cells energetic state seems an efficient strategy in describing regulation of the metabolic fluxes. However, more experimental is required for improving the model structure as well as parameter values which may be regulated with cell physiological state. Finally, the model will be applied to other plant species as well as cell suspensions, and it will be studied as a tool to describe transient processes such as metabolic regulation.

metabolic model
metabolic regulation
plant cells
kinetic model
cell nutrition


A global analysis of NMR distance constraints from the PDB

Information obtained from Nuclear Magnetic Resonance (NMR) experiments is encoded as a set of constraint lists when calculating three-dimensional structures for a protein. With the amount of constraint data from the world wide Protein Data Bank (wwPDB) that is now available, it is possible to do a global, large-scale analysis using only information from the constraints, without taking the coordinate information into account. This article describes such an analysis of distance constraints from NOE data based on a set of 1834 NMR PDB entries containing 1909 protein chains. In order to best represent the quality and extent of the data that is currently deposited at the wwPDB, only the original data as deposited by the authors was used, and no attempt was made to ‘clean up’ and further interpret this information. Because the constraint lists provide a single set of data, and not an ensemble of structural solutions, they are easier to analyse and provide a reduced form of structural information that is relevant for NMR analysis only. The online resource resulting from this analysis (http://www.ebi.ac.uk/msd/srv/docs/NMR/analysis/results/html/comparison.html) makes it possible to check, for example, how often a particular contact occurs when assigning NOESY spectra, or to find out whether a particular sequence fragment is likely to be difficult to assign. In this respect it formalises information that scientists with experience in spectrum analysis are aware of but cannot necessarily quantify. The analysis described here illustrates the importance of depositing constraints (and all other possible NMR derived information) along with the structure coordinates, as this type of information can greatly assist the NMR community.
Introduction
The information contained in the world wide Protein Data Bank (wwPDB) (Berman et al. 2007) is growing steadily, with increasing numbers of structures being deposited from both traditional single laboratory sources and recent structural genomics efforts. The two main methods to determine these structures are X-ray crystallography and Nuclear Magnetic Resonance (NMR). NMR structures account for around 15% of all entries in the wwPDB. While inherent size restrictions limit the method to molecules of lower molecular weight, NMR has still made a significant contribution to protein folds and molecular interaction data. However, NMR structures are less straightforward to use than structures determined by X-ray because they are often represented as ‘ensembles’ of structures, where the whole ensemble (and not individual structures by themselves) represents the solution of the structure determination problem based on the experimental data. The reason for this is that information derived from NMR is insufficient with respect to the structure calculation process and thus cannot lead to a single exact solution. For example, measured distance-related NOE data is ensemble and time averaged, so that the final observed NOE data for a set of multiple distinct conformations in fast exchange will be a degenerate mix of the distance information in each of those conformations. All calculated structures that conform to a set of criteria based on the fit to the experimental data (NMR derived constraints) and physical characteristics encoded in the calculation process (overall energy minimum, inter-atomic packing, …) are therefore in principle equally valid (Spronk et al. 2003). However, there is no ‘standard’ set of criteria, and different programs and researchers use different sets when selecting the ‘best’ structures out of the calculated ones. The quality of the NMR structures deposited at the wwPDB therefore varies widely (Nabuurs et al. 2006). This problem is being addressed by novel structure determination methods like Inferential Structure Determination (ISD) (Rieping et al. 2005) that perform more objective structure calculations and select statistically relevant ensembles as a representative solution to the experimental data. These methods are, however, computationally expensive.
The observed NMR data is used in structure calculations to constrain inter-atomic distances, relative bond orientations and/or dihedral angles. Only just over half of the NMR entries in the wwPDB were deposited together with the constraint lists used in the structure calculation process. These constraint lists provide very valuable information, as, for example, they enable recalculation of the structures with better or different protocols, and a globally consistent comparison of the constraints to the original coordinates for validation purposes. However, a major problem in using this information is that constraint files come in many file formats, and that the atom naming and residue numbering in the coordinate and the constraint files often differs. To handle the problem of different file formats, constraint lists are now continuously converted into the NMR-STAR format at the BioMagResBank (BMRB) (Doreleijers et al. 2003; Ulrich et al. 1989). A further step, as part of the DOCR project (Doreleijers et al. 2005), addresses the atom naming and residue numbering problem by directly relating the constraint atoms to the coordinate atoms and molecular system using the FormatConverter and CCPN data model (Fogh et al. 2002; Vranken et al. 2005). This data is then checked for consistency and redundant constraints are removed using the WATTOS software as part of the FRED project (Doreleijers et al. 2005). In the original implementation the DOCR/FRED project resulted in a set of more than 500 internally consistent constraint lists, molecular system information and structure coordinates. This data led to the construction of the RECOORD (Nederveen et al. 2005) and DRESS (Nabuurs et al. 2004) databanks, where structures from the PDB were respectively recalculated and re-refined based on the cleaned up constraint lists.
