Why are local field potentials generally band-pass filtered?

Why are local field potentials generally band-pass filtered?

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I was wondering what the rationale was behind low-pass or band-pass filtering in local field potential measurements?

It seems to me that we could potentially filter out potentially valuable information by filtering procedures.

Is there a physical limitation for this that would not allow to measure, say, the responses in a frequency range of 0 to 5 kHz?

There is no physical limitation whatsoever on the frequency band you wish to record, other than the hardware limitations on the sampling rate.

Often electrophysiological recordings suffer from noise (mainly in the high-frequencies) and drifts in the baseline (low-frequency range).

In the end, you wish to filter out as much noise as possible, without throwing away the baby with the bathwater. In effect, prior knowledge about the frequency range of the responses of interest are vital. Anything outside that range can, and likely should be filtered out.

For example, FFT analysis of EEGs mainly focuses on bands limited to the frequency range of 1 to 50 Hz. The mains frequency is 50 or 60 Hz, often imposing sinusoidal noise when the room is not shielded. Hence, what reason would there be not to use a low-pass filter with a cutoff around 50 Hz to get rid of it?

Lastly, offline filtering methods are aplenty. My personal preference nowadays is, is to collect the raw data and filter offline. That way you have the baby and the water, and you can focus, with trial and error, on where the baby is and where the water.

Local field potentials reflect multiple spatial scales in V4

Local field potentials (LFP) reflect the properties of neuronal circuits or columns recorded in a volume around a microelectrode (Buzsáki et al., 2012). The extent of this integration volume has been a subject of some debate, with estimates ranging from a few hundred microns (Katzner et al., 2009 Xing et al., 2009) to several millimeters (Kreiman et al., 2006). We estimated receptive fields (RFs) of multi-unit activity (MUA) and LFPs at an intermediate level of visual processing, in area V4 of two macaques. The spatial structure of LFP receptive fields varied greatly as a function of time lag following stimulus onset, with the retinotopy of LFPs matching that of MUAs at a restricted set of time lags. A model-based analysis of the LFPs allowed us to recover two distinct stimulus-triggered components: an MUA-like retinotopic component that originated in a small volume around the microelectrodes (񾍐 μm), and a second component that was shared across the entire V4 region this second component had tuning properties unrelated to those of the MUAs. Our results suggest that the LFP reflects neural activity across multiple spatial scales, which both complicates its interpretation and offers new opportunities for investigating the large-scale structure of network processing.

Regularized Kalman filter for brain-computer interfaces using local field potential signals

Brain-computer interfaces (BCIs) seek to establish a direct connection from brain to computer, to use in applications such as motor prosthesis control, control of a cursor on the monitor, and so on. Hence, the accuracy of movement decoding from brain signals in BCIs is crucial. The Kalman filter (KF) is often used in BCI systems to decode neural activity and estimate kinetic and kinematic parameters. To use the KF, the state transition matrix, the observation matrix and the covariance matrices of the process and measurement noises must be known in advance, however, in many applications these matrices are not known. Typically, to estimate these parameters, the ordinary least squares method and the sample covariance matrix estimator are used. Our purpose is to enhance the decoding performance of the KF in BCI systems by improving the estimation of the mentioned parameters.

New Method

Here, we propose the Regularized Kalman Filter (RKF) which implements two fundamental features: 1) Regularizing the regression estimate of the state equation to improve the estimation of the state transition matrix, and 2) Use of shrinkage method to improve the estimation of the unknown measurement noise covariance matrix. We validated the performance of the proposed method using two datasets of local field potentials obtained from motor cortex of a monkey (Estimation of kinematic parameters during hand movement) and three rats (Estimation of the amount of force applied by hand as a kinetic parameter).


The results demonstrate that the proposed method outperforms the conventional KF, the KF with feature selection, the Partial least squares, and the Ridge regression approaches.


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

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

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. [4]

Bond stretching Edit

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

The bond stretching constant k i j > can be determined from the experimental Infrared spectrum, Raman spectrum, or high-level quantum mechanical calculations. The constant k i j > 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. [5]

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 Edit

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

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. [10] [11] [12] 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. [12] [4] 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.

