**9.1 Mitomycin-C**

*Biophysical Chemistry - Advance Applications*

Cisplatin-DNA sequence selectivity has been given great attention from the research community. Several studies show that cisplatin first binds monofunctionally to guanine N7 and is particularly reactive towards Gn-runs (n ≥ 2) (**Figure 7**) [18, 20, 21]. The high nucleophilicity of Gn-runs attracts the positively charged cisplatin monoaqua specie. The lifetime of the monoadduct is relatively long and it has therefore been suggested that the initial monoadduct is crucial for the type of cross-linked adduct formed and thus for the cytotoxic properties of the Pt complex. The main factors influencing the mono-functional binding affinity in DNA are thought to be [18] the type of bound nucleotide and of the adjacent residues, the steric effects of the Pt complex, the hydro-

The formation of a cisplatin adduct with the GpG bases requires a significant tilting of the bases leading to a perturbation of the regular B-DNA conformation. The structural perturbation has been shown to be specifically recognized by a number of cellular proteins, including proteins with high-mobility group (HMG) binding domains and the TATA box binding protein [22]. It is believed that (some of) these recognition proteins mediate the cellular response which finally induces cell death by apoptosis or necrosis. In some cases, relatively subtle changes in the adduct structure can affect the recognition and the biological effects in a major way. This is exemplified by the cisplatin analogue oxaliplatin which forms similar G\*G\*-Pt adducts as cisplatin [18]. However, the oxaliplatin-G\*G adducts differ in repair efficiency, mutagenesis and translesion synthesis, believed to be related to the differential activity of the two drugs (oxaliplatin is used, in combination with 5-fluorouracil, for the treatment of colorectal cancers against which cisplatin is inactive). The evaluation of the structural details of the platinum-DNA adducts and of their effects on protein, recognition can therefore help to understand why the biological activities of two similar platinum compounds (e.g., cisplatin versus oxaliplatin) are different. So far only nine cisplatin-DNA adducts have been characterized by NMR and/or x-ray crystallography. These structures were extensively reviewed by Ano et al. and found to be basically similar in structure. The cisplatin-GG adduct kinks the double helix approx. Approximately 60 towards the major groove and induces N sugar pucker for

gen binding properties of the Pt-DNA adduct and the DNA conformation.

**8. Sequence specific structural perturbation**

*Assumed mechanism for the formation of cisplatin-DNA adducts.*

X of 5′ XG\*, 5′ G\* and the C complementary to 3′ G\* [18].

**82**

**Figure 7.**

Mitomycin-C is a well-characterized antitumor antibiotic that forms a covalent interaction with DNA after reductive activation (**Figure 8**). The activated antibiotic forms a cross-linking structure between guanine bases on adjacent strands of DNA therefore inhibiting single strand formation [8].


**6. Status**

Potential endophenotypes related with language and social communication

A continuous distribution of social deficits has been described in the general population, being more frequent in boys than in girls and more prevalent in brothers and fathers than in sisters and mothers of patients with ASD [54]. The estimated frequency of such disorders in siblings ranges from 2.6% to 61.7% [55-59].

It has been suggested that siblings later diagnosed with ASD may be distinguished from other siblings and low-risk infants by unusual eye contact, visual tracking, disengagement of visual attention, orienting to name, imitation, and delayed social expressive and receptive language [60].

**i.** Be identified for genetically related disorders [48-51].

phenotypes that may fulfill the requirements of endophenotypes.

proposed for neuropsychiatric disorders.

356 Autism Spectrum Disorder - Recent Advances

**4. Research course**

anatomy, or neurophysiology.

ranges from 2.6% to 61.7% [55-59].

**5. Methods**

**6. Status**

Thus far, the identification of endophenotypes has been successful in several fields of Medi‐ cine. Endophenotypes were useful in the identification of genes for QT syndrome, idiopatic hemochromatosis, juvenile myoclonic epilepsy, and familial adenomatous intestinal polypo‐ sis. Biochemical assays, physiological measures and challenges contribute as primary evidence of pathology in the detection of increased risk to diabetes, hypercholesterolemia, obesity, hypertension, and osteoporosis [48, 52, 53]. Furthermore, different endophenotypes have been

First degree relatives of patients are key elements in the study of endophenotypes. They are considered at-risk individuals. Even so, only a relatively small percentage of siblings of an individual with ASD will develop such disorders, but a larger proportion is expected to exhibit