These efforts, as well as validation software like AQUA (Doreleijers et al. 1998) or Procheck-NMR (Laskowski et al. 1996), are applied on a per-entry basis, where the original or recalculated coordinates are related to the original or standardised constraint lists. With the amount of constraint data that is now available it has become possible to do a global, large-scale analysis using only the information from the constraints, without taking the coordinate information into account. The constraint lists are the ‘final product’ of the usually human analysis of NMR spectra, and as such they represent the experimental NMR-derived information that is relevant for the structure calculation. The constraint lists also provide a single set of data, whereas NMR structures are usually represented as ensembles that can be calculated in many different ways, which complicates their interpretation. Analysing the constraint data on a large scale can thus provide insights into the NMR data analysis process (e.g. which type of inter-atomic contact is often derived from the spectra), and the relation of the constraints to the coordinate data (e.g. does the structure calculation process add any distance information that is relevant for NMR).
The analysis described here relates only to distance constraints derived from NOE data, with a base set of 1834 NMR PDB entries containing 1909 protein chains. Only constraints between protons in protein chains were retained for analysis, and for validation purposes the base set was further divided into subsets for entries that contain intra-residue constraints and entries where all the original constraint and coordinate information was recognised and linked to each other. A coordinate data set based on the original coordinate files was also generated and used for comparison. This article explores some of the issues surrounding distance constraints and the NMR data they are derived from, and hopes to highlight the importance of depositing the constraint lists used for structure calculations along with the molecular coordinates.
Materials and methods
The data was obtained from two sources: the molecular system, coordinate, secondary structure and author information from the wwPDB, and the original constraint information as NMR-STAR files from the NMR Restraints Grid at the BioMagResBank. Each file was directly parsed and combined into the CCPN data model via the FormatConverter software (Vranken et al. 2005), in a process that extends the procedure used in the original DOCR/FRED project. To handle the larger number of entries an automatic mapping procedure was developed that maps the molecule sequence as derived from the PDB file to the atom information and sequence code numbering used within the constraint lists. For some entries manual mapping between the information from the PDB file and the constraint file was required. The original 409 mappings from the RECOORD project (by Aart Nederveen) and a further mappings 124 by the author and 17 by Jurgen Doreleijers were used to correctly set the PDB-constraint file mapping for the entries in the base set. Using the automatic or manual mapping the atom information from the constraints was then connected to that for the molecule. During this process the dependence on string-based atom names for the assignment (as used in all constraint files) was also removed, since the CCPN data model is object-based. The final CCPN project, in which all the information from the original files is now highly organised, was then written out. This process was completed for 2643 PDB entries.
Three subsets of the base set were generated for comparison and validation purposes (Table 1). Sets HIP and AHIP contain only entries with intra-residue constraints, sets AHP and AHIP only include entries where over 99% of relevant constraint information was assigned to atoms. In addition a set was generated based on the coordinates for the entries included in the HP set. Only the HP, HPC and AHIP sets are further referred to in this article, the HIP and AHP sets are available online for reference purposes.
Table 1Overview of the available data sets used in the analysisSet NameData typeDetails1HPConstraintsBase set2HIPConstraintsIntra-residue3AHPConstraintsHigh assignment4AHIPConstraintsIntra-residue, high assignment5HPCCoordinatesOriginal coordinate data
A workflow based on Python (van Rossum 2003) scripts and dictionaries was then developed to handle the information from the CCPN project files for the 2643 entries (Fig. 1). This workflow was run separately for the base set and each subset. In the first step, the original information was filtered so that only valid constraints between protons in protein chains were retained (Fig. 1). Entries were removed for the following reasons (Table 2): (1) No valid protein chains: the entry contained only chains that are sequence fragments or duplicates of other chains (only the chain with the highest number of valid constraints linked to it is retained in the data set), (2) No valid constraint lists: the originally deposited constraint lists could not be parsed or handled correctly, or (for sets HIP and AHIP), did not contain any intra-residue constraints, (3) Insufficient linking: less than 80% (sets HP, HIP) or 99.9% (sets AHP, AHIP) of the constraint information could be linked to the atom information (constraint information belonging to non-protein chains was ignored for this purpose), (4) Insufficient valid constraints: less then 20% of constraints remained for all lists after removing invalid constraints. Constraints were considered invalid if they did not have any valid items, no upper distance limit, an upper distance limit of larger than 10 Å, or had only items between invalid atoms (non-proton, unlinked or non-protein). Note that some entries had specific distance constraint lists and/or constraints removed for these reasons, but were still included in the analysed set.
