Force field (chemistry)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Force_field_(chemistry) 

A force field is used to minimize the bond stretching energy of this ethane molecule.

In the context of chemistry and molecular modelling, a force field is a computational method that is used to estimate the forces between atoms within molecules and also between molecules. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics, molecular dynamics, or Monte Carlo simulations. The parameters for a chosen energy function may be derived from experiments in physics and chemistry, calculations in quantum mechanics, or both. Force fields are interatomic potentials and utilize the same concept as force fields in classical physics, with the difference that the force field parameters in chemistry describe the energy landscape, from which the acting forces on every particle are derived as a gradient of the potential energy with respect to the particle coordinates.

All-atom force fields provide parameters for every type of atom in a system, including hydrogen, while united-atom interatomic potentials treat the hydrogen and carbon atoms in methyl groups and methylene bridges as one interaction center. Coarse-grained potentials, which are often used in long-time simulations of macromolecules such as proteins, nucleic acids, and multi-component complexes, sacrifice chemical details for higher computing efficiency.

Functional form

Molecular mechanics potential energy function with continuum solvent.

The basic functional form of potential energy in molecular mechanics includes bonded terms for interactions of atoms that are linked by covalent bonds, and nonbonded (also termed noncovalent) terms that describe the long-range electrostatic and van der Waals forces. The specific decomposition of the terms depends on the force field, but a general form for the total energy in an additive force field can be written as

${\displaystyle \ E_{\text{total}}=E_{\text{bonded}}+E_{\text{nonbonded}}}$

where the components of the covalent and noncovalent contributions are given by the following summations:

${\displaystyle \ E_{\text{bonded}}=E_{\text{bond}}+E_{\text{angle}}+E_{\text{dihedral}}}$

${\displaystyle \ E_{\text{nonbonded}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}}$

The bond and angle terms are usually modeled by quadratic energy functions that do not allow bond breaking. A more realistic description of a covalent bond at higher stretching is provided by the more expensive Morse potential. The functional form for dihedral energy is variable from one force field to another. Additional, "improper torsional" terms may be added to enforce the planarity of aromatic rings and other conjugated systems, and "cross-terms" that describe the coupling of different internal variables, such as angles and bond lengths. Some force fields also include explicit terms for hydrogen bonds.

The nonbonded terms are computationally most intensive. A popular choice is to limit interactions to pairwise energies. The van der Waals term is usually computed with a Lennard-Jones potential and the electrostatic term with Coulomb's law. However, both can be buffered or scaled by a constant factor to account for electronic polarizability. Studies with this energy expression have focused on biomolecules since the 1970s and were generalized to compounds across the periodic table in the early 2000s, including metals, ceramics, minerals, and organic compounds.

Bond stretching

As it is rare for bonds to deviate significantly from their reference values, the most simplistic approaches utilize a Hooke's law formula:

${\displaystyle E_{\text{bond}}={\frac {k_{ij}}{2}}(l_{ij}-l_{0,ij})^{2}}$

Where ${\displaystyle k_{ij}}$ is the force constant, ${\displaystyle l_{ij}}$ is the bond length and ${\displaystyle l_{0,ij}}$ is the value for the bond length between atoms ${\displaystyle i}$ and ${\displaystyle j}$ when all other terms in the force field are set to 0. The term ${\displaystyle l_{0,ij}}$ is often referred to as the equilibrium bond length, which may cause confusion. The equilibrium bond length is the value adopted in equilibrium at 298 K with all other force field terms and kinetic energy contributing. Therefore, ${\displaystyle l_{0,ij}}$ is often a few percent different from the actual bond length in experiments at 298 K.

The bond stretching constant ${\displaystyle k_{ij}}$ can be determined from the experimental Infrared spectrum, Raman spectrum, or high-level quantum mechanical calculations. The constant ${\displaystyle k_{ij}}$ determines vibrational frequencies in molecular dynamics simulations. The stronger the bond is between atoms, the higher is the value of the force constant, and the higher the wavenumber (energy) in the IR/Raman spectrum. The vibration spectrum according to a given force constant can be computed from short MD trajectories (5 ps) with ~1 fs time steps, calculation of the velocity autocorrelation function, and its Fourier transform.

Though the formula of Hooke's law provides a reasonable level of accuracy at bond lengths near the equilibrium distance, it is less accurate as one moves away. In order to model the Morse curve better one could employ cubic and higher powers.^[2][6] However, for most practical applications these differences are negligible and inaccuracies in predictions of bond lengths are on the order of the thousandth of an angstrom, which is also the limit of reliability for common force fields. A Morse potential can be employed instead to enable bond breaking and higher accuracy, even though it is less efficient to compute.

Electrostatic interactions

Electrostatic interactions are represented by a Coulomb energy, which utilizes atomic charges ${\displaystyle q_{i}}$ to represent chemical bonding ranging from covalent to polar covalent and ionic bonding. The typical formula is the Coulomb law:

${\displaystyle E_{\text{Coulomb}}={1 \over 4\pi \varepsilon _{0}}{\frac {q_{i}q_{j}}{r_{ij}}}}$

Where ${\displaystyle r_{ij}}$ is the distance between two atoms ${\displaystyle i}$ and ${\displaystyle j}$. The total Coulomb energy is a summation over all pairwise combinations of atoms and usually excludes 1, 2 bonded atoms, 1, 3 bonded atoms, as well as 1, 4 bonded atoms.

Atomic charges can make dominant contributions to the potential energy, especially for polar molecules and ionic compounds, and are critical to simulate the geometry, interaction energy, as well as the reactivity. The assignment of atomic charges often still follows empirical and unreliable quantum mechanical protocols, which often lead to several 100% uncertainty relative to physically justified values in agreement with experimental dipole moments and theory. Reproducible atomic charges for force fields based on experimental data for electron deformation densities, internal dipole moments, and an Extended Born model have been developed. Uncertainties <10%, or ±0.1e, enable a consistent representation of chemical bonding and up to hundred times higher accuracy in computed structures and energies along with physical interpretation of other parameters in the force field.

