Cyclic Automated Model Building (CAB) Applied to Nucleic Acids

Abstract

Obtaining high-quality models for nucleic acid structures by automated model building programs (AMB) is still a challenge. The main reasons are the rather low resolution of the diffraction data and the large number of rotatable bonds in the main chains. The application of the most popular and documented AMB programs (e.g., PHENIX.AUTOBUILD, NAUTILUS and ARP/wARP) may provide a good assessment of the state of the art. Quite recently, a cyclic automated model building (CAB) package was described; it is a new AMB approach that makes the use of BUCCANEER for protein model building cyclic without modifying its basic algorithms. The applications showed that CAB improves the efficiency of BUCCANEER. The success suggested an extension of CAB to nucleic acids—in particular, to check if cyclically including NAUTILUS in CAB may improve its effectiveness. To accomplish this task, CAB algorithms designed for protein model building were modified to adapt them to the nucleic acid crystallochemistry. CAB was tested using 29 nucleic acids (DNA and RNA fragments). The phase estimates obtained via molecular replacement (MR) techniques were automatically submitted to phase refinement and then used as input for CAB. The experimental results from CAB were compared with those obtained by NAUTILUS, ARP/wARP and PHENIX.AUTOBUILD.

1. Introduction

Automated model building (AMB) programs try to replace the visual interpretation of the three-dimensional electron density map, which is usually time consuming and subjective, with automatic procedures to speed up the structure determination process and to minimize the modelling errors.

Several successful and well-documented AMB programs are available for proteins (among others, we cite BUCCANEER [1], ARP/wARP [2], PHENIX.AUTOBUILD [3]). Equivalent tools for nucleic acids exist, but most of them are still in progress. Indeed, quite often, such AMB programs aid in detecting errors in crystallographic models [4], or extend and rebuild existing nucleotides chains [5] or perform semi-automatic building [6].

Because the number of solved nucleic acid structures is rapidly increasing, more efforts were spent recently on the specific difficulties in the electron density interpretation due to lower resolution data [7] and the large number of rotatable bonds in the main chain (two in the protein main chain, six in nucleic acids). As a consequence, the conformation at low resolution is often ambiguous, particularly for large nucleic acid structures, and is typically determined at resolutions worse than 2.5Å. It is not uncommon that phosphate and base planes are reliably located, but sugars and part of the backbone are not seen at all [8]. Rebuilding and refining current models is often a time-consuming manual practice, so AMB promise to save time.

In spite of the above limitations, complete or almost complete AMB packages for nucleic acids exist: PHENIX.AUTOBUILD [3], ARP/wARP [9] and NAUTILUS [10]. These programs build nucleotide chains in a rather automatic manner. All such AMB procedures are based on an intensive use of prior crystallochemical knowledge. Indeed, nucleotides contain three rigid groups: the pentose sugar, the phosphate group and the base. Different programs use different tools for the AMB: some programs use the planarity of the base (e.g., in ARP/wARP), others exploit the sugar and the phosphate groups as the first tool for identifying the main chain (e.g., in NAUTILUS). All try to extend possible nucleotide chains and match the built chains to the nucleotide sequence. Models so found may be refined via REFMAC [11] or PHENIX.REFINE [12]; usually, calculations are iterated to obtain more complete models. It is typical that a good percentage of nucleotides are correctly built in the final model.

Recently, the cyclic automated model building (CAB) package for protein-automated model building was described [13]. CAB uses BUCCANEER in a cyclic procedure aimed at increasing its rate of success and the quality of the provided molecular models. In other words, CAB wraps around BUCCANEER. This program is itself cyclic; a standard BUCCANEER run performs five cycles of model building and 10 cycles of model refinement via REFMAC. CAB is highly automated and not very time consuming because BUCCANEER is fast, efficient, simple to use, and rather insensitive to the resolution limit of the data. CAB was tested over 81 protein structures solved via molecular replacement, anomalous dispersion and ab initio methods. The results showed that CAB gave more complete and accurate structures compared to the conventional use of BUCCANEER.

The success of CAB for proteins suggests that similar improvements may be made for nucleic acids. Here, we test whether or not the cyclic application of NAUTILUS by CAB improves the completeness and accuracy of the resulting nucleic acid structures. As was done for proteins, CAB does not modify the basic NAUTILUS algorithms at all; it has to be considered as a tool that allows the synergistic combination of NAUTILUS with some supplementary algorithms, offering more chances for the correct interpretation of the electron density maps. Indeed, in our experience, a starting set with the smallest average phase error is not always the most successful when an AMB program is applied; often, it is the variety of starting sets which allows CAB to improve NAUTILUS results.

