Space-filling model

Last updated November 14, 2024

An example of a three-dimensional, space-filling model of a complex molecule, THC, the active agent in marijuana. Thc.pdb.gif — An example of a three-dimensional, space-filling model of a complex molecule, THC, the active agent in marijuana.

In chemistry, a space-filling model, also known as a calotte model, is a type of three-dimensional (3D) molecular model where the atoms are represented by spheres whose radii are proportional to the radii of the atoms and whose center-to-center distances are proportional to the distances between the atomic nuclei, all in the same scale. Atoms of different chemical elements are usually represented by spheres of different colors.

Space-filling calotte models are also referred to as CPK models after the chemists Robert Corey, Linus Pauling, and Walter Koltun, who over a span of time developed the modeling concept into a useful form.^[1] They are distinguished from other 3D representations, such as the ball-and-stick and skeletal models, by the use of the "full size" space-filling spheres for the atoms. The models are tactile and manually rotatable. They are useful for visualizing the effective shape and relative dimensions of a molecule, and (because of the rotatability) the shapes of the surface of the various conformers. On the other hand, these models mask the chemical bonds between the atoms, and make it difficult to see the structure of the molecule that is obscured by the atoms nearest to the viewer in a particular pose. For this reason, such models are of greater utility if they can be used dynamically, especially when used with complex molecules (e.g., see the greater understanding of the molecules shape given when the THC model is clicked on to rotate).

History

Space-filling models arise out of a desire to represent molecules in ways that reflect the electronic surfaces that molecules present, that dictate how they interact, one with another (or with surfaces, or macromolecules such as enzymes, etc.). Crystallographic data are the starting point for understanding static molecular structure, and these data contain the information rigorously required to generate space-filling representations (e.g., see these crystallographic models); most often, however, crystallographers present the locations of atoms derived from crystallography via "thermal ellipsoids" whose cut-off parameters are set for convenience both to show the atom locations (with anisotropies), and to allow representation of the covalent bonds or other interactions between atoms as lines. In short, for reasons of utility, crystallographic data historically have appeared in presentations closer to ball-and-stick models. Hence, while crystallographic data contain the information to create space-filling models, it remained for individuals interested in modeling an effective static shape of a molecule, and the space it occupied, and the ways in which it might present a surface to another molecule, to develop the formalism shown above.

In 1952, Robert Corey and Linus Pauling described accurate scale models of molecules which they had built at Caltech.^[1] In their models, they envisioned the surface of the molecule as being determined by the van der Waals radius of each atom of the molecule, and crafted atoms as hardwood spheres of diameter proportional to each atom's van der Waals radius, in the scale 1 inch = 1 Å. To allow bonds between atoms a portion of each sphere was cut away to create a pair of matching flat faces, with the cuts dimensioned so that the distance between sphere centers was proportional to the lengths of standard types of chemical bonds.^[1] A connector was designed—a metal bushing that threaded into each sphere at the center of each flat face. The two spheres were then firmly held together by a metal rod inserted into the pair of opposing bushing (with fastening by screws). The models also had special features to allow representation of hydrogen bonds.^[1]^{[ verification needed ]}^[2]

An example of a 3D, space-filling model of a simple molecule, sulfur dioxide, SO2, showing the electrostatic potential surface, computed for the molecule using the Spartan software suite of computational chemistry tools. It is shaded from blue for electropositive areas to red for electronegative areas. The surface was generated by calculating the energy of interaction of a spherical point positive charge (e.g., a proton, H ) with the molecule's atoms and bonding electrons, in a series of discrete computational steps. Here, the electrostatic surface emphasizes the electron deficiency of the sulfur atom, suggesting interactions in which it might engage, and chemical reactions it might undergo. Sulfur-dioxide-elpot.png — An example of a 3D, space-filling model of a simple molecule, sulfur dioxide, SO₂, showing the electrostatic potential surface, computed for the molecule using the *Spartan* software suite of computational chemistry tools. It is shaded from blue for electropositive areas to red for electronegative areas. The surface was generated by calculating the energy of interaction of a spherical point positive charge (e.g., a proton, H ) with the molecule's atoms and bonding electrons, in a series of discrete computational steps. Here, the electrostatic surface emphasizes the electron deficiency of the sulfur atom, suggesting interactions in which it might engage, and chemical reactions it might undergo.