Parameterization

In addition to the functional form of the potentials, force fields define a set of parameters for different types of atoms, chemical bonds, dihedral angles, out-of-plane interactions, nonbond interactions, and possible other terms. Many parameter sets are empirical and some force fields use extensive fitting terms that are difficult to assign a physical interpretation. Atom types are defined for different elements as well as for the same elements in sufficiently different chemical environments. For example, oxygen atoms in water and an oxygen atoms in a carbonyl functional group are classified as different force field types. Typical force field parameter sets include values for atomic mass, atomic charge, Lennard-Jones parameters for every atom type, as well as equilibrium values of bond lengths, bond angles, and dihedral angles. The bonded terms refer to pairs, triplets, and quadruplets of bonded atoms, and include values for the effective spring constant for each potential. Most current force fields parameters use a fixed-charge model by which each atom is assigned one value for the atomic charge that is not affected by the local electrostatic environment.

Force field parameterizations for simulations with maximum accuracy and transferability, e.g., IFF, follow a well-defined protocol. The workflow may involve (1) retrieving an x-ray crystal structure or chemical formula, (2) defining atom types, (3) obtaining atomic charges, (4) assigning initial Lennard-Jones and bonded parameters, (5) computational tests of density and geometry relative to experimental reference data, (6) computational tests of energetic properties (surface energy, hydration energy) relative to experimental reference data, (7) secondary validation and refinement (thermal, mechanical, and diffusion properties). Major iterative loops occur between steps (5) and (4), as well as between (6) and (4)/(3). The chemical interpretation of the parameters and reliable experimental reference data play a critical role.

The parameters for molecular simulations of biological macromolecules such as proteins, DNA, and RNA were often derived from observations for small organic molecules, which are more accessible for experimental studies and quantum calculations. Thereby, multiple issues arise, such as (1) unreliable atomic charges from quantum calculations may affect all computed properties and internal consistency, (2) data different derived from quantum mechanics for molecules in the gas phase may not be transferable for simulations in the condensed phase, (3) use of data for small molecules and application to larger polymeric structures involves uncertainty, (4) dissimilar experimental data with variation in accuracy and reference states (e.g. temperature) can cause deviations. As a result, divergent force field parameters have been reported for biological molecules. Experimental reference data included, for example, the enthalpy of vaporization (OPLS), enthalpy of sublimation, dipole moments, and various spectroscopic parameters. Inconsistencies can be overcome by interpretation of all force field parameters and choosing a consistent reference state, for example, room temperature and atmospheric pressure.

Several force fields also include no clear chemical rationale, parameterization protocol, incomplete validation of key properties (structures and energies), lack of interpretation of parameters, and of a discussion of uncertainties. In these cases, large, random deviations of computed properties have been reported.

Methods

Some force fields include explicit models for polarizability, where a particle's effective charge can be influenced by electrostatic interactions with its neighbors. Core-shell models are common, which consist of a positively charged core particle, representing the polarizable atom, and a negatively charged particle attached to the core atom through a springlike harmonic oscillator potential. Recent examples include polarizable models with virtual electrons that reproduce image charges in metals and polarizable biomolecular force fields. By adding such degrees of freedom for polarizability, the interpretation of the parameters becomes more difficult and increases the risk towards arbitrary fit parameters and decreased compatibility. The computational expense increases due to the need to repeatedly calculate the local electrostatic field.

Polarizable models perform well when it captures essential chemical features and the net atomic charge is relatively accurate (within ±10%). In recent times, such models have been erroneously called "Drude Oscillator potentials". An appropriate term for these models is "Lorentz oscillator models" since Lorentz rather than Drude proposed some form of attachment of electrons to nuclei. Drude models assume unrestricted motion of the electrons, e.g., a free electron gas in metals.

Parameterization

Historically, many approaches to parameterization of a forcefield have been employed. Numerous classical forcefields relied on relatively intransparent parameterization protocols, for example, using approximate quantum mechanical calculations, often in the gas phase, with the expectation of some correlation with condensed phase properties and empirical modifications of potentials to match experimental observables. The protocols may not be reproducible and semi-automation often played a role to generate parameters, optimizing for speedy parameter generation and wide coverage, and not for chemical consistency, interpretability, reliability, and sustainability.

Similar, even more automated tools have become recently available to parameterize new force fields and assist users to develop their own parameter sets for chemistries which are not parameterized to date. Efforts to provide open source codes and methods include openMM and openMD. The use of semi-automation or full automation, without input from chemical knowledge, is likely to increase inconsistencies at the level of atomic charges, for the assignment of remaining parameters, and likely to dilute the interpretability and performance of parameters.

The Interface force field (IFF) assumes one single energy expression for all compounds across the periodic (with 9-6 and 12-6 LJ options) and utilizes rigorous validation with standardized simulation protocols that enable full interpretability and compatibility of the parameters, as well as high accuracy and access to unlimited combinations of compounds.

Transferability

Functional forms and parameter sets have been defined by the developers of interatomic potentials and feature variable degrees of self-consistency and transferability. When functional forms of the potential terms vary, the parameters from one interatomic potential function can typically not be used together with another interatomic potential function. In some cases, modifications can be made with minor effort, for example, between 9-6 Lennard-Jones potentials to 12-6 Lennard-Jones potentials. Transfers from Buckingham potentials to harmonic potentials, or from Embedded Atom Models to harmonic potentials, on the contrary, would require many additional assumptions and may not be possible.

Limitations

All interatomic potentials are based on approximations and experimental data, therefore often termed empirical. The performance varies from higher accuracy than density functional theory calculations, with access to million times larger systems and time scales, to random guesses depending on the force field. The use of accurate representations of chemical bonding, combined with reproducible experimental data and validation, can lead to lasting interatomic potentials of high quality with much less parameters and assumptions in comparison to DFT-level quantum methods.