The criteria we will use for making cyclic NAUTILUS applications cannot coincide with the criteria used for making cyclic BUCCANEER because of the strong differences between protein and nucleic acids crystallochemistry. We describe, in Section 2, the algorithms introduced into CAB for the location of the heavy atoms contained into ligands; in Section 3, we describe the recursive CAB algorithms for nucleic acids and, in Section 4, the experimental tests where we compare the results obtained by CAB with those obtained by NAUTILUS, ARP/wARP and PHENIX.AUTOBUILD.

2. CAB Algorithm for Locating Ligand Heavy Atoms

We suppose that a set of observed structure factor amplitudes with refined ϕ_r phases and w_r weights are available as the starting point for any AMB application. They were first obtained by applying REMO09 [14] to the test structures, and then refined via the SYNERGY approach [15]. The name of the latter procedure arises from the fact that it combines mainstream phase refinement procedures (DM by Cowtan [16]) and out-of-mainstream phase refinement techniques. SYNERGY includes free lunch [17,18], low density Fourier transform [19], vive la difference [20,21], phantom derivative [22,23] and phase-driven model refinement [24]. SYNERGY, as well as REMO09, was included in a modified version of SIR2014 [25].

In nucleic acid structures, sometimes the ligands’ scattering power is a not negligible part of the total scattering power, and often ligands contain (or are constituted by) heavy atoms. If no ligand is taken into account, the final R value may be large even if the nucleic acid model is good. This is mainly due to the fact that any AMB program is more focused on building nucleic acid models than defining the ligand substructure. Because the latter contribution does not enter into the model structure factor calculation, an additional systematic discrepancy occurs between the observed structure factor amplitudes and the calculated nucleic acid amplitudes, thereby causing larger values of R (and of R_f) and, therefore, a larger distrust of the user.

We then decided to modify the standard CAB approach by searching for ligands, including heavy atoms, in the first step. In this step, another task may also be accomplished: the identification of the P atoms belonging to the nucleic acid backbone. This decision is supported by the observation that often the average phase error corresponding to ϕ_r phases (say <|Δϕ_r |>) is low, even if the average phase error at the molecular replacement level is large. This is mainly due to the effectiveness of the SYNERGY step. Indeed, after SYNERGY it may be easier to locate heavy atoms and also to recognize a good percentage of the P atomic positions.

A useful premise for the location of heavy atoms is the following: the number and positions of the heavy atoms are unknown, while their atomic species are assumed to be known due to the known chemical composition of the ligands. Only atoms with an atomic number equal or larger than 20 are considered “heavy”. The above condition is suggested by the following criterion: heavy atoms are not subjected to constraints or restraints during the least-squares refinement, so the optimization of their positions is feasible only if the atomic species is sufficiently heavy. If ligands contain two or more heavy atom species, we associate them with the heaviest atomic species. The following automatic algorithm is used:

(i) An observed electron density map is calculated by using ϕ_r phases and w_r weights. The first candidates for being P atoms in the target structure are the P atoms of the model structure, as refined by SYNERGY. If no heavy atoms are present in ligands, steps (ii) and (iii) are skipped;

(ii) The highest N peaks (where N = 30 × number of nucleotides in the target sequence) are selected and sorted with respect to the intensity (I). All peaks closer than DIST from model atoms are rejected, where DIST corresponds to the covalent radius of the heaviest species in the target. Non-crystallographic occupancy I(i)/I(1) and the heaviest atomic species in the target are associated to the ith peak;

(iii) The structure parameters of 10 peaks with the largest I(i)/I(1) values are refined, one atom at a time, together with the nucleic acid model previously determined, by five REFMAC cycles. Then, a new R value is obtained. If it is smaller than the previous one, the heavy atom is accepted as a reliable candidate of the heavy atom substructure and the next peak is processed; otherwise, the procedure for locating heavy atoms stops.

At the end of the steps (ii) and (iii), a list of heavy atom candidates are available. The final R (and R_f) values and the new phase estimates (denoted by ϕ_rh) are expected to be better than the corresponding values obtained at the end of SYNERGY. Correspondently, the new average phase error (say <|Δ ϕ_rh|>) is expected to be smaller.

Heavy atom candidates added to the SYNERGY model are used to calculate new structure factors by which a new electron density map is calculated. Steps ii) and iii) are repeated and a new model is obtained, which now includes the final estimates of P and heavy atoms’ positions. A new phase set (ϕ_rh) and a new average phase error (<|Δ ϕ_rh|>) correspond to such models.

