Calculation and Specification of the Multiple ChiralityDisplayed by sugar Pyranoid Ring structures Robert S. Shallenberger, Ronald E. Wrolstad' and Laurie E. Kerschner Institute of Food Science, New York State Agricultural Experiment Station, Cornell University. Geneva. NY 14456 The salient features of the various conformations of a sugar pyranoid ring, and the steric disposition of suhstituents about the reference and the anomeric carbon atoms contained within the ring can he described using simple algebraic notation. As a consequence, the nature of these chiral attributes can he calculated. The results obtained afford an unambiguous determination and specification of the pyranoid ring anomeric t h e chiral family (D- or L-),and the conforform (a-or P-), mation of the chair or boat structure. The method for assigning chiral operands and the procedure for calculatine the nature of the . ~.v r a n o i dring chiral attrihutcs in hiwin dewribrd. The prinriplr employed is the s r a u e n t i ~dt:term!narion l (~inlwbwic~ r ~ d u c teach , . 01 which yieid the specification of a; isolated chiral feature. The products are obtained, in turn, by the multiplication of chiral specification operands.
Figure 1. Reference structures for calculating the configurational and cantorrnational structure of pyranoid sugars.
Method lor Pyranoid Chair Conformations The reference structures for the ensuing description of the method of assigning chiral operands and the calculation of the chiral descriptors for pyranoid chair structures are the conformational drawings of the two models shown in Figure 1. The first step is to determine which of the two carbon atoms contiguous to the ring oxygen atom is the anomeric carhon atom and which is the reference carhon atom. For sugars, the reference carbon atom is the highest numhered asymmetric carbon atom in the Fischer projection formula. Therefore, in oentaovranoid form it is carhon atom number four and C-5 hecome, ;I ring mt~thylenecarhm a t m l adjacent t o the ring oxygen atom. F,,r hexapyranoiil structures it is uiually C - 5 and wnsrquently pOSiQSs?-.nn h~druxynlethylenesubstiturnt The anorneric carhon n t ~ mI S t heret'mt. identified hs elimination, and is assigned the numerical descriptor C-1.
the ring oxygen atom is remote and the carbon atom sequence is clockwise. Carbon atoms No. 1 and 4 are then displaced "above" or "below" the average plane for the ring. Current symbols acknowledge this using a superscript for "ahove" and a subscript for "below." The lowest numhered carbon atom corresponding to the Reeves' number is retained and the C l and IC symbols for the ahove structures become 4C1and lCq, respectively. As any one of an enantiomeric pair of sugars may possess either of the mirror image ring forms, the conformational symbols are ambiguous when unaccompanied by a chiral family specification.
Chiral Product I (Indicating the Chair Conformation). Determination of the Rinp Numbering Operand. Observe a model or the str"ctura1 drawing of the pyramid chair conformation and locate the anomeric (hemiacetal) carhon atom (C-1). If the numbering sequence of the carbon atoms contained within the ring is clockwise, the operand n (for numbering) is (+). If the carhon atom sequence is counterclockwise n is (-). Determination of the ring puckermg operand. Without changing the spatial orientation of the model, or by observing the structural drawing, determine if the puckered ring oxygen atom lies "ahove" the average plane for the ring described by carhon atoms 1,2,4, and 5 or is merely written "upwards" in the plane of the paper on which it is drawn. In either case the chiral operand p (for puckering) is (+). If the ring oxygen atom lies "below" the average plane for the ring, or is "downward" in the drawing, p is (-1. Calculat~onof product I. Multiply n by p. if the product is positive (+), assign the Reeves ( I ) chair conformational symbol C1. If it is negative (-1 assign the mirror image symbol 1C. chair conformational symbols in current use The are derived from the Reeves' symbols. In the conventional
'
On sabbatic leave from Oregon State University. Corvallis, 1979-80.
orientation of isometric drawings of pyranoid ring conformations, as shown below,
Chiral Product 11(lndicating the Chiral Family). Determination of the Chiral Family Operand. Again locate the reference carbon atom contained within the ring. When the bulky substituent (either - 0 H o r -CHzOH) lies as that for the ring itself (i.e.. an in the same averaee .. olane . rqunr,.rrrrl ilispoi~tion,,the operilnd r (fur re?crenct carbon to ntom 1 i i T I . \Vhen the hulkv ~uhstituentis .verpendicular the average plane for the ring (i.e., an axla1 disposition), r is (-).
