The diagnosis of BCR/ABL-negative chronic myeloproliferative diseases (CMPD): a comprehensive approach based on morphology, cytogenetics, and molecular markers

Recent years showed significant progress in the molecular characterization of the chronic myeloproliferative disorders (CMPD) which are classified according to the WHO classification of 2001 as polycythemia vera (PV), chronic idiopathic myelofibrosis (CIMF), essential thrombocythemia (ET), CMPD/unclassifiable (CMPD-U), chronic neutrophilic leukemia, and chronic eosinophilic leukemia (CEL)/hypereosinophilic syndrome, all to be delineated from BCR/ABL-positive chronic myeloid leukemia (CML). After 2001, the detection of the high frequency of the JAK2V617F mutation in PV, CIMF, and ET, and of the FIP1L1–PDGFRA fusion gene in CEL further added important information in the diagnosis of CMPD. These findings also enhanced the importance of tyrosine kinase mutations in CMPD and paved the way to a more detailed classification and to an improved definition of prognosis using also novel minimal residual disease (MRD) markers. Simultaneously, the broadening of therapeutic strategies in the CMPD, e.g., due to reduced intensity conditioning in allogeneic hematopoietic stem cell transplantation and the introduction of tyrosine kinase inhibitors in CML, in CEL, and in other ABL and PDGRFB rearrangements, increased the demands to diagnostics. Therefore, today, a multimodal diagnostic approach combining cytomorphology, cytogenetics, and individual molecular methods is needed in BCR/ABL-negative CMPD. A stringent diagnostic algorithm for characterization, choice of treatment, and monitoring of MRD will be proposed in this review.
Introduction
Chronic myeloproliferative disorders (CMPD) are clonal stem cell disorders encompassing a very heterogeneous complex of different entities which are defined by distinct clinical and cytomorphological phenotypes and, in some part, known genetic features. They are characterized by increased and effective proliferation of one to three hematopoietic cell lineages in the bone marrow associated to increased peripheral blood parameters. The recent detection of the high incidence of the JAK2 mutations in polycythemia vera (PV), chronic idiopathic myelofibrosis (CIMF), and essential thrombocythemia (ET) [1–5], the detection of the FIP1L1–PDGFRA gene fusion in chronic eosinophlilic leukemia (CEL) [6, 7], and the introduction of tyrosine kinase inhibitors such as imatinib in chronic myeloid leukemia (CML) or hypereosinophilic syndrome (HES)/CEL shed new interest on molecular diagnostics and detection of minimal residual disease (MRD) in CMPD.
Today, CMPD are primarily separated in CML as defined by the Philadelphia translocation t(9;22)(q34;q11)/BCR–ABL and in all other so-called BCR/ABL-negative CMPD. According to the WHO proposal of 2001 [8], the latter are subdivided into PV, CIMF, ET, and unclassified CMPD (CMPD-U). Some very rare disorders as chronic neutrophilic leukemia (CNL), HES, and CEL are additionally included. This broad spectrum becomes even more heterogeneous due to the continuous progress of stages, as all CMPD have the potential of clonal evolution and stepwise progression. They often terminate in bone marrow failure due to myelofibrosis or ineffective hematopoiesis or in acceleration and finally transformation to blast crisis. Differential diagnosis in CMPD is further hampered by the biologically given overlap of the diverse morphologic phenotypes and the sometimes close relationship to reactive conditions, and even show overlaps to myelodysplastic disorders. The WHO, thus, created a category of disorders combining myeloproliferative and myelodysplastic features in which chronic myelomonocytic leukemia (CMML), unclassified myelodysplastic/myeloproliferative disorder (MDS/MPD, U), and some very rare disorders as juvenile myelomonocytic leukemia (JMML) were incorporated [8, 9].
It is well known that PV has a median survival of 10 years, ET of 10–15 years, but CIMF of only 4 years. However, the clinical course in CMPD ranges from a few months with rapid leukemic transformation to several decades. These uncertainties in prognosis and the similarities in the clinical and morphological phenotypes at diagnosis plead for inclusion of other than clinical and morphologic parameters only into classification.
Although chromosomal abnormalities are not specific for distinct CMPD, they contribute to the definition of the prognosis and to the classification of the CMPD. However, aberrant karyotypes are detectable in only 5–45% of all BCR/ABL-negative CMPD, depending on the specific subtype.
Routinely applied methods further include by now polymerase chain reaction (PCR) screening for the V617F mutation in the JAK2 non-receptor tyrosine kinase [1–5] and will probably soon be included as diagnostic criteria in a revised WHO classification of the CMPD [10]. This novel marker is highly utile for the confirmation of a BCR/ABL-negative CMPD and might contribute to the definition of the prognosis and even for MRD strategies in the future [11]. Molecular methods in the CMPD further encompass PCR analyses of some rare gene fusions, e.g., in HES/CEL [6, 7] or in the 8p11 syndrome [12].
Adaptation of these extensive diagnostic procedures in CMPD to the laboratories’ resources becomes a major challenge. Major goals are standardization of diagnostic workflow, hierarchical order of methods, and combination of single results. This review intends to propose specific diagnostic algorithms for scenarios in BCR/ABL-negative CMPD.
Preanalytic conditions
To achieve optimal conditions in the diagnostic procedures, a standardized preparation of the samples and optimal conditions for transport are essential in the CMPD: Cytomorphology requires 3 ml bone marrow and 2 ml peripheral blood anticoagulated with ethylenediaminetetraacetic acid (EDTA), being aware that cytomorphology is hampered by heparine. Cytogenetics, in contrast, requires 5–10 ml heparinized bone marrow and 10–20 ml heparinized peripheral blood, as cultivation of metaphases is nearly inhibited by EDTA which induces apoptosis of cells. Multiparameter flow cytometry and all molecular genetic methods can be performed either on EDTA or heparinized material. Trephine biopsies should be performed for histomorphology and immunohistochemistry and allow cytomorphological evaluation by smears from the trephine cylinder in case of a dry tap. In the latter case, also for cytogenetics, a trephine cylinder can be transferred to isotone saline solution plus heparine, which, in many cases, makes metaphases after cultivation in cytogenetic medium possible.
Cytomorphology in CMPD
Differential diagnosis in the CMPD should always include investigation of peripheral blood smears, bone marrow aspirates, and trephine biopsies in parallel. Smears from peripheral blood and bone marrow are stained according to May Grunwald Giemsa. This may be completed by other stainings: Myeloperoxidase (MPO) reaction and non-specific-esterase (NSE) should be performed in blast crisis after CMPD and are warranted in cases of CMML. Iron staining may be performed additionally, but is of minor importance for the differential diagnostics, as in an early PV, iron will not always be absent. MPO and iron staining are further helpful in all cases with an overlap between the CMPD and MDS for detection of MPO deficiency and ringed sideroblasts. Cases with suspicious HES or CEL should, in addition, undergo toluidine blue staining for detection of mast cells which are frequently increased in CEL with the FIP1L1–PDGFRA gene fusion.
In PV, cytomorphology shows increased cellularity with trilineage cell proliferation. Stainable iron is completely missing in many cases. PV is further characterized by elevated blood counts in either cell line (Hb > 18.5 g/dl in men, >16.5 g/dl in women, platelets ≥400 × 109/l, WBC ≥12 × 109/l). In addition, other criteria as reduced serum erythropoietin levels below normal ranges [10, 13] or in vitro formation of endogenous erythroid colonies are included in the classification criteria [8]. In CIMF, bone marrow cytology is often hampered by myelofibrosis, and the peripheral blood shows the characteristical poikilocytosis and leukoerythroblastosis. However, these findings are not specific but occur as well in secondary myelofibrosis following other CMPD. ET is characterized by proliferation of the megakaryocytic lineage with clusters of enlarged mostly mature megakaryocytes in normocellular bone marrow. Granulopoiesis and erythropoiesis present as normal. According to the WHO [8], a diagnosis of ET requires a sustained peripheral platelet count ≥600 × 109/l, whereas reactive thrombocytosis must be excluded. Recently, an international expert panel recommended to lower the threshold for the diagnosis of ET to 450 × 109/l [10]. All CMPD, but especially CML, may show the so-called pseudo-Gaucher cells in the bone marrow, which represent glycolipide storing histiocytes resulting from increased cell proliferation [14]. Another specific cytomorphological subentity is represented by refractory anemia with ringed sideroblasts associated with marked thrombocytosis >500 × 109/l (RARS-T). This rare subtype may be included within the category of overlapping myelodysplastic and myeloproliferative diseases in the upcoming WHO classification [15–17].
Histomorphology in CMPD
Bone marrow histology has a central role in the diagnosis of CMPD. Staining is performed according to Giemsa, PAS, and chloroacetate esterase. Gomori silver impregnation allows assessment of reticulin fibers to quantify bone marrow connective tissue.
Thus, a diagnosis of CIMF requires at least a bone marrow histology, as bone marrow aspirates are hampered in most cases. Histology shows variable reticulin or collagen fibrosis, osteosclerosis, and sometimes even decreased cellularity. Sinuses are dilated with intraluminal hematopoiesis and erythrocyte extravasates. Megakaryopoiesis is increased with signs of dysplasia [8, 18].
PV demonstrates increased megakaryopoiesis, increased granulopoiesis, and erythropoiesis without storage iron, sinusoid hyperplasia, and variable myelofibrosis in combination with osteopenia. These characteristics allow discrimination from reactive erythrocytosis [19]. In more detail, differentiation from cases of secondary polycythemia includes the evaluation of megakaryopoiesis which shows clustering and pleomorphous appearance with very small and giant megakaryocytes with the characteristical staghorn-like nuclei neighboring each other [19, 20].
ET is characterized by clusters of enlarged mature megakaryocytes close to the sinusoids, whereas erythropoiesis and granulopoiesis are normal [10, 18]. A specific problem is provided by the differentiation between ET and prefibrotic CIMF, as both might be characterized by thrombocytosis in initial stages, and reticulin fibrosis might be minimal or absent in prefibrotic CIMF. However, prefibrotic CIMF is characterized by marked hypercellularity, left-shifted increased granulopoiesis, and a particular megakaryocyte morphology with nuclear features, whereas ET shows hyperlobulated and mature-appearing megakaryocytes [10, 21].
Cytogenetics in BCR/ABL-negative CMPD
The frequency of clonal karyotype anomalies varies considerably between the different BCR/ABL-negative CMPD entities. The presence of karyotype abnormalities at diagnosis per se seems to be prognostically negative [9]. CIMF has the highest karyotype aberration rate with 33–43% of all cases, followed by PV in 33–35%, whereas in ET, clonal abnormalities are extremely rare (<5%) [22–25]. In CMPD-U, aberrant karyotypes were reported in ∼20% [22], but definition of the true incidence is difficult due to the heterogeneity of subtypes in this category.