There is a special reason why P atoms’ positions are examined. In an experimental version of NAUTILUS (Cowtan, personal communication 2020), it is possible to use two new tools to improve the NAUTILUS default model building: a more extended library of nucleic acid model structures and the previous knowledge of the positions of the triples (O₃’, P, O₅’). A good percentage of such triples may be correctly identified when SYNERGY and the above described algorithm for heavy atom location end with a small R value. Then, a list of triples (O₃’, P, O₅’) is automatically passed to NAUTILUS, which may build the final model of the target nucleic acid more efficiently.

3. The Recursive Algorithm

We briefly summarize, in this section, the main CAB algorithms that make the application of NAUTILUS cyclic. The different characteristics of nucleic acids with respect to proteins suggest that CAB algorithms cannot be the same for the two types of structures.

We suppose that REMO09 molecular replacement techniques were applied to the test structures, and then the corresponding phases were refined by SYNERGY. Let ϕ_r and w_r be phases and weights at the end of the above procedure: they constitute the input for NAUTILUS, CAB, ARP/wARP and PHENIX.AUTOBUILD. Furthermore, let ϕ_b and w_b be phases and weights obtained after the first application of NAUTILUS. We divided the CAB procedure into the following steps:

STEP 1: When a ligand contains heavy atoms, the procedure for locating them starts (see Section 2). ϕ_rh and w_rh are phases and weights corresponding to the combination of the nucleic acid model and the heavy atoms; R_rh is the corresponding crystallographic residual and R_frh the R_free value. ϕ_rh and w_rh coincide with ϕ_r and w_r when ligand heavy atoms are not found;

STEP 2: ϕ_rh and w_rh are used automatically to start the first NAUTILUS application, which provides a new molecular model of the nucleic acid. The Fourier inversion of the new model leads to a set of calculated structure factors to which the contribution of the ligand heavy atoms is added. Let R_b and R_fb be the corresponding crystallographic residuals, ϕ_b and w_b the corresponding model phases and weights. If R_b is smaller than 0.30, then CAB stops and the model is considered not worthy of further improvement;

STEP 3: The w_rh and w_b distributions are fitted through histogram matching, to put them on the same statistical basis. Then, the tangent

$$\tan {\varphi }_C=\frac{w_{rh}\sin {\varphi }_{rh}+S_C{w}_b\sin {\varphi }_b}{w_{rh}\cos {\varphi }_{rh}+S_C{w}_b\cos {\varphi }_b}$$

(1)

is calculated, to derive a set of combined ϕ_c phases. S_C is the parameter that defines how ϕ_rh and ϕ_b should be combined. If the ϕ_b phases are supposed to be reliable, then S_C is expected to be large; if the user is not confident of their quality, then S_C has to be small. At this stage, the quality of the ϕ_b phases may be estimated through the R_b value. We heuristically decided to linearly relate S_C to R_b via Equation (2) (owing to the different quality of the problem, this equation does not coincide with that used for proteins):

S_C = 1.975 − 3.25R_b

(2)

with the conditions that if R_b < 0.30, then S_C = 1, and if R_b > 0.5, then S_C = 0.35.

The reason is the following: when R_b is sufficiently small, then the ϕ_b phases are expected to be reliable and their weights deserve to stay on the same scale of the ϕ_rh phases. If R_b is large, then the contribution of the ϕ_b phases to the tangent expression (1) has to be depleted. The weight

$$w_C=\frac{1}{2}{\left(T^2+B^2\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$$

may be applied to the ϕ_c phases.

However, if R_b is large, then it is very likely that the weakly weighted ϕ_c phases are badly estimated. Accordingly, we decided to eliminate in Equation (1) a percentage (PERC) of the ϕ_b phases (those with lower weights) defined by the following equation:

PERC = 2.4R_fb − 0.84

(3)

with the conditions that if R_fb > 0.6, then PERC = 0.60, and if R_fb < 0.35, no reflection is eliminated.

Equation (3) is equivalent to assigning w_b = 0 to 60% of the weakest estimates from NAUTILUS when R_fb is equal or larger than 0.6, and to assigning w_b = 0 to the 12% of the weakest estimates from NAUTILUS when R_fb = 0.40. ϕ_c phases and w_c weights thus obtained are used as input values for the next NAUTILUS run to produce new ϕ_b phases and w_b weights, which are again combined according to Equation (1) with ϕ_rh phases and w_rh weights in up to six cyclic NAUTILUS runs. The procedure stops if R_b < 0.30;

STEP 4: The cyclic procedure described in STEP 3 is a useful tool that offers a variety of electron density maps to NAUTILUS algorithms, to increase the chance of a good interpretation. The six maps, however, are close to each other: a large variety of maps could make success easier. A total of 12 supplementary cycles are thus introduced in the procedure. The ϕ_b phases and w_b weights obtained at the cycle n are combined via a tangent expression with the ϕ_c phases and w_c weights obtained at the end of the (n − 1)-th tangent cycle. The procedure stops if R_b < 0.30.