Fig. 1Overview of the workflow employed in the analysis. Grey boxes indicate files, white boxes Python scriptsTable 2Overview, for each data set, of the number of removed and analysed entriesHPHIPAHPAHIPNo valid protein chains396396396396No valid constraint lists310409310409Insufficient linking4837677635Insufficient valid constraints55555555Total included entries1834174612031146Total included chains1909181712521192
In the second step, the data from all relevant entries was collated (Fig. 1). After reading in the CCPN projects, non-relevant information was removed based on the filtering information, and the data reorganised into a set of Python dictionaries that contain the overall information on the entry, residue and constraint levels. In the final analysis step these dictionaries were read in, areas and data of interest were marked, and organised HTML output was produced for browsing. A Python dictionary with highly reduced information that can be further used for validation or constraint filtering purposes was also generated.
The same 1834 entries from the HP set were used to generate the HPC set. The original coordinates were analysed using r−6 distance averaging for equivalent and prochiral atom sets over all structures in the ensemble (Nilges 1995). Only individual distances of less then 7 Å were retained, and final averaged distances of less than 5 Å were considered to be equivalent to an observable constraint contact. Atoms without coordinates were ignored in the analysis.
Highlights from the analysis are described in the results section, and complete details are available from a web site (http://www.ebi.ac.uk/msd-srv/docs/NMR/analysis/results/html/comparison.html). For all statistical operations, the R package (Bates et al. 2007) was accessed via the RPy Python module (Moreira and Warnes 2006). Since a contact is either observed or not observed, it was possible to use a binomial analysis to determine, for example, which secondary structure specific contacts were significantly less or more likely to be observed. Binomial analysis was used throughout with a confidence level of 0.99, meaning that only 1 out of every 100 determined outliers is a false positive. The correlations between the coordinate and the constraint data within a data set and correlations between data sets were plotted via RPy, with linear correlation coefficients determined by both the Spearman and Pearson methods. The Spearman method (Spearman 1904) is a non-parametric measure of correlation, which does not make assumptions about the frequency distribution of the variables, and does not require a linear relationship between the variables. The Pearson method (Pearson 1896) on the other hand assesses if the relationship between the variables is linear.
In the analysis, a residue is marked as ‘assigned’ when at least one proton belonging to it is linked to a constraint. The total number of times a particular inter-atomic contact is observed can be a fraction, as for ambiguous constraints each constraint item contributes a fraction of 1 to the total:
The total number of relevant distances for a particular inter-atomic contact (ndist) is always an integer. The occurrence for a particular inter-atomic contact is calculated as: where nactual is the number of times the contact occurs (with ambiguity taken into account), and npossible the total number of times this contact could occur between the relevant residues, either for all residues or only between ‘assigned’ residues. The occurrence is given in percent or as a fraction. The ‘ambiguity’ of an inter-atomic contact is defined as:
If the ambiguity is 0, this means that all contributing contacts are unambiguously assigned. The more highly ambiguous the contributing contacts are, the closer this number will be to 1, which also means it is less dependable. Within secondary structure combinations, the same definitions are used, except that npossible and nactual are now determined within that secondary structure combination as npossible,ss and nactual,ss. The uniqueness of a contact for a secondary structure combination, which indicates how unique the contact is within that combination, is defined as:
For prochiral and possible non-equivalent atom sets, the contacts are divided into the individual atom names (e.g. Hβ2 and Hβ3, or Hδ1 and Hδ2 for Phe) if they occur by themselves in a constraint. If both the atom names occur in different items within the same constraint to the same other atom, then they are grouped (e.g. Hβ*, or Hδ* for Phe). If they occur as a group in one constraint item they are used as is. In order to obtain total statistics for these contacts, they were also combined (e.g. (Hβ2 + Hβ3), or (Hδ1 + Hδ2) for Phe). To get the combined occurrence, the nactual for the group is added to the individual contribution with the highest nactual to obtain the nactual used to calculate the occurrence for the combined contact. The combined distance information is obtained from all contributions, and the ambiguity is then calculated from the total nactual of all contributions.
Results
Information from analysis
The analysis of the data for each set is divided into separate categories (visible on the left-hand side menu in Fig. 2): (1) Contact analysis: Arranges inter-atomic distances by residue–residue combination, secondary structure of those residues, and contact type (intra-residue (i–i), sequential (i–i + 1), medium-range defined here as up to 6 residues separation (i–i + n), and long range (i–i + 6<)). (2) Protein secondary structure analysis: Groups inter-atomic distances by secondary structure combinations. (3) Residue atom analysis: Shows assignment percentages for the atoms in each amino acid. (4) Unassigned fragments breakdown: Lists unassigned sequence fragments. (5) Fragment analysis by residue: Analyses tripeptide fragments based on the assignment status of the central residue.