Possible limitations include atomic charges, also called point charges. Most force fields rely on point charges to reproduce the electrostatic potential around molecules, which works less well for anisotropic charge distributions. The remedy is that point charges have a clear interpretation, and virtual electrons can be added to capture essential features of the electronic structure, such additional polarizability in metallic systems to describe the image potential, internal multipole moments in π-conjugated systems, and lone pairs in water. Electronic polarization of the environment may be better included by using polarizable force fields or using a macroscopic dielectric constant. However, application of one value of dielectric constant is a coarse approximation in the highly heterogeneous environments of proteins, biological membranes, minerals, or electrolytes.

All types of van der Waals forces are also strongly environment-dependent because these forces originate from interactions of induced and "instantaneous" dipoles (see Intermolecular force). The original Fritz London theory of these forces applies only in a vacuum. A more general theory of van der Waals forces in condensed media was developed by A. D. McLachlan in 1963 and included the original London's approach as a special case. The McLachlan theory predicts that van der Waals attractions in media are weaker than in vacuum and follow the like dissolves like rule, which means that different types of atoms interact more weakly than identical types of atoms. This is in contrast to combinatorial rules or Slater-Kirkwood equation applied for development of the classical force fields. The combinatorial rules state that the interaction energy of two dissimilar atoms (e.g., C...N) is an average of the interaction energies of corresponding identical atom pairs (i.e., C...C and N...N). According to McLachlan's theory, the interactions of particles in media can even be fully repulsive, as observed for liquid helium, however, the lack of vaporization and presence of a freezing point contradicts a theory of purely repulsive interactions. Measurements of attractive forces between different materials (Hamaker constant) have been explained by Jacob Israelachvili. For example, "the interaction between hydrocarbons across water is about 10% of that across vacuum". Such effects are represented in molecular dynamics through pairwise interactions that are spatially more dense in the condensed phase relative to the gas phase and reproduced once the parameters for all phases are validated to reproduce chemical bonding, density, and cohesive/surface energy.

Limitations have been strongly felt in protein structure refinement. The major underlying challenge is the huge conformation space of polymeric molecules, which grows beyond current computational feasibility when containing more than ~20 monomers. Participants in Critical Assessment of protein Structure Prediction (CASP) did not try to refine their models to avoid "a central embarrassment of molecular mechanics, namely that energy minimization or molecular dynamics generally leads to a model that is less like the experimental structure". Force fields have been applied successfully for protein structure refinement in different X-ray crystallography and NMR spectroscopy applications, especially using program XPLOR. However, the refinement is driven mainly by a set of experimental constraints and the interatomic potentials serve mainly to remove interatomic hindrances. The results of calculations were practically the same with rigid sphere potentials implemented in program DYANA (calculations from NMR data), or with programs for crystallographic refinement that use no energy functions at all. These shortcomings are related to interatomic potentials and to the inability to sample the conformation space of large molecules effectively. Thereby also the development of parameters to tackle such large-scale problems requires new approaches. A specific problem area is homology modeling of proteins. Meanwhile, alternative empirical scoring functions have been developed for ligand docking, protein folding, homology model refinement, computational protein design, and modeling of proteins in membranes.

It was also argued that some protein force fields operate with energies that are irrelevant to protein folding or ligand binding. The parameters of proteins force fields reproduce the enthalpy of sublimation, i.e., energy of evaporation of molecular crystals. However, protein folding and ligand binding are thermodynamically closer to crystallization, or liquid-solid transitions as these processes represent freezing of mobile molecules in condensed media. Thus, free energy changes during protein folding or ligand binding are expected to represent a combination of an energy similar to heat of fusion (energy absorbed during melting of molecular crystals), a conformational entropy contribution, and solvation free energy. The heat of fusion is significantly smaller than enthalpy of sublimation. Hence, the potentials describing protein folding or ligand binding need more consistent parameterization protocols, e.g., as described for IFF. Indeed, the energies of H-bonds in proteins are ~ -1.5 kcal/mol when estimated from protein engineering or alpha helix to coil transition data, but the same energies estimated from sublimation enthalpy of molecular crystals were -4 to -6 kcal/mol, which is related to re-forming existing hydrogen bonds and not forming hydrogen bonds from scratch. The depths of modified Lennard-Jones potentials derived from protein engineering data were also smaller than in typical potential parameters and followed the like dissolves like rule, as predicted by McLachlan theory.

Widely used force fields

Further information: Comparison of force field implementations, Molecular design software, and Comparison of software for molecular mechanics modeling

Different force fields are designed for different purposes. All are implemented in various computers software.

MM2 was developed by Norman Allinger mainly for conformational analysis of hydrocarbons and other small organic molecules. It is designed to reproduce the equilibrium covalent geometry of molecules as precisely as possible. It implements a large set of parameters that is continuously refined and updated for many different classes of organic compounds (MM3 and MM4).

CFF was developed by Arieh Warshel, Lifson, and coworkers as a general method for unifying studies of energies, structures, and vibration of general molecules and molecular crystals. The CFF program, developed by Levitt and Warshel, is based on the Cartesian representation of all the atoms, and it served as the basis for many subsequent simulation programs.

ECEPP was developed specifically for the modeling of peptides and proteins. It uses fixed geometries of amino acid residues to simplify the potential energy surface. Thus, the energy minimization is conducted in the space of protein torsion angles. Both MM2 and ECEPP include potentials for H-bonds and torsion potentials for describing rotations around single bonds. ECEPP/3 was implemented (with some modifications) in Internal Coordinate Mechanics and FANTOM.

AMBER, CHARMM, and GROMOS have been developed mainly for molecular dynamics of macromolecules, although they are also commonly used for energy minimizing. Thus, the coordinates of all atoms are considered as free variables.

