3.3.1. Embedded Model Accuracy

We analysed the similarity of the outputs from the Keras model and those from its C-compiled version. For this purpose, we assessed the differences on the inference outputs of the models. This was obtained by calculating the relative L2 error:

$$\varepsilon = \frac{||F\_{\text{generated}} - F\_{\text{original}}||}{||F\_{\text{generated}}||},\tag{5}$$

where *Fgenerated* is the flattened array of the generated model last output layer and *Foriginal* the flattened array of the original model. In other words, we compare the reliability results returned by the last layer of the two model implementations, prior to classification.

Results for each model are presented in Table 3. We showed the results when each C-compiled model was compressed to occupy less flash memory in the microcontroller. Compression is carried out using a weight sharing-based algorithm. A clustering technique (K-means) is used to calculate values centroids for the layer weights and bias. The compression with factor x4 uses 256 centroids codified on 8 bits, while the compression with factor x8 uses 16 centroids codified on 4bits. In most of the models the L2 error was very low, under 6.8 × 10−7, which implies the C-compiled models maintain a very close classification behaviour. It should be noted that, for the models with the highest number of nodes in the hidden layer, their more compressed version provides reliability values relatively further from the corresponding model in Keras. Increasing the complexity of the hidden, fully connected layer may have caused this effect. The results obtained may also have been influenced as a consequence of the ov-erfitting effect mentioned above, which could imply an improvement in effectiveness, due to the fact that specific features to classify particular cases of the training set could be forgotten. This may have occurred with the four hidden node compressed model, which has improved its accuracy over the original Keras model. However, the best results continue to be found with the model with three nodes in the hidden layer, obtaining an L2 lower than 1.0 × 10−8.

**Table 3.** L2 error for each model (trained model vs. generated c-model) with different compression factors.


**3.2 Computational approaches**

20 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

There were attempts to relate order parameters to structural characteristics of proteins and ligand-protein complexes. It was observed that amino acids with smaller side chains tend to show – intuitively - greater backbone flexibility than those with bulkier side chains (Goodman *et al.*, 2000). However, the variation of backbone amide 2 *S* parameters is larger than the differences between the averages for different amino acid types. Backbone amide order parameters are also only weakly affected by secondary structure elements, with loops having only slightly smaller average 2 *S* N-H values than helices or beta-turns (Kay et al., 1989). Backbone 2 *S* N-H values can be predicted from structures using a simple model that takes account of local contacts to the N-H and C=O atoms of each peptide group (Zhang and

A more sophisticated model for predicting dynamics from structure has recently been reported (tCONCOORD) (Seeliger *et al.*, 2007). tCONCOORD allows for a fast and efficient sampling of protein's conformational degrees of freedom based on geometrical restraints. Weak correlation between side chain order parameters and contact distance between the methyl carbon and neighboring atoms, with solvent exposure (Ming and Brüschweiler, 2004), and amino acid sequence conservation patterns (Mittermaier *et al.*, 2003) have been reported in literature. These results demonstrate that protein dynamics are strongly affected by the unique architecture of the protein as well as the environment. Thus, it cannot be readily predicted by the bioinformatic techniques, based on the primary/secondary sequence analysis. Developing a fast and reliable method of assessment of protein dynamics is, nevertheless, crucial for predictions of ligand-protein interactions - as it will be shown in the course of this chapter, dynamics affects all stages of molecular recognition events.

Order parameters can be related to entropy through the relationship developed by Yang and Kay (1996). This formalism quantifies the conformational entropy associated with observable protein motions by means of a specific motion model. For a wide range of motion models, the functional dependence of entropy on the 2 *S* parameter was demonstrated to be similar (Yang and Kay, 1996). This suggests that changes in 2 *S* can be related to the conformational entropy change in a model-independent manner. This approach has many advantages: it is straightforward, relatively free of assumptions (the requirement is that the internal motions are uncorrelated with the global tumbling of the macromolecule), and applicable to both NMR experiments and theoretical approaches (MD simulations). Moreover, since 2 *S* parameters are measured per bond vector, this approach enables site-specific reporting of any loses, gains, and redistributions of conformational

However, the model-free formalism can give only a qualitative view of micro-to-millisecond time scale motions. Failure to correctly account for anisotropic molecular tumbling and the assumption that all motions are un-correlated seriously compromises the usefulness of this approach for studying dynamics associated with large conformational changes or concerted motions. Because of the time scales, alternative approaches must be implemented to study

As described, ITC obtains free energy as the global parameter, thus, effects like ligandinduced conformational changes, domain-swapping, or protein oligomerisation, which

*G* , will not be resolved. In order to assess the role those factors

entropy through different dynamic states of the ligand-protein complex.

motions occurring at a millisecond time scale (e.g. R2 relaxation dispersion).

**3.1.3 Combination of ITC and NMR**

contribute to the overall

Brüschweiler, 2002).

Computational approaches to ligand-protein interaction studies have great potential and the development of various methods, briefly described in this chapter, have been truly outstanding. However, every method – computational, experimental alike - has its limitations and computational methods should not be used in a 'black box' manner; one should beware of the 'Garbage In Garbage Out' phenomenon. Yet it is evident that theoretical approaches have finally come to the stage that makes rational molecular design truly rational.

During a binding event, the ligand may bind in multiple orientations. The conformation of either of the interacting partners can change significantly upon association. The network of intramolecular interactions (e.g. hydrogen bonds, salt bridges) can dramatically change (breaking and/or creating new contacts), and new intermolecular interactions occur. Water molecules and ions can be expelled upon binding, or – on the contrary – bind more tightly. Finally, conformational or solvation entropic contributions may play significant role, affecting the free energy in a way which is difficult to predict.

Growing amount of calorimetric data available allows the investigation of the thermodynamic profiles for many ligand-protein complexes in detail. When structural data (crystal, NMR) are available as well – and often it is the case - it is very appealing to speculate about the link between the structure of the complex and the thermodynamics of the binding event. However, such speculations are challenging. It is important to bear in mind that both enthalpic and entropic contributions to the free energy terms obtained from ITC experiments are global parameters, containing a mixture of different contributions, which can have either equal or opposing signs and different magnitudes. This may lead to various thermodynamic signatures of a binding event. Moreover, 'structural' interpretation of intrinsic entropic contributions is notoriously difficult. Hence, the experimental thermodynamic data cannot be easily interpreted on the basis of structural information alone. Last but not least, the contribution from the solvation effects is difficult to get insight into, and although direct experimental estimations of solvation free energy have been attempted, these always require additional assumptions (Homans, 2007, Shimokhina *et al.*, 2006).

No doubt, a great advantage of theoretical approaches lies with gaining an insight about each of those contributions and their de-convolution. Binding events (ligand-protein

(Klepeis *et al.*, 2009 and references therein). MD methods rely on quality of the force field (parameters, inclusion of non-additive effects, etc), description of solvent effects, adequate sampling, and quality of initial structures used for the simulations. The quality of the results relies also on the duration of the simulation. There are limits on the time scales at which the system of interest can be considered. Simulation runs are fairly short: typically nanoseconds to microseconds, rarely extending to miliseconds, if super-fast computers are employed. Since biological processes (ligand-protein binding, large conformational changes, etc) typically occur ar micro-to-milisecond scales, one needs to assess whether or not a simulation has reached equilibrium before the averages calculated can be trusted. Furthermore, the averages obtained need to be subjected to a statistical analysis, to make an

MD methods have been widely employed to study ligand-protein binding phenomena, conformational changes, solvent effects, and to assess individual contributions to the binding free energy. These methods are particularly useful in assessing the conformational entropic contribution to the free energy. Information about ps-to-ns time scale molecular motions can be readily obtained from the MD simulation trajectory and analysed either through diagonalisation of the covariance matrix of displacements of atomic Cartesian coordinates - quasi-harmonic analysis, Schlitter's approach (7,8), analysed through principal component analysis (PCA), or quantified NMR-like via generalised order parameters. Entropy changes can be estimated from the MD trajectory through Yang and Kay's relationship (9). The order parameter analysis has the advantage of being able to calculate order parameters by-vector, thus providing site-specific information on flexibility and hence intrinsic entropic contribution. Computed parameters can be also directly compared to the experimental results of NMR relaxation analysis (Best and Vendruscolo, 2004). In last few years several studies proved the success of this methodology in estimating of entropic

> 1 ' lndet 2

*B k Te SS k*

chemical/molecular mechanical (QM/MM) (Senn and Thiel, 2009) methods.

2 22 2 2 22 3 1 222 222

MD-based approaches used for binding thermodynamics calculations include free energy perturbation (FEP) (Foloppe and Hubbard, 2006), thermodynamic integration (TI) (Straatsma and Berendsen, 1988), lambda-dynamics simulations (Knight and Brooks, 2009), Molecular Mechanics-Poisson-Boltzmann Surface Area (MM-PBSA) (Gilson and Zhou, 2007), Linear Interaction Energy (LIE) (Gilson and Zhou, 2007), and hybrid quantum

Free energy perturbation (FEP) is used to calculate free energy differences between two states from MD simulations. These two states can represent, for instance, unbound (apo) protein and a ligand-protein complex (holo), or two ligand-protein complexes with different ligands. In the framework of FEP, the difference in the free energy difference for two states

2 2

2 2 *S x y z xy yz yz* (9)

*ij i i j j xxx x* (8)

(7)

*B*

**1 M**

estimate of the errors.

contributions to the binding thermodynamics.

is obtained from the Zwanzig equation (10).

binding pose and the strength of their interactions) can be predicted by molecular docking, albeit intrinsic entropic contributions and solvation effects are usually ignored. Dynamic behaviour of proteins and ligands can be studied using extensive molecular dynamics (MD) simulation, which, combined with experimental NMR and ITC data, provide extremely valuable information on configurational entropy changes upon binding event, and hence about the intrinsic entropic contribution to the free energy. The global free energy changes can be studied by free energy perturbation (FEP) calculations, or related methods, such as thermodynamic integration (TI). Molecular docking methods allow for a quick assessment of enthalpic contributions, while solvent effects can be studied either by quantum chemical (QM) calculations (e.g. COSMO model), hybrid QM/MM schemes, or FEP-related methods.