Chromosomal changes in the CMPD are not specific, but their presence at least confirms the diagnosis of a malignant hematopoietic disorder and contributes additional aspects to differential diagnosis. This can be exemplified in the 9p-aberrations which are closely associated to PV and to CIMF. In addition, translocations involving ABL, PDGFRA, PDGFRB or other tyrosine kinases can be detected by chromosome banding analyses, allowing the identification of patients who probably benefit from treatment with tyrosine kinase inhibitors.
Thus, chromosome banding analyses contribute a lot at diagnosis in many in cases with a suspicious or proven CMPD. However, they do not lead to important information for clinically clearly proven cases of ET. Cytogenetics may also be needed for the follow-up of the CMPD, as leukemic transformation is characterized in many cases by clonal evolution to more complex karyotypes resulting in higher rates of chromosomal abnormalities of ≥90% [9, 23, 26].
Interphase (IP-), metaphase (HMF-), and 24-color fluorescence in situ hybridization (FISH) may further confirm and clarify the results of the chromosome banding analyses. IP-FISH probes can be used for future MRD studies. Nearly all typically observed aberrations—e.g., +8, +9, gain of 9p, or del(20q)—can be monitored.
Trisomy 8 is the most frequent aberration in the CMPD being detected in ∼20% of all cytogenetic aberrant PV cases and in ∼10% in chromosomally aberrant CIMF—mostly as sole abnormality or in combination with +9. This is followed by trisomy 9 in ∼10% of all cytogenetically aberrant cases. Partial trisomies of 9p are equally frequent with a special association to PV [27–30]. Other recurrent aberrations are deletions of 13q and 20q and partial trisomies of 1q [9, 22, 31], whereas +19, +21, −7, −Y, del(12p), and i(17q) are less frequent.
Chromosomal changes show a characteristic distribution within the diverse CMPD. In detail, PV shows, as the most frequent changes, +9, followed by +8 and by del(20q) [23, 26]. CIMF has a more heterogeneous pattern with deletions of 13q and of 20q both in ∼9% of all cases [9, 25], structural abnormalities of 1q and 5q, and chromosome 7 abnormalities [23, 31]. In ET, chromosomal abnormalities are found in <5% of cases only, mostly represented by numerical gain of chromosome 9. Table 1 presents an overview on recurrent cytogenetic and molecular markers in the CMPD.
Table 1Chromosomal and molecular markers in CMPD [8, 9, 22, 23, 52, 69] Karyotype abnormalitiesMolecular markersMolecular MRD markersCMLt(9;22)(q34;q11), in all cases BCR–ABLBCR/ABL+PVIn some cases: +8, +9, del(20q), del(13q), del(1p)JAK2V617F+JAK2 exon 12 in V617F-negative casesCIMFIn some cases: del(13q), del(20q), +8, +9, partial trisomy 1qJAK2V617F+MPLW515ETIn rare cases +8, +9, del(13q), JAK2V617F+MPLW515CMPD-UIn some cases +8, +9, del(20q)JAK2V617F+In rare cases 8p11 translocationsFGFR1 rearrangementsCEL/HESin some cases: +8, i(17q),PDGFRA/FIP1L1 in CEL+CNLin some cases: +8, +9, del(20q)−−CMML−7, +8, del(20q)NRAS in some cases+
Balanced translocations as revealed by cytogenetics are rare in the CMPD. Many of these lead to the disruption of genes encoding tyrosine kinases. The breakpoints cluster in two regions at 5q31-33 and 8p11 which target the platelet-derived growth factor receptor beta [e.g., in the t(5;12)(q31q33;p12)/ETV6-PDGFRB)] and the fibroblast growth factor receptor 1 kinase [e.g., in t(8;13)(p11;q12)/FGFR1-ZNF198)]. Further, the ABL non-receptor tyrosine kinase might be involved in these rare rearrangements as in the t(9;12)(q34;p13)/ETV6-ABL [32]. The 8p11 myeloproliferative syndrome shows a specific profile outlined by frequent association to Non-Hodgkin’s lymphoma, high leukemic transformation rates, eosinophilia, and CML-like findings in bone marrow cytomorphology. It is most frequently caused by the t(8;13)(p11;q12)/FGFR1-ZNF198, but many other variants all involving 8p11/FGFR1 have been described. Bone marrow cytomorphology shows CML-like findings and eosinophilia [12]. As patients with PDFRB and ABL rearrangements are all candidates for tyrosine kinase inhibitor treatment, detection of these rare rearrangements by cytogenetics in combination with FISH and PCR is obligatory. For an overview on these reciprocal gene fusions, we refer to Cross and Reiter [32].
Molecular mutations in BCR/ABL-negative CMPD
As published in 2005 by several study groups, a high proportion of patients with BCR/ABL-negative CMPD have a somatic point mutation in the JAK2 gene on 9p24 (V617F) which codes for the JAK2 kinase. In detail, the mutation was found in 80–97% of all patients with PV, in >50% of all patients with CIMF, and in 40–57% in ET [1–5]. Janus kinases are non-receptor TKs which regulate the phosphorylation of several signaling pathways, e.g., JAK/STAT, whose activity is increased by the JAK2 mutation [3, 5]. Interestingly, JAK2V617F-positive ET cases were found to show considerable clinical similarities to PV. This pleads for common pathogenetic pathways in part of the ET cases and in PV [33]. It has to be expected that the JAK2V617F mutation will soon be included as a major criterion for PV diagnosis in a revised WHO classification, as nearly all cases were found to be positive [10]. According to this proposal, also in ET or in CIMF, the respective mutation will serve likewise to any other clonal marker as criterion for the diagnosis of ET or CIMF, which further emphasizes its value for diagnostics in the CMPD.
A positive mutation status seemed correlated with further advanced stages. Homozygous JAK2 mutations are more frequent in PV and CIMF than in ET [26] and are associated with a longer history of disease than heterozygous mutations [34]. Thus, a homozygous mutation status correlates with a more aggressive course and might indicate an inferior outcome.
Different assays were developed for JAK2 mutational analyses, e.g., allele specific PCR, real-time PCR, or pyrosequencing, which is able to convey information on the frequency of mutated alleles [35]. Kroger et al. [11] showed that quantitative assessment of the JAK2 mutation with real-time PCR after allogeneic hematopoietic stem cell transplantation was valid as minimal residual disease parameter allowing the adaptation of adoptive immunotherapy accordingly. Thus, determination of the JAK2V617F mutation status is highly valuable for all cases with a suspicious or proven BCR/ABL-negative CMPD and even contributes to determination of the prognosis and to MRD strategies.
The role of the JAK2V617F mutation is not limited to the “classical” CMPD but was detected in other myeloid malignancies as well, e.g., in 3–10% of all MDS cases [1, 36, 37] or in 50–90% in RARS-T representing an ambiguous subentity with overlapping myeloproliferative and myelodysplastic features [17, 38]. Interestingly, the JAK2V617F mutation was as well found in 20–30% of patients with abdominal vein thromboses and in 5% of patients with cerebral vein thromboses without signs of an overt hematologic disorder [39, 40].
Since the detection of the JAK2617F, the panel of known activating mutations in the CMPD is continuously increasing: PV patients who were JAK2V617F-negative were detected to carry somatic gain-of-function mutations within exon 12 of the JAK2 gene in 40% of cases in a recent study. This mutation subtype was shown to stimulate erythroid proliferation in in vitro experiments [40, 41]. Further on, ∼5% of CIMF and ∼1% of all ET cases show somatic mutations in codon 515 within the transmembrane domain of the MPL gene which encodes the thrombopoietin receptor. The respective point mutations lead to single amino exchanges (W515L and W515K) and induce constitutive cytokine-independent activation of the JAK-STAT pathway as gain-of-function-mutations likewise to the V617F [42–44].
Chronic neutrophilic leukemia
CNL is a very rare CMPD defined by persistent leukocytosis in pB ≥25 × 109/l, segmented neutrophils and bands >80% of WBC, immature WBC <10%, and myeloblasts <1% [8]. Survival is extremely heterogeneous and was reported from a few months to 20 years. Cytogenetic aberrations are rare and include +8, +9, del(20q), and del(11q) [8, 45, 46]. The JAK2 mutation was described in few cases of CNL [4, 22, 37, 45–48], but determination of the true incidence is extremely difficult due to the rare occurrence. Some CNL cases were identified to bear rare BCR–ABL fusion transcripts with a breakpoint between exons c3 and c4 of the BCR gene leading to a 230-kDa fusion protein [49, 50].
Hypereosinophilic syndrome/chronic eosinophilic leukemia
Persisting hypereosinophilia is, in most cases, reactive and is only rarely caused by a malignant disorder such as HES or CEL or other eosinophilia-associated CMPD [6, 7, 51–53]. HES is defined by persistent eosinophilia ≥1.5 × 109/l in peripheral blood >6 months and an increased number of bone marrow eosinophils of unknown origin; this is accompanied by organ involvement and dysfunction. Classification as HES requires exclusion of all other causes and failure of detection of the underlying genetic defect by cytogenetic and/or molecular screening.
A diagnosis of CEL requires >2% blasts in peripheral blood and >5–19% bone marrow blasts or evidence of clonality [8, 54]. The most frequent aberration in CEL is the FIP1L1–PDGFRA fusion which results from a cryptic interstitial deletion on chromosome 4q12. Whereas chromosome banding analyses fail to detect the respective cytogenetic correlate, it is revealed by IP-FISH with differently marked probes for CHIC2, FIP1L1, and PDGFRA, and with reverse transcription (RT)-PCR for FIP1L1–PDGFRA [55, 56].
Some more rare TK gene fusions were detected in eosinophilia-associated CMPD, which involve the tyrosine receptor kinases PDGFRA on 4q12, PDGFRB on 5q31, FGFR1 on 8p11, and the non-receptor kinase JAK2 on 9p24 [9, 57]. The beneficial response of patients with PDGFRA and PDGFRB rearrangements to imatinib makes the detection of these rearrangements obligatory [6, 7, 53, 58]. Therefore, a combination of cytomorphology, cytogenetics, IP-FISH, and RT-PCR based on the patient’s history provides the basis for optimized diagnosis in eosinophilia-associated CMPD followed by targeted therapy [32, 59, 60].
Chronic myelomonocytic leukemia
Due to its ambiguous character, CMML was incorporated by the WHO into a category which overlaps between myelodysplastic and myeloproliferative disorders [8] and was defined by peripheral monocytes >1 × 109/l and by dysgranulopoiesis >10%. Blasts and promonocytes were defined by <20% of WBC and by <20% of all nucleated cells in bone marrow. NSE was strongly recommended for bone marrow examination. Clonal karyotype abnormalities occur in 25–35% of all cases. Most frequent are changes of chromosome 7, trisomy 8, and complex aberrant karyotype which is defined by three or more chromosomal aberrations [9, 22, 61]. Mutations of the NRAS protooncogene are the most frequent so far identified molecular markers with variable incidences of 10–66% in this entity. Although there was a wide range in these studies (probably due to the limited samples size in the different studies), this high incidences suggest parallels to MDS or AML [61–63]. The JAK2 mutation was detected in 3–13% of all cases with CMML [1, 4, 37], which illustrates the vicinity to the CMPD in another part of CMML cases. This molecular heterogeneity correlates with the clinical and morphological diversity of CMML and supports the ambiguous position as suggested in the WHO classification.