Interface Force Field (IFF) was developed as the first consistent force field for compounds across the periodic table. It overcomes the known limitations of assigning consistent charges, utilizes standard conditions as a reference state, reproduces structures, energies, and energy derivatives, and quantifies limitations for all included compounds. It is compatible with multiple force fields to simulate hybrid materials (CHARMM, AMBER, OPLS-AA, CFF, CVFF, GROMOS).

Classical

• AMBER (Assisted Model Building and Energy Refinement) – widely used for proteins and DNA.
• CFF (Consistent Force Field) – a family of forcefields adapted to a broad variety of organic compounds, includes force fields for polymers, metals, etc.
• CHARMM (Chemistry at HARvard Molecular Mechanics) – originally developed at Harvard, widely used for both small molecules and macromolecules
• COSMOS-NMR – hybrid QM/MM force field adapted to various inorganic compounds, organic compounds, and biological macromolecules, including semi-empirical calculation of atomic charges NMR properties. COSMOS-NMR is optimized for NMR-based structure elucidation and implemented in COSMOS molecular modelling package.
• CVFF – also used broadly for small molecules and macromolecules.
• ECEPP – first force field for polypeptide molecules - developed by F.A. Momany, H.A. Scheraga and colleagues.
• GROMOS (GROningen MOlecular Simulation) – a force field that comes as part of the GROMOS software, a general-purpose molecular dynamics computer simulation package for the study of biomolecular systems. GROMOS force field A-version has been developed for application to aqueous or apolar solutions of proteins, nucleotides, and sugars. A B-version to simulate gas phase isolated molecules is also available.
• IFF (Interface Force Field) – First force field to cover metals, minerals, 2D materials, and polymers in one platform with cutting-edge accuracy and compatibility with many other force fields (CHARMM, AMBER, OPLS-AA, CFF, CVFF, GROMOS), includes 12-6 LJ and 9-6 LJ options
• MMFF (Merck Molecular Force Field) – developed at Merck for a broad range of molecules.
• OPLS (Optimized Potential for Liquid Simulations) (variants include OPLS-AA, OPLS-UA, OPLS-2001, OPLS-2005, OPLS3e, OPLS4) – developed by William L. Jorgensen at the Yale University Department of Chemistry.
• QCFF/PI – A general force fields for conjugated molecules.
• UFF (Universal Force Field) – A general force field with parameters for the full periodic table up to and including the actinoids, developed at Colorado State University. The reliability is known to be poor due to lack of validation and interpretation of the parameters for nearly all claimed compounds, especially metals and inorganic compounds.

Polarizable

• AMBER – polarizable force field developed by Jim Caldwell and coworkers.
• AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) – force field developed by Pengyu Ren (University of Texas at Austin) and Jay W. Ponder (Washington University). AMOEBA force field is gradually moving to more physics-rich AMOEBA+.
• CHARMM – polarizable force field developed by S. Patel (University of Delaware) and C. L. Brooks III (University of Michigan). Based on the classical Drude oscillator developed by A. MacKerell (University of Maryland, Baltimore) and B. Roux (University of Chicago).
• CFF/ind and ENZYMIX – The first polarizable force field which has subsequently been used in many applications to biological systems.
• COSMOS-NMR (Computer Simulation of Molecular Structure) – developed by Ulrich Sternberg and coworkers. Hybrid QM/MM force field enables explicit quantum-mechanical calculation of electrostatic properties using localized bond orbitals with fast BPT formalism. Atomic charge fluctuation is possible in each molecular dynamics step.
• DRF90 developed by P. Th. van Duijnen and coworkers.
• IFF (Interface Force Field) – includes polarizability for metals (Au, W) and pi-conjugated molecules
• NEMO (Non-Empirical Molecular Orbital) – procedure developed by Gunnar Karlström and coworkers at Lund University (Sweden)
• PIPF – The polarizable intermolecular potential for fluids is an induced point-dipole force field for organic liquids and biopolymers. The molecular polarization is based on Thole's interacting dipole (TID) model and was developed by Jiali Gao Gao Research Group | at the University of Minnesota.
• Polarizable Force Field (PFF) – developed by Richard A. Friesner and coworkers.
• SP-basis Chemical Potential Equalization (CPE) – approach developed by R. Chelli and P. Procacci.
• PHAST - polarizable potential developed by Chris Cioce and coworkers.
• ORIENT – procedure developed by Anthony J. Stone (Cambridge University) and coworkers.
• Gaussian Electrostatic Model (GEM) – a polarizable force field based on Density Fitting developed by Thomas A. Darden and G. Andrés Cisneros at NIEHS; and Jean-Philip Piquemal at Paris VI University.
• Atomistic Polarizable Potential for Liquids, Electrolytes, and Polymers(APPLE&P), developed by Oleg Borogin, Dmitry Bedrov and coworkers, which is distributed by Wasatch Molecular Incorporated.
• Polarizable procedure based on the Kim-Gordon approach developed by Jürg Hutter and coworkers (University of Zürich)
• GFN-FF (Geometry, Frequency, and Noncovalent Interaction Force-Field) - a completely automated partially polarizable generic force-field for the accurate description of structures and dynamics of large molecules across the periodic table developed by Stefan Grimme and Sebastian Spicher at the University of Bonn.

Reactive

• EVB (Empirical valence bond) – this reactive force field, introduced by Warshel and coworkers, is probably the most reliable and physically consistent way to use force fields in modeling chemical reactions in different environments. The EVB facilitates calculating activation free energies in condensed phases and in enzymes.
• ReaxFF – reactive force field (interatomic potential) developed by Adri van Duin, William Goddard and coworkers. It is slower than classical MD (50x), needs parameter sets with specific validation, and has no validation for surface and interfacial energies. Parameters are non-interpretable. It can be used atomistic-scale dynamical simulations of chemical reactions. Parallelized ReaxFF allows reactive simulations on >>1,000,000 atoms on large supercomputers.