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. [4] Many parameter sets are empirical and some force fields use extensive fitting terms that are difficult to assign a physical interpretation. [13] 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. [14] 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. [15] 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. [12] [16]

Force field parameterizations for simulations with maximum accuracy and transferability, e.g., IFF, follow a well-defined protocol. [4] 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, [17] hydration energy [18] ) relative to experimental reference data, (7) secondary validation and refinement (thermal, mechanical, and diffusion properties). [19] 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. [20] [6] [14] Inconsistencies can be overcome by interpretation of all force field parameters and choosing a consistent reference state, for example, room temperature and atmospheric pressure. [4]

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. [21] In these cases, large, random deviations of computed properties have been reported.

Methods Edit

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. [22] [23] [24] Recent examples include polarizable models with virtual electrons that reproduce image charges in metals [25] and polarizable biomolecular force fields. [26] 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%). [4] [27] In recent times, such models have been erroneously called "Drude Oscillator potentials". [28] An appropriate term for these models is "Lorentz oscillator models" since Lorentz [29] rather than Drude [30] proposed some form of attachment of electrons to nuclei. [25] Drude models assume unrestricted motion of the electrons, e.g., a free electron gas in metals. [30]

Parameterization Edit

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. [31] [32] [33] 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. [34] [35] 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. [4]

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. [19] In some cases, modifications can be made with minor effort, for example, between 9-6 Lennard-Jones potentials to 12-6 Lennard-Jones potentials. [9] 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.

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. [36] 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. [37] [38]

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. [39] The remedy is that point charges have a clear interpretation, [12] 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. [40] [41] [42] Electronic polarization of the environment may be better included by using polarizable force fields [43] [44] 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. [45]

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. [46] 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. [47] 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, [46] 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. [46] For example, "the interaction between hydrocarbons across water is about 10% of that across vacuum". [46] 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. [48] 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". [49] Force fields have been applied successfully for protein structure refinement in different X-ray crystallography and NMR spectroscopy applications, especially using program XPLOR. [50] 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 [51] (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. [52] Thereby also the development of parameters to tackle such large-scale problems requires new approaches. A specific problem area is homology modeling of proteins. [53] Meanwhile, alternative empirical scoring functions have been developed for ligand docking, [54] protein folding, [55] [56] [57] homology model refinement, [58] computational protein design, [59] [60] [61] and modeling of proteins in membranes. [62]

It was also argued that some protein force fields operate with energies that are irrelevant to protein folding or ligand binding. [43] 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. [63] [64] [65] 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. [46] 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, [66] [67] but the same energies estimated from sublimation enthalpy of molecular crystals were -4 to -6 kcal/mol, [68] 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. [43]

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). [69] [70] [71] [72] [73]

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. [74]

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) [75] 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. [4] [76] It is compatible with multiple force fields to simulate hybrid materials (CHARMM, AMBER, OPLS-AA, CFF, CVFF, GROMOS).

Classical Edit

    (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. (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. [77]
  • CVFF – also used broadly for small molecules and macromolecules. [14]
  • ECEPP [78] – first force field for polypeptide molecules - developed by F.A. Momany, H.A. Scheraga and colleagues. [79][80] (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. [81] 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 [4][75]
  • MMFF (Merck Molecular Force Field) – developed at Merck for a broad range of molecules. (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. [82][83]
  • 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. [21] 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. [5][76]

Polarizable Edit

  • AMBER – polarizable force field developed by Jim Caldwell and coworkers. [84]
  • 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). [85] AMOEBA force field is gradually moving to more physics-rich AMOEBA+. [86][87]
  • CHARMM – polarizable force field developed by S. Patel (University of Delaware) and C. L. Brooks III (University of Michigan). [26][88] Based on the classical Drude oscillator developed by A. MacKerell (University of Maryland, Baltimore) and B. Roux (University of Chicago). [89][90]
  • CFF/ind and ENZYMIX – The first polarizable force field [91] which has subsequently been used in many applications to biological systems. [44]
  • 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. [92] Atomic charge fluctuation is possible in each molecular dynamics step.
  • DRF90 developed by P. Th. van Duijnen and coworkers. [93]
  • IFF (Interface Force Field) – includes polarizability for metals (Au, W) and pi-conjugated molecules [25][42][41]
  • NEMO (Non-Empirical Molecular Orbital) – procedure developed by Gunnar Karlström and coworkers at Lund University (Sweden) [94]
  • 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. [95][96]
  • Polarizable Force Field (PFF) – developed by Richard A. Friesner and coworkers. [97]
  • SP-basis Chemical Potential Equalization (CPE) – approach developed by R. Chelli and P. Procacci. [98]
  • PHAST - polarizable potential developed by Chris Cioce and coworkers. [99]
  • ORIENT – procedure developed by Anthony J. Stone (Cambridge University) and coworkers. [100]
  • 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. [101][102][103]
  • 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. [104]
  • Polarizable procedure based on the Kim-Gordon approach developed by Jürg Hutter and coworkers (University of Zürich) [citation needed]
  • 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. [105]

Reactive Edit

  • 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. [according to whom?] The EVB facilitates calculating activation free energies in condensed phases and in enzymes. – 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. [13] Parallelized ReaxFF allows reactive simulations on >>1,000,000 atoms on large supercomputers.