At the end of the above procedure, the minimum R_b value is selected (and denoted as R_C); the corresponding model is considered the most accurate.

A special case, not very rare in nucleic acid crystallography, occurs when the model and target sequences are identical or differ by one nucleotide. Among the 29 test structures, seven cases (4xqz, 5ihd, 5jua, 5nt5, 5t4w, 2a0p, 5tpg) have identical nucleotides and four cases (3n4o, 1iha, 2fd0, 4enc) differ by one nucleotide. In the latter case, the lengths of the two sequences may be the same or may differ by one nucleotide. If R_rh < 0.35 and R_rh < R_C, then SYNERGY and STEP 1 models are preferred to the CAB model (see Section 4).

4. Applications

In a previous paper [26], we selected from the Protein Data Bank (PDB) 38 nucleic acid structures for which phase solution attempts were made via molecular replacement (MR) techniques: we downloaded the observed diffraction data, unit cell dimensions, the space group symmetry, nucleotide sequence, and the structural models. We submitted the test structures to default runs of REMO09; for nine of them, REMO09 did not provide a sufficiently good model (i.e., the average phase error for such structures was larger than 80°). The remaining 29 structures, quoted in

Table 1. For the 29 nucleic acid test structures, the following abbreviations are used: Protein Data Bank (PDB) for the structure code, space group (SG) and the diffraction data resolution (RES) (Å). The number of nucleotides in the asymmetric unit (nN) is reported by the symbol n·N, where n is the number of chains per asymmetric unit, N is the number of nucleotides per chain. N is replaced by a sum of two numbers if chains with different type or different number of nucleotides are present. The model used in the MR step (column model) is reported as p·CODE, where CODE is the PDB code of the molecular fragment and p is the number of fragments originally used in the MR process. The information on the ligands is given in the corresponding column, in the form of m·CODE, where CODE is the PDB code of a ligand, and m is the number of ligands in the asymmetric unit of the target structure. The chemical formula for each ligand CODE is also specified at the bottom of the Table, from which the presence of heavy atoms may be deduced.

PDB	SG	RES	nN	Model	Ligand(s)
3ce5 [27]	I 4	2.50	2·12	1k8p	2·K + BRA
3eil [28]	P 32	2.60	6·12	3·463d	7·Mn
3n4o [29]	P 21 21 21	2.90	2·12	1dnh	2·B7C + HT
3tok [30]	C 2	1.74	10 + 10	2org	Na
4gsg [31]	C 2	2.00	2·(10 + 10)	2·2org	UCL
4ms5 [32]	P 43 21 2	2.23	1·10	3qrn	Ba + RKF
4xqz [33]	P 21	2.15	8·6	2·5ihd	6·Cu + 4·Ca + 7·Cl + MES + MOH
5dwx [34]	P 4 21 2	2.71	24 + 8	1kf1	K
5i4s [35]	R 3	2.46	2·12	476d	8·Ca + 2·1W5
5ihd [33]	P 21	1.57	4·6	2·2dcg	4·Cu + 2·Ca + 2·2OP + SIN
5ju4 [36]	P 21 21 21	2.00	2·12	1d29	Mg + Cl
5lj4 [37]	R 3	2.17	2·12	463d	4·Ca + 2·1W5 + 2·1WA
5mvt [38]	P 31 2 1	1.89	2·12	5mvl	3·Co
5nt5 [39]	P 21 21 21	2.30	2·12	1d29	Na + CAC
5t4w [40]	P 21 21 21	2.30	2·12	5jua	DAP
1iha [41]	C 2	1.60	2·9	165d	2·Cl + 2·BRU + 2·RHD
1z7f [42]	P 31 2 1	2.10	3·16	1yrm	2·Sr
2a0p [43]	R 3 2	1.95	2·8	259d	S4C
2fd0 [44]	C 2 2 21	1.80	2·23	2fcy	K + Cl + 5BU + LIV
2pn4 [45]	P 21 21 21	2.32	2·(24 + 20)	2·2pn3	10·Sr + 4·5BU
3d2v [46]	P 21 21 2	2.00	2·77	2cky	10·Mg + 2·PYI
3fs0 [47]	P 31	2.30	10 + 11	½·3ftm	3·Mg
4enc [48]	P 21 21 2	2.27	52	4enb	5·Mg + K + F
5kvj [49]	R 3	2.26	16 + 16	2·3nd3	ARG
5l4o [50]	P 32 1 2	2.80	77	3cw5	Na + PSU + OMC + 4SU + 5MU + H2U
5nz6 [51]	P 32 1 2	2.94	41	½·5nwq	2·CBV + GAI
5tgp [52]	P 61	1.60	2·8	2·1dns	4·US3
5uz6 [53]	C 2	2.10	3·(25 + 8)	3·5ux3	8OS + LCC
6az4 [53]	P 41 21 2	2.98	32 + 9	4fnj	GP3
Ligand Information
Code	Formula	Code	Formula	Code	Formula
1W5	C10 H14 N3 O9 P	BRU	C9 H12 Br N2 O8 P	MES	C6 H13 N O4 S
1WA	C10 H16 N5 O7 P	CAC	C2 H6 As O2	MOH	C H4 O
2OP	C3 H6 O3	CBV	C9 H13 Br N3 O8 P	OMC	C10 H16 N3 O8 P
4SU	C9 H13 N2 O8 P S	DAP	C16 H15 N5	PSU	C9 H13 N2 O9 P
5BU	C9 H12 Br N2 O9 P	GAI	C H5 N3	PYI	C14 H21 N4 O7 P2
5MU	C10 H15 N2 O9 P	GP3	C20 H27 N10 O18 P3	RHD	Rh3 H18 N6
8OS	C14 H18 N7 O7 P	H2U	C9 H15 N2 O9 P	RKF	C38 H20 F2 N13 Ru
ARG	C6 H15 N4 O2	HT	C25 H24 N6 O	S4C	C9 H14 N3 O7 P S
B7C	C12 H16 N3 O7 P	LCC	C11 H16 N3 O8 P	SIN	C4 H6 O4
BRA	C35 H43 N7 O2	LIV	C29 H55 N5 O18	UCL	C9 H12 Cl N2 O8 P
				US3	C10 H15 N2 O7 P Se