Coarse-grained

• DPD (Dissipative particle dynamics) - This is a method commonly applied in chemical engineering. It is typically used for studying the hydrodynamics of various simple and complex fluids which require consideration of time and length scales larger than those accessible to classical Molecular dynamics. The potential was originally proposed by Hoogerbrugge and Koelman  with later modifications by Español and Warren.  The current state of the art was well documented in a CECAM workshop in 2008. Recently, work has been undertaken to capture some of the chemical subtitles relevant to solutions. This has led to work considering automated parameterisation of the DPD interaction potentials against experimental observables.
• MARTINI – a coarse-grained potential developed by Marrink and coworkers at the University of Groningen, initially developed for molecular dynamics simulations of lipids, later extended to various other molecules. The force field applies a mapping of four heavy atoms to one CG interaction site and is parameterized with the aim of reproducing thermodynamic properties.
• SAFT - A top-down coarse-grained model developed in the Molecular Systems Engineering group at Imperial College London fitted to liquid phase densities and vapor pressures of pure compounds by using the SAFT equation of state.
• SIRAH – a coarse-grained force field developed by Pantano and coworkers of the Biomolecular Simulations Group, Institut Pasteur of Montevideo, Uruguay; developed for molecular dynamics of water, DNA, and proteins. Free available for AMBER and GROMACS packages.
• VAMM (Virtual atom molecular mechanics) – a coarse-grained force field developed by Korkut and Hendrickson for molecular mechanics calculations such as large scale conformational transitions based on the virtual interactions of C-alpha atoms. It is a knowledge based force field and formulated to capture features dependent on secondary structure and on residue-specific contact information in proteins.

Machine learning

• ANI is a transferable neural network potential, built from atomic environment vectors, and able to provide DFT accuracy in terms of energies.
• FFLUX (originally QCTFF)  A set of trained Kriging models which operate together to provide a molecular force field trained on Atoms in molecules or Quantum chemical topology energy terms including electrostatic, exchange and electron correlation.
• TensorMol, a mixed model, a Neural network provides a short-range potential, whilst more traditional potentials add screened long range terms.
• Δ-ML not a force field method but a model that adds learnt correctional energy terms to approximate and relatively computationally cheap quantum chemical methods in order to provide an accuracy level of a higher order, more computationally expensive quantum chemical model.
• SchNet a Neural network utilising continuous-filter convolutional layers, to predict chemical properties and potential energy surfaces.
• PhysNet is a Neural Network-based energy function to predict energies, forces and (fluctuating) partial charges.

Water

Main article: Water model

The set of parameters used to model water or aqueous solutions (basically a force field for water) is called a water model. Water has attracted a great deal of attention due to its unusual properties and its importance as a solvent. Many water models have been proposed; some examples are TIP3P, TIP4P, SPC, flexible simple point charge water model (flexible SPC), ST2, and mW. Other solvents and methods of solvent representation are also applied within computational chemistry and physics some examples are given on page Solvent model. Recently, novel methods for generating water models have been published.

Modified amino acids

• Forcefield_PTM – An AMBER-based forcefield and webtool for modeling common post-translational modifications of amino acids in proteins developed by Chris Floudas and coworkers. It uses the ff03 charge model and has several side-chain torsion corrections parameterized to match the quantum chemical rotational surface.
• Forcefield_NCAA - An AMBER-based forcefield and webtool for modeling common non-natural amino acids in proteins in condensed-phase simulations using the ff03 charge model. The charges have been reported to be correlated with hydration free energies of corresponding side-chain analogs.

Other

• LFMM (Ligand Field Molecular Mechanics) - functions for the coordination sphere around transition metals based on the angular overlap model (AOM). Implemented in the Molecular Operating Environment (MOE) as DommiMOE and in Tinker
• VALBOND - a function for angle bending that is based on valence bond theory and works for large angular distortions, hypervalent molecules, and transition metal complexes. It can be incorporated into other force fields such as CHARMM and UFF.

Abdominal obesity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Abdominal_obesity 

 

Abdominal obesity
Other names	Central obesity, truncal obesity; see also § Colloquialisms
An abdominous obese male Weight: 182 kg/400 lbs Height: 185 cm/6 ft 1 in. Body mass index: 53

Specialty	Endocrinology
Complications	Heart disease, asthma, stroke, diabetes
Causes	Sedentary lifestyle, Overeating, Cushing's syndrome, Alcoholism, Polycystic ovarian syndrome, Prader-Willi syndrome

Abdominal obesity, also known as central obesity and truncal obesity, is a condition when excessive abdominal fat around the stomach and abdomen has built up to the extent that it is likely to have a negative impact on health. Abdominal obesity has been strongly linked to cardiovascular disease, Alzheimer's disease, and other metabolic and vascular diseases.

Visceral and central abdominal fat and waist circumference show a strong association with type 2 diabetes.

Visceral fat, also known as organ fat or intra-abdominal fat, is located inside the peritoneal cavity, packed in between internal organs and torso, as opposed to subcutaneous fat, which is found underneath the skin, and intramuscular fat, which is found interspersed in skeletal muscle. Visceral fat is composed of several adipose depots including mesenteric, epididymal white adipose tissue (EWAT), and perirenal fat. An excess of adipose visceral fat is known as central obesity, the "pot belly" or "beer belly" effect, in which the abdomen protrudes excessively. This body type is also known as "apple shaped", as opposed to "pear shaped" in which fat is deposited on the hips and buttocks.

Researchers first started to focus on abdominal obesity in the 1980s when they realized it had an important connection to cardiovascular disease, diabetes, and dyslipidemia. Abdominal obesity was more closely related with metabolic dysfunctions connected with cardiovascular disease than was general obesity. In the late 1980s and early 1990s insightful and powerful imaging techniques were discovered that would further help advance the understanding of the health risks associated with body fat accumulation. Techniques such as computed tomography and magnetic resonance imaging made it possible to categorize mass of adipose tissue located at the abdominal level into intra-abdominal fat and subcutaneous fat.

