A Theoretical Exploration of Single-Molecule Mixture Through Combinatorial Method
AA Theoretical Exploration of Single-Molecule Mixture Through Combinatorial Method
Yu Tang* State Key Laboratory of Bioorganic and Natural Products Chemistry, Center for Excellence in Molecular Synthesis, Shanghai Institute of Organic Chemistry, University of Chinese Academy of Sciences, Chinese Academy of Sciences, 345 Lingling Road, Shanghai 200032 (China), Email: [email protected]
Abstract : Single-molecule mixture, which contains a mixture of molecules that have molecularly different structures, represent an extreme form of molecules that remain unexplored both theoretically and experimentally. In this article, a theoretical approach that combined model construction, thought experiment, and mathematical analysis was developed to study this elusive form of molecules. It was found that in a model substituted oligo-D-mannitol system, only 30 minimally different alkyl substitute group are needed for the construction of a structural space that enables single-molecule mixtures to exist in macroscopic quantities, the probabilities of individually and randomly take N A molecules from the trimer or higher oligomer structural space to get single-molecule mixture are larger than 0.999. This study opens a new way to for the exploration of this elusive form of molecules. A possible route for the preparation of such form of molecules was also provided. There exist two extreme forms of molecules: pure form and single-molecule mixture. As is shown in Figure . Pure form contains only one kind of molecule. Ultrapure substances, such as ultrapure water, have find wide applications, however, “absolute pure” form of molecules can hardly be reached experimentally. Single-molecule mixture, on the other hand, contains a mixture of molecules that have molecularly different structures. In a given amount of single-molecule mixture sample, the number of molecular structures equals the number of molecules. In nature, at cell levels, each cell is different, at molecular levels, single-molecule mixture, in that each olecule has different structure, to the best of our knowledge, has not yet been explored, both theoretically and experimentally. In this paper, I wish to report a primary theoretical exploration of this form of molecules and provide a possible route for its preparation. Figure 1. Two extreme forms of molecules: pure form and single-molecule mixture
To start our exploration, the first problem we met is how to generate a structural space that contain sufficient huge number of chemical structures (1-5) to enable single-molecule mixtures to exist in macroscopic quantities, for example, at gram scale. Our goal is to generate a “synthesizable low-molecular-weight structural space”, in that this space is conveniently accessible from a synthetic point of view, not just a purely theoretical model. After many attempts, we choose substituted oligo- D -mannitol as a model system; the structures of the related substances are shown in Figure 2. The –OH groups in the chain of oligo-D-mannitol are substituted by substituted benzyl group, in which the substitutes are selected 30 isomers of decanyl group (-C H ). Two extreme forms of molecules
Pure form Mixtures Single-molecule mixturea molecule
Figure 2. The model system of the present study: substituted oligo- D -mannitol The overall numbers of possible structures of the substituted benzyl group were calculated to be 1.395 × . Thus, the number of possible structures of the tetra-substituted monomer unit of oligo-D-mannitol are (1.395 × ) , namely, about 3.787 × . Based on these calculated results, the numbers of possible structures of oligo-D-mannitol (n = 2-6) in the present model system, together with their molecular weight, were calculated, and the results are shown in Table 1. Table 1. Calculated numbers of possible structures and molecular weight of the oligo-D-mannitol (n = 2-6) in the present model system.
HO OHOHOHOHOH
D-mannitol
O O O O ORO RO OR RO OR ORRORO OR RO OR OR OR OR O OR R = R = R : 30R = R ≠ R : 870R = R ≠ R or R = R ≠ R : 870R ≠ R ≠ R : 12180over all: 13950R: Selected 30 isomers of -C H Number of structures:Number of structures: 3.787*10 O O O O ORO RO OR OR ORORRORO RO RO OR ORH OMe n H OMe n R = C H , Selected 30 isomers ligomer Number of Structures Molecular Weight 3.787 × × × × × × × possible structures exist in the structural space of the hexamers. A very interesting question occurs: if we take a given number ( n ) of molecules for the above structural space individually and randomly (which means that the same structure may be taken more than once), what’s the probability to get single-molecule mixture, in that each structures we takes are different? This problem can be solved through probability calculation. In our case, we choose n = N A as the given number of molecules taken from the structural space. The calculated results are summarized in Table 2. Table 2. Calculated probabilities to get single-molecule mixture from each model system, the number of molecules taken from each structure space are n = N A Oligomer P 0 < (1-4.20 × -10 ) N A > 0.999 H OMe1