Remission criteria in the CMPD
New therapeutic strategies including allogeneic stem cell transplantation as potentially curative option or targeted therapies in the CMPD implicate the need for more differentiated and sensitive criteria of remission. For CIMF, an international working group formulated new consensus criteria for response to treatment [64]. These criteria are based on a combination of clinical and laboratory parameters and include cyto- and histomorphological, cytogenetic, and molecular findings. Thus, highest so far applicable sensitivity is achieved. Clinical criteria include disappearance of clinical symptoms as palpable hepatosplenomegaly. The laboratory and cytomorphological criteria of complete remission imply normalization of trilineage peripheral blood count and the absence of blasts, immature progenitor cells, or nucleated erythroid precursors in peripheral blood. Bone marrow histologic remission criteria apply to cellularity, myeloblast percentage, and osteomyelofibrosis. Finally, cytogenetic response criteria discriminate major cytogenetic response, meaning absence of chromosomal abnormalities in cases with a preexisting aberration from minor cytogenetic response requiring a ≥50% reduction of abnormal metaphases. As the most sensitive criterion, major molecular response defines absence of a specific disease-associated mutation in previously positive cases [64].
Approach to a diagnostic algorithm in the CMPD
A diagnostic algorithm for all cases with diagnosis or suspicion of CMPD (Fig. 1) should start with the cytomorphologic evaluation of peripheral blood and bone marrow. This allows, in many, cases a differentiation between CML and a BCR/ABL-negative CMPD. In parallel, all cases should be evaluated by histomorphology.
Fig. 1Proposal for a diagnostic algorithm in BCR/ABL-negative CMPD. HES Idiopathic hypereosinophilic syndrome, CEL chronic eosinophilic leukemia, PV polycythemia vera, CIMF chronic idiopathic myelofibrosis, CMPD-U unclassifiable CMPD, ET essential thrombocytosis, RARS-T refractory anemia with ringed sideroblasts, CMML chronic myelomonocytic leukemia, MFC multiparameter flow cytometry, RT-PCR reverse transcription polymerase chain reaction. Dashed line may add information in difficult cases, but not obligatory
Chromosome banding analyses might gain important information in PV, CIMF, and also in CMPD-U, as chromosomal aberration rates of ∼20–45% were reported [22]. According to the recent guidelines of a British Committee, cytogenetics are considered as “stage 2 investigations” in case of PV and erythrocytosis which should be performed in dependence on the results of clinical evaluation, blood count, and the JAK2 mutation as well as other laboratory parameters such as serum ferritin which are obligatory as “stage 1 investigations” [65]. In contrast, cytogenetics can be neglected in clinically clear cases of ET due to the extremely low incidence of aberrant karyotypes. In cases in which the discrimination of a CMPD from a reactive disorder is not possible according to clinical, laboratory, and cyto-/histomorphological aspects, cytogenetics might contribute to differential diagnosis, as, in some cases, clonal abnormalities confirm the diagnosis of a hematologic malignancy. CMML should as well undergo cytogenetic analyses; in addition, molecular screening for NRAS mutations might be discussed due to their frequent occurrence and new drugs that may come up. This also includes the investigation of PDGF receptors expression.
The chromosomal aberrations as revealed by chromosome banding analyses—e.g., +8, +9, del(20q)—can be verified by FISH techniques. This further allows the selection of IP probes for distinct numerical and structural aberrations to provide parameters for MRD diagnostics.
Today, the backbone in all cases of suspicious or proven CMPD should be screening for the JAK2V617F mutation status by PCR, e.g., by a melting curve light cycler assay [66]. According to the proposals for a revised WHO classification, evidence of the JAK2V617F mutation (localized in exon 14 of the JAK2 gene) or a functionally similar mutation will be required as major criterion for the diagnosis of PV. This might justify additional screening for JAK2 mutations in exon 12 in cases which are highly suspicious for PV from morphological aspects but are negative for the JAK2V617F [10].
Finally, all cases with a suspected or proven CMPD should be evaluated by IP-FISH or PCR for BCR–ABL to exclude a diagnosis of CML due to the therapeutic consequences. This is even more emphasized by single cases showing a coincidence of the BCR–ABL fusion and the JAK2V617F mutation where the cytomorphological features of the CMPD can mask the CML aspect [67].
In cases with diagnosis or suspicion of HES/CEL, cytogenetic analysis is informative only in very few cases and may be omitted, whereas molecular diagnostics in search of the FIP1L1–PDGFRA gene fusion by IP-FISH and/or RT-PCR is obligatory.
Conclusions
For many years, diagnostics in the BCR/ABL-negative CMPD were mainly based on clinical symptoms, cytomorphology, and histomorphological findings. This has dramatically changed in recent years. The WHO (2001) [8] included cytogenetic aspects directly and indirectly in their classification system. This can be exemplified in ET which is excluded by evidence of a del(5q) or an inv(3)(q21q26), as both the 5q- syndrome in MDS or AML with the respective inversion 3 can show microkaryocytes and high thrombocytes. Clonal chromosomal abnormalities other than the Philadelphia translocation support the diagnosis of CMPD and allow to discriminate this from reactive conditions.
Additionally, the spectrum of molecular mutations considerably increased. Most molecular events target receptor TK (such as FGFR1, PDGFRA, and PDGFRA) and non-receptor-TK (such as ABL or JAK2). Especially, the detection of the JAK2 mutation in the majority of patients with a CMPD has revolutionized diagnostics in the CMPD [13] and allows, in many cases, now a rapid and clear discrimination of the CMPD from reactive conditions. It further may abolish the measurement of the PRV1 expression in cases with suspected PV. JAK2 mutated cases seem to be associated with higher complication rates and an increased need for therapeutic interventions when compared to wild-type patients [3]. This might play a role for the choice of therapy in the future. Finally, JAK2 might represent a target for specific compounds with anti-tyrosine kinase activity [2, 34]. The recent description of JAK2 mutations in exon 12 in V617F-negative PV cases [40, 41] and of the W515 mutations of the MPL gene in a low frequency in ET and CIMF [42–44] illustrate that we have to assume a complex network of activating mutations in the CMPD of which only parts are so far identified. Thus, a new classification of the CMPD according to the molecular substrate, e.g., the JAK2 mutation, likewise to the definition of CML, will be more appropriate [10, 68]. The inclusion of JAK2 mutation analysis as a major criterion for the PV diagnosis within the current and upcoming World Health Organization (WHO) diagnostic criteria was suggested [10].
The detection of the FIP1L1–PDGFRA fusion in CEL/HES in association to the good response to imatinib [6, 52] and the increasing detection of rare fusion transcript in the BCR/ABL-negative CMPD [32] contributed as well significantly to an improved molecular classification in CMPD.
MRD strategies are so far poorly established in the Philadelphia negative CMPD when compared to the acute leukemias or to CML. This might change in the near future, as it was already shown in a post-transplantation setting that quantitative assessment of the JAK2 mutation qualifies as MRD marker [11]. In CML, the definition of remission criteria allowed an international standardization in clinical studies and was helpful for clinical routine. This approach is increasingly important also for the BCR/ABL-negative CMPD as realized by an international working group proposing cytogenetic and molecular response criteria in CIMF [64].
In conclusion, diagnostics in the BCR/ABL-negative CMPD have abandoned the former perception which classified these complex disorders mainly on clinical and morphological aspects and are on the way to a comprehensive approach focussing increasingly on cyto- and molecular genetic aspects. Individual treatment is already available or will hopefully follow.

cmpd
molecular marker
cytomorphology
bcr/abl


Overdiagnosis and overtreatment of early detected prostate cancer

Early detection of prostate cancer is associated with the diagnosis of a considerable proportion of cancers that are indolent, and that will hardly ever become symptomatic during lifetime. Such overdiagnosis should be avoided in all forms of screening because of potential adverse psychological and somatic side effects. The main threat of overdiagnosis is overtreatment of indolent disease. Men with prostate cancer that is likely to be indolent may be offered active surveillance. Evaluation of active surveillance studies and validation of new biological parameters for risk assessment are expected.
Introduction
What is the rationale for screening?
Screening for diseases, especially cancer, has become part of modern medicine. Screening for breast, cervical and colorectal cancer is already normal practice in some countries, and will probably become routine in other countries in the future. Screening for prostate, melanoma and lung cancer are subject to ongoing studies [1–5]. The rationale behind screening is simple: to detect cancers at an early stage, when they are still curable. Screening is currently performed using one of the three methods: mass screening (i.e. large scale screening of an entire population), selective screening (i.e. screening of high-risk populations) or opportunistic screening (e.g. incorporated as part of a medical consultation). Diagnostic testing differs from screening because it attempts to identify the disease in the presence of symptoms, while screening is offered to symptom-free individuals.
In any population screened for cancer, four basic groups of patients exist: those diagnosed with cancer who would not have developed cancer symptoms during their lifetime (overdiagnosis); those diagnosed with cancer at an early stage that might otherwise have led to symptoms and/or the need for more aggressive curative treatment; those diagnosed with cancer at a curable stage with aggressive disease that might otherwise have progressed to metastatic disease at the time of diagnosis; and those whose cancer is diagnosed by screening at the same stage as it would have been diagnosed through clinical routines, and that involves cancers that are too late for curative therapy. Ideally, screening should reduce the number of patients in the fourth group (that cannot be cured), and increase those in the second and third group. The window of opportunity for decreasing cancer-mortality by screening for cancer lies with the second and third group. Randomized clinical trials, considered the gold standard for the evaluation of a screening test, have to show how sizeable the window of opportunity is. The difference between the first group and the second is however not always clear at the time of initial diagnosis. Any screening procedure carries a risk of overdiagnosis and overtreatment, which should be balanced against the benefits for those in which the cancers are diagnosed at a curative stage. Whether this balance is justifiable depends on more than mortality differences of randomized study groups only, but also on quality of life issues measured against the cultural background of the population studied.
Incidence
Does screening influence prostate cancer incidence?
Since the potential value of PSA for the early detection of prostate cancer was described in the early 1990s, both prostate cancer incidence and mortality rates have changed profoundly [6]. Between 1989 and 2003, for example, the age-standardized incidence rate of prostate cancer increased by 48.4% in The Netherlands (reaching an incidence of 93.2 cases per 100,000 men). Based on rates from 2001 to 2003, 17.1% of U.S. men born today will be diagnosed with cancer of the prostate at some time during their lifetime [http://www.cancer.gov]. It is now the most frequently diagnosed non-cutaneous cancer, with 225,000 new cases reported each year in Europe alone [7]. This increase of incidence suggests that this is due to the detection of cancers in the first three groups described above. This is supported by the reports on autopsy studies. These autopsy studies have revealed that histologic prostate cancer occurs in an even larger proportion of men compared to the screening incidence: up to 55% of men in their fifties, and 64% of men in their seventies have prostate cancer diagnosed at autopsy, while only 5–10% are detectable in a screening setting during life [8].