Fig. 2Example web page for Ala → Ala i → i + 2 contact information from http://www.ebi.ac.uk/msd-srv/docs/NMR/analysis/results/html/comparison.html. The different data sets, comparisons between them, and analysis categories can be accessed via the left hand side menu. In this contact information page, overall statistics for the individual Ala residues involved in this contact are shown in the ‘Residue 1’ and ‘Residue 2’ tables at the top, statistics for the combined Ala–Ala residues in the ‘Residue combination’ table. The information on an atom level is listed in the ‘Breakdown per contact’ table. Outliers per secondary structure combination based on a binomial analysis are highlighted in red (higher than expected) and blue (lower than expected). This colour coding is used throughout the web pages for other types of analyses
Validation of data sets
The relevance of the base set (HP) was validated by comparison with the most restricted AHIP set. This is necessary because the HP set contains entries without intra-residue constraints and entries where less constraint information is linked to atoms. The correlation between the occurrences of contacts between both sets is very high (0.97) (Fig. 3), and in a breakdown per contact type no correlation is less than 0.91 (results on web pages). A further detailed analysis shows that out of 43,984 compared contacts only 5 differ significantly at a confidence level of 0.999. Of these, 3 are His → His contacts where the differences are most likely introduced by changes in the number of His residues that are assigned in the data sets (from 71.66% in HP to 68.47% in AHIP). The other 2 are long-range contacts involving side chain protons between Leu → Phe and Phe → Val, which are uncommon, and these differences can be attributed to accidental variations in the number of entries that have these contacts and are included in the data set. Overall, this data shows that including the additional 688 entries does not introduce major changes in the occurrence levels. The HP set was therefore chosen as the reference set, as estimates of, for example, significant differences between contacts in secondary structure elements tend to become more reliable as more data is included. Information on correlations between all data sets is available from the web pages (Fig. 2, the ‘Comparison’ link in the left-hand side menu).
Fig. 3Correlation between the foccurrence for the HP and AHIP data sets (correlation Spearman 0.971, Pearson 0.996)
A further way to validate the constraint information is that it should reproduce the typical contacts that are observed in secondary structure elements. The secondary structure definitions as determined by DSSP (Kabsch and Sander 1983) were taken from the PDB file header for each entry. Because of the size of the data that is generated by the analysis, only the Ala residue is used here as an example. The complete information can be accessed via the web pages (Fig. 2). The numbers that are relevant in order to determine whether a contact is significant for a particular secondary structure element are the occurrence within that particular secondary structure element (which has to be significantly higher than expected from the overall occurrence), the ambiguity of the contact (if it is high it comes, by definition, from highly ambiguous constraints and is therefore unreliable), and the uniqueness of the contact (which indicates how often the contact is seen within that secondary structure element compared to the total number of times it is observed).
For intra-residue contacts there are not many significant differences in the observed occurrence within different secondary structure elements, although overall fewer contacts are observed when secondary structure is absent (Table 3). This is likely due to higher signal overlap for atoms in ‘random coil’ fragments, which complicates assignment. The information from the coordinate-derived HPC set is provided throughout for comparison: there are, as expected when using a distance cutoff of 5 Å, no differences for this HPC set between the occurrence for different secondary structure elements, and only minor differences in the average and mean distance are observed (data available on web pages).
Table 3foccurrence for selected backbone Ala–Ala contactsTypeAtom 1Atom 2α-helixβ-sheetNo secondary structurei → iHHα0.50/1.000.51/1.000.43/1.00HHβ*0.73/1.000.68/1.000.57/1.00HαHβ*0.32/1.000.33/1.000.29/1.00i → i + 1HH0.84/1.000.50/1.000.57/1.00HHβ*0.22/0.990.07/0.690.10/0.83HαH0.52/1.000.90/1.000.67/1.00HαHβ*0.03/0.420.30/1.000.11/0.93i → i + 2HH0.47/0.990.00/0.000.16/0.45HHβ*0.09/0.790.00/0.000.03/0.25HαH0.28/0.970.04/0.040.17/0.60HαHβ*0.02/0.630.00/0.000.02/0.27Hβ*H0.22/0.980.09/0.450.17/0.77Hβ*Hβ*0.02/0.120.05/0.700.01/0.51i → i + 3HH0.09/0.860.04/0.120.04/0.16HHβ*0.12/0.840.04/0.120.04/0.22HαH0.66/0.990.00/0.040.14/0.28HαHβ*0.58/0.990.00/0.040.14/0.33Hβ*H0.14/0.910.04/0.160.06/0.34Hβ*Hβ*0.11/0.970.04/0.120.07/0.46i → i + 4 HH0.02/0.010.00/0.000.02/0.03HHβ*0.01/0.010.05/0.090.02/0.07HαH0.32/0.940.00/0.000.07/0.16HαHβ*0.02/0.790.00/0.000.02/0.23Hβ*H0.09/0.850.00/0.090.02/0.22Hβ*Hβ*0.03/0.930.00/0.090.01/0.37In the secondary structure columns, the first value is from the HP set, the second from the HPC set. A bold value indicates a contact that occurs significantly more than average, a italic value significantly less