Calculation of Product 11. Multiply (np) by r. When the product is positive (+),the chiral family indicated is D-. When it is (-) the family indicated is L-. Chiral Product 111(Indicating the Anomerlc Form) Determination of the Anomeric Operand. Observe the two suhstituents on the anomeric carbon atom. When the hydroxyl, or substituted hydroxyl suhstituent is equatorial, the operand a (for anomeric carbon atom) is assigned a (+)value. When it is axial, the assignment is (-1. Calculation of Product IIZ. Multiply (np) by (npr) and then again by a. When the product is (+I, the anomer indicated is 0. When the product is (-), the anomer is a-. As n 2 and p 2 are +I in the above equation, it reduces to (ra). This fact is convenient for working the procedure in reverse in order to construct a desired pyranoid structure. It also serves to emphasize that the steric description of just what constitutes an a- or 0-anomer is directly related to the handedness of the reference carhon atom and that an anomeric designation is Volume 58
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Determination of Sequential Chiral Products and Comparison ot Calculated Structures for Compounds Shown In Figure 2 with Those of Selected Reference Comnounds.
("1
i Chair Conformation (PI @PI
1
i r ~
1 I
111
Chiral Family i w )
Anomeric Form Ira)
1
(a)
1
Calculated Structure
Reference Compound
also ambiguous unless it is accompanied by a D- or L- de~criptor.~ Method for Pyranoid Boat Conformations
Except for minor changes in specification, the procedure for determiningspecific (as opposed to skewed) boat conformations parallels that for calculating pyranoid chair chirality. A reference structure (Reeves' B2 conformation) is shown below. noopm/.
Chiral Product I (Indicating the Boat Conformation). The numbering operand is obtained in the same manner as described for the chair conformations. The puckering operand is determined from the lowest numhered carbon atom (C-1, C-2, or C-3) that occupies a stem position on the boat. If the lowest numbered carhon atom is directed upward, the operand is (+). If downward, it is (-). A positive (np) product will then indicate either a BI, 8 2 , or 8 3 conformation and a negative result will indicate either the I B , 28,or 38 mirror image conformation. Chiral Product /I (Indicating the Chiral Family). When the hulky substituent on the reference carhon atom is equatorial, or a t aflagpole position, r is (+).When it is axial, or at a bowsprit position, it is (-).Then, when (np) (r) is (+), the sugar belongs to the D-series, and when (-) it belongs to the L-series. Chiral Product ill (Indicating the Anomeric Form). When the hulky suhstituent a t the anomeric center is equatorial, or a t a flagpole position, the operand a is (+). Otherwise, it is (-). Then when ( r ) (a) is positive, the anomer is p- and when negative it is a-. Application ol the Method
Chair Conformations An application of the method to the determination of the basic chair conformation, the chiral family, and the anomeric form of an obscure structure, such as that shown below, is as follows cn,oH H
/
L
O
A
/
0
/
W
Operand n is (-I a n d p is (-I. Theproduct (npl is (+I. Therefore the conformation is Ci. Product 11. Operand r is (-1, and the p r o d u c t ( n p ) (r) is also (-1. Therefore the c h i d family is L-. Product 111. Operand a is (+I, and ( n p ) ( n p r ) ( a ) is (-), as is (rl ( a ) . Therefore the anomerie form is a-.
Product 1.
Assemhlying the information derived from the calculations indicates that the structure shown above is an a-L-aldohex600
Journal of Chemical Education
Figure 2. Selected configurational and canformational shuctures used for the calculations given in the table.
opyranose, and when drawn in the conventional manner in the C1 conformation it becomes a-L-'C1 as shown below.
Application of the method to the variety of pyranoid structures shown in Fieure 2 is resented in the tahle. The first structure shown is th'e framework form for the entire series of the n-aldohexa~vranoidsucars. It is shown because the reference compound given, 0-D-glucopyranose in the 'C1 conformation serves not onlv as the example of the most favored chair conformationai form for these structures (all bulky carhon atom suhstituents equatorial), but also as a mnemonic for the chiral operand assignments and for the significance of the algebraic products. All chiral operands are positive. Thus, all products are positive, leading to an equatorial disposition of all bulky suhstituents for the favored 4C1 conformational structure. The second structure is the framework form for the D-series of the ketohexapyranoid sugars. It demonstrates (see table) that the method is valid even though the reference carhon atom is not contieuous to the rine oxveen ." atom. The third and fourth structures in Figure 2 and the tahle show the application of the method to an anhvdro-suear and an aldooenta" pyranoid sugar respectively. The final structure shows that a deoxy sugar may have several names, and in addition to the names given in the tahle, structure 5 is also the framework structure for the 1,5anhydro-D-alditols. Boat Conformations The application of the method to the specific boat structure shown in the method section is as follows:
Operand n is I + ) andp is (+I. The product (np)is (+I. Therefbre the conformation is R2. ProduetlI. Operand r is (+) and the product (np) ( r ) is (+I. Therefore, the family is D-. Product 111. Operand o is (+) and the product (np) lnpr) lo) is I+). Therefore the anomeric form is 0.. Product I.