A number of influences might have contributed to the increase of cancer diagnosis over the last decades, apart from the structured screening studies that have been initiated at various places. First, the PSA thresholds for biopsy appears to have been reduced gradually in some areas of the world due to the detection of significant cancers in the low PSA range [9]. Most guidelines, however, still mention the traditional cut-off of 4 ng/ml as an indication for biopsy. Secondly, an increase in the number of core samples per biopsy have been advocated, based on the observation that more cancers are diagnosed when more biopsies are taken. Thirdly, awareness of prostate cancer within the general population has increased stimulated by the information obtained predominantly from the urologic profession [10]. If these current trends continue, the number of living men diagnosed with prostate cancer will increase even further [11].
Mortality
What happens to prostate cancer mortality by screening and detecting indolent tumors?
Despite this rising incidence, the age-standardized prostate cancer mortality rate has decreased in many countries around the world with or without early detection programs. In The Netherlands, for example, rates fell by 11% between 1989 and 2003, to 28.4 deaths per 100,000 men or 2,349 in total [http://www.cancer.gov]. It is however unclear whether the stage and grade migration observed in screening studies results in a reduction in the mortality, although case-control studies with conflicting results are available [12–14]. A decrease of mortality shown in randomized studies would form a strong argument in favor of population screening.
Screening results in the more frequent detection of small volume, low grade and organ confined prostate cancers, which are diagnosed earlier in their course [6, 15]. Many of these tumors have the histological characteristic of autopsy tumors, that is, tumors that have not become symptomatic during life [16]. They have been called indolent or clinically insignificant cancers. Various definitions of clinically insignificant tumors have been designed based on the characteristics of the autopsy studies, of which the Epstein definition is widely known [17]. Detecting such tumors will increase the detection frequency of cancer, but it is unlikely that they will influence the prostate cancer specific mortality, as they do not alter the course of life.
Early diagnosis
Screen detected tumors are diagnosed more early
Screen detected tumors are not only diagnosed more often, but can be expected more early during their natural course. Lead-time is defined as the time period from detection by a screening procedure to the time of diagnosis in absence of screening due to symptoms. If the patient dies during the lead-time period of the tumor, the lead-time is indefinite and therefore equal to overdiagnosis.
Early detection by PSA advances prostate cancer diagnosis in time (i.e. lead time) [18]. For men aged 55–75 years lead time amounts to 12.3 years in a screening setting [19]. The lead-time is likely to be shorter for aggressive cancers and longer for indolent ones. Early detection also causes a significant stage shift towards more locally confined and less aggressive cancers [20]. The long lead-time, stage reduction and natural history data cited above indicate that for properly selected cases there is a long ‘time-window’ during which observation is safe without losing the opportunity for cure. This is supported by evidence from nomograms, prognostic tables, and by the only available randomized study of observation against radical prostatectomy [21].
The impact of overdiagnosis and unnecessary treatment and of its side effects on patient health is also unclear; however, application of a mathematical model (the Miscan model) on data from the ERSPC has shown that, in an annual screening program for men aged 55–67 years, 56% of diagnosed cases would constitute instances of overdiagnosis [22]. If this estimate proves to be realistic (as it appears to be the case), nationwide screening programs may not be acceptable using the present screening regimens, even if benefits in terms of mortality reduction were shown. Research aimed at the development of more selective screening tools is therefore very important.
The natural course of screen-detected cancers
The current knowledge of the natural history of prostate cancer is mainly based on clinically detected cases, diagnosed by disease-related symptoms, or coincidentally at the time of unrelated symptoms of the urinary tract. Natural history data on screen-detected cases of prostate cancer will be created as a result of the large ongoing screening studies worldwide in which tumors might have been treated without invasive therapy [1]. Most studies show histological and cytological grade to be the most important prognostic variable [23, 24]. There is a steep decline in the 5-, 10- and 15-year cancer-specific survival with increasing grade. Most prostate cancer cases diagnosed with present diagnostic techniques fall into the moderately differentiated group (grade 2, Gleason 6), of which the cancer-specific 10–15-year mortality is 18–30%. This is even lower in the group of prostate cancers diagnosed with grade 1 and 2 or Gleason 4–6, and there are subgroups of patients who are not at risk of dying from prostate cancer even within 15 years. Overall mortality is then determined by comorbidity. The majority of these men are currently treated for their prostatic disease with invasive procedures, which might not be needed. Adequate prediction of the outcome of comorbid diseases would be of great support in predicting the outcome of the prostate cancer patient.
Overdiagnosis
Overdiagnosis and overtreatment, what does it mean?
During recent years, increased interest has risen to the possibility that increased detection of prostate cancer may lead to the diagnosis of cancers that rather should not have been diagnosed, and certainly should not have been treated, as their detection and subsequent treatment is unlikely to benefit patients, or even might harm them. Related to this, the terms ‘overdiagnosis’ and ‘overtreatment’ are being used. So, when is prostate cancer overdiagnosed?
By using the clinical definition of overdiagnosis, that is diagnosing tumors that would otherwise remain clinically unrecognized until the individual died from other causes, it is clear that this definition can only be applied in retrospect in the evaluation of studies. There are currently no clinical or biological parameters that can identify such tumors 100% adequately at the time of diagnosis. By studying the natural course of prostate cancer, and comparing autopsy results with findings from screened populations, clinical and histological parameters can be identified that predict indolent tumors best. Those indolent tumors are likely to be only a subset of the tumors that are overdiagnosed in retrospect.
Overdiagnosis is predominantly being associated with early detection or screening programs. Overdiagnosis appears to be especially harmful when it results in invasive treatment of the tumors that would unlikely to be harmful. This is called overtreatment.
Overdiagnosis occurs when screening detects small tumors that would otherwise remain clinically unrecognized until the individual dies from other causes. Such tumors are predominantly found in the low PSA ranges. Unfortunately, an unknown number of biologically more aggressive cancers may hide between the larger number of detectable tumors with favorable stages. Though some of the aggressive tumors can be diagnosed by adverse histological criteria such as high Gleason score in the biopsy, some of these features might be missed due to the heterogeneity of prostate cancers and their representation in the biopsy sampling. This might justify the amount of overtreatment that has been practiced in various areas of the world. Overtreatment is thus defined as unnecessary invasive treatment with respect to the outcome of the natural course of the tumor in combination with its host.
One can wonder what number needed-to-treat to prevent one prostate cancer death we are prepared to accept. Based on the Swedish randomized trial of radical prostatectomy versus watchful waiting [22], the Connecticut observation series [15], and the Toronto active surveillance experience [25], a number needed to treat analysis of the benefit of radical treatment of all newly diagnosed favorable-risk prostate cancer patients, compared with a strategy of active surveillance with selective delayed intervention, has been presented by Klotz [25]. This suggested that approximately 73 patients will require radical treatment for each prostate cancer death averted. This translates into a 3- to 4-week survival benefit, unadjusted for quality of life. If any, the number of life-years gained will be small, because of the fact that prostate cancer is a disease of old age. This should be contrasted to the side-effects of all applied treatments. As a minimum, the number of men needed to treat should be higher than the number of men dying from intervention related causes.
Informed decision making, reduction of unnecessary prostate biopsies
The increasing number of diagnostic procedures and subsequently of prostate cancer diagnosis in various areas of the world is partly fed by an increased awareness of prostate cancer and the anxiety raised of suffering from a devastating disease at the end of life. Men should ask themselves if they are at specific risk for having prostate cancer, and if they want to follow the step wise procedure of PSA testing, urologic investigations, prostate biopsies, and potential treatment. Balanced information regarding this procedure and its consequences should be offered to every man considering prostate testing. Validated information (that is: well understandable text that delivers the information that is required) has been made available in several countries around the world, and it has been shown that such information reduces the number of men who initially wanted to be screened.
Based on population data it is possible to provide risk assessments for every step of the screening procedure. Such assessments produce an individual risk calculation based on relevant risk parameters. This might support patients and doctors in their decision to follow or refrain from further steps, dependent on their interpretation of the risk calculated. At the time of cancer diagnosis, it may provide information on the risk of the presence of an indolent tumor, as discussed above.
Current risk calculators have incorporated family history, age, micturition complaints, PSA, DRE, TRUS results, and histologic features of the prostate biopsies into their assessment. With an increasing number of relevant parameters, the level of predictive accuracy is enhanced. It is likely that new parameters might be added once tested in population-based biorepositories. Candidate parameters therefore obviously are serum and urine markers for the early diagnostic steps, and histologic markers at the time that biopsies have been taken.
Much interest has been given to the increase of specificity of the biopsy procedure in the general population with serum markers like PSA isoforms and kallekreins in order to diminish the number of false negative biopsies [26, 27]. Enhancing specificity always resulted in a reduction of sensitivity of prostate cancers. As we have seen based on autopsy incidence, the number of potentially detectable tumors is manifold the number of currently diagnosed cancers. It is therefore not the absolute number, but the number of clinically relevant cancers that is of interest [28]. The PSA isoforms and kallekreins should therefore ideally be related to the characteristics of the cancers detected.
Screening efficiency
A small number of studies already have provided evidence that supports strategies to reduce the number of screens in the general population. Such strategies will inevitably lead to the reduction of overdiagnosis of prostate cancer.
Information obtained from population based screening studies illustrates that the absolute value of serum PSA is related to the proportion of detectable carcinomas in subsequent screening rounds. Data from the ERSPC as well as from the PLCO [29, 30] showed that men with a PSA less than 1 ng/ml did not develop invasive cancer over the time period of more than 5 years of repeated check-ups. In the Rotterdam site of the ERSPC, 1703 men with an initial PSA of less than 1 ng/ml men were followed during two consecutive 4 year screening rounds. Eighty percent of men attended the second screening round, and 77% the third round. In total, only 8 cancers were found in 47 prostate biopsies on the indication of PSA of >3 ng/ml. In the PLCO screening, every 5 years for baseline PSA less than 1 ng/ml and every 2 years for PSA 1–2 ng/ml could result in a 50% reduction in PSA tests and in less than 1.5% of men missing earlier positive screens.
In men who were enrolled onto a cardiovascular study in Sweden, 21,277 men aged <50 years old were assessed over a period of more than 20 years starting between 1974 and 1986. Two decades later, 498 (2.3%) were eventually diagnosed with prostate cancer (outside a structured screening procedure). In retrospect, the level of serum kallikreins (hK2, total PSA, and free PSA) at baseline and thereafter were strongly associated with emerging prostate cancer. This supports the idea of risk stratification for screening on prostate cancer in an early age, that is during the fourth decade of life. Men at low risk may refrain from frequent serum testing for long periods of time based on their individual risk assessment that incorporates the information obtained from currently available and newly validated parameters.
Overtreatment
Side effects of treatment are substantial
Treatment for prostate cancer may involve surgery, external beam radiation therapy, brachytherapy, high intensity focused ultrasound (HIFU), watchful waiting, active surveillance, chemotherapy, cryosurgery, hormonal therapy, or combinations. The most frequently applied treatments for organ confined prostate cancer are radical prostatectomy, external beam radiotherapy and brachytherapy.