Coarse-grained Edit

  • 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 [106][107] with later modifications by Español and Warren [108] The current state of the art was well documented in a CECAM workshop in 2008. [109] 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. [35] – a coarse-grained potential developed by Marrink and coworkers at the University of Groningen, initially developed for molecular dynamics simulations of lipids, [3] 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.
  • 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. [110]

Machine learning Edit

  • ANI is a transferable neural network potential, built from atomic environment vectors, and able to provide DFT accuracy in terms of energies. [111]
  • FFLUX (originally QCTFF) [112] 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. [113][114]
  • TensorMol, a mixed model, a Neural network provides a short-range potential, whilst more traditional potentials add screened long range terms. [114]
  • 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. [115]
  • SchNet a Neural network utilising continuous-filter convolutional layers, to predict chemical properties and potential energy surfaces. [116]
  • PhysNet is a Neural Network-based energy function to predict energies, forces and (fluctuating) partial charges. [117]

Water Edit

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, [118] SPC, flexible simple point charge water model (flexible SPC), ST2, and mW. [119] 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. [120]


Locomotor activity levels following pseudoephedrine and morphine treatments

The exploratory movements of animals were monitored by using a web-based camera. Patterns of ambulatory behavior were computed by using a tracking system (Fig. 4). The movement patterns of 4 representative animals, during a 60-90 min period, are shown. The effects of treatments were compared to the levels in mice treated with saline control. The results showed that morphine increased animal movements, whereas PSE did not appear to affect animal movements, at either 50 or 100 mg/kg body weight (BW). A one-way ANOVA also confirmed a significant increase in locomotor counts induced by morphine (F(3,35)=31.350, p<0.05) (Fig. 5). No significant difference in locomotor counts was observed following PSE treatments.

Fig. 4.

Monitoring locomotor activity following saline, 50 and 100 mg/kg pseudoephedrine, and 15 mg/kg morphine treatments. A web-based camera was used to record animal movement. The levels of animal movements were detected by a tracking system. Movements within a specific area of the recording chamber are represented by grayscale code.

Fig. 5.

Effects of morphine and pseudoephedrine treatments on locomotor activity levels. Locomotor counts were averaged and expressed as the mean ± S.E.M. The effects of treatment were determined using a one-way ANOVA, followed by multiple comparisons with the Student-Newman-Keuls post hoc test. n=9. *P≤0.05 compared with the control group.

Local field potential oscillations in the striatum following pseudoephedrine and morphine treatments

Following morphine or PSE treatments, the raw signals of local field potential oscillations were subjected to visual inspection. Brain waves from representative animals, under the four different treatment conditions, were compared (Fig. 6). The results showed that the brain waves from all animals contained both slow and fast activities within the raw signals. PSE treatment, at both 50 and 100 mg/kg BW, appeared to produce similar local field potential patterns as saline treatment. In contrast, differential signaling patterns were observed following 15 mg/kg BW morphine treatment, including additional fast activities, with gamma activity superimposed on basic slow-wave signals.

Fig. 6.

Raw LFP signals in the striatum, following saline, 50 and 100 mg/kg pseudoephedrine, and 15 mg/kg morphine treatments. Representative LFPs of 4 mice per treatment are displayed in the time-domain.

Raw signals were also expressed as spectrograms for inspection of frequency activities in time domain. Spectrograms of representative animals that received four different treatments were shown (Fig. 7). In comparison with the spectrogram for control animals, PSE-treated animals (both 50 and 100 mg/kg BW) appeared to show baseline levels of local field potentials. Relatively similar activities were observed for frequencies below 50 Hz. In contrast, dominant gamma frequency activity was observed following morphine treatment. Gamma activity clearly increased and ebbed within 3 h following morphine treatment.

Fig. 7.