Theoretical approaches allow also for investigations of transient phenomena, e.g. shortliving alternative conformers from an ensemble that contribute to the binding event but which cannot be readily observed. In a situation – which is not uncommon – when an experimental structure of the protein target or a part of it is missing (such as in cases of most G-protein-coupled receptors), computational approaches allow the generation of such structures (e.g. by homology modelling, threading, or *ab initio* predictions) and its use for predictions which can be validated experimentally, despite of the absence of protein structural data. Therefore, usage of theoretical methods is indispensable – not only for the interpretation of the existing experimental data, but also to direct and design new experiments.

Because of space limitations, only two theoretical methods, which are the most relevant for thermodynamics of molecular binding events, will be briefly discussed: MD-related methods (which includes MD simulations, FEP-like approaches, methods which use MD algorithms with enhanced sampling, and hybrid QM/MM schemes), and quantum chemical (QM) calculations. This division is not strict and many of these methods overlap, e.g. QM/MM methods use both MD simulations and QM calculations, and FEP-like methods have many flavours, including hybrid QM/MM-FEP.

#### **3.2.1 Molecular Dynamics (MD) simulations**

Molecular dynamics (MD) simulation consists of the numerical solution of the Newton's equations of motion of a system (e.g. protein, or a ligand-protein complex in water environment). The potential energy of the particle system is described by a function called force field (6). The potential energy of the system (U) is described as a sum of energy terms for covalent bonds, angles, dihedral angles, a van der Waals non-bonded term, and a nonbonded electrostatic term (Cornell *et al.*, 1995). Since the kinetic energy is also taken into account, the system is able to move across the energy barriers on the potential energy surface, which implies substantial changes (e.g. conformational) during the simulation.

$$\begin{split} \mathcal{U} &= \sum\_{\text{bonds}} k\_r \left( r - r\_0 \right)^2 + \sum\_{\text{angles}} k\_\theta \left( \theta - \theta\_0 \right)^2 + \sum\_{\text{dihedrals}} k \phi \left[ 1 + \cos \left( n \phi + \phi\_0 \right) \right] \\ &+ \sum\_{\text{atom } i} \sum\_{j \neq i} 4 \varepsilon\_{i,j} \left[ \left( \frac{\sigma\_{i,j}}{r\_{i,j}} \right)^{12} - \left( \frac{\sigma\_{i,j}}{r\_{i,j}} \right)^6 \right] + \sum\_i \sum\_{j \neq i} \frac{q\_i q\_j}{\varepsilon\_0 r\_{i,j}} \end{split} \tag{6}$$

The principles of MD simulations, algorithms used, and different types of force fields applied (all-atom, united atom, coarse-grain, etc) have been described in many publications

binding pose and the strength of their interactions) can be predicted by molecular docking, albeit intrinsic entropic contributions and solvation effects are usually ignored. Dynamic behaviour of proteins and ligands can be studied using extensive molecular dynamics (MD) simulation, which, combined with experimental NMR and ITC data, provide extremely valuable information on configurational entropy changes upon binding event, and hence about the intrinsic entropic contribution to the free energy. The global free energy changes can be studied by free energy perturbation (FEP) calculations, or related methods, such as thermodynamic integration (TI). Molecular docking methods allow for a quick assessment of enthalpic contributions, while solvent effects can be studied either by quantum chemical (QM) calculations (e.g. COSMO model), hybrid QM/MM schemes, or FEP-related methods. Theoretical approaches allow also for investigations of transient phenomena, e.g. shortliving alternative conformers from an ensemble that contribute to the binding event but which cannot be readily observed. In a situation – which is not uncommon – when an experimental structure of the protein target or a part of it is missing (such as in cases of most G-protein-coupled receptors), computational approaches allow the generation of such structures (e.g. by homology modelling, threading, or *ab initio* predictions) and its use for predictions which can be validated experimentally, despite of the absence of protein structural data. Therefore, usage of theoretical methods is indispensable – not only for the interpretation of the existing experimental data, but also to direct and design new

Because of space limitations, only two theoretical methods, which are the most relevant for thermodynamics of molecular binding events, will be briefly discussed: MD-related methods (which includes MD simulations, FEP-like approaches, methods which use MD algorithms with enhanced sampling, and hybrid QM/MM schemes), and quantum chemical (QM) calculations. This division is not strict and many of these methods overlap, e.g. QM/MM methods use both MD simulations and QM calculations, and FEP-like methods

Molecular dynamics (MD) simulation consists of the numerical solution of the Newton's equations of motion of a system (e.g. protein, or a ligand-protein complex in water environment). The potential energy of the particle system is described by a function called force field (6). The potential energy of the system (U) is described as a sum of energy terms for covalent bonds, angles, dihedral angles, a van der Waals non-bonded term, and a nonbonded electrostatic term (Cornell *et al.*, 1995). Since the kinetic energy is also taken into account, the system is able to move across the energy barriers on the potential energy surface, which implies substantial changes (e.g. conformational) during the simulation.

> 2 2 0 0 0

The principles of MD simulations, algorithms used, and different types of force fields applied (all-atom, united atom, coarse-grain, etc) have been described in many publications

*q q*

  1 cos

(6)

bonds angles dihedrals 12 6 , ,

*ij i ij ij i ji i j*

*ij ij i j*

*rr r*

*U krr k k n*

atom ,, 0 ,

have many flavours, including hybrid QM/MM-FEP.

**3.2.1 Molecular Dynamics (MD) simulations**

,

*i j*

4

*r*

experiments.

(Klepeis *et al.*, 2009 and references therein). MD methods rely on quality of the force field (parameters, inclusion of non-additive effects, etc), description of solvent effects, adequate sampling, and quality of initial structures used for the simulations. The quality of the results relies also on the duration of the simulation. There are limits on the time scales at which the system of interest can be considered. Simulation runs are fairly short: typically nanoseconds to microseconds, rarely extending to miliseconds, if super-fast computers are employed. Since biological processes (ligand-protein binding, large conformational changes, etc) typically occur ar micro-to-milisecond scales, one needs to assess whether or not a simulation has reached equilibrium before the averages calculated can be trusted. Furthermore, the averages obtained need to be subjected to a statistical analysis, to make an estimate of the errors.

MD methods have been widely employed to study ligand-protein binding phenomena, conformational changes, solvent effects, and to assess individual contributions to the binding free energy. These methods are particularly useful in assessing the conformational entropic contribution to the free energy. Information about ps-to-ns time scale molecular motions can be readily obtained from the MD simulation trajectory and analysed either through diagonalisation of the covariance matrix of displacements of atomic Cartesian coordinates - quasi-harmonic analysis, Schlitter's approach (7,8), analysed through principal component analysis (PCA), or quantified NMR-like via generalised order parameters. Entropy changes can be estimated from the MD trajectory through Yang and Kay's relationship (9). The order parameter analysis has the advantage of being able to calculate order parameters by-vector, thus providing site-specific information on flexibility and hence intrinsic entropic contribution. Computed parameters can be also directly compared to the experimental results of NMR relaxation analysis (Best and Vendruscolo, 2004). In last few years several studies proved the success of this methodology in estimating of entropic contributions to the binding thermodynamics.

$$S < S' = \frac{1}{2} k\_B \ln \det \left[ \mathbf{1} + \frac{k\_B T e^2}{\hbar^2} \mathbf{M} \sigma \right] \tag{7}$$

$$
\sigma\_{ij} = \left\langle \left( \mathbf{x}\_i - \left\langle \mathbf{x}\_i \right\rangle \right) \left( \mathbf{x}\_j - \left\langle \mathbf{x}\_j \right\rangle \right) \right\rangle \tag{8}
$$

$$S^2 = \frac{3}{2} \left[ \left< \mathbf{x}^2 \right>^2 + \left< y^2 \right>^2 + \left< z^2 \right>^2 + 2\left< xy \right>^2 + 2\left< yz \right>^2 + 2\left< yz \right>^2 \right] - \frac{1}{2} \tag{9}$$

MD-based approaches used for binding thermodynamics calculations include free energy perturbation (FEP) (Foloppe and Hubbard, 2006), thermodynamic integration (TI) (Straatsma and Berendsen, 1988), lambda-dynamics simulations (Knight and Brooks, 2009), Molecular Mechanics-Poisson-Boltzmann Surface Area (MM-PBSA) (Gilson and Zhou, 2007), Linear Interaction Energy (LIE) (Gilson and Zhou, 2007), and hybrid quantum chemical/molecular mechanical (QM/MM) (Senn and Thiel, 2009) methods.

Free energy perturbation (FEP) is used to calculate free energy differences between two states from MD simulations. These two states can represent, for instance, unbound (apo) protein and a ligand-protein complex (holo), or two ligand-protein complexes with different ligands. In the framework of FEP, the difference in the free energy difference for two states is obtained from the Zwanzig equation (10).