CHiRAL OPERATIONS
The basic form of the boat structure is therefore that of an aldohexopyranose in the Reeves B2 conformation, i.e., it is 8-D-B (2,5). Discussion Numbering and Puckering a s Chirai Operations The fact that the puckered pyranoid sugar ring is in itself a chiral structure forms the basis for the sequential calculation of monosaccharide chirality. The proof of the chiral nature of the ring is as follows. Two operations are needed to impart handedness to a symmetrical five- or six-membered heterocyclic ring. If the ring is planar, e.g., a regular hexagon, the numbering operation is a two-dimensional chiral oneration. The numbered but planar ring has an "enantiomeric" form upon which it is not superposable in a hypothetical two-dimensional realm. In three-dimensional space, however, the "enantiomers" are indistinguishable since rotation is avalid C2 symmetry operation leading to superposability. To impart three dimensional chiralitv to a numhered danar ring reqkres that a puckering mode be invoked. ~ i s t o r t i n g one segment only from the plane of the ring itself is the second chiral operation. Conversely, a puckered but symmetrical ring is rendered chiral by a numbering operation. These two fundamental but abstract chiral operations neatly lend themselves (for pedagogical purposes) to a display of numbered and folded hexagonal templates cut from a piece of paper (cf. Pigman and Horton (3)as shown in Figure 3 in order to prove the point. Two puckering modes are invoked in Figure 3 in order to draw an analoev to the case for the ~ v r a n o i drines. If one of the planar templates had been folded in a manner opposite to that of the instructions for both ~ l a n atemdates. r then the numhered and puckered structureswould have beenidentical. ring. This o~erationhas a~plicationto demonstrating.~yranoid .. conformational i n t r ~ k v e r t i b i l i t y . As applied to furanoid and pyranoid sugar ring structures, the numbering and puckering operations are not abstract, but are instead quite real. The intrinsic puckering mode is due to the 109"28' bond angle between contiguous carbon atoms. The intrinsic numbering mode is due to the fact that the electronic distribution about the carbon atoms contiguous to the ring oxygen atom is entirely different. This is brought about because the substitution on the contiguous carbon atoms differs thereby generating two-dimensional chirality for this tripartite unit, as shown below. The intrinsic num-
Figure 3. Diagammatic representatim of W e prmf U-at numbwing and puckering generates chirality far pyranoid ring rhucturel.
Assignment of Algebraic Signs to the Operands and Products After the assignment of the pyranoid conformational form, the method of calculating the chiral family indicated and also the anomeric form is a straightforward application of the configurational relationships established for the FischerTollens or the Haworth structures for the sugars (2). The D-configuration a t the hiehest numbered asvmmetric carbon atom iathen carried in& an equatorial disposition for the bulky substituent on the pyranoid ring when the ring oxygen atom is "above" the average plane of the ring and the carbon atom sequence numbers clockwise when viewed from "above." This is, of course, the basic CI conformation, and the assignment of a (+) operand for an equatorial -CH20H aldohexapyranoid substituent matches the known absolute handedness of that chiral center. On the other hand, the assignment of a (+) product to indicate the &configuration, whether D- or L-,and a (+) operand to indicate an equatorial suhstituent a t the anomeric carbon atom was an arbitrary choice. A (-) product for a p-anomer would have been more consistent with Hudson's rules of isorotation, but then the operands a t the anomeric center would have needed to be (-1 for an equatorial substituent and (+) for an axial suhstituent. This did not seem to be consistent with the chiral familv omrand assienment nor with the mnemonic purpose of having an "all conformational structure and o ~ e r a n dassienment for the most favored " aldohexapyranoid structure, i.e., 8-D-glucopyranose
-
>
+"
Literature Cited hering mode also exists by virtue of the fact that the acidity of the ring carbon atom hydroxyl substituents varies.
i l l Resula.R. E.. J. Amer Chem. Soe..7t.Zl5(l~Bi 121 Rule of Carklhydrste Nomenclature. J. Org. Chem ,28.281 119631. (31 Pieman. Ward, and Harton. Derek."TheCsrbohydratos,"Acadomie P r a . New York. 1972. p. 68. I41 Hud8nn.C. S.. J Amer Chem S o c , 31,66(1909)
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