Representative LFP spectrograms, displaying the dynamics of brain wave frequencies, for saline, 50 and 100 mg/kg pseudoephedrine, and morphine treatments. In spectrograms, the values of EEG powers are expressed as a grayscale of frequency against time.

Finally, frequency analyses of local field potentials during a 60-90 min period were focused to reveal the spectral powers in the frequency and time domains. Local field potentials were analyzed and expressed as percent total power every 30 mins (Fig. 8A-F). The results showed increases in the frequency ranges for low-gamma and high-gamma bands, starting from 0-30 min until 150-180 min. Therefore, data from all time periods were collected for statistical analyses. Significant differences in low-gamma and high-gamma powers were found during all examined periods, including 0-30 min [low-gamma (F(3,35)=7.487, p<0.05), high-gamma (F(3,35)=4.261, p<0.05)], 30-60 min [low-gamma (F(3,35)=11.662, p<0.05), high-gamma (F(3,35)=6.262, p<0.05)], 60-90 min [low-gamma (F(3,35)=6.401, p<0.05), high-gamma (F(3,35)=11.755, p<0.05)], 90-120 min [low-gamma (F(3,35)= 4.670, p<0.05), high-gamma (F(3,35)=5.292, p<0.05)], 120-150 min [low-gamma (F(3,35)=7.979, p<0.05), high-gamma (F(3,35)=10.503, p<0.05)], and 150-180 min [low-gamma (F(3,35)=5.709, p<0.05), high-gamma (F(3,35)=7.731, p<0.05)] (Fig. 9). Multiple comparisons also indicated that significant increases in low-gamma and high-gamma powers were only produced by morphine treatment. Neither the 50 nor 100 mg/kg BW PSE dose produced significant differences in power for these frequency bands. Moreover, the gamma powers of a wide frequency range of (35–100 Hz) were analyzed and expressed in the time domain. Gamma power was clearly increased by morphine but not by PSE treatment (Fig. 10A). Both the 50 and 100 mg/kg BW PSE treatment doses produced only baseline levels of gamma activity. Therefore, the averaged gamma powers during the 60–180 min period were statistically analyzed (Fig. 10B). A one-way ANOVA revealed that gamma activity was significantly increased only by the morphine treatment (F(3,35)=9.975, p<0.05). No significant effects on gamma activity were produced by PSE treatments.

Fig. 8.

Frequency analyses of striatal LFP oscillations. Spectral powers following saline, 50 and 100 mg/kg pseudoephedrine, and morphine treatments were analyzed every 30 mins and expressed as a percentage of total power in the frequency domain (A–F).

Fig. 9.

Effects of saline, 50 and 100 mg/kg pseudoephedrine, and 15 mg/kg morphine treatments on low- and high-gamma frequency waves. Data are expressed as the mean ± S.E.M. The effects of treatments were determined using a one-way ANOVA, followed by multiple comparisons (Student-Newman-Keuls post hoc test). n=10. * P≤0.05 compared with control levels.

Fig. 10.

Time-course analysis of the effects of 50 and 100 mg/kg pseudoephedrine and 15 mg/kg morphine treatments on gamma oscillations (35–100 Hz) in the striatum during a 3 h period. Values were normalized and expressed as a percent of total power (A). The inset values were calculated from the period of 60–180 min (B). Data are expressed as the mean ± S.E.M. The effects of treatments were determined by using a one-way ANOVA, followed by multiple comparisons (Student-Newman-Keuls post hoc test). n=9. * P≤0.05 compared with control levels.

Sleep-wakefulness following pseudoephedrine and morphine treatments

The effects of PSE and morphine treatments on sleep-wake patterns were analyzed. Data were scored and expressed as the total times of wake, NREM, and REM sleep (Fig. 11). One-way ANOVA revealed significant differences in the wake (F(2,17)=19.263, p<0.05), NREM (F(2,17)= 16.478, p<0.05), and REM (F(2,17)=7.369, p<0.05) sleep periods. Multiple comparisons also indicated that significant increases in the total time spent in all brain states were induced by morphine but not PSE.

Fig. 11.

Effects of 50 and 100 mg/kg pseudoephedrine and 15 mg/kg morphine treatments on sleep-wake cycles. The mean time spent in each brain state is shown. Sleep-wake data were analyzed from EEG signals recorded for 3 h following treatment. Data are expressed as the mean ± S.E.M. The effects of treatment were determined by using a one-way ANOVA, followed by multiple comparisons (Student-Newman-Keuls post hoc test). n=9. * P≤0.05 compared with control levels.