For sequential Ala–Ala contacts, the H–H contact is observed significantly more in α-helices than in β-sheets (Table 3), and is also highly unique (0.65). This situation is, as expected, reversed for the Hα–H contact, which is observed significantly less in α-helices and more in β-sheets. Overall, however, this contact is more uniquely observed in α-helices (0.49 compared to 0.08 for β-sheets), which is due to the prevalence of Ala–Ala fragments in α-helices (56.2% compared to 5.35%). Interestingly, however, an H–Hβ* contact is also observed significantly more in α-helices than in β-sheets or when no secondary structure is present, and has a uniqueness of 0.71, so within a sequential Ala–Ala fragment this type of contact is highly predictive of α-helical structure. The sequential Hα–Hβ* contact is, on the other hand, highly predictive of β-sheet with a uniqueness of 0.20, although it is on average mostly observed when no secondary structure is present (0.38). This illustrates that the uniqueness of a contact is strongly related to the prevalence of a particular sequence combination in a particular secondary structure element, and is not necessarily indicative of the kind of secondary structure element a particular contact usually occurs in. The information from the constraints and the coordinates show clear differences, as illustrated by comparison with some of the contacts described earlier. The H–Hβ* contact occurs quite often in β-sheets based on the coordinate data, with a median distance that is slightly higher than in α-helices (4.63 Å compared to 4.31 Å). The Hα–Hβ* contact, which would generally be difficult to identify due to overlap in the aliphatic region of a NOESY spectrum, is always present based on the coordinate data, but is only seen in 0.30 cases based on the constraints. These differences illustrate that the NOE constraint data not only incorporates distance information, but also encodes NMR-specific information such as the difficulty with which a particular contact can be assigned.
For i–i + 2 and i–i + 3 contacts, as expected, the typical H–H, Hα–H, Hα–Hβ* and Hβ*–H contacts are highly prevalent for α-helices (Table 3), with generally high uniqueness and low ambiguity. An H–Hβ* contact is also more often observed than average (respectively in 0.09 and 0.12 cases), while Hβ*–Hβ* contacts are very rarely seen for i–i + 2 contacts in an α-helix. Note that based on the coordinate data the i–i + 2 Hβ*–Hβ* contact is highly relevant for β-sheets (0.70), but it is in practice rarely observed (0.05), probably because it falls in a densely populated region of a typical NOESY spectrum. For 310 helices the percentages are often similar to the α-helical ones, but there are often not enough data to determine whether a difference is significant (data on web pages). Also of interest is the i–i + 3 contact between Hβ*–H, which occurs in 0.04 cases for β-sheets and 0.06 cases where secondary structure is absent. The binomial analysis indicates that the 0.06 fraction is observed significantly less, while it does not mark the 0.04 fraction. This is because this type of analysis is dependent on sample size (only 1 sample for the 0.04 fraction, 12 for the 0.06 fraction).
For the i–i + 4 contacts, Hα–H and Hβ*–H connections are again highly prevalent for α-helices, while Hα–Hβ* and Hβ*–Hβ* contacts are present in the coordinate set but are seldom observed in practice (Table 3). All contacts with a separation of 5 residues or higher are very rarely observed in α-helices, but become highly prevalent for β-sheets (data not shown). The only exception to this are long range Hα–Hβ* and Hβ*–Hβ* contacts, which are seen in significantly higher percentages between α-helices as compared to the average.
Contact data highlights
Traditionally, and as described above, identifying secondary structure contacts is based on the commonly observed contacts between protons from the backbone and the β position (Wüthrich 1986). However, with experience in assigning NOE peaks comes the knowledge that other contacts are also often observed (e.g. i → i + 2 contacts between side chain protons in a β-sheet). In this analysis, such contacts are readily observed (Table 4). For example, the sequential Trp Hε3–Gly H contact is quite common based on the coordinate data, but is in practice particularly observed in a β-sheet. The sequential Trp Hε3–Phe Hα contact is seemingly more often observed in an α-helix, but the differences are not significant. This is a case that could be clarified if more relevant data were available. The Thr Hγ2*–Tyr Hε* i–i + 2 contact is clearly observed in mostly β-sheet. Interesting in this case is that according to the constraint data it can occur in an α-helix, while this is not the case based on the coordinate data, even though the ambiguity of the contact is 0.00. This is possible because this data point is based on one contact with an upper distance limit of 6 Å, whereas the cutoff used for coordinates is 5 Å. Generally speaking this type of situation can occur for highly ambiguous constraints, where other constraint items satisfy the upper distance limit. An Hα–Hδ1* i–i + 3 contact between Ala and Ile is observed almost exclusively in an α-helix (and never in a β-sheet), and is very unique (0.78). To be able to discern whether this contact is very common from the Hα of any amino acid to the Hδ1* of an Ile, the data was joined as Xxx residues to produce generic information to and from each amino acid (data on web pages). The specific information for the i–i + 3 Hα–Hδ1* contact from all residues to Ile is shown in Table 4 and shows that this contact is common in α-helices. Finally, some other interesting i–i + 4 side chain contacts that often occur in helices are listed in Table 4.
