I Donald B. Boyd Lilly Research Laboratories Eli Lillv and Cornoanv , Indianapolis. Indiana 46206
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Space-Filling Molecular Models of Four-Membered Rings
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I
Three-dimensionql aspects in the design of penicillin and c6pha/osporinantibiotics
The utility of hand-held molecular models in appreciating the three-dimensional structure of molecules, understanding chemical rearrangements, elucidating crystal packings, visualizing drug-receptor interactions, and planning molecular modifications hardly needs emphasizing here. Among the more useful commercially available types of models (I) is the Corey-Pauling-Koltun (CPK) (2)set of space-filling atomic models. Until now a cons~icuousgap in this set was the lack of atomic models for building small cyclic structures, such as four-membered rines of carhon, nitroeen, or oxwen. This article presents designs for the requisitestc&, makes known the availability1 of the new atomic models, and demonstrates their use in the construction of some 8-lactam antibiotic structures. Owing to the scope of the presently available CPK molecular model set, their principal application has been to nucleic acids and proteins (see, e.g., ref. (3)).Their application to organic molecules of general interest has not been infrequent, however. The success of the original CPK designs ( 2 ) is exemplified by the fact that there have been relatively few innovations since their inception in 1965. Some of these innotions have dealt with easier and more accurate ways of setting dihedral angles ( 4 ) . whereas others have dealt with better modeling ofhydrogenbonding, fused ringsystems,and ionic honding LO metals. Cases of cleverly improvising space-filling modelsof four-membered rings have been reported. In one instance, plastic foam halls were simply glued together (51, and in another case, regular CPK atomic models were held together with rubber bands (6).Neither of these alternatives has the advantages which can he derived from having sturdy, reusable, color coded, precision atomic models specifically desiened for four-membered rines. 1'i;e prime motivation of our &fort was to he ahle to construcr space-filling models uf venirillinr 11) and Ax-re-
(11
(11)
These therapeutically important and widely used antibiotics (7) have in common the four-membered &lactam (01 a h din-2-one) ring. This ring is, in fact, believed to be the key to the compounds' antibacterial activities hecause the ring acts
Bask Considerations Three criteria were kept in mind throughout the design and construction of the new atomic models: (1)they should fit with
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Eli Lilly and Company has concluded an agreement with Ealing Corporation whereby the latter organizationwill handle subsequent manufacture and distribution of the new atomic models.All inquiries a b u t obtaining these models, along with the other CPK items, should be addressed to Ealing Cor~oration,22 Pleasant St., South Natick. Mass. 01760.
the commercially available CPK set in terms of scale and appearance; (2) they should he connectable to other CPK atomic models with the usual CPK connector links; (3) the designs should he amenable for use in as many situations as possible. That is, we want a minimum number of new patterns to machine and a maximum number of chemical structures for which the models are usable. As seen below, we are ahle to meet this obiective vew well with onlv two new model patterns of appropri&e dimensions. Castings bf the new modeis, which can he done in more than one color, satisfy the first two criteria also. We now briefly survey the relevant structural information which must go into our designs. We begin by considering the molecular geometry of the &lactam ring. Bond lengths and angles from X-ray crystallographic studies (9) on individual penicillins and cephalosporins may he amalgamated through averaging over the most pertinent structures into the dimensions shown below in (111). rm8,
"1/
,2011
tm) One may ascertain that most of the bond lengths and angles in and around the 8-lactam ring are not very dissimilar t o those determined for some of the less biologically interesting p-lactam structures, such as the A2-cephalosporins (IV), anhydropenicillins (V), and other exotic variations (9,10).
Hydrogens on the ol face of C3 and CI in (111) are frequently not located precisely from the X-ray diffraction data, and, even when they are, the apparent C-H hond lengths can he sFtematically too short (11). Therefore, these hydrogens may he nositinned hv assmine standard hnnd leneths (-1.1 A. see. following angles: CyC3-H 1 1 P , N-C3-H 104O, CaC3-H 116', C3-C4-H 116°, S-C4-H llZO,and NIC4-H 116O. Most of these are larger than 109.5' because of the strain imposed by the four-membered ring. The three atoms bonded to the carhonyl carbon (Cz) of (111) are essentially coplanar. In the antibiotics the fourth atom in the 8-lactam ring (C4) lies above the plane of the other atoms hy 0.1-0.3 A (9). The hond radiating from the 8-lactam nitrogen N1 (into the thiazolidine ring of penicillins or the dihydrothiazine ring of cephalosporins) has been found to he Volume 53. Number 8, August 1976 / 483
coplanar in the biologically inactive analogs, such as (IV), and out of plane in the active compounds, such as (I) and (11) (9). This distineuishine feature stems from the fact that enhancemen; of conjugation between the carhonyl group and the 0-lactam nitrogen strenethens the C-NY hond and renders the nitrog& with &re nearly s 2 hybridization. However, the opposite effect of minimizing this conjugation and weakening the 6-lactam C-N hond is desired for priming the molecule for antibacterial activity (12). Thus, in any atomic model design we will want two types of nitrogen: one with nearly sp3 hyhridization and another with spz hybridization. Many simple four-membered ring structures have also been determined, usually by microwave or electron diffraction methods. These include cyclohutane (VI) (13), azetidine (VII) (14), trimethylene oxide (VIII) (15), methylenecyclobutane (IX) (161, cyclobutanone (X) (17), and cyclobutene (XI) (18).