Ligand-protein interactions can be driven by quantum effects. These include charge transfer, halogen bonds, or polarisation. Stabilisation energy related to charge transfer can be several

'Conventional' QM calculations, using HF, DFT, or semi-empirical methods provide a way to obtain the ground state energy of a ligand-protein system or a part of it. Most programs based on these are capable of studying molecular properties such as atomic charges, multipole moments, vibrational frequencies, and spectroscopic constants. In addition, there are methods allowing the study of excited-state processes, such as time-dependent DFT or

The application area of QM methods is vast. QM calculations are used for charge derivation for molecular dynamics simulations, for description of direct interactions (hydrogen bonds, halogen bonds, aromatic stacking), for calculations of pKa, protonation, redox states, and for

Derivation of accurate charges for a system being studied is an important step in preparation for MD simulation. Failure in charge representation will inevitably lead to incorrect results. Derivation of charges is done using QM calculations, usually in several steps, involving optimisation, electrostatic potential generation, and fitting charges into atoms. RESP methodology, based on charges derived from *ab initio* HF/6-31G\* level of theory has been for many years a standard in deriving charges for MD simulations (Bayly *et*

Charge distribution is also required for the calculation of the solvation properties using conductor-like screening model (COSMO) (Klamt and Schüürmann, 1993). COSMO, just like any other continuum solvent approach, approximates the solvent by a dielectric continuum, surrounding the solute molecules outside of a molecular cavity. In COSMO, the polarisation charges of the continuum, caused by the polarity of the solute molecule, is derived from a scaled-conductor approximation (hence the name). In this way, the charge distribution of the molecule, which can be obtained from the QM calculations, and the energy of the

QM calculations are also used for force field development, such as adding new parameters and incorporating non-additive effects. Several studies indicate that non-additive effects (.e.g. electronic polarisation) significantly affect binding affinities of many ligands (Ji and Zhang, 2008, 2009 and references therein). Electrostatic interactions are critically dependent on charge distribution around both interacting species, and this distribution is heavily dependent on the conformation (geometry) of the complex. Description of hydrogen bonding is also affected by electronic polarisation – some hydrogen bonds, which are found broken during MD simulation using 'conventional' force fields are found to be stable, when non-additive force field is used (Ji and Zhang, 2009). Corrections for polarisation can be added to MD force fields in order to derive protein charges more accurately and provide a better description of electrostatic interactions. Protein polarisation is important for stabilisation of the native structures of proteins. MD simulations indicate that inclusion of polarisation effects not only improves the description of protein native structures, but also distinguishes native from decoy dynamically: the former are more stable than the latter under the polarised force fields. These observations provide strong evidence that inclusion of polarisation effects in calculations of ligand-protein interactions is likely to greatly

kcal/mol and force field-based schemes cannot describe this stabilisation correctly.

**3.2.2 Quantum mechanical (QM) calculations**

*al.*, 1993, Cieplak *et al.*, 1995, Cornell *et al*., 1993).

improve accuracy of such calculations.

restricted open-shell Kohn-Sham (ROKS) (Li and Liu, 2010).

studying solvation effects, such as computing free solvation energies.

interaction between the solvent and the solute molecule can be determined.

$$
\Delta G \left( A \to B \right) = G\_B - G\_A = -k\_B T \ln \left\langle \exp \left( -\frac{E\_B - E\_A}{k\_B T} \right) \right\rangle\_A \tag{10}
$$

where A and B represent two states (e.g. apo and holo protein), G is the difference between free energies of both states, *Bk* is the Boltzmann's constant, T is the temperature, and the triangular brackets denote an average over a simulation run for state A.

FEP calculations converge properly only when the difference between these two states is small enough; therefore it is usually necessary to divide a perturbation into a series of smaller 'steps', which are calculated independently.

Thermodynamic integration (TI) is a related method to calculate free energy differences. Since the free energy can be expressed by its relation to the canonical partition function, the free energy difference in two different states can be used to calculate the difference of potential energy. TI calculations are usually executed by designing a thermodynamic cycle (Figure 1), and integrating along the relevant path. The path can be either a real chemical process or an artificial change (e.g. substitution of a methyl group by hydrogen atom).

The MD methods, despite their numerous successes, suffer of two major bottlenecks. One is the results are critically dependent on the force field used, therefore requires caution when use of appropriate force field and parameters. Many modern force fields are parametrised on experimental NMR data, some are able to include – to some extent – non-additive effects (electronic polarisation). Application of QM/MM schemes allow the inclusion of quantum effects to some extent. Another bottleneck is related to the adequacy of sampling. It is known that – due to relatively short time scales investigated – only some subsets of potential conformational changes can be observed, and often the system gets 'stuck' in a minimum, which does not have to be the global one. This makes the results heavily biased towards the starting structure and is very likely to underestimate the degree of molecular motions observed in the system. Prolonging the simulation time helps to solve the sampling problem only to some extent, and significantly increases the computational cost of MD simulations. Thus, in order to overcome the sampling issue, various enhanced sampling techniques have been employed. One of such methods, frequently used, is replica exchange MD (REMD), which attempts to overcome the problem of multiple-minima by exchanging temperatures of several replicas of the system. These replicas are non-interacting with each other and they run at different temperatures. REMD is also called "parallel tempering" (Earl and Deem, 2005). Another approach used to improve sampling is to construct the bias potential and add it to the potential energy function of the system (force field). This group of methods, referred to as umbrella sampling methods, consist of metadynamics (Laio and Gervasio, 2008), conformational flooding, and accelerated dynamics (Lange et al., 2006). The core feature of metadynamics is the construction of so-called reference potential, which is one that is the most similar to the actual potential. That is, repulsive markers are placed in a coarse time line in a space that is spanned by a small number of relevant collective variables. These markers are then placed on top of the underlying free energy landscape in order to push the system to rapidly accumulate in the initial basin by discouraging it from revisiting points in configurational space. In this way, the system is allowed to escape the lowest transition state as soon as the growing biasing potential and the underlying free energy well exactly counterbalance each other, effectively allowing the simulation to escape free energy minima.

### **3.2.2 Quantum mechanical (QM) calculations**

24 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

where A and B represent two states (e.g. apo and holo protein), G is the difference between free energies of both states, *Bk* is the Boltzmann's constant, T is the temperature, and the

FEP calculations converge properly only when the difference between these two states is small enough; therefore it is usually necessary to divide a perturbation into a series of

Thermodynamic integration (TI) is a related method to calculate free energy differences. Since the free energy can be expressed by its relation to the canonical partition function, the free energy difference in two different states can be used to calculate the difference of potential energy. TI calculations are usually executed by designing a thermodynamic cycle (Figure 1), and integrating along the relevant path. The path can be either a real chemical process or an artificial change (e.g. substitution of a methyl group by hydrogen atom). The MD methods, despite their numerous successes, suffer of two major bottlenecks. One is the results are critically dependent on the force field used, therefore requires caution when use of appropriate force field and parameters. Many modern force fields are parametrised on experimental NMR data, some are able to include – to some extent – non-additive effects (electronic polarisation). Application of QM/MM schemes allow the inclusion of quantum effects to some extent. Another bottleneck is related to the adequacy of sampling. It is known that – due to relatively short time scales investigated – only some subsets of potential conformational changes can be observed, and often the system gets 'stuck' in a minimum, which does not have to be the global one. This makes the results heavily biased towards the starting structure and is very likely to underestimate the degree of molecular motions observed in the system. Prolonging the simulation time helps to solve the sampling problem only to some extent, and significantly increases the computational cost of MD simulations. Thus, in order to overcome the sampling issue, various enhanced sampling techniques have been employed. One of such methods, frequently used, is replica exchange MD (REMD), which attempts to overcome the problem of multiple-minima by exchanging temperatures of several replicas of the system. These replicas are non-interacting with each other and they run at different temperatures. REMD is also called "parallel tempering" (Earl and Deem, 2005). Another approach used to improve sampling is to construct the bias potential and add it to the potential energy function of the system (force field). This group of methods, referred to as umbrella sampling methods, consist of metadynamics (Laio and Gervasio, 2008), conformational flooding, and accelerated dynamics (Lange et al., 2006). The core feature of metadynamics is the construction of so-called reference potential, which is one that is the most similar to the actual potential. That is, repulsive markers are placed in a coarse time line in a space that is spanned by a small number of relevant collective variables. These markers are then placed on top of the underlying free energy landscape in order to push the system to rapidly accumulate in the initial basin by discouraging it from revisiting points in configurational space. In this way, the system is allowed to escape the lowest transition state as soon as the growing biasing potential and the underlying free energy well exactly counterbalance each other, effectively allowing the simulation to escape free energy

*kBT*

*A* (10)

*G A B GB GA kBT* ln exp *EB EA*

triangular brackets denote an average over a simulation run for state A.

smaller 'steps', which are calculated independently.

minima.

Ligand-protein interactions can be driven by quantum effects. These include charge transfer, halogen bonds, or polarisation. Stabilisation energy related to charge transfer can be several kcal/mol and force field-based schemes cannot describe this stabilisation correctly.

'Conventional' QM calculations, using HF, DFT, or semi-empirical methods provide a way to obtain the ground state energy of a ligand-protein system or a part of it. Most programs based on these are capable of studying molecular properties such as atomic charges, multipole moments, vibrational frequencies, and spectroscopic constants. In addition, there are methods allowing the study of excited-state processes, such as time-dependent DFT or restricted open-shell Kohn-Sham (ROKS) (Li and Liu, 2010).

The application area of QM methods is vast. QM calculations are used for charge derivation for molecular dynamics simulations, for description of direct interactions (hydrogen bonds, halogen bonds, aromatic stacking), for calculations of pKa, protonation, redox states, and for studying solvation effects, such as computing free solvation energies.