An example of a 3D, space-filling model of a very complex macromolecule, a protein, the cell membrane-spanning b2 adrenoreceptor, a G protein-coupled receptor, in this image, viewed as if looking down onto the extracellular surface. The electrostatic potential surface was applied to a model with atom positions determined by crystallography (PDB code 2RH1); the electrostatic surface was computed using Adaptive Poisson-Boltzmann Solver (APBS) freeware. It is again shaded blue for electropositive areas to red for electronegative areas. Somewhat apparent, in stick representation in yellow, red and blue, in a groove at the top of the receptor, is a small molecule ligand bound to it, the agent carazolol, a partial inverse agonist which, through this binding, antagonizes binding of the normal ligand, the neurotransmitter/hormone epinephrine. In response to binding epinephrine, this receptor, in conjunction with an L-type calcium channel, mediates physiologic responses such as smooth muscle relaxation and bronchodilation. All of such binding interactions and the function of the receptor in signal transduction are mediated by electrostatic effects, and in modern structure work they are often studied using similar space filling models. Beta-2-adrenergic-receptor-electrostatic-top.png — An example of a 3D, space-filling model of a very complex macromolecule, a protein, the cell membrane-spanning β2 adrenoreceptor, a G protein-coupled receptor, in this image, viewed as if looking down onto the extracellular surface. The electrostatic potential surface was applied to a model with atom positions determined by crystallography (PDB code 2RH1); the electrostatic surface was computed using *Adaptive Poisson-Boltzmann Solver* (APBS) freeware. It is again shaded blue for electropositive areas to red for electronegative areas. Somewhat apparent, in stick representation in yellow, red and blue, in a groove at the top of the receptor, is a small molecule ligand bound to it, the agent carazolol, a partial inverse agonist which, through this binding, antagonizes binding of the normal ligand, the neurotransmitter/hormone epinephrine. In response to binding epinephrine, this receptor, in conjunction with an L-type calcium channel, mediates physiologic responses such as smooth muscle relaxation and bronchodilation. All of such binding interactions and the function of the receptor in signal transduction are mediated by electrostatic effects, and in modern structure work they are often studied using similar space filling models.

In 1965, Walter L. Koltun designed and patented a simplified system with molded plastic atoms of various colours, which were joined by specially designed snap connectors; this simpler system accomplished essentially the same ends as the Corey-Pauling system,^[4]^[5] and allowed for the development of the models as a popular way of working with molecules in training and research environments. Such colour-coded, bond length-defined, van der Waals-type space-filling models are now commonly known as CPK models, after these three developers of the specific concept.

In modern research efforts, attention returned to use of data-rich crystallographic models in combination with traditional and new computational methods to provide space-filling models of molecules, both simple and complex, where added information such as which portions of the surface of the molecule were readily accessible to solvent, or how the electrostatic characteristics of a space-filling representation—which in the CPK case is almost fully left to the imagination—could be added to the visual models created. The two closing images give examples of the latter type of calculation and representation, and its utility.

Related Research Articles

<span class="mw-page-title-main">Chemical bond</span> Association of atoms to form chemical compounds

A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds, or some combination of these effects. Chemical bonds are described as having different strengths: there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force, and hydrogen bonding.

Electronegativity, symbolized as χ, is the tendency for an atom of a given chemical element to attract shared electrons when forming a chemical bond. An atom's electronegativity is affected by both its atomic number and the distance at which its valence electrons reside from the charged nucleus. The higher the associated electronegativity, the more an atom or a substituent group attracts electrons. Electronegativity serves as a simple way to quantitatively estimate the bond energy, and the sign and magnitude of a bond's chemical polarity, which characterizes a bond along the continuous scale from covalent to ionic bonding. The loosely defined term electropositivity is the opposite of electronegativity: it characterizes an element's tendency to donate valence electrons.