, are used as test cases for our applications: the first 16 of them are DNA, the other 13 are RNA fragments. For each structure, we show their PDB code (PDB), the space group (SG), and the data resolution (RES) in Table 1. The number of nucleotides in the asymmetric unit is reported in the form n·N, where n is the number of chains in the asymmetric unit and N is the number of nucleotides per chain. N is replaced by a sum of two numbers if two chains with a different type or number of nucleotides are present. The model used in the MR step (column model) is reported as p·CODE, where CODE is the PDB code of the molecular fragment and p is the number of fragments originally used in the MR process. The information on the ligands is given in the corresponding column, in the form of m·CODE, where CODE is the PDB code of a ligand and m is the number of ligands in the asymmetric unit of the target structure. The chemical formula for each ligand CODE is also specified at the bottom of Table 1, from which the possible presence of heavy atoms may be deduced.

Model phases obtained by REMO09 and refined by SYNERGY (ϕ_r and w_r, respectively) constitute the input for CAB, ARP/wARP and PHENIX.AUTOBUILD. Because we are interested in procedures for the automatic crystal structure solution, we used default directives for all three AMB programs. The available documentation for these programs suggested the following instructions (adapted to the 3eil test structure, as an example):

for CAB-NAUTILUS

nautilus_pipeline–stdin < 3eil_nautilus.inp, where 3eil_nautilus.inp contains

seqin 3eil.pir

mtzin 3eil_synergy.mtz

colin-fo F, SIGF

colin-phifom PHIC, FOM

colin-free FreeR_flag

pdbin 3eil_po3o5_out.pdb

pdbin-ref nautilus_lib_dna.pdb

pdbout 3eil_nautilus.pdb

cycles 5

for ARP/wARP:

auto_nuce.sh \

datafile 3eil_synergy.mtz \

nucleotides 72 \

fp F sigfp SIGF phib PHIC fom FOM

for PHENIX.AUTOBUILD:

phenix.autobuild write_run_directory_to_file = 3eil_phenix.log \

seq_file = 3eil.pir \

input_data_fil e=3eil_synergy.mtz \

input_labels ="F SIGF PHIC FOM HLA HLB HLC HLD FreeR_flag" \

chain type =DNA \

ncs_copies = 1 \

nproc = 12

We are conscious that the above instructions do not correspond to the optimized ways of applying the mentioned AMB programs. Indeed, any of them may be more effective if suitable instructions are introduced to treat special types of DNA or RNA and/or to explore different building approaches. The directives we used are only simple tools for automatic runs, which, if successful, constitute important achievements by themselves.