It has been shown that siblings of patients with ASD as well as other first degree relatives sometimes exhibit social, communication, and/or learning deficits, and ASD are more frequent in them than in the general population. Several possible endophentoypes for ASD have been proposed so far and are related with language and communication and/or with cognition,

Medline database was searched for articles related with autism and autism spectrum disorder endophenotypes (query terms: autism spectrum disorders and endophenotypes, neuroanat‐ omy, neurophysiology, endocrinology, cognition, social communication, and language. OMIM compendium was searched for disease and gene names. We will discuss potential endophenotypes based on studies in which one or more of their characteristics were fulfilled.

A continuous distribution of social deficits has been described in the general population, being more frequent in boys than in girls and more prevalent in brothers and fathers than in sisters and mothers of patients with ASD [54]. The estimated frequency of such disorders in siblings

It has been suggested that siblings later diagnosed with ASD may be distinguished from other siblings and low-risk infants by unusual eye contact, visual tracking, disengagement of visual

Potential endophenotypes related with language and social communication

Moreover, there are reports of poor social and communicative performance in parents without a diagnosis of ASD and siblings of children with such disorders [61]. Families with multiple affected individuals were compared with single-incidence autism families, and Down syndrome families as controls. In most cases with multiple affected relatives, both parents had autism-related characteristics. This was not observed in single-incidence families [62].

Furthermore, children with ASD and their parents have been shown to have an impaired performance in rapid automatized naming. Siblings of patients had intermediate performances when compared with controls [62, 63].

Poor verbal imitation and reduced response to vocal approaches have also been described in children with ASD or children who later developed ASD [64, 65]. In a study, 100% of the 12 month-old infants with no risk for ASD responded on the first or second name call, but 14% of at risk infants responded later. At two years of age developmental problems were identified in many of the children who failed to respond [66].

Impairment in joint attention abilities at age 20 months was also associated with later social and language symptoms [67]. At that same age, children with ASD failed to orient towards biological motion [68]. In addition, affected children who were three to four years old per‐ formed worse not only in social orienting and joint attention, but also in attention to the distress of someone else when compared with children without ASD [69].

There are genes that have been associated with language and social impairment in children with ASD and their siblings. This may be illustrated by a familial mutation of the MET gene. The mutation consists of a deletion of 4 exons that cause a frameshift and a premature stop codon. On the homologous chromosome 7 the patient carried an allele that was associated with a decrease in MET expression.

A sibling who was also a carrier of the deletion had language and social impairment [70]. MECP2 gene has been associated with difficulty in recognizing emotional expressions and less time spent looking at facial features [71]; it has also been described as a regulator of the expression of genes involved in social behavior [72]. In animal models, social deficits are observed when the activity of specific genes is lacking, such as FMR1 and Mu-opiod recepetor gene (OPRM1) [73].

#### **Cognitive, anatomical and neurophysiological candidate endophenotypes**

Atypical patterns of brain activation, for example, in the fusiform gyrus and the amygdala have been identified in individuals with ASD during face processing [74, 75]. In adults, parents and siblings of individuals with ASD were less able to discriminate subtle differences between faces than control individuals, but performed better than adults with ASD. Relatives were significantly worse at identifying expressions of fear and disgust than controls and did not show the typical sensitivity to direct eye gaze direction as opposed to averted eye-gaze, a characteristic observed in adults with ASD [76]. In a prospective study, 6 to 10 month-old infants were asked to view faces with eye gaze directed toward or away from the infant. Characteristic components of event-related potentials were associated with ASD diagnosed later, at 36 months [77]. In one study, functional magnetic resonance imaging and eye tracking in unaffected siblings of individuals with ASD were performed. There were important differences in gaze fixation and brain activity in response to images of human faces when unaffected siblings were compared with typically developing controls. Siblings performed in a similar way than the ASD patients. When amygdala volume was compared, individuals with ASD and their siblings had similar volumes, which were significantly reduced when compared with volumes in the control group [78]. Small differences were independently found in the left amygdala when subjects with ASD or siblings were compared with controls [79]. Moreover, boys with ASD and unaffected brothers of individuals with ASD showed deficits in a visual attention task. Atypical fronto-cerebellar activation was identified in patients and unaffected brothers when they were compared with controls [80, 81].