Table 4foccurrence for selected secondary structure related contactsTypeAtom 1Atom 2α-helixβ-sheetNo secondary structurei → i + 1Trp Hε3Gly H0.05/0.450.56/0.880.24/0.63Trp Hε3Phe Hα0.55/0.680.11/0.160.13/0.47i → i + 2Thr Hγ2*Tyr Hε*0.02/0.000.46/0.800.12/0.41i → i + 3Ala HαIle Hδ10.66/0.930.00/0.000.11/0.21Xxx HαIle Hδ10.57/0.920.00/0.020.09/0.22i → i + 4Trp Hζ2Thr Hγ20.52/0.560.00/0.000.00/0.00Tyr Hε1 + Hε2Val Hγ20.47/0.740.00/0.050.06/0.21In the secondary structure columns, the first value is from the HP set, the second from the HPC set. A bold value indicates a contact that occurs significantly more than average, an italic value significantly less
It is not possible to describe all information in detail in this article, and the web pages serve as the reference resource for any investigations. However, to provide a better overview of the overall trends in secondary structure elements, all backbone contacts were grouped by atom type (H, Hα, Hβ) and secondary structure combinations (Table 5, full data from web site). For intra-residue contacts, more contacts involving Hβ protons are defined in β sheets. Sequential contacts in α helices originating from the H and Hβ protons are observed significantly more often, whereas ones originating from the Hα proton are less common. This situation is reversed in β sheets (except for Hβ–H contacts). There are, only for sequential contacts, some discrepancies between the data from the HP and HPC sets, with, for example, the rate at which sequential H–Hα contacts are observed being reversed in the HPC set as compared to the HP set. The reasons for this are not immediately clear, but are likely related to overlap. Most i–i + 2 contacts are more common in α helices, except for ones to the Hα proton and between Hβ protons. The latter contact is more often observed in β sheets. As expected most i–i + 3 contacts are commonly observed in α helices, except for Hβ–Hα and H–Hα. The latter is again more frequently seen for β sheets, but in this case this is expected to be between different strands in the hairpin area. The trends are not as clear for i–i + 4 contacts, where Hα–H, Hα–Hβ and Hβ–H contacts are more frequent in α helices, and all other ones more frequent in β sheets. This is again likely related to hairpin contacts. All contacts from i → i + 5 and more are very infrequent for α helices but relatively very frequent for β sheets.
Table 5Brief overview of general trends in joint secondary structure information for all contactsTypeSSH (i)Hα (i)Hβ (i)HHαHβHHαHβHHαHβi–iHelix. . + .. .− .− .+ .− .− .Sheet. .+ .. .. .+ .+ .+ .+ .i–i + 1Helix+ .+ −+ +− .− +−−+ .+ ++ +Sheet− .− +−−+ .+ ++ ++ .−−−−i–i + 2Helix+ +−−+ ++ +- -. ++ +−−−−Sheet−−. −−−−−. −. −−−+ .+ +i–i + 3Helix+ +. −+ ++ ++ ++ ++ +−−+ +Sheet−−+ +−−−−. −−−−−. −−−i–i + 4Helix. .−−−−++. .+ ++ +−−. +Sheet+++ ++ .−−+ −. −. −+ .+ −i–i + 4<Helix−−−−−−−−−−−−−−−−−−Sheet+ ++ ++ ++ ++ ++ ++ ++ ++ ++ Indicates that signals observed more than average, − less than average, . signifies that there is no trend. The first character in each cell contains the constraint HP set information, the second the coordinate HPC set
An analysis of the percentage of atoms that were assigned within each residue type (Residue atom analysis on the website) shows that generally atoms are significantly higher assigned in α-helices and β-sheets, and lower when no secondary structure is present. This finding is not surprising as the secondary structure elements are defined by constraints, and the atoms have to be assigned to obtain those. Another general trend is that prochiral methylenes are within α-helices significantly more degenerated, i.e. the HB2 and HB3 atoms exists as a QB pseudoatom or an HB* type atom set. This type of analysis can be significantly improved by cleaning up the stereospecific assignment status based on the coordinates.