<span class="mw-page-title-main">Ionic bonding</span> Chemical bonding involving attraction between ions

Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds. It is one of the main types of bonding, along with covalent bonding and metallic bonding. Ions are atoms with an electrostatic charge. Atoms that gain electrons make negatively charged ions. Atoms that lose electrons make positively charged ions. This transfer of electrons is known as electrovalence in contrast to covalence. In the simplest case, the cation is a metal atom and the anion is a nonmetal atom, but these ions can be more complex, e.g. molecular ions like NH⁺
₄ or SO²⁻
₄. In simpler words, an ionic bond results from the transfer of electrons from a metal to a non-metal to obtain a full valence shell for both atoms.

An intermolecular force is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics.

A molecule is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when referring to polyatomic ions.

<span class="mw-page-title-main">Molecular orbital</span> Wave-like behavior of an electron in a molecule

In chemistry, a molecular orbital is a mathematical function describing the location and wave-like behavior of an electron in a molecule. This function can be used to calculate chemical and physical properties such as the probability of finding an electron in any specific region. The terms atomic orbital and molecular orbital were introduced by Robert S. Mulliken in 1932 to mean one-electron orbital wave functions. At an elementary level, they are used to describe the region of space in which a function has a significant amplitude.

The van der Waals radius, r_w, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals equation of state.

<span class="mw-page-title-main">Van der Waals force</span> Interactions between groups of atoms that do not arise from chemical bonds

In molecular physics and chemistry, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and therefore more susceptible to disturbance. The van der Waals force quickly vanishes at longer distances between interacting molecules.

<span class="mw-page-title-main">Molecular modelling</span> Discovering chemical properties by physical simulations

Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials science to study molecular systems ranging from small chemical systems to large biological molecules and material assemblies. The simplest calculations can be performed by hand, but inevitably computers are required to perform molecular modelling of any reasonably sized system. The common feature of molecular modelling methods is the atomistic level description of the molecular systems. This may include treating atoms as the smallest individual unit, or explicitly modelling protons and neutrons with its quarks, anti-quarks and gluons and electrons with its photons.

In chemistry, valence bond (VB) theory is one of the two basic theories, along with molecular orbital (MO) theory, that were developed to use the methods of quantum mechanics to explain chemical bonding. It focuses on how the atomic orbitals of the dissociated atoms combine to give individual chemical bonds when a molecule is formed. In contrast, molecular orbital theory has orbitals that cover the whole molecule.

Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. For example, in a carbon atom which forms four single bonds, the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp³ mixtures in a tetrahedral arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.

In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.

In the context of chemistry, molecular physics, physical chemistry, and molecular modelling, a force field is a computational model that is used to describe the forces between atoms within molecules or between molecules as well as in crystals. Force fields are a variety of interatomic potentials. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system on the atomistic level. Force fields are usually used in molecular dynamics or Monte Carlo simulations. The parameters for a chosen energy function may be derived from classical laboratory experiment data, calculations in quantum mechanics, or both. Force fields utilize the same concept as force fields in classical physics, with the main difference being that the force field parameters in chemistry describe the energy landscape on the atomistic level. From a force field, the acting forces on every particle are derived as a gradient of the potential energy with respect to the particle coordinates.

In chemistry, the CPK coloring is a popular color convention for distinguishing atoms of different chemical elements in molecular models.

Molecular graphics is the discipline and philosophy of studying molecules and their properties through graphical representation. IUPAC limits the definition to representations on a "graphical display device". Ever since Dalton's atoms and Kekulé's benzene, there has been a rich history of hand-drawn atoms and molecules, and these representations have had an important influence on modern molecular graphics.

A molecular model is a physical model of an atomistic system that represents molecules and their processes. They play an important role in understanding chemistry and generating and testing hypotheses. The creation of mathematical models of molecular properties and behavior is referred to as molecular modeling, and their graphical depiction is referred to as molecular graphics.

In chemistry, the ball-and-stick model is a molecular model of a chemical substance which displays both the three-dimensional position of the atoms and the bonds between them. The atoms are typically represented by spheres, connected by rods which represent the bonds. Double and triple bonds are usually represented by two or three curved rods, respectively, or alternately by correctly positioned sticks for the sigma and pi bonds. In a good model, the angles between the rods should be the same as the angles between the bonds, and the distances between the centers of the spheres should be proportional to the distances between the corresponding atomic nuclei. The chemical element of each atom is often indicated by the sphere's color.