Differences in gray matter in the cerebellum, parietal lobe, and left occipital lobe have been described between patients with ASD and controls. In some cases, differences between siblings without ASD and controls have also been reported [79, 82]. Furthermore, deficits in frontal, temporal, and occipital lobes have been identified in discordant monozygotic twins. Eight out of nine of the unaffected twins showed a social or language delay [83]. The functional magnetic resonance imaging response to happy facial expression was different between unaffected siblings and healthy controls without a family history of ASD. Here there were no statistically differences in response between unaffected siblings and patients with ASD [84].

The CNTNAP-2 gene (at 7q35 region) is mutated in individuals with intellectual disability, seizures, autistic features, and language impairment. Connectivity in the frontal lobe has been associated with CNTNAP-2 genetic variants [85].

White matter structure was analyzed in a voxel-based diffusion tensor imaging study. Children with ASD and their unaffected siblings had significantly reduced white matter fractional anisotropy values in the frontal parietal and temporal lobes when compared with controls. There were no significant differences in white matter structure between the ASD and sibling groups [86].

In other studies, children with ASD and their parents showed eye movement abnormalities that suggested a poorer spatial accuracy with respect to controls. The authors proposed that the spatial working memory may be affected in parents [87].

It has been suggested that ASD is characterized by a tendency towards local rather than global information processing. This has been called weak central coherence, which has also been reported in fathers of boys with ASD, as indicated by piecemeal processing in four tests [88]. In addition, some parents preferred nonsocial activities and ability in detail-focused process‐ ing, as is expected in subjects with ASD. A questionnaire completed by parents discriminated between ASD individuals and controls, but did not differentiate siblings [89]. In addition, atypical activation of temporal and frontal regions during the Embedded Figures Task was found in subjects with ASD and in unaffected siblings. The reduced activation on the ASD group when compared with controls was correlated with the severity of reciprocal social interaction deficits [90].

infants were asked to view faces with eye gaze directed toward or away from the infant. Characteristic components of event-related potentials were associated with ASD diagnosed later, at 36 months [77]. In one study, functional magnetic resonance imaging and eye tracking in unaffected siblings of individuals with ASD were performed. There were important differences in gaze fixation and brain activity in response to images of human faces when unaffected siblings were compared with typically developing controls. Siblings performed in a similar way than the ASD patients. When amygdala volume was compared, individuals with ASD and their siblings had similar volumes, which were significantly reduced when compared with volumes in the control group [78]. Small differences were independently found in the left amygdala when subjects with ASD or siblings were compared with controls [79]. Moreover, boys with ASD and unaffected brothers of individuals with ASD showed deficits in a visual attention task. Atypical fronto-cerebellar activation was identified in patients and unaffected

Differences in gray matter in the cerebellum, parietal lobe, and left occipital lobe have been described between patients with ASD and controls. In some cases, differences between siblings without ASD and controls have also been reported [79, 82]. Furthermore, deficits in frontal, temporal, and occipital lobes have been identified in discordant monozygotic twins. Eight out of nine of the unaffected twins showed a social or language delay [83]. The functional magnetic resonance imaging response to happy facial expression was different between unaffected siblings and healthy controls without a family history of ASD. Here there were no statistically

The CNTNAP-2 gene (at 7q35 region) is mutated in individuals with intellectual disability, seizures, autistic features, and language impairment. Connectivity in the frontal lobe has been

White matter structure was analyzed in a voxel-based diffusion tensor imaging study. Children with ASD and their unaffected siblings had significantly reduced white matter fractional anisotropy values in the frontal parietal and temporal lobes when compared with controls. There were no significant differences in white matter structure between the ASD and

In other studies, children with ASD and their parents showed eye movement abnormalities that suggested a poorer spatial accuracy with respect to controls. The authors proposed that

It has been suggested that ASD is characterized by a tendency towards local rather than global information processing. This has been called weak central coherence, which has also been reported in fathers of boys with ASD, as indicated by piecemeal processing in four tests [88]. In addition, some parents preferred nonsocial activities and ability in detail-focused process‐ ing, as is expected in subjects with ASD. A questionnaire completed by parents discriminated between ASD individuals and controls, but did not differentiate siblings [89]. In addition, atypical activation of temporal and frontal regions during the Embedded Figures Task was found in subjects with ASD and in unaffected siblings. The reduced activation on the ASD

differences in response between unaffected siblings and patients with ASD [84].

brothers when they were compared with controls [80, 81].