Derivation of accurate charges for a system being studied is an important step in preparation for MD simulation. Failure in charge representation will inevitably lead to incorrect results. Derivation of charges is done using QM calculations, usually in several steps, involving optimisation, electrostatic potential generation, and fitting charges into atoms. RESP methodology, based on charges derived from *ab initio* HF/6-31G\* level of theory has been for many years a standard in deriving charges for MD simulations (Bayly *et al.*, 1993, Cieplak *et al.*, 1995, Cornell *et al*., 1993).

Charge distribution is also required for the calculation of the solvation properties using conductor-like screening model (COSMO) (Klamt and Schüürmann, 1993). COSMO, just like any other continuum solvent approach, approximates the solvent by a dielectric continuum, surrounding the solute molecules outside of a molecular cavity. In COSMO, the polarisation charges of the continuum, caused by the polarity of the solute molecule, is derived from a scaled-conductor approximation (hence the name). In this way, the charge distribution of the molecule, which can be obtained from the QM calculations, and the energy of the interaction between the solvent and the solute molecule can be determined.

QM calculations are also used for force field development, such as adding new parameters and incorporating non-additive effects. Several studies indicate that non-additive effects (.e.g. electronic polarisation) significantly affect binding affinities of many ligands (Ji and Zhang, 2008, 2009 and references therein). Electrostatic interactions are critically dependent on charge distribution around both interacting species, and this distribution is heavily dependent on the conformation (geometry) of the complex. Description of hydrogen bonding is also affected by electronic polarisation – some hydrogen bonds, which are found broken during MD simulation using 'conventional' force fields are found to be stable, when non-additive force field is used (Ji and Zhang, 2009). Corrections for polarisation can be added to MD force fields in order to derive protein charges more accurately and provide a better description of electrostatic interactions. Protein polarisation is important for stabilisation of the native structures of proteins. MD simulations indicate that inclusion of polarisation effects not only improves the description of protein native structures, but also distinguishes native from decoy dynamically: the former are more stable than the latter under the polarised force fields. These observations provide strong evidence that inclusion of polarisation effects in calculations of ligand-protein interactions is likely to greatly improve accuracy of such calculations.

binding pocket of HBP contains a number of polar and charged residues, hence it is an example of a 'hydrophilic' binder. In contrast to HBP, the binding pocket of MUP is very 'hydrophobic'. Surprisingly, both HBP and MUP are characterised by similar overall entropy

In our recent study (Syme *et al*., 2010) we compared the driving forces for binding between these two proteins in terms of entropic contributions from ligand, protein, and solvent. We performed an extensive study combining x-ray crystallography, NMR spectroscopy, ITC,

The structure of MUP was solved both by x-ray crystallography and solution NMR (Barratt *et al.*, 2005, Kuser *et al.*, 2001, Timm *et al.*, 2001). Several ligand-MUP complexes were studied, including long-chain alcohols, pyrazine derivatives, and pheromones as ligands. Regardless of the chemical nature of ligand, the protein structures are very similar to each other: the desolvated ligand, which occupies the central, hydrophobic binding pocket,

The crystal structure of HBP complexed with histamine revealed two binding sites for the ligand: one of them possessing considerably higher affinity than the other (Figure 4, right panel) (Syme *et al*., 2010). Therefore, in order to simplify the thermodynamic analysis of ligand binding, a mutant of HBP was designed. In this mutant, denoted as HBP-D24R, negatively charged aspartic acid D24 inside the "low" affinity site was replaced by larger and positively charged arginine. This abolished binding of ligand to the "low" affinity site.

Fig. 4. Crystal structures of MUP (left panel) and HBP (right panel). Both MUP and HBP are displayed with their ligands bound: octanediol (purple), and histamine (pink). Ligands are represented as VDW spheres. For MUP, superimposed structures of apo (blue) and holo (dark cyan) protein are showed, in order to display a lack of major conformational changes associated with ligand binding. For HBP, the second (low affinity) binding site is showed

Given that the binding pocket of MUP is very hydrophobic, an entropy-driven binding signature might have been expected for ligand-MUP interactions. Surprisingly, global

of ligand binding.

and coloured yellow.

**4.1.2 Calorimetric studies of MUP**

MD simulations, and QM calculations.

causes very few conformational changes (Figure 4, left panel).

**4.1.1 Structures of HBP and MUP**

QM methods are also used in molecular docking. The application of QM methods to molecular docking was pioneered by Raha and Merz (2004), who developed a semiempirical QM-based scoring function and studied ion-mediated ligand binding processes. Their conclusion was that quantum chemical description is required for metal-containing systems, mainly because of poorly-defined atom types of metal atoms in most of the force field parameters, which cannot describe the interactions between a small molecule ligand and a metal ion in the active site of the protein.

Applicability of QM methods to study ligand-protein system has been discussed in literature (Raha *et al.*, 2007, Stewart, 2007). As well as these successes, many examples of the failure of QM approaches have been demonstrated. However, it should be kept in mind that most of these studies were based on either DFT, or semi-empirical Hamiltonians, which do not describe van der Waals interactions and hydrogen bonding terms of ligand-protein interactions correctly. This is, indeed, a serious limitation of "fast", hence more popular QM methods. A straightforward way to solve this problem is to add additional correction terms to the QM energy. It has been demonstrated that the addition of the dispersion energy and corrections for hydrogen bonds improved the performance of semi-empirical QM methods dramatically (Rezac *et al.,* 2009). The recently developed PM6-DH2 method (Fanfrlik *et al.,* 2010) yields, to date, the most accurate results for non-covalent interactions among the semiempirical QM methods. For small non-covalent complexes, the results obtained were comparable to the high-level wave-function theory-based calculations within chemical accuracy (1 kcal/mol) (Rezac *et al.*, 2009).

Another major bottleneck of QM methods applied to studying ligand-protein interactions thermodynamics is the size of the system. DFT can handle up to 150 atoms, highly-accurate methods such as coupled-clusters can handle a few tens of atoms and require very fast computers and long computing times. This limitation of the size of the systems that can be studied seriously compromises its usage in the study of ligand-protein thermodynamics. For instance, the usage of the linear scaling algorithm MOZYME (Stewart, 2009) based on the localised orbitals allows size increases to systems as large as 18 000 atoms and above, which allows calculation of very large ligand-protein complexes. Due to these developments QM methods have become, therefore, very useful for fast and highly accurate predictions of ligand-protein interactions energetics.

An alternative approach is to use so-called divide-and-conquer (DIVCON) algorithm (Dixon and Merz, 1996, 1997). The principle is to divide a large system into many smaller subsystems, separately determine the electron density of each of these subsystems, and then to add the corresponding contributions from each subsystem in order to obtain the total electron density and the energy.


Preface

Chapter 10 **Urticarial Syndromes 117**

**VI** Contents

Chapter 11 **Hereditary Angioedema 133**

and Teresa Caballero

Sevgi Akarsu and Ecem Canturk

Chapter 15 **Pseudoangioedema 227**

Hilal Gokalp and Isil Bulur

Asli Gelincik and Semra Demir

Chapter 12 **Pathophysiology of Bradykinin-Mediated Angioedema: The**

Chapter 13 **Short‐Term Prophylaxis in Odontostomatological, Maxillofacial**

Chapter 14 **Bradykinin-Mediated Angioedema Across the History 205**

**and ENT Procedures in Patients with Hereditary Angioedema**

Jesús Jurado-Palomo, Irina Diana Bobolea, Alexandru Daniel Vlagea

**Role of the Complement System 151** Jesús Jurado‐Palomo and Teresa Caballero

**Due to C1‐Inhibitor Deficiency 177** Jesús Jurado‐Palomo and Teresa Caballero The aim of this book is to give readers a broad review of urticaria and angioedema, which may affect people from birth to death, and their treatment options. The book contains the latest advances and scientific knowledge from the leading experts.

The book consists of 15 chapters in which urticaria classification, urticaria etiopathogenesis, urticaria clinics, urticarial syndromes, angioedemas, diagnosis, pathogenesis and patho‐ physiology of urticaria, and treatment options are discussed. This book also emphasizes on the various laboratory tests necessary for urticarias. One chapter of the book is devoted to comorbidities in chronic spontaneous urticaria. Another chapter is related with pathophysi‐ ology and treatment of hereditary angioedema.

We are thankful to our families for understanding our missed family time and grateful to all the contributors and leading experts for their valuable chapters, which provide an in-depth view of all aspects of the content.

We express our heartfelt gratitude to magnificent Ataturk who said "Our true mentor in life is science" and inspired us the importance of working on positive science.

> **Assoc. Prof. Dr. Selda Pelin Kartal** University of Health Sciences, Department of Dermatology, Dışkapı Yıldırım Beyazıt Training and Research Hospital in Ankara, Turkey

#### **Assoc. Prof. Dr. Zekayi Kutlubay**

Istanbul Cerrahpasa University, Department of Dermatology, Turkey

**Section 1**


*2.3. Mixed-Integer Second-Order Cone Programming (MISOCP) Model*

After the introduction of SOCP approximations and linearization of the OLTC transformer model, the complete set of equations used in this model is represented as follows:

1. By introducing (9) into (1), the objective function is given as:

$$\text{Minimize } \sum\_{i \in \mathbb{B}^{\mathsf{T}}, s \in \mathcal{S}} P\_{\text{Ii}, \text{s}} - \sum\_{i \in \text{DI}, j \in \text{DI}^{\text{task}}\_i, s \in \mathcal{S}} \mathbf{P}\_{i \mid s}^{\text{DI}, \text{inst}} + \sum\_{(ij) \in \text{IV}, s \in \mathcal{S}} r\_{ij} \cdot \mathbf{L}\_{ij, \text{s}} \tag{18}$$

subject to:


*2.2. Constitutive Relations*

The gas-phase constitutive equation is characterized by the effective viscosity of the gas. The solid-phase constitutive relationship is expressed in terms of solid stress. Tables 1 and 2 summarize a detailed description of the constitutive relations [37–42].