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.

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Altogether, the present findings demonstrated clear evidence of the psychostimulatory effects produced by morphine but found no similar effects for PSE. Previous studies have reported that cellular activity in the striatum was induced by PSE treatment. However, the present study confirmed that CNS activities induced by PSE have no detectable output at the levels of locomotor activity and local field potential oscillations in the striatum following acute treatment. Further studies might be necessary to examine the chronic effects of PSE on oscillations in the basal ganglia and locomotion compared with the levels produced by standard stimulant drugs. At this stage, these data support the use of PSE for the acute treatment of occasional nasal congestion. The continuous use of PSE for chronic diseases, such as allergic rhinitis or allergic with asthma, may not be recommended.


Historically, the mammalian neocortex has been viewed as the pinnacle of brain evolution. The highly structured six-layered laminar cytoarchitecture of the neocortex and the associated computational properties contributing to complex cognition added to this view. However, exactly how laminar cytoarchitecture and associated neurophysiological processes mediate complex cognition remains poorly understood. Our understanding of how the neocortex works can be informed by comparisons with other animals. Notably, comparisons with non-mammalian groups lacking laminar cytoarchitecture, as is the case in birds, can be used to isolate traits that depend upon laminar cytoarchitecture from those that do not. In this study, we use this comparative approach to gain insight into the neocortex by examining sleep-related neuronal activity in the avian brain.

A growing body of research suggests that the brain rhythms occurring during sleep are involved in processing information acquired during wakefulness [1]. Notably, the slow (typically <1 Hz) oscillation of neocortical neuronal membrane potentials between a depolarized “up-state” with action potentials, and a hyperpolarized “down-state” with neuronal quiescence occurring during non-rapid eye movement (NREM) sleep and some types of anesthesia is the focus of several hypotheses for the function of sleep [2–4]. The term ‘slow-oscillation’ is in wide-spread use even though the interval between down-states is variable and individual cycles of the slow-oscillation originate from different neocortical locations [5–8]. Slow-oscillations manifest in electroencephalogram (EEG) or local field potential (LFP) recordings as high-amplitude, slow-waves that propagate across the mammalian neocortex as traveling waves [5, 7–15], raising the possibility that they are involved in processing spatially distributed information [1, 16] via processes such as spike timing-dependent plasticity [17]. However, it remains unknown whether the traveling nature of slow-oscillations reflects a feature unique to the laminar cytoarchitecture and associated computational properties of the neocortex [18] or a more general aspect of sleep-related neuronal activity.

To distinguish between these alternatives, we studied brain activity in birds, the only non-mammalian group known to exhibit slow-oscillations [19] and associated EEG slow-waves comparable to those observed in mammals during NREM sleep [20, 21]. This similarity between mammals and birds is particularly interesting because unlike the laminar mammalian neocortex, neurons in the avian forebrain are arranged in a largely nuclear manner [22]. Specifically, the hyperpallium, a region developmentally homologous and functionally similar to the mammalian primary visual and somatosensory/motor cortices [23, 24], lacks the laminar arrangement of neurons, including pyramidal neurons with long trans-layer apical dendrites found in the six-layered mammalian neocortex and in the three-layered dorsal cortex of the closest living reptilian relatives to birds [24]. Instead, the hyperpallium is composed of long flat nuclei stacked one on top of the other running along the dorsal-medial-anterior surface of the brain, each of which is composed of stellate neurons with short spiny dendrites and axonal projections within and between nuclei [24, 25]. Interestingly, this cytoarchitecture is even found within high-order association regions in the avian brain (that is, mesopallium and nidopallium) involved in orchestrating complex cognitive tasks, in some cases comparable to those performed by primates [26].

We recorded intracerebral potentials in the zebra finch (Taeniopygia guttata) hyperpallium and nidopallium to evaluate whether traveling slow-waves are unique to mammals, or are shared with birds irrespective of fundamental differences in cytoarchitectonic organization.


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Band-pass and band-stop filters

Note that filters do not remove all of the energy outside of their pass band (the pass band is the frequencies between X and Y for a band pass filter, and below X and above Y for a band stop filter). Generally, the further away from the cut off frequencies (X and Y), the greater the attenuation of the energy. How fast the attenuation increases as a function of frequency is established by parameters (primarily “Q”) of the filter. Real filters will also attenuate within the pass band, and there are some tradeoffs in the selection of parameters.

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