Health risks

Heart disease

Abdominal obesity is associated with a statistically higher risk of heart disease, hypertension, insulin resistance, and type 2 diabetes (see below). With an increase in the waist to hip ratio and overall waist circumference the risk of death increases as well. Metabolic syndrome is associated with abdominal obesity, blood lipid disorders, inflammation, insulin resistance, full-blown diabetes, and increased risk of developing cardiovascular disease. It is now generally believed that intra-abdominal fat is the depot that conveys the biggest health risk.

Recent validation has concluded that total and regional body volume estimates correlate positively and significantly with biomarkers of cardiovascular risk and BVI calculations correlate significantly with all biomarkers of cardio-vascular risk.

Diabetes

There are numerous theories as to the exact cause and mechanism in type 2 diabetes. Central obesity is known to predispose individuals for insulin resistance. Abdominal fat is especially active hormonally, secreting a group of hormones called that may possibly impair glucose tolerance. But adiponectin, an anti-inflammatory adipokine, which is found in lower concentration in obese and diabetic individuals has shown to be beneficial and protective in type 2 diabetes mellitus (T2DM).

Insulin resistance is a major feature of diabetes mellitus type 2 , and central obesity is correlated with both insulin resistance and T2DM itself. Increased adiposity (obesity) raises serum resistin levels, which in turn directly correlate to insulin resistance. Studies have also confirmed a direct correlation between resistin levels and T2DM. And it is waistline adipose tissue (central obesity) which seems to be the foremost type of fat deposits contributing to rising levels of serum resistin. Conversely, serum resistin levels have been found to decline with decreased adiposity following medical treatment.

Asthma

Developing asthma due to abdominal obesity is also a main concern. As a result of breathing at low lung volume, the muscles are tighter and the airway is narrower. Obesity causes decreased tidal volumes due to reduced in chest expansion that is caused both by the weight on the chest itself and the effect of abdominal obesity on flattening the diaphragms. It is commonly seen that people who are obese breathe quickly and often, while inhaling small volumes of air. People with obesity are also more likely to be hospitalized for asthma. A study has stated that 75% of patients treated for asthma in the emergency room were either overweight or obese.

Alzheimer's disease

Based on studies, it is evident that obesity has a strong association with vascular and metabolic disease which could potentially be linked to Alzheimer's disease. Recent studies have also shown an association between mid-life obesity and dementia, but the relationship between later life obesity and dementia is less clear. A study by Debette et al. (2010) examining over 700 adults found evidence to suggest higher volumes of visceral fat, regardless of overall weight, were associated with smaller brain volumes and increased risk of dementia. Alzheimer's disease and abdominal obesity has a strong correlation and with metabolic factors added in, the risk of developing Alzheimer's disease was even higher. Based on logistic regression analyses, it was found that obesity was associated with an almost 10-fold increase risk of Alzheimer's disease.

Other health risks

Central obesity can be a feature of lipodystrophies, a group of diseases that is either inherited, or due to secondary causes (often protease inhibitors, a group of medications against AIDS). Central obesity is a symptom of Cushing's syndrome and is also common in patients with polycystic ovary syndrome (PCOS). Central obesity is associated with glucose intolerance and dyslipidemia. Once dyslipidemia becomes a severe problem, an individual's abdominal cavity would generate elevated free fatty acid flux to the liver. The effect of abdominal adiposity occurs not just in those who are obese, but also affects people who are non-obese and it also contributes to insulin sensitivity.

Ghroubi et al. (2007) examined whether abdominal circumference is a more reliable indicator than BMI of the presence of knee osteoarthritis in obese patients. They found that it actually appears to be a factor linked with the presence of knee pain as well as osteoarthritis in obese study subjects. Ghroubi et al. (2007) concluded that a high abdominal circumference is associated with great functional repercussion.

Causes

Diet

See also: Diet and obesity

The currently prevalent belief is that the immediate cause of obesity is net energy imbalance—the organism consumes more usable calories than it expends, wastes, or discards through elimination. Some studies indicate that visceral adiposity, together with lipid dysregulation and decreased insulin sensitivity, is related to the excessive consumption of fructose. Some evidence shows that in regards to juveniles, when free fructose is present as children's fat cells mature, it makes more of these cells mature into fat cells in the abdominal region. It also caused both visceral fat and subcutaneous fat to be less sensitive to insulin. These effects were not attenuated when compared to similar glucose consumption.

Intake of trans fat from industrial oils has been associated with increased abdominal obesity in men and increased weight and waist circumference in women. These associations were not attenuated when fat intake and calorie intake was accounted for. Greater meat (processed meat, red meat, & poultry) consumption has also been positively associated with greater weight gain, and specifically abdominal obesity, even when accounting for calories. Conversely, studies suggest that oily fish consumption is negatively associated with total body fat and abdominal fat distribution even when body mass remains constant. Similarly, increased soy protein consumption is correlated with lower amounts of abdominal fat in postmenopausal women even when calorie consumption is controlled.

Numerous large studies have demonstrated that eating ultraprocessed food has a positive dose-dependent relationship with both abdominal obesity and general obesity in both men and women. Consuming a diet rich in unprocessed food and minimally processed food is linked with lower obesity risk, lower waist circumference and less chronic disease. These findings are consistent among American, Canadian, Latin American, British, Australian, French, Spaniard, South Korean, Chinese, and Sub-Saharan African populations.

Obesity plays an important role in the impairment of lipid and carbohydrate metabolism shown in high-carbohydrate diets. It has also been shown that quality protein intake during a 24-hour period and the number of times the essential amino acid threshold of approximately 10 g has been achieved is inversely related to the percentage of central abdominal fat. Quality protein uptake is defined as the ratio of essential amino acids to daily dietary protein.