**Table 1.** Gas constitutive relations.

**Table 2.** Solid constitutive relations.


**4. Bioactivity**

Bioactive materials can be used to repair diseases or damage to bone tissue and can remain in place indefinitely. An indication of bioactivity is the ability to develop a stable binding with living tissues in contact with simulated body fluid solution [22] via deposition of hydroxyapatite on the surface of a substrate [23].

The bioactivity of endodontic bioceramic materials was confirmed in the Bioaggregate [21], EndoSequence Root Repair Material [21], Pro RootMTA [21], and iRoot SP [24].

After the SCR closure, direct contact between the obturator material and the periapical tissues occurs, such as the periodontal ligament (PDL) and the bone, making a three-dimensional hermetic sealing to prevent recurrent infections of the periapical space, both of endodontic or coronal origin. This seal may be mechanical with materials that provide an airtight seal, but may also be of biological origin. In this case, the filling material induces the formation of hard tissue through the cells of the periodontal ligament, isolating the root canal from the surrounding tissues and stimulating the healing processes of damaged apical tissues [25].

According to Camps et al. [26], tricalcium silicate-based materials have a recognized bioactivity property, that is, the ability to induce hard tissue formation in both the dental pulp in the periapical region. In this regard, interactions of newly developed tricalcium silicate (BioRoot, Septodont, Saint Maur Des Fosses, France)

with apical tissue were compared with a standard zinc oxide-eugenol cement (Pulp Channel Sealer [PCS]; SybronEndo Orange, CA). Cell viability was investigated by direct contact between human periodontal ligament (PDL) cells and BioRoot or PCS. For this, the extracted human incisors were sectioned at the enamel-cement junction; root canals were prepared, sterilized, and filled with lateral condensation with both materials. The root apexes were submerged in the culture medium for 24 h. These conditioned media were used to investigate their effects on human PDL cells. BioRoot had less toxic effects on PDL cells than PCS and induced a higher secretion of angiogenic and osteogenic growth factors than PCS. Given the results of the present study, it is suggested that calcium silicate cement (BioRoot) has a higher bioactivity than zinc oxide eugenol cement (PCS) in human PDL cells.

According to Niu et al. [27], a particularity of tricalcium silicate-based materials is their potential to express bioactivity, which is considered an important property for bone binding capacity. In this sense, Moinzadeh et al. [28] conducted a study to evaluate the interaction of EndoSequence BC RRM (Brasseler USA, Savannah, GA) in contact with simulated blood and tissue fluids, as these materials come into direct contact with the periapical region. These materials are hydrophilic; therefore, its properties improve in the presence of moisture, either from the periodontal ligament or dentinal tubules. However, specific environmental conditions may modify the material configuration. The reaction of tricalcium silicate with tissue fluids led to the formation of calcium hydroxide, and this was evident in the mass in contact with water and Hank's balanced salt solution. In this case, there was also the formation of globular crystals synonymous with hydroxyapatite formation. The material in contact with blood had a non-crystalline surface with additional peaks of calcium, phosphorus, and chlorine. However, in vitro material evaluation may not be representative of the clinical situation, because carbon dioxide present in the bloodstream leads to the formation of calcium carbonate rather than hydroxyapatite reported in in vitro studies.

### **5. Cytotoxicity**

All endodontic treatment will be impaired if the sealing cement is irritating to the tissues of the periapical region, causing larger inflammation or promoting large tissue necrosis, which may lead to reduction in apical repair capacity. Hence, the great importance of knowing the biocompatibility and cytotoxicity of obturator cements [21]. The cytotoxicity of endodontic cements can cause cell degeneration and delay healing due to the direct contact of the cements with the periapical tissues [29]. Cements with satisfactory biocompatibility must have low or no toxicity to the periapical tissues.

When compared to their cytotoxicity, some bioceramic cements exhibit minimal levels of cytotoxicity (EndoSequence Root Repair Material) and Mineral Trioxide Aggregate (MTA) [11]. In a study by Fayyad [30] that compared cytotoxicity, some bioceramic cements exhibited minimal levels of cytotoxicity (EndoSequence Root Repair Material) and Mineral Trioxide Aggregate (MTA) of two materials, BioAggregate and iRoot (Innovative Bioceramix, IBC, Vancouver, Canada) on human fibroblast MRC-5 cells found that both showed acceptable biocompatibility and that the cytotoxic effect of the materials was concentration dependent.

According to Candeiro et al. [12], comparing the characteristics of biodegradable EndoSequence sealer with AH Plus, bioceramic cement presented lower cytotoxicity and was unlikely to damage the genetic information inside a cell compared to AH Plus.

The results involving the biological response of MTA Fillapex (Angelus, Londrina, Brazil) seem to be conflicting. This cement showed high cytotoxicity and

**183**

**7. Color change**

*Bioceramic Cements in Endodontics*

human osteoblast cells [29].

**6. Antimicrobian activity**

*DOI: http://dx.doi.org/10.5772/intechopen.89015*

genotoxicity, shortly after the manipulation. Another study reported that when implanted into subcutaneous tissue in rats for a period of 90 days, it remained toxic [31]. However, another study has shown that despite these initial toxic effects in the early stage the cytotoxicity of Fillapex MTA decreases over time, exhibiting activity adequate to the stimulation of the formation of hydroxyapatite crystals in cultured

some studies have shown that cytotoxicity levels are identical.

eliminating residual microorganisms within the dentinal tubules [33].

According to Damas et al. [2], bioceramic cements have several applications and

Much research has been conducted proving the relationship between microorganisms and periodontitis, as well as the presence of endodontic biofilm in the process of periapical diseases. Thus, during root canal treatment, the main objective is sanitation through chemical-mechanical preparation [32], which may be associated with intra-canal medication, ending with the three-dimensional obturation. As is known, the total eradication of bacteria in all root spaces is not always achieved due to the limitation of the mechanical action of the instruments. Ideally, the obturator materials should have an antimicrobial component to assist in the process of

Bukhari and Karabucak [34] carried out a study to test the antibacterial activity of bioceramic cement compared to AH Plus (Dentsply International Inc., York, PA) in a biofilm composed of 8-week-old *Enterococcus faecalis* adhered to surfaces using a model of dentin infection. The surfaces of the unirradicular intact extracted canals were infected by *E. faecalis* biofilm. Cement AH Plus and EndoSequence BC Sealer (Brasseler USA, Savannah, GA) were placed on the wall of the root canal of the specimens during a period of 24 h and another of 2 weeks in humid conditions at 37°C. Infected samples incubated without shutter cement for similar periods were used as negative controls. In order to test the sealing cements, the specimens were labeled with fluorescence viability staining and confocal laser scanning microscopy to evaluate the proportions of dead and living bacteria in the canal walls during the determined periods. The EndoSequence BC Sealer significantly killed more *E. faecalis* in biofilm bound to channel surfaces when compared to AH Plus and control at both time points (P, 0.05–0.0005). In this sense, they concluded that the EndoSequence BC Sealer exhibited significant antimicrobial ability in the presence of dentin for up to 2 weeks in an 8 week old *E. faecalis* biofilm, compared to the AH Plus cement.

The aim of endodontic interventions is to prevent and treat apical periodontitis. However, the esthetic result is equally important, especially in the anterior region. Pulpal therapy procedures, such as direct pulp capping, repair of perforations, and regenerative endodontics involve the placement of materials in the coronal third of the tooth, which may have potential for discoloration [35]. In this sense, Kohli et al. [36] carried out a study with the objective of evaluating the in vitro tooth discoloration induced by bioceramic materials, EndoSequence RRM and BD in comparison with other materials used during endodontic treatment, such as gray MTA (GMDTA, Dentsply, York, PA, USA). The aim of this study was to evaluate in vitro the biomarker-induced coronal tooth discoloration, EndoSequence RRM and BD, in comparison with other materials used during endodontic treatment, such as gray MTA (GMTA); MTA white (WMTA, Dentsply), triple antibiotic paste

*Bioceramic Cements in Endodontics DOI: http://dx.doi.org/10.5772/intechopen.89015*

*Oral Diseases*

reported in in vitro studies.

**5. Cytotoxicity**

periapical tissues.

with apical tissue were compared with a standard zinc oxide-eugenol cement (Pulp Channel Sealer [PCS]; SybronEndo Orange, CA). Cell viability was investigated by direct contact between human periodontal ligament (PDL) cells and BioRoot or PCS. For this, the extracted human incisors were sectioned at the enamel-cement junction; root canals were prepared, sterilized, and filled with lateral condensation with both materials. The root apexes were submerged in the culture medium for 24 h. These conditioned media were used to investigate their effects on human PDL cells. BioRoot had less toxic effects on PDL cells than PCS and induced a higher secretion of angiogenic and osteogenic growth factors than PCS. Given the results of the present study, it is suggested that calcium silicate cement (BioRoot) has a higher bioactivity than zinc oxide eugenol cement (PCS) in human PDL cells.