In

Table 2. NAUTILUS and cyclic automated model building (CAB) results. For the 29 test structures, PDB is their PDB code, <|Δϕ_r|>° is the average phase error at the end of SYNERGY, R_r and R_f are the crystallographic residuals (for all of the data) and the Rfree value. The corresponding ϕ_r phases are the input for NAUTILUS and CAB. R_N, R_fN, MA_N and MA_MN are the R, R_f, MA and MA_M values obtained after the application of NAUTILUS; R_C, R_fC, MA_C and MA_MC are the corresponding values obtained at the end of CAB. R and MA values are percentages.

PDB	<|Δϕr|>°	Rr	Rf	RN	RfN	MAN	MAMN	RC	RfC	MAC	MAMC
3ce5	50	41	43	54	59	36	16	52	53	41	18
3eil	46	31	36	47	50	59	43	36	38	82	76
3n4o	33	23	26	44	45	55	36	23	26	91	69
3tok	49	35	35	57	58	44	15	52	56	72	24
4gsg	53	34	38	45	45	17	9	42	46	44	17
4ms5	59	46	64	56	57	0	4	37	41	78	57
4xqz	48	32	35	58	58	30	22	27	30	80	94
5dwx	58	41	44	57	58	18	5	48	59	32	25
5i4s	35	25	29	36	37	59	49	35	34	82	51
5ihd	39	34	36	51	52	50	39	25	29	100	92
5ju4	26	26	28	37	37	95	83	26	28	100	100
5lj4	29	25	29	44	48	86	58	41	45	82	58
5mvt	28	29	28	38	37	82	79	31	31	95	92
5nt5	24	27	28	46	47	86	64	27	28	100	99
5t4w	25	25	29	43	42	86	64	25	29	100	96
1iha	41	34	35	36	37	94	77	23	25	88	81
1z7f	34	32	34	42	43	69	71	30	30	100	100
2a0p	31	27	35	32	39	100	93	27	35	100	99
2fd0	33	32	36	37	38	89	78	32	36	95	85
2pn4	40	34	40	41	48	87	68	36	41	86	74
3d2v	57	47	51	49	51	34	29	49	50	32	30
3fs0	63	42	47	40	41	68	51	29	33	89	86
4enc	28	25	28	36	39	83	74	25	28	98	95
5kvj	49	31	39	37	46	94	55	32	41	94	63
5l4o	40	31	36	35	39	74	51	34	39	74	53
5nz6	45	23	23	39	43	75	44	31	32	90	53
5tgp	26	28	29	51	51	43	40	27	27	100	100
5uz6	34	34	36	30	33	99	88	30	33	99	88
6az4	51	36	40	28	30	87	63	28	30	87	63

, we show the experimental results obtained by NAUTILUS and CAB, both obtained by using the new NAUTILUS library and the knowledge of the positions of the triples (O₃’, P, O₅’), when detected after the SYNERGY step. The results obtained without such tools were poorer and are not shown for brevity. <|Δϕ_r|>° is the average phase error at the end of SYNERGY, R_r and R_f are the corresponding crystallographic residual (for all of the data) and Rfree value. R_N, R_fN, R_C and R_fC are the R and R_f values at the end of NAUTILUS and CAB, respectively. During any AMB process, only the residuals R and R_f are known. They are efficient figures of merit for establishing the overall accuracy of the proposed models, but they are not sufficient for assessing their true quality. We, therefore, used two a posteriori additional figures of merit, MA and MA_M, to check the quality of the models provided by NAUTILUS and CAB (denoted as MA_N and MA_MN for the NAUTILUS case, and MA_C and MA_MC for CAB).

Table 2 suggests the following conclusions:

(1) MA_N and MA_C only deal with the quality of the P chains; their usefulness as figures of merit has to be confirmed by MA_MN and by MA_MC, respectively, which define the overall quality of the structural model. Even if there is a good correlation between MA and MA_M for all the tested AMB programs, their indications do not always agree;

(2) The inequality MA_N > MA_C is rare (only in four cases, 5lj4, 1iha, 2pn4, 3d2v), and in all cases MA_MN ≤ MA_MC;

(3) For a high percentage of test structures, the quality of the NAUTILUS model is largely improved by CAB (examples are not given for brevity). Frequently, quite poor initial models are transformed by CAB into almost complete models. These cases correspond to poor values of MA_N and MA_MN, and to large values of MA_C and MA_MC;

(4) In all test cases, R_N ≥ R_C. That increases the confidence of CAB users in the quality of the built model. In some cases, the final residuals are large because of the unmodeled contribution to the diffraction from ligands that are missing in the model;

(5) Eleven test cases (in bold) represent situations where the model and target sequences are identical or differ by only one residue and where the conditions R_rh < 0.35 and R_rh < R_C are satisfied. The program automatically checks the sequence relationships and verifies if the numerical conditions are satisfied. As stated before, in all eleven cases, the program automatically chooses the models at the end of STEP 1 rather than the final CAB models. As an example, in Figure 1, we show the structure 2fd0, for which MA_C = 0.95 and MA_MC = 0.85. The CAB model is on the left and the published model on the right; the main difference concerns a nucleotide close to a chain terminal.