Visceral fat cells will release their metabolic by-products in the portal circulation, where the blood leads straight to the liver. Thus, the excess of triglycerides and fatty acids created by the visceral fat cells will go into the liver and accumulate there. In the liver, most of it will be stored as fat. This concept is known as 'lipotoxicity'.

Alcohol consumption

A study has shown that alcohol consumption is directly associated with waist circumference and with a higher risk of abdominal obesity in men, but not in women. After controlling for energy under-reporting, which have slightly attenuated these associations, it was observed that increasing alcohol consumption significantly increased the risk of exceeding recommended energy intakes in male participants – but not in the small number of female participants (2.13%) with elevated alcohol consumption, even after establishing a lower number of drinks per day to characterize women as consuming a high quantity of alcohol. Further research is needed to determine whether a significant relationship between alcohol consumption and abdominal obesity exists among women who consume higher amounts of alcohol.

A systemic review and meta-analysis failed to find data pointing towards a dose-dependent relationship between beer intake and general obesity or abdominal obesity at low or moderate intake levels (under∼500 mL/day). However, high beer intake (above ∼4 L/wk) appeared to be associated with a higher degree of abdominal obesity specifically, particularly among men.

Other factors

Other environmental factors, such as maternal smoking, estrogenic compounds in the diet, and endocrine-disrupting chemicals may be important also.

Hypercortisolism, such as in Cushing's syndrome, also leads to central obesity. Many prescription drugs, such as dexamethasone and other steroids, can also have side effects resulting in central obesity, especially in the presence of elevated insulin levels.

The prevalence of abdominal obesity is increasing in Western populations, possibly due to a combination of low physical activity and high-calorie diets, and also in developing countries, where it is associated with the urbanization of populations.

Waist measurement (e.g., for BFP standard) is more prone to errors than measuring height and weight (e.g., for BMI standard). It is recommended to use both standards. BMI will illustrate the best estimate of one's total body fatness, while waist measurement gives an estimate of visceral fat and risk of obesity-related disease.

Diagnosis

Silhouettes and waist circumferences representing normal, overweight, and obese

There are various ways of measuring abdominal obesity including:

• Absolute waist circumference (>102 cm (40 in) in men and >88 cm (35 in) in women)
• Waist–hip ratio (the circumference of the waist divided by that of the hips of >0.9 for men and >0.85 for women)
• Waist-stature ratio (waist circumference divided by their height, >0.5 for adults under 40 and >0.6 for adults over 50)
• Sagittal Abdominal Diameter

Overweight teenage boy holding his excess abdominal fat.

In those with a body mass index (BMI) under 35, intra-abdominal body fat is related to negative health outcomes independent of total body fat. Intra-abdominal or visceral fat has a particularly strong correlation with cardiovascular disease.

BMI and waist measurements are well recognized ways to characterize obesity. However, waist measurements are not as accurate as BMI measurements. For this reason, it is recommended to use both methods of measurements.

An adult man with abdominal obesity.

While central obesity can be obvious just by looking at the naked body (see the picture), the severity of central obesity is determined by taking waist and hip measurements. The absolute waist circumference 102 centimetres (40 in) in men and 88 centimetres (35 in) in women and the waist-hip ratio (>0.9 for men and >0.85 for women) are both used as measures of central obesity. A differential diagnosis includes distinguishing central obesity from ascites and intestinal bloating. In the cohort of 15,000 people participating in the National Health and Nutrition Examination Survey (NHANES III), waist circumference explained obesity-related health risk better than BMI when metabolic syndrome was taken as an outcome measure and this difference was statistically significant. In other words, excessive waist circumference appears to be more of a risk factor for metabolic syndrome than BMI. Another measure of central obesity which has shown superiority to BMI in predicting cardiovascular disease risk is the Index of Central Obesity (waist-to-height ratio, WHtR), where a ratio of >=0.5 (i.e. a waist circumference at least half of the individual's height) is predictive of increased risk. Another diagnosis of obesity is the analysis of intra-abdominal fat having the most risk to one's personal health. The increased amount of fat in this region relates to the higher levels of plasma lipid and lipoproteins as per studies mentioned by Eric Poehlman (1998) review. An increasing acceptance of the importance of central obesity within the medical profession as an indicator of health risk has led to new developments in obesity diagnosis such as the Body Volume Index, which measures central obesity by measuring a person's body shape and their weight distribution. The effect of abdominal adiposity occurs not just in those who are obese, but also affects people who are non-obese and it also contributes to insulin sensitivity.

Index of central obesity

Index of Central Obesity (ICO) is the ratio of waist circumference and height first proposed by a Parikh et al. in 2007 as a better substitute to the widely used waist circumference in defining metabolic syndrome. The National Cholesterol Education Program Adult Treatment Panel III suggested cutoff of 102 cm (40 in) and 88 cm (35 in) for males and females as a marker of central obesity. The same was used in defining metabolic syndrome. Misra et al. suggested that these cutoffs are not applicable among Indians and the cutoffs be lowered to 90 cm (35 in) and 80 cm (31 in) for males and females. Various race specific cutoffs were suggested by different groups. The International Diabetes Federation defined central obesity based on these various race and gender specific cutoffs. The other limitation of waist circumference is that it the measurement procedure has not been standardized and in children there are no, or few, comparison standards or reference data.

Parikh et al. looked at the average heights of various races and suggested that by using ICO various race- and gender-specific cutoffs of waist circumference can be discarded. An ICO cutoff of 0.53 was suggested as a criterion to define central obesity. Parikh et al. further tested a modified definition of metabolic syndrome in which waist circumference was replaced with ICO in the National Health and Nutrition Examination Survey (NHANES) database and found the modified definition to be more specific and sensitive.