According to Niu et al. [27], a particularity of tricalcium silicate-based materials is their potential to express bioactivity, which is considered an important property for bone binding capacity. In this sense, Moinzadeh et al. [28] conducted a study to evaluate the interaction of EndoSequence BC RRM (Brasseler USA, Savannah, GA) in contact with simulated blood and tissue fluids, as these materials come into direct contact with the periapical region. These materials are hydrophilic; therefore, its properties improve in the presence of moisture, either from the periodontal ligament or dentinal tubules. However, specific environmental conditions may modify the material configuration. The reaction of tricalcium silicate with tissue fluids led to the formation of calcium hydroxide, and this was evident in the mass in contact with water and Hank's balanced salt solution. In this case, there was also the formation of globular crystals synonymous with hydroxyapatite formation. The material in contact with blood had a non-crystalline surface with additional peaks of calcium, phosphorus, and chlorine. However, in vitro material evaluation may not be representative of the clinical situation, because carbon dioxide present in the bloodstream leads to the formation of calcium carbonate rather than hydroxyapatite

All endodontic treatment will be impaired if the sealing cement is irritating to the tissues of the periapical region, causing larger inflammation or promoting large tissue necrosis, which may lead to reduction in apical repair capacity. Hence, the great importance of knowing the biocompatibility and cytotoxicity of obturator cements [21]. The cytotoxicity of endodontic cements can cause cell degeneration and delay healing due to the direct contact of the cements with the periapical tissues [29]. Cements with satisfactory biocompatibility must have low or no toxicity to the

When compared to their cytotoxicity, some bioceramic cements exhibit minimal levels of cytotoxicity (EndoSequence Root Repair Material) and Mineral Trioxide Aggregate (MTA) [11]. In a study by Fayyad [30] that compared cytotoxicity, some bioceramic cements exhibited minimal levels of cytotoxicity (EndoSequence Root Repair Material) and Mineral Trioxide Aggregate (MTA) of two materials, BioAggregate and iRoot (Innovative Bioceramix, IBC, Vancouver, Canada) on human fibroblast MRC-5 cells found that both showed acceptable biocompatibility

According to Candeiro et al. [12], comparing the characteristics of biodegradable EndoSequence sealer with AH Plus, bioceramic cement presented lower cytotoxicity and was unlikely to damage the genetic information inside a cell compared to AH Plus. The results involving the biological response of MTA Fillapex (Angelus, Londrina, Brazil) seem to be conflicting. This cement showed high cytotoxicity and

and that the cytotoxic effect of the materials was concentration dependent.

**182**

genotoxicity, shortly after the manipulation. Another study reported that when implanted into subcutaneous tissue in rats for a period of 90 days, it remained toxic [31]. However, another study has shown that despite these initial toxic effects in the early stage the cytotoxicity of Fillapex MTA decreases over time, exhibiting activity adequate to the stimulation of the formation of hydroxyapatite crystals in cultured human osteoblast cells [29].

According to Damas et al. [2], bioceramic cements have several applications and some studies have shown that cytotoxicity levels are identical.

#### **6. Antimicrobian activity**

Much research has been conducted proving the relationship between microorganisms and periodontitis, as well as the presence of endodontic biofilm in the process of periapical diseases. Thus, during root canal treatment, the main objective is sanitation through chemical-mechanical preparation [32], which may be associated with intra-canal medication, ending with the three-dimensional obturation. As is known, the total eradication of bacteria in all root spaces is not always achieved due to the limitation of the mechanical action of the instruments. Ideally, the obturator materials should have an antimicrobial component to assist in the process of eliminating residual microorganisms within the dentinal tubules [33].

Bukhari and Karabucak [34] carried out a study to test the antibacterial activity of bioceramic cement compared to AH Plus (Dentsply International Inc., York, PA) in a biofilm composed of 8-week-old *Enterococcus faecalis* adhered to surfaces using a model of dentin infection. The surfaces of the unirradicular intact extracted canals were infected by *E. faecalis* biofilm. Cement AH Plus and EndoSequence BC Sealer (Brasseler USA, Savannah, GA) were placed on the wall of the root canal of the specimens during a period of 24 h and another of 2 weeks in humid conditions at 37°C. Infected samples incubated without shutter cement for similar periods were used as negative controls. In order to test the sealing cements, the specimens were labeled with fluorescence viability staining and confocal laser scanning microscopy to evaluate the proportions of dead and living bacteria in the canal walls during the determined periods. The EndoSequence BC Sealer significantly killed more *E. faecalis* in biofilm bound to channel surfaces when compared to AH Plus and control at both time points (P, 0.05–0.0005). In this sense, they concluded that the EndoSequence BC Sealer exhibited significant antimicrobial ability in the presence of dentin for up to 2 weeks in an 8 week old *E. faecalis* biofilm, compared to the AH Plus cement.

#### **7. Color change**

The aim of endodontic interventions is to prevent and treat apical periodontitis. However, the esthetic result is equally important, especially in the anterior region. Pulpal therapy procedures, such as direct pulp capping, repair of perforations, and regenerative endodontics involve the placement of materials in the coronal third of the tooth, which may have potential for discoloration [35]. In this sense, Kohli et al. [36] carried out a study with the objective of evaluating the in vitro tooth discoloration induced by bioceramic materials, EndoSequence RRM and BD in comparison with other materials used during endodontic treatment, such as gray MTA (GMDTA, Dentsply, York, PA, USA). The aim of this study was to evaluate in vitro the biomarker-induced coronal tooth discoloration, EndoSequence RRM and BD, in comparison with other materials used during endodontic treatment, such as gray MTA (GMTA); MTA white (WMTA, Dentsply), triple antibiotic paste

(TAP), and AH Plus sealant (AH+, Dentsply). Visual discoloration was observed in all specimens in the GMTA, WMTA, and TAP groups over 7 days, which increased over time. Significant coronary tooth discoloration was caused by TAP, GMTA, and WMTA, but not by BD, RRM or RRMF at the end of the experiment.

Discoloration of the crown such as the one present in the MTA is one of the disadvantages of restorative cement used in dentistry. This has to be taken into account when repairing furcation injuries or in cases where pulp protection is required. According to the literature, the bismuth oxide present in the MTA composition reacts with the residual sodium hypochlorite that remains inside the dentinal tubules after mechanical chemical preparation, resulting in dark precipitations and staining of the tooth. In the composition of the EndoSequence, the zirconia oxide is the opacifier used, preventing the unwanted darkening [37].

According to Kholi et al. [36], the bio-based materials Biodentine (Septodont, Saint-Maur-des-Fosses, France), ERRM, EndoSequence, ERRM putty (Brasseler, Savannah, GA), RMF, EndoSequence ERRM fast set paste (Brasseler), and AH+, AH Plus sealer (Dentsply), when left in the pulp chamber for periods of up to 6 months do not induce color change in the tooth structure. Alsubait et al. [37] compared the potential for discoloration of the Endosequence Bioceramic Root Repair Material Fast Putty Set (ERRM) and ProRootMTA (PMTA) by placing them on the crown of extracted human teeth for a period of 4 months and found progressive discoloration in teeth when treated with PMTA, whereas those with ERRM had no change in color stability.

## **8. Mechanism of action**

The bioceramic cement is hydrophilic; therefore, it uses water present in the dentin tubules to initiate the firming reaction. The hydration of the material decreases the working time, consequently the amount of water mixed can reduce the time required; but the bioceramics only harden when present in a humid environment. After hydration, the calcium silicate gel and the calcium hydroxide are produced by the calcium silicate present in the mixture. Calcium hydroxide reacts with phosphate ions and produces hydroxyapatite and water. The continuous interaction of calcium silicate and water leads to the formation of hydrated calcium silicate [38]. The amount of water in the reaction is a critical factor in controlling the rate of hydration. The pH is similar when compared to the reaction time of calcium hydroxide. As this is highly alkaline, it reaches a value of 12.8 during the placement time, decreasing progressively over a period of 1 week [2]. The pH is affected by the release of calcium ions and by alkalinizing the medium, a condition that can influence the repair, besides promoting the mineralization process and its concentration. The release of hydroxyl ions can alter the dissociation [12].

Candeiro et al. [12] carried out a study with the purpose of evaluating the physicochemical properties of a bioceramic. Radiopacity, pH, calcium ion release, and flowability were studied and compared with AH Plus® cement (resin-based cement). The radiopacity and flow were evaluated by using ISO 6876/2001 standards. For the analysis of the radiopacity, metal discs with 10 mm diameter and 1 mm thickness were used and were covered with sealer cement. The flowability test was performed with 0.005 ml of cement on a glass plate. The release of calcium ions and pH were evaluated in periods of 3, 24, 72, 180, and 240 h with a spectrometer and pH meter, respectively. Radiopacity was then found to be significantly lower than AH Plus®, pH analysis, and calcium ion release were significantly higher than AH Plus®, and it was demonstrated that there were no significant differences in

**185**

*Bioceramic Cements in Endodontics*

*DOI: http://dx.doi.org/10.5772/intechopen.89015*

very favorable values for a sealant cement.

(BC-RRM) showed similar sealing ability.

adaptation in this region [19, 40, 41].