The van der Waals surface of a molecule is an abstract representation or model of that molecule, illustrating where, in very rough terms, a surface might reside for the molecule based on the hard cutoffs of van der Waals radii for individual atoms, and it represents a surface through which the molecule might be conceived as interacting with other molecules. Also referred to as a van der Waals envelope, the van der Waals surface is named for Johannes Diderik van der Waals, a Dutch theoretical physicist and thermodynamicist who developed theory to provide a liquid-gas equation of state that accounted for the non-zero volume of atoms and molecules, and on their exhibiting an attractive force when they interacted. van der Waals surfaces are therefore a tool used in the abstract representations of molecules, whether accessed, as they were originally, via hand calculation, or via physical wood/plastic models, or now digitally, via computational chemistry software. Practically speaking, CPK models, developed by and named for Robert Corey, Linus Pauling, and Walter Koltun, were the first widely used physical molecular models based on van der Waals radii, and allowed broad pedagogical and research use of a model showing the van der Waals surfaces of molecules.

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively charged nucleus, with a cloud of negatively charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

References

1 2 3 4 Corey, Robert B.; Pauling, Linus (1953). "Molecular models of amino acids, peptides, and proteins" (PDF). Review of Scientific Instruments. 8 (24): 621–627. Bibcode:1953RScI...24..621C. doi:10.1063/1.1770803 . Retrieved 9 March 2020.
↑ In the same paper Corey and Pauling also briefly describe a much simpler but less accurate type of model, with rubber-like polyvinyl plastic spheres in the scale 1 inch = 2Å and connected by snap fasteners. See Corey & Pauling, 1953, op. cit.
↑ Baker, N.A., Sept, D., Joseph, S., Holst, M.J. & McCammon, J.A., 2001, "Electrostatics of nanosystems: Application to microtubules and the ribosome," Proc. Natl. Acad. Sci. U.S.A.98: pp. 10037-10041, see , and "Calculating Electrostatics". Archived from the original on 2015-06-24. Retrieved 2015-06-23., and , accessed 23 June 2015.
↑ Koltun, Walter L. (1965). "Precision space-filling atomic models". Biopolymers. 3 (6): 665–679. doi:10.1002/bip.360030606. ISSN 0006-3525.
↑ USpatent 3170246,Koltun, Walter L.,"Space filling atomic units and connectors for molecular models",issued 1965-02-23

External links

More on molecular models and a couple of examples from chemistry and biology (article is in German)

Gallery

A space-filling model of cyclohexane C
6H
12. Carbon atoms, partially masked, are in grey, and hydrogen atoms are presented as white spheres. Cyclohexanmolekulmodell.png — A space-filling model of cyclohexane C
₆H
₁₂. Carbon atoms, partially masked, are in grey, and hydrogen atoms are presented as white spheres.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[corpau-1] 1 2 3 4 Corey, Robert B.; Pauling, Linus (1953). "Molecular models of amino acids, peptides, and proteins" (PDF). Review of Scientific Instruments. 8 (24): 621–627. Bibcode:1953RScI...24..621C. doi:10.1063/1.1770803 . Retrieved 9 March 2020.

[2] In the same paper Corey and Pauling also briefly describe a much simpler but less accurate type of model, with rubber-like polyvinyl plastic spheres in the scale 1 inch = 2Å and connected by snap fasteners. See Corey & Pauling, 1953, op. cit.

[3] Baker, N.A., Sept, D., Joseph, S., Holst, M.J. & McCammon, J.A., 2001, "Electrostatics of nanosystems: Application to microtubules and the ribosome," Proc. Natl. Acad. Sci. U.S.A.98: pp. 10037-10041, see , and "Calculating Electrostatics". Archived from the original on 2015-06-24. Retrieved 2015-06-23., and , accessed 23 June 2015.

[4] Koltun, Walter L. (1965). "Precision space-filling atomic models". Biopolymers. 3 (6): 665–679. doi:10.1002/bip.360030606. ISSN 0006-3525.

[5] USpatent 3170246,Koltun, Walter L.,"Space filling atomic units and connectors for molecular models",issued 1965-02-23

[1]

[2]

[4]

[5]