Although, severe or life-threatening complications with radical prostatectomy are rare, the adverse effects of greatest concern are damage to the urinary sphincter and erectile nerves (nervi erigenti), resulting in urinary incontinence and impotence, respectively. Complete incontinence is uncommon after radical prostatectomy, although a significant number of men experience some degree of stress-urinary incontinence [31–33]. In the Prostate Cancer Outcomes Study, a population-based study of 1,291 men who underwent radical prostatectomy for localized prostate cancer and were followed for 2 years, 1.6% reported no urinary control at 24 months following surgery (compared with 0.7% at baseline prior to surgery), while 7 and 42% reported frequent and occasional leakage, respectively (compared with 2 and 9% at baseline) [32]. Age had an impact on the degree of incontinence; 14% of men aged between 75 and 79 years experienced the highest level of incontinence compared with 0.7–4% of younger men. In the Prostate Cancer Outcomes Study, 42% of men reported that sexual performance was a moderate to large problem at 24 months (compared with 18% at baseline); 60% were not able to have erections firm enough for sexual intercourse (compared with 16% at baseline) [32]. At 24 months postoperatively, men over the age of 60 were more likely to be impotent than younger men (78–85 vs. 61%, respectively).
Complications after external beam radiotherapy include bladder irritation (urgency, pain, frequency) in up to 5% of men, and impotence in 40–50% [34]. In contrast to surgery, these complications tend to increase over time. The reported incidence of radiation proctitis ranges from 2 to 39%, depending upon the definition used, and the dose field, and technique of radiotherapy. Prostate inflammation and swelling can occur acutely following brachytherapy, suggesting that men with significant urinary symptoms or a large prostate are not good candidates. Urinary retention can be severe enough to require self-catheterization; transurethral resection to improve micturition is contraindicated until a substantial portion of the radioactivity (usually five half-lives) has dissipated because of the risk of incontinence and radiation risks to the surgeon and pathologist. Later complications include irritative voiding symptoms, urinary retention, rectal urgency, bowel frequency, rectal bleeding or ulceration, and prostatorectal fistulas [35–37]. The incidence of erectile dysfunction ranges from 14 to 52%, depending on whether it is physician- or patient-reported.
It is obvious that invasive treatment may influence the quality of life of men with prostate cancer and their families substantially. But so does a potential threat of prostate cancer that is not actively treated or not even diagnosed yet. It is unlikely that quality of life studies will be able to indicate the best balance between these points of view for management decisions on an individual patient level.
Active surveillance as alternative to invasive treatment
Because not all cancers diagnosed require treatment, one of the major challenges for the future is to determine which diagnosed cancers should be treated, and which can be managed by active surveillance. Active Surveillance manages selected men with prostate cancer expectantly with curative intent. This means men are carefully selected and subsequently actively observed in order to have the possibility to offer them deferred curative treatment once the tumor seems to progress. Active surveillance should be clearly differentiated from watchful waiting. Watchful waiting entails a strategy for all men who are managed expectantly, whereas active surveillance focuses on men for whom therapy is delayed until the tumor becomes progressive and curative treatment can be offered. This offers an attitude of active control over the cancer diagnosed for patients and their doctors. The stage migration that screening provides has resulted in an over-representation of low-risk cancers. Therefore, studies which validate monitoring algorithms in active surveillance regimens are ongoing [38].
Risk stratification for indolent disease
Over the last decade, a number of nomograms have been composed to predict the presence of an indolent cancer [39, 40]. The identification of indolent cancers was strongly based on histologic information of prostate biopsies, and power of Gleason score as a predictive parameter for aggressiveness of prostate cancer was unsurpassed. As a single serum parameter at the time of diagnosis, the level of PSA contributed most to prognosis.
These nomograms were based on extensive clinical series. A new nomogram recently appeared based on information obtained from a screening series of the general population [41]. Screening series differ from clinical studies, as the incidence of indolent cancer is almost 50% compared to maximal 20% in multicentred clinical series. With the use of the nomogram, at a 70% probability cut-off, at least 69% of all indolent cancers would be diagnosed as such, and be treated with active surveillance.
Conclusions
It is still too early to say whether population-based prostate cancer screening is a useful tool with regard to cancer mortality. We must wait until the results of ongoing prostate cancer screening trials are available. Until then, opportunistic screening should not be encouraged and those men who do want a PSA test should participate in carefully designed, balanced information program. Even if PSA screening is found to reduce prostate-cancer-specific mortality, levels of overdiagnosis may remain unacceptable for population-based screening.
To reduce overdiagnosis in a screening setting, markers are needed that reduce the risk on a positive prostate biopsy, increasing the specificity of this procedure. Men from the age of forty, as well as their advising doctors, need instruments to reduce their doubts and anxiety of the potential presence of a prostate cancer. This, together with balanced information about the benefits and risks of the individual outcome of screening procedures, might induce a more selective and step-wise screening action. Risk assessment, incorporating the main determinants known for the presence of prostate cancer from the age of 50, such as age, family history, and micturition complaints, should form the base of an individual screening approach. Objective values of serum markers might enhance the accuracy of such of risk predictors.
Various efforts are performed to find new markers in the proteome and genome of blood and urine. Based on large and longitudinal serum collections of men diagnosed with prostate cancer in screening settings, the EC-sponsored P-MARK consortium evaluates candidate markers as prognostic tools [42].
Until alternative screening tools are found, PSA will continue to be used, and overdiagnosis will remain an unavoidable drawback of prostate cancer screening. The current challenge is to ensure that in the still growing numbers of men diagnosed with prostate cancer world-wide, overdiagnosis does not result in overtreatment. To this end, research efforts presently focus on clarifying which cancers can be managed through active surveillance.

overdiagnosis
overtreatment
prostate cancer
active surveillance
rationale for screening


π-π stacking tackled with density functional theory

Through comparison with ab initio reference data, we have evaluated the performance of various density functionals for describing π-π interactions as a function of the geometry between two stacked benzenes or benzene analogs, between two stacked DNA bases, and between two stacked Watson–Crick pairs. Our main purpose is to find a robust and computationally efficient density functional to be used specifically and only for describing π-π stacking interactions in DNA and other biological molecules in the framework of our recently developed QM/QM approach "QUILD". In line with previous studies, most standard density functionals recover, at best, only part of the favorable stacking interactions. An exception is the new KT1 functional, which correctly yields bound π-stacked structures. Surprisingly, a similarly good performance is achieved with the computationally very robust and efficient local density approximation (LDA). Furthermore, we show that classical electrostatic interactions determine the shape and depth of the π-π stacking potential energy surface.
Introduction
Two major factors for the structure and stability of DNA are the hydrogen bonds between two adjacent bases from opposite strands (forming a Watson-Crick pair), and the π-π stacking interactions between two bases within each of the two DNA strands. The hydrogen bonding interactions in DNA are well understood by high-level Density Functional Theory (DFT) calculations [1–3]. They were shown to be provided by nearly equally important contributions from electrostatic attraction and donor-acceptor orbital interactions (e.g., from an N lone pair to an N-H σ* orbital), and to be sensitive to effects from the molecular environment (counter-ions, solvent) [1, 2]. A similar understanding of the π-stacking interactions is currently lacking due to several reasons: (1) π-π stacking interactions have proven to be sensitive to the methodology used (see below); (2) π-π stacking interactions have proven to be very dependent on the size of the basis set used in (ab initio) calculations, resulting in a large basis-set superposition error (BSSE); (3) high-level ab initio benchmark studies (CCSD(T) with at least triple-zeta basis sets) have only recently become available; and (4) the notorious problems of DFT to correctly describe dispersion interactions, [4–16] which constitute one of the components involved in π-stacking interactions (see below). The latter problems of DFT resulted in potential energy surfaces (PES) that, erroneously, lack any equilibrium configuration, i.e., the stacked systems were incorrectly described as being purely repulsive.
Because of the technical difficulties involved in obtaining accurate benchmarks (CCSD(T) using large basis sets), Sponer, Hobza and co-workers have studied in a ground-breaking series of papers [17–22] the stacking energies of DNA bases and DNA base analogs using a variety of ab initio methods and basis sets. Earlier studies showed that reasonable interaction energies could be obtained when employing the MP2/6-31G*(0.25) method, which was confirmed by later and more accurate studies [17–22]; in the aforementioned 6-31G*(0.25) basis set, the standard d-polarization functions (with exponent of 0.80) were replaced by more diffuse ones (exponent of 0.25) with the aim to improve description of the dispersion attraction [22]. Thus, for the anti-parallel displaced pyrimidine dimer, the MP2/6-31G*(0.25) energy is only 1.1 kcal mol−1 lower than the CCSD(T)/6-31++G*(0.25,0.15) energy, for the anti-parallel cytosine dimer it is 0.6 kcal mol−1 higher than the CCSD(T)/6-31++G**(0.25,0.15) energy, and for the twisted uracil dimer the MP2/6-31G*(0.25) is equal to the CCSD(T)/6-31++G**(0.25,0.15) energy. Although there seems to be no systematic shift in energy when comparing MP2/6-31G*(0.25) with the more elaborate CCSD(T) stacking energies, the MP2 stacking energies are always larger in magnitude than the corresponding CCSD(T) ones when using the same basis set for both methods. Interestingly, in connection with the quest for reliable ab initio benchmarks, preliminary results [23–27] indicate that the recently developed spin-component scaled MP2 (SCS-MP2) yields systematically lower stacking energies than MP2. This suggests that SCS-MP2 is in good agreement with the CCSD(T) results at only a fraction of the computational cost.
Several approaches have been proposed to remedy the “dispersion problem” of DFT, ranging from Time-Dependent DFT frameworks [28] to more ad-hoc procedures such as including (C6) van der Waals terms in the interaction energy (DFT-D) [29] or fitting (reparameterizing) the form of the density functional to some reference energies and/or distances. A more elegant solution was recently proposed by Tozer and co-workers [30], who analyzed the DFT exchange-correlation (xc) potential in comparison with the near-exact multiplicative Zhang-Morrison-Parr (ZMP) potential from coupled cluster Brueckner doubles (BD) densities. Their resulting KT1, and the related KT2, functional [30] produces xc potentials that closely resemble those from ZMP. As a result, KT1 and KT2 produce NMR chemical shifts [4, 31] that in general show smaller deviations from experimental values than those from standard density functionals. Furthermore, the ZMP potential from Brueckner (BD(T)) coupled cluster densities gives dispersion forces in good agreement with near-exact dispersion forces [32]. It is therefore to be expected that the KT1 and KT2 functionals behave properly for dispersion forces as well. However, the application of these new functionals to π-stacking interactions has so far not appeared in the literature.