**10. Resistance of union**

**9. Marginal adaptation/sealing capacity**

flowability. Thus, the bioceramics present values of radiopacity and fluidity within the limits of ISO standards and the other physicochemical properties analyzed show

According to Shokouhinejad et al. [39], the marginal adaptation of the EndoSequence Root Repair Material (ERRM) was similar to that of the MTA. However, bioceramic-based cements when compared with resin-based cements (AH PLUS) exhibited more regions containing gaps. Bioceramic endodontic cements also showed infiltration results similar to MTA. In relation to sealing and its ability, the Bioceramic Root-end Repair (BCRR) is equivalent to the MTA [13]. Antunes et al. [14] reported that MTA and BioCeramic Root Repair Material

To what concerns bioceramics and the hydration of the material during the setting process, the formation of hydroxyapatite crystals occurs between the surface of the material and the dentin wall, which can provide adequate sealing and marginal

The ability of a root canal sealer to adhere intra-radicular dentin through micromechanical retention or resistance to friction is advantageous in maintaining the integrity of the sealant interface and dentin during mechanical stresses caused by flexion of the teeth, surgical procedures or preparation of the space for intra radicular retainers [42]. It has been shown that the release of calcium and hydroxyl ions from calcium silicate-containing material results in the formation of a layer of hydroxyapatite when it comes in contact with the fluids of the dentinal tubules. The formation of this interfacial layer develops a chemical bond between calcium and dentin walls [43]. Therefore, it is expected that the bioceramic cements, which are based on a calcium silicate composition, have the potential to chemically adhere to the dentin. Shokouhinejad et al. [44] conducted an investigation to compare the bond strength of bioceramic (EndoSequence BC Sealer) and resin cement AH Plus in the presence and absence of smear layer. Uniradicular ex vivo specimens were used in this experiment using 5.25% sodium hypochlorite and 17% EDTA protocols for smear layer removal and in the other specimens no debris removal protocol, only 5.25% sodium hypochlorite irrigation. The modes of adhesion strength and failure were evaluated. No statistically significant differences were found between the groups filled with gutta percha and AH Plus sealant and gutta percha and bioceramic sealant. The presence or absence of smear layer does not appear to signifi-

Antunes et al. [14] evaluated the sealing capacity of MTA cement and EndoSequence BC RRM-Fast Set Putty in an ex vivo study, in roots of 60 instrumented lower central incisors, which were sectioned in the apical region and ultrasonic tip retroinstruments, and using a new model of bacterial nutrient infiltration. Retrograde obturation was performed with the MTA and BC-RRM Putty in two sets of teeth. In the MTA group, 50% of viable species were detected while in the Putty BC-RRM group, 28% of the samples were positive for cultured bacteria. However, in the comparison analysis of the quantitative or presence/absence of bacteria, no significant difference was identified between the groups, leading the authors to

conclude that the cements studied have similar sealing capacity.

cantly affect the bond strength of filler materials.

*Oral Diseases*

no change in color stability.

**8. Mechanism of action**

dissociation [12].

(TAP), and AH Plus sealant (AH+, Dentsply). Visual discoloration was observed in all specimens in the GMTA, WMTA, and TAP groups over 7 days, which increased over time. Significant coronary tooth discoloration was caused by TAP, GMTA, and

Discoloration of the crown such as the one present in the MTA is one of the disadvantages of restorative cement used in dentistry. This has to be taken into account when repairing furcation injuries or in cases where pulp protection is required. According to the literature, the bismuth oxide present in the MTA composition reacts with the residual sodium hypochlorite that remains inside the dentinal tubules after mechanical chemical preparation, resulting in dark precipitations and staining of the tooth. In the composition of the EndoSequence, the zirconia oxide is

According to Kholi et al. [36], the bio-based materials Biodentine (Septodont, Saint-Maur-des-Fosses, France), ERRM, EndoSequence, ERRM putty (Brasseler, Savannah, GA), RMF, EndoSequence ERRM fast set paste (Brasseler), and AH+, AH Plus sealer (Dentsply), when left in the pulp chamber for periods of up to 6 months do not induce color change in the tooth structure. Alsubait et al. [37] compared the potential for discoloration of the Endosequence Bioceramic Root Repair Material Fast Putty Set (ERRM) and ProRootMTA (PMTA) by placing them on the crown of extracted human teeth for a period of 4 months and found progressive discoloration in teeth when treated with PMTA, whereas those with ERRM had

The bioceramic cement is hydrophilic; therefore, it uses water present in the dentin tubules to initiate the firming reaction. The hydration of the material decreases the working time, consequently the amount of water mixed can reduce the time required; but the bioceramics only harden when present in a humid environment. After hydration, the calcium silicate gel and the calcium hydroxide are produced by the calcium silicate present in the mixture. Calcium hydroxide reacts with phosphate ions and produces hydroxyapatite and water. The continuous interaction of calcium silicate and water leads to the formation of hydrated calcium silicate [38]. The amount of water in the reaction is a critical factor in controlling the rate of hydration. The pH is similar when compared to the reaction time of calcium hydroxide. As this is highly alkaline, it reaches a value of 12.8 during the placement time, decreasing progressively over a period of 1 week [2]. The pH is affected by the release of calcium ions and by alkalinizing the medium, a condition that can influence the repair, besides promoting the mineralization process and its concentration. The release of hydroxyl ions can alter the

Candeiro et al. [12] carried out a study with the purpose of evaluating the physicochemical properties of a bioceramic. Radiopacity, pH, calcium ion release, and flowability were studied and compared with AH Plus® cement (resin-based cement). The radiopacity and flow were evaluated by using ISO 6876/2001 standards. For the analysis of the radiopacity, metal discs with 10 mm diameter and 1 mm thickness were used and were covered with sealer cement. The flowability test was performed with 0.005 ml of cement on a glass plate. The release of calcium ions and pH were evaluated in periods of 3, 24, 72, 180, and 240 h with a spectrometer and pH meter, respectively. Radiopacity was then found to be significantly lower than AH Plus®, pH analysis, and calcium ion release were significantly higher than AH Plus®, and it was demonstrated that there were no significant differences in

WMTA, but not by BD, RRM or RRMF at the end of the experiment.

the opacifier used, preventing the unwanted darkening [37].

**184**

flowability. Thus, the bioceramics present values of radiopacity and fluidity within the limits of ISO standards and the other physicochemical properties analyzed show very favorable values for a sealant cement.


**5. Bacterial invasion of the skin**

For as long as microorganisms that colonize the skin of importance to skin diseases and microbiology; I have been collecting our knowledge of these organisms live accurate until recently through the existing studies on the culture. Historically, it is *Staphylococcus aureus* and other *Staphylococcus aureus* negative coagulation as the primary bacterial colonies of the skin. Other microorganisms that are generally regarded as skin colonizers include coryneforms of the phylum Actinobacteria (the genera *Corynebacterium*, *Propionibacterium* and *Brevibacterium*) and the genus *Micrococcus*. Gram-negative bacteria, with the exception of some *Acinetobacter* spp., are generally not isolated from the skin, but are thought to arise in cultures owing to contamination from the gastrointestinal tract [30].

It was isolated from non-bacterial microorganisms from the skin. *Fungal species* are the most common *Malassezia* spp., which is particularly widespread in the fatty areas. Considered mite *Demodex* (such as *Demodex* follicle and *Demodex* brevis), a microscopic arthropods, part of the natural skin flora. They feed on mites *Demodex* sebum and be more prevalent after puberty, preferring to colonize the oily areas of the face. *Demodex* mites may also feed on epithelial cells lining the unit sunscreens space, or even other organisms (such as acne Brobbeoneptariom) that live in the same place. It is not the role of the experimental study of viruses, and is limited research on the molecular and microbiological methods available for the identification and characterization of viruses [31].

Historically, culture-based approach is the standard to describe the microbial diversity. It is now clear that only a minority of bacteria able to thrive in isolation [32]. Choose mainly culture-based laboratory techniques "herbs": species that thrive under conditions typical nutritional and physiological use of diagnostic microbiology laboratories. This is not necessarily the most abundant organisms in society. This bias is particularly evident when trying to isolate the organisms living in micro skin, which adapted to the nature of cold, dry and acidic environment. Moreover, the hair follicles and sebaceous glands are an oxygen-free environment and are home to the anaerobic microorganisms. Isolate the problem especially anaerobic using routine methods based on culture. These are often slow-growing organisms and require special conditions for growth and during the transfer and processing of samples [33, 34].

#### *Bacterial Skin Abscess DOI: http://dx.doi.org/10.5772/intechopen.91657*

The development of molecular techniques to identify and quantify microorganisms has revolutionized our view of the world Microbial. Characterization of genetic diversity of bacterial depends on the sequence of genes for RNA ribosomal 16S, found in all bacteria and analyzes antique, but not in eukaryotes. Genes rRNA contain 16S in highly variable regions of certain types, which allows the classification of classification, and the spaces reserved for the one who, operating Xaah molecular site linking the primers PCR. The emergence of new sequencing technologies (such as pyrosequencing) is to increase productivity significantly while reducing the cost of sequencing. More importantly, the living organism culture does not need to determine the sequence of its kind by 16S rRNA [35].

The skin is the largest organ in the human body, colonized by a variety of tiny, mostly harmless organisms or even beneficial to their hosts. Colonialism is the motivation behind the surface of the skin environment, which is highly variable depending on the site topography, and host factors internal factors, the external environment. The responses can be innate immune and lead to a modified adaptive skin microorganisms in the skin, but microorganisms are also working to educate the immune system. Molecular road development has led to the identification of microorganisms to see the emerging skin bacteria resident are very diverse and variable. The improved understanding of the microbes in the skin is necessary to gain insight into the involvement of microbes in human skin disorders and to enable new methods for therapeutic drugs antimicrobial and antimicrobial therapy [36].

The main barrier against microbial invasion is the skin. It interacts continuously with the external environment, a colonizer with a variety of microbes. The vast majority of plants colony consists of bacteria. To help organize the distribution of plants, one that divides the body into two halves at the waist. The usual things that colonizes the skin above the waist are usually positive types of Gram such as *Staphylococcus epidermidis*, *Corynebacterium species*, *S. aureus* and *Streptococcus pyogenes* [37].

*Staphylococcus aureus* and *Corynebacterium* spp. It is the most abundant organisms that colonize humid areas, consistent with the data culture that indicate that these organisms prefer high humidity areas. These include navel wet sites (navel), and the basement axillary, and wrinkling inguinal (side thigh) and wrinkling brigades (the upper part of the fold between the buttocks), insole foot, hole popliteal (behind the knee) and the pit antecubital (elbow inner). *Staphylococcus aureus* occupies air position on the skin and may use urea in the race as a source of nitrogen. Insect bacteria are highly sensitive organisms that have slow growth in culture, and such as the role of the skin accurate objects has been appreciated until recently. Treatment of sweat by bacteria and *Staphylococcus* (along with the minute in the basement of underarm living organisms), resulting in a transient characteristic odor associated with sweating in humans [38].