The unique sequence fragments for which no assignments were found are also listed on the website (Unassigned fragments breakdown). An example from this data is that often no constraints are found for His tags. The LEHHHHH fragment, for example, was not assigned in 13 entries. A general overview of the percentage of residues that are assigned confirms that His residues, for example, are assigned in only 71.66% of cases, while Trp is assigned in 97.87% of cases (Fragment analysis by residue).
To examine this in more detail, all tripeptide fragments where a particular amino acid is the central residue are listed (for the N- and C-terminus these are dipeptide fragments). Listed for each fragment are (1) the total number of times the tripeptide fragment occurs in the data set, (2) the percentage of times it is unassigned compared to the total number of times the amino acid occurs, (3) the number of times the amino acid is not assigned, (4) the number of times the tripeptide fragment occurs overall, and (5) the assignment percentages per secondary structure element. The entries in which the fragments are unassigned are also listed. Continuing with His as an example, it is not assigned when part of the EHH fragment in 69% of cases, and when part of a C-terminal HH fragment it is not assigned in 96% of all times the fragment occurs. To get a better overall view of the sequence fragments that are difficult to assign, they were grouped by joining, respectively, the i − 1 and i + 1 residues. The results for His and some selected other fragments are shown in Table 6. A Ser residue preceded or followed by a Gly, for example, is often unassigned. This type of information could be useful for predicting which areas of a protein sequence are difficult to assign from an NMR perspective.
Table 6Selected sequence fragments where the central residue is often unassigned. The unassigned percentages are relative to the total number of times the fragment occursFragmentUnassigned (%)TotalXxx–His–His62756Xxx–His–Met583Gly–His–Xxx234His–His–Xxx63740Ser–His–Xxx8114Xxx–Ser–Gly18365Gly–Ser–Xxx19479Xxx–Pro–Ser8157
Discussion
In this analysis only the original data as deposited by the authors was used, and no attempt was made to ‘clean up’ and further interpret this information, except for linking the constraint with the coordinate data and removing identical sequences from the data set pool (where only the entry with the highest number of constraints linked to atoms was kept). This approach is intentional, as it best represents the quality and extent of the data that is currently deposited at the PDB. Only the distance constraint information was included in the analysis, and the information from dihedral, H-bond and RDC constraints was ignored. Even though these constraints contain important structural information, they were, as experimental data, recorded independently from the NOE data. They are used in the structure determination process, however, and it was not investigated whether their presence influences the quality of the final distance constraint lists. There are several other issues that can still be addressed, and although these are likely to improve some of the aspects of this type of study, it is also important to start with the original information so that a comparison point is available.
The first issue is that stereospecific assignments can be swapped or deassigned based on the original coordinates, similar to the approach in the RECOORD project. This could in principle reveal preferences related to stereospecifically assigned atoms in secondary structure elements. The second issue concerns the distances that were provided with the constraints. These are often ‘binned’ in weak/medium/strong classes with fixed distance cutoffs, so that the resulting distance distributions often show spikes at these distances. In Fig. 4, for example, it is clear that spikes occur at 3.0, 3.5 and 5.0 Å. Recalibrating the distances based on the deposited coordinates should improve the quality of the resulting information, and reveal relationships between distance and occurrence. The third issue concerns the sequences that are included: the current data sets include protein sequences with a high homology. This is clearly not an ideal situation, but there is currently not enough data available for a cleaner analysis. It is therefore important to check whether a particular contact appears in a large amount of entries, or the observed occurrence might be due to systematic error from homologous proteins produced by the same laboratory. The fourth problem is the identification of the secondary structure fragments. This is now based on the PDB DSSP analysis from the original coordinates for only the first or representative model so that secondary structure elements are not always identified properly. If chemical shifts were available an identification based on CSI (Wishart et al. 1992) would become possible so secondary structure stretches can be included that are more flexible and less defined on the coordinate level. More refined secondary structure identifications from the coordinates could also reveal patterns related to, for example, turns. Overall, the best way to improve this analysis remains to increase the sample size by encouraging deposition of constraint lists and all related NMR information (peak lists, chemical shifts, spectra), and ensuring that the data is consistent when deposited by the authors. Efforts like the CCPN project (Fogh et al. 2002, 2005), which allow data harvesting from NMR data collection to structure calculation, should provide this kind of data without requiring any additional effort by the scientists who produce the data.
Fig. 4Distance distribution from the constraint information for sequential Ala–Ala contacts between backbone H protons
In this analysis a particular inter-atomic contact between two residues from one PDB entry is either observed or not observed. The reason why a contact is observed (or not) implicitly includes distance information, peak overlap, water exchange line broadening, and all other factors that can lead to not observing or assigning a contact during analysis of a spectrum. This is different from the traditional meaning of an ‘assigned atom’ on the chemical shift level, where it means that the chemical shift value for the resonance that arises from the atom is known. However, this does not necessarily mean that these assigned atoms produce any valid inter-atomic distance information. Thus, an ‘assigned atom’ (or residue) on the constraint level means that a chemical shift assignment also produced useful and valid information related to the inter-atomic distances within the molecule.