Here, we report the results of a systematic investigation of π-stacking interaction energies, potential energy surfaces (PES) and stacking distances for dimers of, among others, the five DNA/RNA bases. A long list of standard as well as recent density functionals (including the KT1 and KT2 functionals) has been considered in this study, ranging from the Local Density Approximation (LDA), via the Generalized Gradient Approximation (GGA), and meta-GGA, to hybrid functionals. We have also examined BHandH, which was recently [12] shown to give reasonable agreement with ab initio data. The DFT results are compared to benchmark data that were taken from the literature, which in some cases contained energy profiles as a function of the torsion associated with the rotation of one base with respect to the other.
The present investigation is part of a larger undertaking. We aim at developing an extended QM/QM scheme, designated QUILD [33], which allows a (complex) molecular system to be decomposed into arbitrary, interpenetrating domains such that each type of interaction can be described with a different method, i.e., the density functional that performs best for that type of interaction or process, for example, electron-pair as well as hydrogen bonding (BP86: see [2, 3]), π-π stacking (LDA, KT1, KT2: this work) or reaction barriers (OLYP, OPBE: see [34, 35]). This is a pragmatic (of course not a fundamental) approach to cope with the present-day shortcomings of DFT, which features density functionals that perform satisfactorily for a number but not all types of interactions and phenomena. The present study focuses on identifying which DFT approaches serve best to describe the π-π stacking interactions in the above-mentioned QM/QM scheme.
Furthermore, we have analyzed the π-stacking interactions in more detail by decomposing the interaction energy into three physically meaningful components, namely, electrostatic energy, Pauli repulsion (i.e., the destabilizing interactions between occupied orbitals), and bonding orbital interactions [36]. Our analyses reveal, among others, that the electrostatic attraction between the stacked molecules is the most important component of the π-π stacking interaction (see also [37]) which determines the shape and depth of the PES. We have also analyzed the π-π interactions between two stacked Watson–Crick base pairs with the purpose to differentiate between inter- and intra-strand stacking interactions.
Methods
Computational details
All calculations were performed with the Amsterdam Density Functional (ADF) program. [38–49] Molecular orbitals (MOs) were expanded using a large, uncontracted set of Slater-type orbitals: TZ2P [40]. The TZ2P basis is an all-electron basis of triple-ζ quality, augmented by two sets of polarization functions (2p and 3d on H; d and f on heavy atoms). An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately in each SCF cycle.
The equilibrium structure of individual benzene analogs, DNA bases and Watson-Crick base pairs were optimized at the BP86 level of DFT, i.e., using the local density approximation (LDA; Slater exchange and VWN [42] correlation) with non-local corrections due to Becke [43] (exchange) and Perdew [44] (correlation) added self-consistently, which was previously shown to be one of the best DFT methods for the accuracy of geometries [41, 45] and hydrogen-bonding interactions [1–3]. The π-π stacking interaction energies for all density functionals were evaluated post-SCF using LDA as SCF functional. This procedure was recently shown to introduce an error of only a few tenths of a kcal mol−1 [46].
Stacking distances (vertical separation) and orientations (twist angle) were explored with the various density functionals through scans of the potential energy surface (PES) in which the BP86 geometries of the monomers (e.g., DNA bases or Watson–Crick base pairs) were kept frozen. PES scans as a function of the twist angle (see below) were done using steps of 30° in case of homo-base stacks, 60° in the case of hetero-base stacks and 36° for stacks of Watson–Crick base pairs. PES scans as a function of the vertical separation (see below) were done in steps of 0.1 Å.
The interaction energy (see below) was studied as a function of the vertical separation between the two monomers in the π-stacked dimer, and as a function of the twist angle between these monomers. The latter is defined as the right-handed rotation of the upper base around the axis that runs through the center of mass of both the upper and lower base, and perpendicular to the plane of the base (see Scheme 1).
Scheme 1Definition of the twist angle (TW). The black dot is the center of mass
In the stacked DNA systems, the twist angle of 0° is defined as that twist angle at which the respective “glycosidic” N-H bonds (more precisely, the N-H bonds that replace the glycosidic N-C bonds to the sugar in the backbone) are oriented in parallel.
Bond-energy decomposition
The overall π-stacking energy ΔE is made up of two major components [36] (Equation 1):
In this formula, the preparation energy ΔEprep is the energy needed to deform the separate molecular fragments from their equilibrium structure to the geometry that they attain in the overall molecular system. The interaction energy ΔEint is the energy released when the prepared fragments are brought together into the position they have in the overall molecule. It is analyzed for our model systems in the framework of the KS-MO model using a Morokuma-type decomposition [47] into electrostatic interaction, Pauli repulsion (or exchange repulsion), and (attractive) orbital interactions (Equation 2).
The term ΔVelstat corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the prepared (i.e. deformed) fragments and is usually attractive. The Pauli-repulsion, ΔEPauli, comprises the destabilizing interactions between occupied orbitals and is responsible for the steric repulsion. The orbital interaction ΔEoi in any MO model, and therefore also in Kohn-Sham theory, accounts for electron-pair bonding, charge transfer (i.e., donor-acceptor interactions between occupied orbitals on one fragment with unoccupied orbitals of the other, including the HOMO-LUMO interactions), and polarization (empty-occupied orbital mixing on one fragment due to the presence of another fragment). The orbital interaction energy can be further decomposed into the contributions from each irreducible representation ℘ of the interacting system (Equation 3) using the extended transition state (ETS) scheme developed by Ziegler and Rauk [48, 49].
Results and discussion
We have analyzed π-π stacking interactions using different systems that were taken mainly from reference data present in the literature. We start with the prototypical system for studying π-π stacking, namely, the benzene dimer. The second set of reference data was taken from the supporting information of a paper by Mignon and co-workers [50], who studied hydrogen bonding and stacking in complexes of substituted benzene C6H5X with pyridine at MP2/6-31G*(0.25) with substituents X = H, F, NH2, Cl, CH3, OH, CN, COOH, CHO and NO2. All substitutions of H by another X in benzene were done at the para-position with respect to the nitrogen of pyridine (see Scheme 2). The third set of reference data was taken from a paper by Jurecka and co-workers [21], who investigated hydrogen bonding and stacking interactions in the cytosine dimer with MP2 and CCSD(T) methods, using several orientations (see Scheme 3) to investigate the potential energy surfaces. The fourth set of reference data was taken from a paper by Wu and Yang [14] (based on previous work by Hobza, Sponer and co-workers [17, 19, 22]) who studied the dependence of the stacking energy of DNA bases on the twist angle (see Scheme 4) and vertical separation using MP2/6-31G*(0.25) calculations.
Scheme 2Stack of substituted benzene and pyridineScheme 3Orientations of the stacked cytosine dimer from Jurecka and co-workers ([21]). The upper base is drawn in bold, the center of mass is indicated by a black dot, and the carbonylic oxygen and the hydrogen replacing the glycosidic bond are indicated for clarityScheme 4Geometries of stacked base dimers with a twist angle of 0 and 120 degrees. The upper base is drawn in bold, the center of mass is indicated by a black dot, and the hydrogens replacing the glycosidic bond are indicated for clarity. Note that for the homo dimers at zero twist angle the lower base is hidden behind the upper base
As mentioned already, the prototypical system for studying π-π stacking interactions is posed by the (parallel sandwich) benzene dimer. Because of its high symmetry (D6h), CCSD(T) energies using large basis sets (aug-cc-pVQZ) are available [51] to compare with (see Table 1). The minimum is found at 3.9 Å for this system with a stacking energy of −1.7 kcal mol−1. The standard density functionals are unable to give a proper description of this system, i.e., they either predict a purely repulsive energy surface (e.g., BP86; see Table 1), or give a shallow well (e.g., OLYP). Interestingly, the KT1 functional predicts a minimum that is very close (3.8–3.9 Å) to that of the CCSD(T) method, and has a well depth that is equally close (−1.6 kcal mol−1; see Table 1). The related KT2 and, surprisingly, the LDA functionals have a minimum at the same distance as CCSD(T) and KT1, but with a somewhat smaller well depth (−1.3 kcal mol−1). Also, the BHandH functional performs reasonably well with a similar equilibrium distance, but a reduced well depth (−0.9 kcal mol−1; see Table 1).
Table 1Stacking energy (in kcal mol−1) of the benzene-benzene complex as a function of the vertical separation Rvert (in Å), computed with various density functionalsa and CCSD(T)/aug-cc-pVQZ*bRvertCCSD(T)bLDAKT1KT2BHandHPW91BLYPBP86OLYPB3LYPX3LYP2.913.5314.5914.0817.0824.4131.6327.4638.6730.1328.923.08.609.299.0411.2717.9824.2020.8430.9322.7821.653.15.115.525.477.1313.1818.5315.8724.8517.2316.173.23.712.702.902.984.239.6014.2212.1420.0513.0412.063.31.681.061.101.292.246.9310.949.3416.229.898.983.40.30−0.01−0.090.170.924.958.457.2513.147.526.683.5−0.62−0.68−0.83−0.540.063.486.555.6810.655.734.963.6−1.19−1.07−1.27−0.96−0.452.405.104.508.634.403.693.7−1.51−1.27−1.50−1.17−0.741.593.993.626.983.392.743.8−1.66−1.33−1.58−1.25−0.861.003.152.945.622.632.043.9−1.70−1.31−1.56−1.25−0.890.572.502.434.512.061.524.0−1.67−1.24−1.48−1.18−0.850.252.002.033.601.631.144.1−1.58−1.13−1.37−1.09−0.780.021.611.722.851.300.854.2−1.46−1.02−1.24−0.98−0.68−0.151.311.472.241.050.644.3−0.90−1.11−0.86−0.58−0.271.071.271.750.860.494.4−0.78−0.97−0.75−0.48−0.360.881.111.350.710.374.5−1.08−0.67−0.85−0.64−0.39−0.420.730.971.030.590.285.0−0.58−0.28−0.39−0.26−0.06−0.450.300.520.200.260.095.5−0.27−0.09−0.15−0.070.08−0.310.130.280.000.140.046.0−0.11−0.01−0.050.000.12−0.160.050.15−0.030.080.036.5−0.040.020.000.030.12−0.060.020.08−0.030.050.037.00.030.020.040.11−0.010.000.05−0.010.040.037.50.030.020.040.090.020.000.03−0.010.030.038.00.030.020.090.080.01−0.010.020.000.020.02aPost-SCF using LDA/TZ2P orbitals and densities, see Computational detailsbFrom supporting information of [51]
Reference data from Mignon and co-workers
Scheme 2 shows the structure of the π-stacked complexes of pyridine with (substituted) benzene, i.e. with benzene, fluorobenzene, aminobenzene, chlorobenzene, toluene, phenol, cyanobenzene, benzoic acid, benzaldehyde and nitrobenzene. For all of these complexes the coordinates were taken from the supporting information of the original paper by Mignon and co-workers [50]. The geometry of each dimer had been fully optimized and therefore the vertical separation is different for each complex; it is found in the range of 3.2–3.4 Å.