On the other hand, the typical living organisms colonize the skin below the waist Gram-positive and Gram-negative. It is expected that this will be a minor near the anal area difference. Attracted intestinal species, such as the intestinal bacteria, to this region of the skin so-called "Fecal Crust" [36].

Normal distribution pattern consists of the largest population areas in the armpit and groin and thigh, where there is moisture level higher. Microflora tend to fill the upper layer of the cornea and parts of the hair follicles. Specific microbes tend to colonize the anatomical structures based on tropical stimuli and biochemical interactions of the site and the formation of specific tissues of biological membranes. Plants can be significantly by climate group differ, genetics, age, sex, stress, hygiene, nutrition, hospitalization [37].

Skin abscess is the most common manifestations of bacterial infection. Abscess may appear in painful blocks degrade transient without medical intervention, or

in severe cases, such as large deep cysts associated with the spread of the blood stream. Although many of the bacteria, causing Gram-positive and Gram-negative cysts, but *Staphylococcus aureus*, especially MRSA associated with the community, it is the causative agent of the most common. Once configured, it can interfere with pus in the lesion Walled significantly with the activity of antibiotics to the extent this makes antibiotic treatment effective to some extent when the abscess exceeds a certain size, with the emergence of the problem of additional scarring. In the case of *EBioMedicine* [39].

Hancock and his colleagues have positive peptide targeted basically describing the formation of cysts. Developed peptides screen anti-biofilm. In the laboratory, which prevent or eliminate biofilms formed by bacteria both Gram-positive and Gram-negative. In non-vertebrate models of infection *P. aeruginosa*, boosted the survival of the host [40].

The main question that arises from the study is the relationship between the strict response and abscess formation. It was responsible for the formation mechanisms kharaj an important topic for research in this field *aureus*. While some defense mechanisms for stress, such as reducing metals and oxidative stress and nitric, appear to have a role in the ability of *S. aureus* to form abscesses, the stringent response in this context has not been clarified yet. It is likely to be the primary contact due to the direct impact of the stringent response CodY regulator. CodY has proven that it affects the severity of the disease in many animal models by changing the expression of the organizers of key, such as agr (RNAIII and RNAII) and saeR, hemolysins (hla), leukocidins (lukSF), the synthesis of the capsule (icaADBC), as well as genes that show it is important to form an abscess. Expression PSMα, which shows that it prevents installed by DJK-5, independently organized through RSH for CodY. Specific factors that regulate the formation of abscess under the strict response remains identified in *Staphylococcus aureus* and other microbes [41].

From a clinical perspective, the siege imposed on the composition of the abscess would be a useful assistant to kill pathogens. Often, infected individuals already infected a large abscess requires Tbarva surgically. For those who provide abscesses smaller or in the early stages which are not viable after discharge surgical, antibiotics are used routinely, but may not be enough to stop the progress of formation of abscess, especially if the pathogen offending is relatively resistant to antibiotics. It can be strict inhibition of the response to the formation of mass abscess useful, and will compare the use of helper inhibitors of protein synthesis inhibition in the treatment of inflammatory toxin mediated by poison. Inhibitors will be particularly useful if they also prevent chronic or recurrent cysts including cases related to chronic bacteria gold that are difficult to treat, such as inflammation of the sweat glands Almqih. Future studies will need to prove that the inhibitors are still effective when used with antibiotics effective or marginal [42].

*Other Bacteriologic characteristics*. In the monomicrobial form, the pathogens are *S. pyogenes*, *S. aureus*, *V. vulnificus*, *A. hydrophila*, and anaerobic streptococci (i.e., *Peptostreptococcus* species). Can *Staphylococcus aureus* and Streptococcus hemolytic occur simultaneously? Most injuries are obtained from the community and there in the limbs, with nearly two-thirds of cases in the lower limbs. There is often an underlying cause, such as diabetes or vascular disease, atherosclerosis or venous insufficiency with edema. Sometimes, chronic vascular ulcers turn into a more intense process. Fasciitis cases of necrotizing that arise after infection varicella or trivial injuries, such as minor scratches and insect bites, always be the result of bacteria *S. pyogenes*. The mortality rate in this group is high, where close to 50–70% in patients with low blood pressure and organ failure [43].


**1. Introduction**

Ultra-wide band systems transmit and receive ultra-short electromagnetic pulses having limited effective radiated power. The system performance is determined primarily by the characteristics of the radiators that have to conform with stringent frequency and time domain requirements in the entire operating band [1]. These requirements are namely, a non-dispersive phase centre; constant radiation and impedance over the frequency range with no excitation of higher order modes [2]. Planar monopole antennas with wide operating bands are most often well matched multi-resonant structures. In [3], Ma et al. have described the time domain performance of a printed dipole antenna employing a tapered slot feed. It is reported that the received pulses are distorted and broadened to more than 1 ns in spite of the antenna being well matched over the entire band. The higher order modes generated tends to shift the antenna phase centers with frequency and can lead to

broadening of the radiated pulse. The same authors in [4] reports a much lesser pulse distortion for a tapered slot antenna operating in the 3.1–10.6 GHz UWB band. The present chapter intends to outline the design, simulation and measurement steps followed to characterize UWB antennas in the time domain.

*U* !

*Tx*ð Þ¼ *t*, *θ*, *φ*

*Rx*ð Þ *t*, *θ*, *φ* . As a result, an ideal antenna (with *h*

!

*Tx*ð Þ¼ *ω*, *θ*, *φ jω*

The time domain relation between the transmitted electric field pulse

1 2*πc*

impulse response *h*

the received pulse.

**2.2 Transient radiation**

and,

antenna is,

*e* !

where,

response *h*

**111**

*rad*ð Þ *t*,*r*, *θ*, *φ* ffiffiffiffiffi *z*0 p ¼ 1

transmit impulse response *h*

!

input voltage pulse.

*e* !

the applied voltage pulse is,

*E* ! *Rx*ð Þ *ω*,*r*, *θ*, *φ* ffiffiffiffi *zc* p ¼ *h*

*Time Domain Performance Evaluation of UWB Antennas*

In the time domain, the corresponding relation is,

*Rx*ð Þ *t*,*r*, *θ*, *φ* ffiffiffiffi *zc* p ¼ *h*

and azimuth angles, the receive antenna transfer function *h*

!

!

*Rx*ð Þ *ω*, *θ*, *φ*

*Rx*ð Þ *t*, *θ*, *φ* ⊗

*zc* and *z*0 are the antenna port and free–space characteristic impedance respectively, while ⊗ indicates convolution operation. If ð Þ *θ*, *φ* represents the elevation

An ideal receiving antenna should receive a voltage pulse of the same shape as the one incident on it from any direction. This means that it should have a Dirac– delta impulse response which is also be independent of the angle of arrival. In other words, the antenna transfer function should have a uniform amplitude and a linear phase response (or constant group delay). However, in practice, the receiving

The frequency domain relation between the transmitted electric field pulse and

2*πc h* !

*∂ ∂t h* !

1 2*πc*

The convolution with the delta function in Eq. (5) represents the time delay attributed to the finite speed of light, denoted by *c*. Eq. (6) indicates that the

radiate an electric field pulse which would be a first–order time derivative of the

*∂ ∂t h* !

!

*Rx*ð Þ *t*, *θ*, *φ* � � ⊗

*Tx*ð Þ *t*, *θ*, *φ* is a time derivative of the receive impulse

!

*e*�*jωr=c r*

*Tx*ð Þ *ω*, *θ*, *φ*

*E* !

> *e* !

*Rx*ð Þ *t*, *θ*, *φ* are considered as a function of the angle of arrival of

*rad*ð Þ *ω*,*r*, *θ*, *φ* ffiffiffiffiffi *z*0

*rad*ð Þ *t*,*r*, *θ*, *φ* ffiffiffiffiffi *z*0

!

*UTx*ð Þ *ω*,*r*, *θ*, *φ* ffiffiffiffi *zc*

*Tx*ð Þ *t*,*r*, *θ*, *φ* at the transmitting

*Rx*ð Þ *ω*, *θ*, *φ* (4)

*uTx*ð Þ *t*,*r*, *θ*, *φ* ffiffiffiffi *zc*

*Rx*ð Þ *t*, *θ*, *φ* (6)

*Rx*ð Þ¼ *t*, *θ*, *σ δ*ð Þ*t* ) will

p (5)

p (3)

p (1)

p (2)

*Rx*ð Þ *ω*, *θ*, *φ* and its

Two monopole antennas with similar design topology is considered for the present analysis: the SQMA with a square radiator and RMA with a rectangular radiator. In both the antennas, the ground plane is optimally designed for a wide impedance bandwidth. The general practice to realize ultra wide-bandwidth in square/rectangular radiating elements is to modify the ground–radiator interface [5–10]. In SQMA, the inherent resonances of a square patch is matched over the wide band by incorporating cuts in the ground plane at specific locations [11]. The designs proposed in [11, 12] have been contemplated to design the RMA. In RMA, the PCB footprint is greatly reduced and radiation patterns in the 3.1–10.6 UWB is stable without much radiation squinting which is otherise observed in wideband antennas at higher frequencies primarily due to the current distribution on the antenna ground plane [13]. Incase of RMA, this aspect is taken into consideration in the design ensuring broadside radiation all through the band of operation. This is further confirmed from the spatio-temporal transfer characteristics and the transient response analysis, making it suitable for UWB applications.