This parameter has been used in the study of metabolic syndrome and cardiovascular disease.

Central obesity in individuals with normal BMI is referred to as normal weight obesity.

Sex differences

50% of men and 70% of women in the United States between the ages of 50 and 79 years now exceed the waist circumference threshold for central obesity. 

When comparing the body fat of men and women it is seen that men have close to twice the visceral fat as that of pre-menopausal women.

Central obesity is positively associated with coronary heart disease risk in women and men. It has been hypothesized that the sex differences in fat distribution may explain the sex difference in coronary heart disease risk.

There are sex-dependent differences in regional fat distribution. In women, estrogen is believed to cause fat to be stored in the buttocks, thighs, and hips. When women reach menopause and the estrogen produced by ovaries declines, fat migrates from their buttocks, hips, and thighs to their belly.

Males are more susceptible to upper-body fat accumulation, most likely in the belly, due to sex hormone differences. Abdominal obesity in males is correlated with comparatively low testosterone levels. Testosterone administration significantly increased thigh muscle area, reduced subcutaneous fat deposition at all levels measured, but slightly increased the visceral fat area.

Even with the differences, at any given level of central obesity measured as waist circumference or waist to hip ratio, coronary artery disease rates are identical in men and women.

Management

A permanent routine of exercise, eating healthily, and, during periods of being overweight, consuming the same number or fewer calories than used will prevent and help fight obesity. A single pound of fat yields approximately 3500 calories of energy (32 000 kJ energy per kilogram of fat), and weight loss is achieved by reducing energy intake, or increasing energy expenditure, thus achieving a negative balance. Adjunctive therapies which may be prescribed by a physician are orlistat or sibutramine, although the latter has been associated with increased cardiovascular events and strokes and has been withdrawn from the market in the US, the UK, the EU, Australia, Canada, Hong Kong, and Thailand.

A 2006 study published in the International Journal of Sport Nutrition and Exercise Metabolism, suggests that combining cardiovascular (aerobic) exercise with resistance training is more effective than cardiovascular training alone in getting rid of abdominal fat. An additional benefit to exercising is that it reduces stress and insulin levels, which reduce the presence of cortisol, a hormone that leads to more belly fat deposits and leptin resistance.

Self-motivation by understanding the risks associated with abdominal obesity is widely regarded as being far more important than worries about cosmetics. In addition, understanding the health issues linked with abdominal obesity can help in the self-motivation process of losing the abdominal fat. As mentioned above, abdominal fat is linked with cardiovascular disease, diabetes, and cancer. Specifically it's the deepest layer of belly fat (the fat that cannot seen or grabbed) that poses health risks, as these "visceral" fat cells produce hormones that can affect health (e.g. increased insulin resistance and/or breast cancer risk). The risk increases considering the fact that they are located in the proximity or in between organs in the abdominal cavity. For example, fat next to the liver drains into it, causing a fatty liver, which is a risk factor for insulin resistance, setting the stage for type 2 diabetes. However, visceral fat is more responsive to the circulation of catecholamines.

In the presence of type 2 diabetes, the physician might instead prescribe metformin and thiazolidinediones (rosiglitazone or pioglitazone) as antidiabetic drugs rather than sulfonylurea derivatives. Thiazolidinediones may cause slight weight gain but decrease "pathologic" abdominal fat (visceral fat), and therefore may be prescribed for diabetics with central obesity. Thiazolidinedione has been associated with heart failure and increased cardiovascular risk; so it has been withdrawn from the market in Europe by EMA in 2010.

Low-fat diets may not be an effective long-term intervention for obesity: as Bacon and Aphramor wrote, "The majority of individuals regain virtually all of the weight that was lost during treatment." The Women's Health Initiative ("the largest and longest randomized, controlled dietary intervention clinical trial") found that long-term dietary intervention increased the waist circumference of both the intervention group and the control group, though the increase was smaller for the intervention group. The conclusion was that mean weight decreased significantly in the intervention group from baseline to year 1 by 2.2 kg (P<.001) and was 2.2 kg less than the control group change from baseline at year 1. This difference from baseline between control and intervention groups diminished over time, but a significant difference in weight was maintained through year 9, the end of the study.

Society and culture

Myths

There is a common misconception that spot exercise (that is, exercising a specific muscle or location of the body) most effectively burns fat at the desired location, but this is not the case. Spot exercise is beneficial for building specific muscles, but it has little effect, if any, on fat in that area of the body, or on the body's distribution of body fat. The same logic applies to sit-ups and belly fat. Sit-ups, crunches and other abdominal exercises are useful in building the abdominal muscles, but they have little effect, if any, on the adipose tissue located there.

Colloquialisms

A large central adiposity deposit has been assigned many common use names, including; "spare tire", "paunch", and "potbelly". Several colloquial terms used to refer to central obesity, and to people who have it, refer to beer drinking. However, there is little scientific evidence that beer drinkers are more prone to central obesity, despite its being known colloquially as "beer belly", "beer gut", or "beer pot". One of the few studies conducted on the subject did not find that beer drinkers are more prone to central obesity than nondrinkers or drinkers of wine or spirits. Chronic alcoholism can lead to cirrhosis, symptoms of which include gynecomastia (enlarged breasts) and ascites (abdominal fluid). These symptoms can suggest the appearance of central obesity.

Deposits of excess fat at the sides of one's waistline or obliques are commonly referred to as "love handles".

Economics

Researchers in Copenhagen examined the relationship between waist circumferences and costs among 31,840 subjects aged 50–64 years of age with different waist circumferences. Their study showed that an increase in just an additional centimetre above normal waistline caused a 1.25% and 2.08% rise in health care costs in women and men respectively. To put this in perspective, a woman with a waistline of 95 cm (approx 37.4 in) and without underlying health problems or co-morbidities can incur economic costs that are 22%, or US$397, higher per year than a woman with a normal waist circumference.