1x1 IXII We cannot take the space here to repeat all the structural parameters for each of these molecules. but the observed hond lengths may he summarized as follows: Cgpa-CQp3 1.55-1.57 A, C,,a-N 1.48 A, C,,s-0 1.45 A, Clnz-Can2 1.51-1.53 A. C=C 1.34 A, C=O 1.20 A, and ~ - ~ i . 0 9 - l i 3A. It will be noticed that these are close to various sets of "standard" bond lengths (19). Intraring bond angles are 84-93". The HC,,-H hond angles are 10~%114~. The rings are puckered tc varying degrees depending on the system,so that the angle between planes defined by the three atoms of each flap is 0-40'. The amount of puckering depends on the conflicting forces for reducing the eclipsing interactions ofthe hydrogens and maintaining the intraring bond angles as large as possible. Note that these geometrical data are similar to the corresponding ones in (Ill), except, of course, for the NI-C2 and NI-C bonds in (1111, which are unique to the 8-lactam structure because they participate in amide resonance (XII) in (I) and (11) and in enamine resonance (XIII) in (11). 11X)
pK, -- pN
0
0
+\
-NQ
IXIII
-
N n
IXIIIJ
Design of the New Models
From the above molecular dimensions we distill covalent radii and hond angles for two new atomic models which can best meet the intended purposes. The first model called BL -tetrahedral2 is for a tetrahedral atom with the distortedsp3 hyhridization specified in (XIV). The covalent radii turn out to be essentially the same as for a normal tetrahedral carhon in the CPK set (0.77 A). Note that the intrarine hond anele " is 88" and that the average oiall six bond angles in XI\' is only a ieu, tenthi of a degrei, less than 109.5".
(XNl
The model of this atom has Cz, symmetry and is cut from a sphere of radius 1.25 A like that for the CPK model of a normal retrahedral carbon. In a four-membered ring t hat ir rather geometrical \.ariahilitv due small and strained and of limited . Because each new atomic model shape can be used for more than one chemical element as explained in the text, they are referred to as Boyd-Lilly or Beta-Lactam (BL)atomic models. 484 / Journal of Chemical Education
Figure 1. Four views of the new atomic model for tetrahedral bonding in a fourmembered ring. Castings of BL-tetrahedral are in blue and black in this figure.
Figure 2. mree views of the new atomic model for trigonal bonding in a burmembered ring. The blue model of BL-trigonal shows b e two intraring faces.
to the requirements of the CPK connector links, the dimensions of (XIV) should work adequately not only for carhon, but also for nitrogen. Covalent radii for nitrogens in various bonding situations are shorter than those of analogous carbons by no more than 0.07 A, adifference hardly noticeable a t the scale to he used. A precedent for assuming the dimensions of certain other carhon and nitrogen atomic models in the CPK set to he the same has already been set (2). As will he discussed below, a lone-pair will occupy one position about (XIV) when it is used to model a trivalent nitrogen. The second new model is for a trigonal atom called BLtrigona12 with distorted sp2 hybridization as shown in (XV).
3h ailA
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lil.
mvi
The three bond axes are coplanar giving the model Cz, symmetry. A van der Waals radius of 1.48 .&waschosen as interm e d k e betwpcn that fora normnlamiderarhon (1.snA) and a n w n d nmide nitmnen (1.15.&I in the CI'K set. The triaonal model is again suitedfor either carbon or nitrogen in afourmembered ring, although its dimensions are somewhat closer to those of carbon. By way of comparison, an amide carhon in the CPK set has covalent radii of 0.67-0.75 A, and an amide nitrogen has covalent radii of 0.60-0.70 A (2). The specifications of (XIV) and (XV) were made into the space-filling atomic models shown in Figures 1 and 2. They are fabricated of durable plastic a t a scale of 1.25 an/.&. The color of the plastic is keyed to the atom represented, e.g., black for carbon, blue for nitrogen, as in the CPK set. For both our new atomic models, machining of the aluminum mold patterns and casting of the plastic models were done carefully to keep their accuracy within +0°30' for hond angles, f0.01 A for covalent radii, and f0.03 .& for van der Wads radii as specified ahove in (XIV) and (XV). In constructing the mold patterns, the length that the standard CPK connectors adds to the interatomic distances was taken into account. This amounts to cutting the faces of each pattern approximately 0.04 cm closer to the center of the spheres from which they were machined. I t will he noticed (Fig. 2) that the trigonal atom model is built with one permanent male connector link and one female ronnecror socket for the intraring connections. This design was necessitated hv the fact that the dimensions o f a four-
membered ring atom do not permit two connector holes to be set deep enough to give the desired bond lengths when the angle separating the two intraring bond axes is only 9Z0. The male connector link is an integral part of the model and has the same dimensions as afforded by a standard CPK connector link. Another feature of the trigonal atomic model is that the exocyclic face is tapered like the surface of a sphere of radius 4 A. The faces of the ethylenic double-bonded carbon in the CPK are similarly tapered. The purpose of rounding this face of the BL-trigonal model is to allow the substituent connected t o this face more freedom for bending distortions. Such distortions must occur to complete certain five- or six-membered rings fused to a four-membered ring. The other two faces of BL-trieonal. as well as all the faces of BL-tetrahedral. are flat because they cannot be tapered without imparting excessive conformational flexibilitv to the four-memhered rinr. Not immediately apparent from Figure 2 is the fact that