The interaction energies for several typical density functionals are compared to the original MP2 data in Table 2. Consistent with previous reports, the mean absolute deviations (MAD) with respect to the reference MP2 data are much larger for density functionals containing the Becke88 [43] exchange functional (e.g., BP86, MAD value 7.68 kcal mol−1) than for functionals based on PW91 [52] or PBE [53] exchange (e.g., PW91, MAD value 5.33 kcal mol−1). However, these standard density functionals all show repulsive interactions, in contrast to the MP2 results that indicate bound systems (see Table 2). Much better agreement with the MP2 data is observed for the KT1, KT2 and, surprisingly, LDA functionals, with MAD values of 0.25 kcal mol−1 (see Table 2). The BHandH functional, recently [12] shown to give good agreement with MP2/CCSD(T) energies, shows a larger MAD value of 0.4 kcal mol−1 (see Table 2). Because of the uncertainty of ca. ± 0.5 kcal mol−1 in the reference MP2 data with respect to the high-level CCSD(T) data (see above), it is uncertain which of the four density functionals (LDA, KT1 , KT2 or BHandH) performs best. However, the improvement over standard density functionals is obvious and promising.
Table 2Stacking energy (in kcal mol−1) of substituted benzene-pyridine complexes (see Scheme 2), computed with various density functionalsa and MP2/6-31G*(0.25)bX=MP2bLDAKT1KT2BHandHPW91BLYPBP86OLYPB3LYPX3LYPH−2.8−3.4−3.4−3.2−2.72.36.14.611.15.04.1F−2.9−3.4−3.3−3.2−2.82.56.44.911.55.14.2NH2−3.2−3.6−3.6−3.3−3.02.26.14.711.24.93.9Cl−3.4−3.4−3.4−3.2−2.82.66.75.111.95.44.4CH3−3.3−3.3−3.4−3.2−2.81.24.53.58.73.52.7OH−2.7−3.2−3.1−3.0−2.52.86.85.211.95.54.6CN−4.1−3.9−3.9−3.7−3.50.94.23.18.43.12.3COOH−3.5−3.6−3.6−3.4−3.02.46.44.811.55.14.2CHO−3.9−3.8−3.8−3.6−3.30.94.23.28.43.22.4NO2−3.8−3.8−3.7−3.6−3.32.05.84.310.84.63.7MADc0.260.250.240.395.339.077.6813.907.896.99aPost-SCF on LDA/TZ2P orbitals and densities, see Computational detailsbFrom [50]cMean Absolute Deviation (in kcal mol−1) of DFT energies from reference MP2 data
Reference data from Jurecka and co-workers
Scheme 3 shows the fourteen orientations of the stacked cytosine dimer that have been considered in the paper by Jurecka and co-workers [21] (with a vertical separation of 3.3 Å for the first orientation, and 3.4 Å for all others). The corresponding reference energies and our DFT interaction energies are collected in Table 3. The latter also contains the MAD values with respect to two sets of reference energies, i.e. the usual MP2/6-31G*(0.25) results (MAD1) as well as the MP2 energies obtained after complete-basis-set (CBS) extrapolation corrected for the difference between MP2 and CCSD(T) with the 6-31G*(0.25) basis set (MAD2). Similar to what was found for the benzene-pyridine systems (see above), the MAD values for standard density functionals are found between 5 and 14 kcal mol−1, resulting in many cases in erroneous repulsive stacking interactions between the cytosine fragments (see Table 3). Improved results are again obtained with LDA, KT1, KT2, and to a lesser extent BHandH, which have MAD1 values (i.e. deviations with respect to MP2/6-31G*(0.25)) of 0.9, 0.8, 0.6 and 1.5 kcal mol−1 respectively, and MAD2 values of 0.4, 0.5, 0.7 and 0.5 kcal mol−1 respectively with the CCSD(T) data (see Table 3).
Table 3Stacking energies (in kcal mol−1) for several orientations of the cytosine dimer (see Scheme 3), computed with various density functionals and MP2a,borientationMP2b,cMP2ccb,dLDAKT1KT2BHandHPW91BLYPBP86OLYPB3LYPX3LYP12.22.52.72.32.73.98.011.710.916.510.99.92−3.1−3.8−3.7−3.9−3.5−3.32.66.55.412.35.24.13−7.2−8.9−8.8−8.7−8.3−9.0−2.11.70.78.00.2−1.04−8.3−9.9−9.4−9.2−8.9−10.1−2.90.8−0.16.9−0.9−2.150.20.30.60.10.61.56.410.39.315.79.38.360.50.60.80.40.81.86.810.89.716.39.88.87−0.5−1.0−0.7−0.9−0.60.22.85.55.28.75.04.28−7.3−9.1−8.4−8.3−7.9−8.8−3.00.2−0.25.6−1.2−2.29−7.6−9.1−8.7−8.5−8.2−9.4−2.31.50.57.3−0.2−1.410−6.6−8.3−7.9−7.7−7.5−8.3−1.81.80.97.60.3−0.811−7.6−9.4−8.8−8.5−8.3−9.5−2.80.6−0.16.2−1.0−2.112−5.5−7.4−6.7−6.6−6.2−7.0−3.6−1.6−1.41.5−2.4−3.113−7.4−8.8−8.3−8.1−7.9−8.6−3.00.4−0.45.2−1.0−2.014−7.0−9.1−8.8−8.7−8.4−9.4−2.11.60.78.0−0.1−1.3MAD1e0.940.810.601.494.878.357.5813.637.066.03MAD2f0.380.470.720.526.049.528.7514.808.247.21aPost-SCF on LDA/TZ2P orbitals and densities, see Computational detailsbFrom [21]cMP2/6-31G*(0.25) resultsdMP2 with complete-basis-set (CBS) extrapolation, i.e. MP2/CBS, corrected for Δ[CCSD(T)/6-31G*(0.25) - MP2/6-31G*(0.25)]eMean Absolute Deviation (in kcal mol−1) of DFT energies from MP2/6-31G*(0.25) datafMean Absolute Deviation (in kcal mol−1) of DFT energies from MP2/CBS corrected for Δ[CCSD(T)/6-31G*(0.25) - MP2/6-31G*(0.25)]
Reference data from Wu and Yang
In the paper by Wu and Yang, [14] the potential energy surface (PES) was calculated as a function of the twist angle between two stacked bases (see Scheme 1 and methodological section for the definition of the twist angle) using MP2/6-31G*(0.25), which was chosen as a reliable reference method based on the paper by Hobza and co-workers [22]. Although thymine was not included by Wu and Yang, we report here the energy profiles for all combinations of the five RNA/DNA bases, i.e., thymine, adenine, guanine, cytosine, uracil (see Scheme 4 for the geometries). The vertical separation is 3.4 Å for the C-C, G-C and G-G stacked base dimers, and 3.3 Å for all other systems. This difference in vertical separations was chosen based on earlier papers by Sponer and co-workers [19].
From the tests with the benzene dimer (Table 1), the Mignon (Table 2) and Jurecka reference data (Table 3), it is already evident that standard density functionals do not give reliable interaction energies, which is now shown to be true also for the energy profiles as function of the twist angle. Figure 1 shows the PES for two stacked bases, namely C-C and G-U, which are representative for all possible base pair combinations (the complete figure for all combinations of stacked bases can be found in the Supporting Information). Interestingly, although the standard density functionals typically underestimate the interaction energy, the shape of the PES is in all cases highly similar to that based on the more accurate MP2 data. This suggests that, at least trends and qualitative features in the rotational energy profile can be correctly reproduced with DFT which otherwise shows a (functional and basis-set dependent) constant shift with respect to the more accurate MP2 rotational profile.
Fig. 1Stacking interaction (in kcal mol−1) as function of the twist angle (in degree) for π-π stacks of two bases, C-C and G-U, computed with various density functionals. The thick lineswithfilled circles, triangles, squaresand diamonds show the results obtained with LDA, PW91, BLYP, and BP86, respectively. The dashed lines with open squares, trianglesand diamonds show the results obtained with OLYP, B3LYP and X3LYP, respectively. The bold linewithcrosses represents the MP2/6-31G*(0.25) reference data
It is, however, more instructive to look at functionals that by themselves already give accurate interaction energies, such as LDA, KT1, KT2 and BHandH. Figure 2 shows the corresponding rotational-energy profiles, again for the stacked bases C-C and G-U. From Fig. 2 it is evident that the LDA, KT1, KT2, and to a lesser extent BHandH are visually (and virtually) indistinguishable from the reference MP2 data.
Fig. 2Stacking interaction (in kcal mol−1) as function of the twist angle (in degree) for π-π stacks of two bases, C-C and G-U, computed with various density functionals. The red, blue and green lines show the results obtained with BHandH, KT1 and KT2, respectively. The bold line with crosses represents the MP2/6-31G*(0.25) reference data
Figure 3 shows the interaction energy as a function of the vertical separation for both the standard (upper diagrams) and promising (lower diagrams) density functionals, together with MP2 reference curve in each of the four diagrams. Not surprisingly, the density functionals that gave larger errors for the rotational energy profile, also give larger errors for the vertical separation profiles: almost all standard density functionals show potential energy surfaces that are repulsive, or at best weakly attractive with a very shallow minimum at elongated distances. In contrast, the promising functionals (i.e., KT1, KT2, LDA and BHandH) do provide well-defined minima with equilibrium distances (3.2–3.3 Å) close to the reference MP2 data. Similar to the uncertainty in the reference energy data of some 0.5–1.0 kcal mol−1 (see above), we may expect a similar uncertainty for the vertical separation, which we very roughly estimate at 0.1–0.2 Å. The differences between the equilibrium distance of the promising density functionals and that of the reference MP2 falls well within this estimated uncertainty. Thus, KT1, KT2, LDA and BHandH perform well not only for rotational energy profiles but also for the PES as a function of the vertical separation.
Fig. 3Stacking interaction (in kcal mol−1) as function of the vertical separation (in Å) for π-π stacks of two bases, A-A and G-G, computed with various density functionals. The thick lines with filled triangles, squares and diamonds in the upper diagrams show the results obtained with PW91, BLYP, and BP86, respectively. The dashed lines with open squares, triangles and diamonds in the upper diagrams show the results obtained with OLYP, B3LYP and X3LYP, respectively. The red, blue, green and orange lines in the lower diagrams that truly show well-defined minima are obtained with BHandH, KT1, KT2 and LDA respectively. The bold black line with crosses represents the MP2/6-31G*(0.25) reference data
Decomposition of interaction energy
Now that we have established the reliability of the KT1, KT2, LDA and BHandH functionals for the interaction energy of stacked DNA bases, it is interesting to study the actual interaction into greater detail. This is done through a quantitative decomposition of the interaction energy ΔEint into electrostatic attraction ΔVelstat, Pauli repulsion ΔEPauli and orbital interactions ΔEoi (see Methods). Table 4 provides the results of the energy decomposition at KT1/TZ2P for the five π-stacked homo dimers, for each one at a twist angle of 0° and 180° (which is the lowest-energy conformation) and at two different vertical separations. Note that the lowest-energy conformation is always achieved at a twist angle of 180° but that the optimal stacking distance (vertical separation) varies by 0.1 – 0.2 Å between the different π-stacked homo dimers. The energy changes by −6.8 (A-A), −11.8 (C-C), −10.2 (G–G), −11.2 (T-T) and −7.9 (U-U) kcal mol−1, respectively, when going from a twist angle of 0° to 180° (the lowest-energy conformation). This change in energy is almost completely resulting from a change in electrostatics that change by −5.4 (A-A), −13.1 (C-C), −10.3 (G-G), −6.6 (T-T) and −8.3 (U-U) kcal mol−1 respectively. The sum of Pauli repulsion and orbital interactions changes much less, by ca. 1.4 kcal mol−1 or less, except for T-T where the sum of Pauli repulsion and orbital interactions changes by 4.6 kcal mol−1 due to the influence of the peripheral methyl groups. But also the changes in each term individually, i.e., either ΔEPauli or ΔEoi, are much smaller (typically 2 to 5 times, but in some cases even more) than the changes in ΔVelstat (again, only in the case of T-T, the change in ΔEPauli is nearly as large as that in ΔVelstat). Here we note that the same energy decomposition analyses for the five π-stacked homo dimers at LDA/TZ2P instead of KT1/TZ2P yield values that differ by only 1 kcal mol−1 or less (not shown in Table 4).