The original study that defined the inter-atomic contacts relevant for assigning secondary structure elements with NMR used a set of 19 high-resolution protein crystal structures comprising about 3,200 residues (Wüthrich et al. 1984). In this study the extent of identification was defined as the percentage of times a distance was smaller than a particular cutoff value within a secondary structure element, while the uniqueness of identification is the percentage of times the distance is observed within a particular secondary structure element out of the total number of times it is observed. The extent is equivalent to the foccurence used in this study for the constraint sets, with the exception that no distance cutoff is used (although some distance information is, as mentioned, implicitly included because the reason a constraint is observed or not is very dependent on distance), and that values are labelled as significant based on a binomial analysis. The uniqueness has the same definition, except that again it is based on the amount of constraints that are observed.
Also of interest is the relationship between the information that comes directly from the deposited constraints and the information that comes from the deposited coordinates. Here, the constraint information is compared to the distances from the originally deposited coordinates. Although a set of recalculated coordinates (as in RECOORD) or X-ray structures could have equally well been used, the originally deposited coordinates were chosen because they should best match the content of the constraint lists. All comparisons between constraint and coordinate information are intended for informative purposes only: the constraints represent the experimental NMR side of the information contained in the coordinates, and are in effect only a subset of the information contained therein. However, a dependable determination of whether a particular NOE contact is observed or not is not possible based on an NMR structural ensemble, but is trivial based on the constraints because they inherently contain NMR-specific information like signal overlap, dynamics, etc.
From Fig. 5 it is clear that the contact occurrence is almost always higher for the HPC set compared to the HP set. This is related to the use of a direct distance cutoff of 5.0 Å in the HPC set: contacts with long distances could give rise to peaks that are too weak to be seen in a real spectrum but are still included. Also, many contacts have an foccurrence of 1.0 in the HPC set because of conformational constraints from covalent bonds. Not all of these contacts are seen in real spectra because of, for example, peak overlap or line broadening. The correlations between the occurrences overall are not very high (Spearman 0.770, Pearson 0.694), with especially the intra-residue contacts giving bad correlations (Spearman 0.451, Pearson 0.356, see web site), and i–i + 2 (Spearman 0.720, Pearson 0.783) and i + 3 (Spearman 0.711, Pearson 0.659) contacts giving the best results. An indication that the main reason for the bad correlation between the occurrences is distance related comes from the large improvement that is observed in the overall correlations if only coordinate distances of less than 3.6 Å are considered (Spearman 0.906, Pearson 0.916). However, results from using both the HP and HPC information to filter ambiguous constraints lists show that both sets essentially give the same results (personal data), even though the constraints are available in a much more ‘compressed’ form than the coordinates, and no force field information was used.
Fig. 5Correlation between the foccurrence from the HPC (Coordinates) and HP (Constraint) sets
In the KNOWNOE (Gronwald et al. 2002) X-ray structure based approach to obtain probabilities for assignments, the distance distributions for inter-atomic contacts are used to generate volume-based probabilities in addition to the atom identity based probabilities. This approach improves the probabilities that are generated, but it does require that the original peak list with volumes is available. This is not possible within the current analysis, although this will be pursued if a meaningful way to recalibrate the distance constraint bounds is available. This would also allow a better comparison between the NMR constraint data and any coordinate data (from NMR or X-ray structures).
Conclusion
A resource is now available where it is possible to check how likely a particular contact is when assigning NOESY spectra, or if a particular sequence fragment is likely to be difficult to assign. In this respect it formalises information that scientists with experience in spectrum analysis are aware of but cannot quantify. The amount of information provided here is extensive, however, and is even more useful when used as ‘knowledge based’ probabilities in automatic assignment strategies, to filter and/or validate ambiguous constraint possibilities, and as a tool to rank assignment possibilities in spectrum analysis programs. These are being implemented as part of the CCPN framework.
Finally, the NMR constraint lists encompass the experimental NMR data encoded in the NMR structural ensembles, and comprise a single set of data that is much easier to analyse than an ensemble of solutions. As such, they provide a reduced form of structural information that is relevant for NMR analysis only. For this reason, and to allow a basic level of scientific reproducibility and validation, it is important that constraints, and all other possible NMR derived information, are deposited along with the structure coordinates. It is very likely that a lot more information than described in this article can be gained from it, which in turn can assist the NMR community and can help to understand the relationships between NMR and structure.

pdb
nuclear magnetic resonance (nmr)
constraint analysis
noe assignment
noe distances