H OMe2
H OMe3
H OMe4
H OMe5
H OMe6
H OMe1
H OMe2
H OMe3 > 1-1.76 × -20 > 1-4.64 × -37 > 1-1.23 × -53 From these calculated results we can see that, for monomers and dimers, the probabilities to get single-molecule mixture corresponds to 0 (for monomers) or nearly 0 (for dimers). However, for trimers, the probability is larger than 0.999, implying that if we individually and randomly take n = N A molecules from the trimer structure space, we have larger than 0.999 probability to get single-molecule mixture. For higher oligomer structures - tetramers, pentamers and hexamers, the probabilities to get single-molecule mixtures even close to 1. A schematic diagram showing the single-molecule mixtures of the substituted oligo-D-mannitol system is illustrated in Figure 3. Figure 3. Schematic diagram showing single-molecule mixtures of substituted oligo- D -mannitol system H OMe4
H OMe5
H OMe6 nother interesting question arise is how to understand the macroscopic structure of the single-molecule mixture obtained from the above thought experiment. Although the structure of each molecules is different, in that the R group in each substitute site varied, they come randomly from the same structure space, thus, macroscopically, the R group can be viewed as a hybrid structure of the 30 possible isomers of the decanyl group (-C H ). Based on this analysis, we can expect that some physical proprieties of the single-molecule mixture sample obtained from the trimer (or higher oligomer) space, such as density, will be consistent, just like in pure substance. Finally, a possible route for the preparation of single-molecule mixture is provided, as illustrated in Figure 4. This route starts from readily available methyl galloate and D-mannitol and 30 equal mixtures of alkyl bromide . Since the substitutes changes at bromide is only minimal at remote position, these bromides are expected to have essentially the same reactivity and polarity. Thus, the synthetic and purification procedure are expected to be similar to handling pure materials (6-8). Figure 4. A Possible Route for The Preparation of Single-Molecule Mixture
In summary, single-molecule mixture, the opposite extreme form of molecules Br R
30 equimolar mixtures
R = R -R HO OHOHOHOHOH TrClO OMeHO OH OH + BaseAlkylation O OMeO O O
R RR
1. Reduction2. Bromination BrO O O
R RRR = R -R R = R -R BrO O O
R RR R = R -R TrO OTrOHOHOHOH
Protection Alkylation TrO O O O OO O O O OOOO O O O OOTr
R R R R RRRRRRRR R = R -R Deprotection TrO O O O OO O O O OOOO O O O OOH
R R R R RRRRRRRR R = R -R & HO O O O OO O O O OOOO O O O OOH R R R R RRRRRRRR R = R -R Tf OTriflation TfO O O O OO O O O OOOO O O O OOTf
R R R R RRRRRRRR R = R -R + R R R R RRRRRRRR H C O O O OO O O O OOOO O O O OO
R R R R RRRRRRRR
O O O OO O O O OOOO O O O OOTr
R R R R RRRRRRRR11
Number of possible structures: 5.431 × single-molecule mixture even at kilogram scale R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R R × randomly-distributed mixtures ompared to “absolute pure” form, have been theoretically studied by a combination of model construction, thought experiment, and mathematical analysis, and some interesting results were obtained from this study. A possible route for its preparation is also provided. It is expected that this form of matters will exhibit unique, perhaps unprecedented, physical properties. It is hoped that this study will inspire further exploration of this intriguing and new area. Acknowledgement
The author would like to thank Prof. Biao Yu at SIOC for his helpful guidance. Financial support from the Shanghai Sailing Program (17YF1424000) and the China Postdoctoral Science Foundation (2017LH038) is acknowledged.
Competing interests
The authors declare no competing financial interest.
References and Notes W. P. Walters, Virtual Chemical Libraries
J. Med. Chem. , 62 , 1116–1124 2.
J-L. Reymond, The Chemical Space Project.
Acc. Chem. Res . , 48, 722 −
730 3.
R.Visini, J. Aru ś -Pous, M. Awale, J-L Reymond, Virtual Exploration of the Ring Systems Chemical Universe. J. Chem. Inf. Model. , 57, 2707–2718 4.
D. Weininger, Combinatorics of Small Molecular Structures. In Encyclopedia of Computational Chemistry; von Ragué Schleyer, P., Ed.; (John Wiley & Sons, Ltd: Chichester, U.K.,2002) Vol. 8, p 1056. 5.
K. Ogata, T. Isomura, H. Yamashita, H. Kubodera, A Quantitative Approach to the Estimation of Chemical Space From a Given Geometry by the Combination of Atomic Species. QSAR Comb. Sci. , 26, 596 − V. S. K. Balagurusamy, G. Ungar, V. Percec, G. Johansson, Rational Design of the First Spherical Supramolecular Dendrimers Self-Organized in a Novel Thermotropic Cubic Liquid-Crystalline Phase and the Determination of Their Shape by X-ray Analysis.
J. Am. Chem. Soc. , F. Xu, C. Yu, A. Tries, H. Zhang, M. Kläui, K. Basse, M. R. Hansen, N. Bilbao, M. Bonn, H. Wang, Y. Mai, Tunable Superstructures of Dendronized Graphene Nanoribbons in Liquid Phase.
J. Am. Chem. Soc. , , 10972–10977. 8. X-Q. Wang, W-J. Li, W. Wang, J. Wen, Y. Zhang, H. Tan, H-B. Yang, Construction of Type III-C Rotaxane-Branched Dendrimers and Their Anion-Induced Dimension Modulation Feature.
J. Am. Chem. Soc.141