Table 4Decomposition of interaction energiesa (in kcal mol−1) between stacked DNA bases in different geometries, computed at KT1/TZ2P A-AC-CG-GT-TU-UTwist angle 0°(TW, Rvert)(0°, 3.3 Å)(0°, 3.4 Å)(0°, 3.4 Å)(0°, 3.3 Å)(0°, 3.3 Å)ΔEPauli5.352.432.1311.003.72ΔVelstat−3.311.801.97−2.48−0.07ΔEoi−2.30−1.88−2.49−5.66−2.11ΔEint−0.262.351.612.861.54Lowest energy conformation(TW, Rvert)(180°, 3.2 Å)(180°, 3.1 Å)(180°, 3.2 Å)(180°, 3.3 Å)(180°, 3.1 Å)ΔEPauli5.867.014.524.286.13ΔVelstat−8.72−11.32−8.33−9.04−8.38ΔEoi−4.17−5.12−4.80−3.58−4.12ΔEint−7.02−9.44−8.61−8.34−6.36aSee Computational details
Additivity of interaction energies of stacked base pair dimers
With the good performance of KT1 for stacking interactions kept in mind, we went one step further, and looked also at the interactions within stacked dimersof hydrogen-bonded base pairs (see Scheme 5) [54]. The geometry was obtained by taking the geometry of one hydrogen-bonded base pair and putting another one at 3.4 Å on top of the former. The base pair dimer is stabilized by hydrogen bonding between the bases within one layer, and stacking interactions between the bases in different layers of the stack. In this case, because there are two bases per layer, there are also interactions present between bases that are, in a sense diagonally, on opposite sides and in different layers [55], the so-called cross terms. For example for the AT-AT system as shown in Scheme 5, this refers to the interaction between the thymine of the top layer with the adenine of the bottom layer.
Scheme 5Structure of stacked DNA base pair dimer AT-AT with twist angle of 36°. The dot represents the B-DNA helical axis of rotation.[54]
In order to investigate in more detail the importance of the various energy terms, in particular, the cross-terms, we approximate the total stacking interaction between the base pairs in the stacked base pair dimer by the sum of four pairwise interactions between two bases, i.e., we approximate the total (stacking) interaction energy ΔEint between the layers AB and CD in Scheme 6 by the sum ΔEadd of interactions A-C, B-D, A-D and B-C as shown in Equations 4a,b:
Scheme 6Additivity approximation for the π-π interaction between two stacked Watson-Crick base pairs in terms of pairwise interactions between individual bases
The remaining term ΔEcoop that, added to the approximate ΔEadd yields again the real stacking interaction ΔEint, consists of cooperativity effects between the different interactions.
In Table 5, we report the energy values resulting from the additivity scheme for the stacked AT-AT, GC-GC and AU-AU base pair dimers at three different values of the twist angle (0, 36 and 180°). Importantly, the additive approximation ΔEadd of the real stacking interaction ΔEint largely accounts for the latter. ΔEcoop has in most cases a positive sign and is small compared to either ΔEadd or ΔEint. Furthermore, the dependence of the ΔEcoop term on the twist angle is much smaller than that of the interaction energy ΔEint. For example, ΔEcoop varies from 1.0 to 1.6 kcal mol−1 whereas ΔEint varies from −1.4 to −10.7 kcal mol−1 for the stacked AT-AT base pair dimer (see Table 5). Larger cooperativity effects are found in the case of the stacked GC-GC base pair dimer, where ΔEcoop values are found between 2.0 and 4.4 kcal mol−1. Note however that the changes in ΔEcoop are again small compared to the changes in ΔEint.
Table 5Interaction energy (kcal mol−1) between stacked DNA base pairs in terms of the additivity scheme, computed at KT1/TZ2Pa,bSystemTWΔEACΔEBDΔEADΔEBCΔEaddΔEcoopΔEintAT-AT0−1.23+1.26−1.24−1.24−2.45+1.04−1.41AT-AT36−5.27−3.93−1.11−0.93−11.24+1.11−10.13AT-AT180−1.84+0.39−5.44−5.44−12.33+1.62−10.71AU-AU0−1.23+0.94−1.37−1.37−3.03+1.17−1.86AU-AU36−5.27−3.00−1.20−1.08−10.55+1.20−9.35AU-AU180−1.84+0.28−4.67−4.67−10.90+1.73−9.17GC-GC0+2.15+2.83−4.90−4.90−4.82+4.42−0.40GC-GC36−2.08−1.32−3.44−4.71−11.55+3.92−7.63GC-GC180−7.59−2.60−1.52−1.52−13.23+1.98−11.25aSee Scheme 6: bPost-SCF on LDA/TZ2P orbitals / densities.
The cross-terms in the additivity scheme are as important as the non-cross terms, especially when rotating the base pair dimer from a twist angle of 0 degrees to finally a twist angle of 180 degrees. At the end point of 180°, the A and B base have switched, and the cross terms are no longer AD and BC, but AC and BD; this switch occurs after a twist angle of 90°. For instance for the AT-AT base pair dimer at 0°, the cross terms are stabilizing (−2.5 kcal mol−1) and dominate the ΔEadd of −2.2 kcal mol−1. At 180°, the non-cross terms dominate (−10.9 kcal mol−1) with still a substantial contribution from the cross terms (−1.4 kcal mol−1). Note also the dominance of the cross terms (−10.2 kcal mol−1) over the non-cross terms (−3.0 kcal mol−1) for the GC-GC base pair dimer at 180°. This is mainly due to favorable hydrogen-bonding interactions between the cross G-G pair.
When rotating base pair dimers from a twist angle of 0° to 36°, the cross terms in the additivity scheme reduce slightly. However, this is dominated by the increase of favorable interactions between the stacked bases. For instance for AT-AT, the cross terms drop from −2.5 to −2.0 kcal mol−1, but the non-cross terms increase from +0.0 to −9.2 kcal mol−1. The same trend is observed for the AU-AU and GC-GC base pair dimers.
Again we note that the same energy decomposition analyses for stacked DNA base pairs at LDA/TZ2P instead of KT1/TZ2P yield values that differ by only 1 kcal mol−1 or less (not shown in Table 5).
Significance of the observed trends for the structure of DNA
The stabilizing interactions for the structure of DNA mainly originate from hydrogen-bonding interactions between bases in one plane and the π-π stacking interactions between stacked bases. However, we have shown here that in addition to these terms there is also an important contribution of the cross terms that arise between bases that are neither hydrogen-bonded within one layer, nor stacked above each other. All these interaction energies can now be understood and quantified with density functional theory using appropriate functionals. For the hydrogen-bonding interactions, the BP86 and PW91 functionals seem to perform best, [3] while for π-stacking interactions KT1, KT2 and (surprisingly) LDA work well.
The experimentally observed value for the twist angle (36°) is retrieved in our study on base pair dimers as the orientation with optimal stacking interactions. We have shown that this is predominantly determined by the classical electrostatic component of the stacking energy. The rotation to a twist angle of 36° destroys part of the favorable cross terms (see above), which is however completely overcome by the increase in favorable stacking interactions between the stacked bases. The twist angle and vertical separation that are experimentally observed are of course influenced by both the sugar-phosphate backbone and the presence of solvent and/or counter ions. These factors will be tackled in forthcoming work.
Conclusions
We have analyzed π-π stacking interactions between two benzenes or benzene analogs, between two DNA bases, and between two Watson-Crick base pairs using Density Functional Theory (DFT) in combination with large basis sets. The interaction energies for a large number of density functionals have been compared with ab initio reference data. In line with previous studies, most standard density functionals recover, at best, only part of the favorable stacking interactions.
An exception is the new KT1 functional, which has been constructed to closely resemble the near-exact Zhao–Morrison–Parr (ZMP) exchange-correlation potential. Thus, not unexpectedly, KT1 gives a good description for π-π stacking energies and potential energy surfaces (PES) resulting in bound systems. Surprisingly, however, a similarly good performance is achieved with the Local Density Approximation (LDA). In view of the accurate prediction of PESes and the low computational cost, we recommend the use of either KT1 or LDA for treating the π-π stacking interactions in larger systems, using a QM/QM approach (e.g., our QUILD approach which is under development [33]) that allows this type of interaction to be separated from other types of interaction, such as hydrogen bonding but also regular covalent bonds.
To gain insight into the origin of π-π stacking interactions, we have decomposed the interaction energies into the classical electrostatic attraction, Pauli repulsion and orbital interactions. Interestingly, the electrostatic interactions appear to be the most important factor that determines the shape and depth of the PES. In the case of two stacked Watson-Crick base pairs, this classical electrostatic attraction causes a minimum to occur along the energy profile at a twist angle of 36°. Furthermore, the stabilizing contributions to the stacking interaction between two Watson-Crick base pairs is shown to originate from the inter-strand stacking terms, that is, from the interaction between two bases that are in different Watson-Crick pairs and also not directly stacked on top of each other.
The above-mentioned insight that electrostatic attraction plays an essential role in π-π stacking interactions nicely consolidates and extends the recent finding by Krapp, Bickelhaupt and Frenking [56] that classical electrostatic attraction is essential for understanding trends in bond strength of diatomic molecules. It is interesting to note that qualitative models of both “regular” chemical bonds and those of π-π stacking interactions often completely ignore classical electrostatic attraction. These qualitative models attempt to rationalize trends in bonding entirely in terms of orbital interactions (in the case of regular bonds) and dispersion interactions (in the case of π-π stacking).
Electronic supplementary material
Below is the link to the electronic supplementary material.
Supporting Information
Energy profiles for various π-π stacked systems as a function of the twist angle and the vertical separation computed with MP2 and various density functionals (PDF 1.90 mb)

density functional theory
π-π stacking interactions
hydrogen bonding
dna stability
dna structure