In

Table 3. MA_C and MA_MC for the eleven structures for which model and target sequences are equal or differ in one position, and for which the conditions R_rh < 0.35 and R_rh < R_C are satisfied. WITH and WITHOUT indicate if the control on the sequences has been applied or not. MA values are percentages.

	With		Without
PDB	MAC	MAMC	MAC	MAMC
3n4o	91	69	77	38
4xqz	80	94	43	30
5ihd	100	92	70	47
5ju4	100	100	95	83
5nt5	100	99	100	87
5t4w	100	96	91	64
1iha	88	81	81	77
2a0p	100	99	100	99
2fd0	95	85	95	81
4enc	98	95	83	78
5tgp	100	100	100	75

, we quote MA_C and MA_MC values obtained with and without the application of the algorithm for the sequence control, to allow the reader to understand how these values differ from each other. It is easily seen that MA_C and MA_MC values without the control are much worse;

(6) CAB (and NAUTILUS, of course) usually fails when $\left|\mathsf{\Delta }{\varphi }_r\right|°$ is close or larger than 50° (this is the case for 3ce5, 3tok, 4gsg, 4ms5, 5dwx, 3d2v), even if two cases can be found in which it has success (3eil and 3fs0). This error limit is usually exceeded when CAB is applied to proteins.

In

Table 4. ARP/wARP and PHENIX.AUTOBUILD experimental results for the 29 test structures. PDB is their PDB code; $\left|\mathsf{\Delta }{\varphi }_r\right|°$ is the average phase error available at the end of the SYNERGY refinement process. The corresponding ϕ_r phases are the input for ARP/wARP and PHENIX.AUTOBUILD. R_A, R_fA, MA_A and MA_MA are the R, R_f, MA and MA_M values obtained at the end of the automatic runs of ARP/wARP; R_P, R_fP, MA_P and MA_MP are the corresponding values obtained at the end of the automatic runs of PHENIX.AUTOBUILD. R and MA values are percentages.

		ARP/wARP				PHENIX.AUTOBUILD
PDB	<|Δϕr|>°	RA	RfA	MAA	MAMA	RP	RfP	MAP	MAMP
3ce5	50	53	56	23	11	45	47	50	40
3eil	46	48	56	26	15	43	47	73	53
3n4o	33	33	52	64	25	33	37	82	57
3tok	49	52	53	28	10	45	47	94	34
4gsg	53	37	43	44	16	38	38	39	17
4ms5	59	0	0	0	0	48	53	44	29
4xqz	48	53	54	13	5	57	60	10	11
5dwx	58	40	47	36	10	49	53	27	27
5i4s	35	34	44	50	20	36	39	50	49
5ihd	39	51	51	10	5	52	56	25	19
5ju4	26	49	58	59	14	35	33	100	84
5lj4	29	41	52	55	25	40	41	68	65
5mvt	28	45	51	50	22	46	44	91	60
5nt5	24	35	48	91	43	35	38	100	84
5t4w	25	31	45	91	49	31	33	95	83
1iha	41	41	41	75	51	36	33	81	64
1z7f	34	40	46	69	32	35	36	91	82
2a0p	31	39	53	86	40	31	37	93	93
2fd0	33	45	52	73	30	37	36	95	80
2pn4	40	47	55	32	13	42	48	57	52
3d2v	57	56	57	6	3	47	48	26	23
3fs0	63	0	0	0	0	29	34	74	69
4enc	28	33	46	79	34	40	41	71	67
5kvj	49	39	55	59	20	35	40	84	63
5l4o	40	44	53	46	16	45	50	54	49
5nz6	45	34	38	53	29	35	37	78	56
5tgp	26	45	51	86	45	34	33	100	89
5uz6	34	34	40	91	53	33	33	91	82
6az4	51	42	46	38	15	39	40	67	53

we show, for all test structures, the values of R, R_f, MA and MA_M obtained after the application of ARP/wARP (say R_A, R_fA, MA_A and MA_MA, respectively), and the analogous values obtained by the application of PHENIX.AUTOBUILD (say R_P, R_fP, MA_P and MA_MP, respectively). Comparing the quartet R_A, R_fA, MA_A and MA_MA with the quartet R_P, R_fP, MA_P and MA_MP clearly suggests the larger effectiveness of PHENIX.AUTOBUILD: usually R_P < R_A, R_fP < R_fA, MA_P > MA_A and MA_MP > MA_MA. The cpu time, however, is much larger for PHENIX.AUTOBUILD.

PHENIX.AUTOBUILD and CAB results may be easily compared via their corresponding quartet (R, R_f, MA, MA_M). Usually R_P > R_C, R_fP > R_fC, MA_P < MA_C, MA_MP < MA_MC, but there are also few cases in which PHENIX.AUTOBUILD alone performes better.

Figure 2 and Figure 3 synthetically represent the results quoted in Table 2 and Table 4. Figure 2 shows the MA values corresponding to the default application of NAUTILUS, CAB, ARP/wARP and PHENIX.AUTOBUILD. In this condition, ARP/wARP seems the least efficient program: MA_A > MA_C only in one case (5dwx) and MA_A = MA_C also in one case (4gsg). The NAUTILUS and PHENIX.AUTOBUILD lines are closer to the CAB line. For NAUTILUS, MA_N > MA_C in four cases (5kvj, 5l4o, 5uz6, 6az4) and MA_N = MA_C in three cases (1iha, 2pn4, 3d2v). For PHENIX.AUTOBUILD, MA_P > MA_C in only two cases (3ce5, 3tok) and MA_P = MA_C in four cases (5ju4, 5nt5, 2fd0, 5tgp).

As previously stated, MA values are not in themselves indisputable estimates of the quality of the built models, because they register only the correctness of the P atoms. MA_M may be considered a more general figure of merit involving all the non-H atoms. The MA_M values obtained by the four tested programs are plotted in Figure 3. A common feature, no matter the algorithm used for AMB, is that usually MA > MA_M; the P positions are more easily located than the other atoms.

Even in this case, ARP/wARP seems the least efficient program, while the NAUTILUS and PHENIX.AUTOBUILD lines are closer to the CAB line, but the quality of the CAB models is markedly higher. In most cases, the CAB percentage of non-H atoms at a distance less than 0.6Å from the published positions is greater than 50.

A final observation is mandatory. This paper is mainly concerned with the full automation of the model building tools. However, the role of CAB for nucleic acids in the present scientific panorama may be better appreciated by including it in

Table 5. Most popular automated or semi-automated tools for model building of nucleic acids. SUB1: automated model building into electron density map from sequence; SUB2: guided semi-automated model building into electron density maps; SUB3: completing and rebuilding existing models into electron density maps; SUB4: building models from sequences without electron density.

SUB1	SUB2	SUB3	SUB4
NAUTILUS [10]	RCRANE [6] in COOT [54]	NAFIT, NABUILD in LAFIRE [5]	AMBER [55]
ARP/wARP [9]		ERRASER [56]	FARFAR [57,58]
PHENIX.AUTOB [3]			ROSETTA [59]
NUT/DHL/RSR [60,61]			3DNA [62]
CAB

, where the most popular automated or semi-automated tools for model building are cited.

5. Discussion

The CAB approach, originally designed for making the BUCCANEER application to proteins cyclic, was modified for use as an AMB tool for nucleic acids. In the new CAB version, we included NAUTILUS; the purpose was to improve the AMB effectiveness without changing NAUTILUS algorithms.

We applied CAB to a set of 29 nucleic acids (DNA and RNA) and compared the models thus obtained with those available after the mere application of NAUTILUS. We also applied ARP/wARP and PHENIX.AUTOBUILD to the same set of test structures. The procedures were fully automatic: a set of default instructions were given as inputs to any AMB program. Obviously, more appropriate input directives may improve the experimental results described in this paper. The results thus obtained show that the CAB cyclic approach remarkably increases NAUTILUS effectiveness and it is quite competitive with ARP/wARP and PHENIX.AUTOBUILD.

The AMB programs tested in this paper clearly show that their efficiency for nucleic acids is much smaller than for proteins. This partly depends on the particular difficulties to overcome for nucleic acids (see Section 1), but also on the smaller efforts spent in this field. This conclusion is supported by the following observation: quite often, SYNERGY ends with <|Δϕ_r|>° ≤ 40° (16 times out of 29). This situation is usually very favourable for AMB programs when applied to proteins; on the contrary, Table 2 and Table 3 show that MA and MA_M values are often far from the expected values. Further efforts are needed for a complete and satisfactory AMB automation. Some of these efforts may be spent on improving the ϕ_r phases, but most of them should concern the improvement of the AMB algorithms.

CAB for nucleic acids is part of an experimental version of SIR2014. Its full use requires that an experimental version of NAUTILUS, on which it is based, is also available. Hopefully, CAB will be released in late 2020.