358 Autism Spectrum Disorder - Recent Advances

associated with CNTNAP-2 genetic variants [85].

the spatial working memory may be affected in parents [87].

sibling groups [86].

Regarding body measurements, although there is a high degree of variability in head circum‐ ference of children with ASD, the rate of macrocephaly is increased in these patients, if compared with the general population. Mean standardized head circumference and frequency of macrocephaly were similar in patients with ASD and their parents. Increased head circum‐ ference was associated with ASD severity and with a late onset of language [91]. Macrocephaly appearing in the first year of life has been described in subgroups of patients with ASD, mental retardation, and/or language delay who carry mutations on the Phosphatase and tensin homolog (PTEN) gene.  Mutations in the hepatocyte cell adhesion molecule gene (HEPACAM) have also been associated with macrocephaly and ASD [95].

Other researchers have documented impairment in cortical sensory processing in ASD cases. For example, it has been suggested that early auditory responses as well as transient memory are impaired in some children with ASD; auditory stimuli produce messages that are sent from the brainstem to the thalamus and into the auditory cortex. Event related potentials were found to be delayed in affected children, and indicated a deficiency to achieve typical maturational development of the auditory system in individuals with ASD [96, 97]. In addition, children who were at risk for ASD showed atypical neural lateralization to speech in their first year of life [98].

Impairment in cortical sensory processing has been found in patients with Rett syndrome. In addition, auditory and visual evoked potentials in mice that were heterozygous for a loss of function variant of the MeCP2 gene demonstrated impairments in sensory processing. For example, increased N1 amplitude, latency of auditory P2 component, and suppression of betaband activity were identified. There was a decreased suppression of induced gamma-band activity [99]. Gamma-band activity differences have been identified between parents of children with ASD and control adults [100].

Another area of potential endophenotypes is related with movement. There have been reports that suggest that specific motor developmental clues may be identified early in infants who will develop ASD. These signs tend to be persistent, and may be associated with abnormalities at the cerebellar, vestibular, cortical or fronto-striatal level [101]. Moreover, infants who were 18-month old and who had an older sibling with ASD were at higher risk for a delay in postural change and stability, language production and comprehension if compared with infants with no risk for ASD [56]. An association of motor anomalies and specific genes has been proposed. MeCP2, SHANK3, 22q13.3, Neurexin 1 (NRXN1) deletion, 15q11.1-q13.3, and KIAA0442 gene (known as Autism Susceptibility Candidate 2 or AUTS2) have been associated with hypotonia, stereotypes and/or motor delay; RNA-binding protein FOX1 (RBFOX1) has been associated with motor assymetry [102].


*2.4. Cell Viability Assay*

HaCaT cells (5 ×104 cells/well) were seeded in a 24-well plate containing DMEM and supplemented with 10% FBS and varying concentrations of Ectoine (0.5–1.5 μM, 24 h). Then it was irradiated in the absence or presence of UVA (3 J/cm2). B16F10 cells (5 × 104 cells/well) were seeded in a 24-well plate containing DMEM and supplemented with 10% FBS and varying concentrations of Ectoine (100–400 μM, 72 h). The cells were washed with PBS and an MTT cell viability assay was conducted [21].


**5. Hormonal signals**

6 Steroids – Basic Science

gonads. The expression of 3β-HSDs is enhanced by ACTH and LH. These isomerases catalyze the formation of Δ4-3-ketosteroids from A5-3β-hydroxysteroids, an obligate step in the biosynthesis of progestins, androgens, estrogens, mineralocorticoids and glucocorticoids. 3β-HSDs catalyze the dehydrogenation of the 3B-equatorial hydroxyl group and the subsequent isomerization of the olefinic bond to yield the A4 3-ketone structure; converting pregnenolone into progesterone, l7α-hydroxypregnenolone into 17α-

Protein kinase A signaling activators (forskolin, dibutyrylcAMP) increase the synthesis of dehydroepiandrosterone and A4, as well as the levels of 3β-HSD and P-450c17 mRNA transcripts. Activation of the protein kinase C pathway by phorbol ester treatment also elevates 3β-HSD mRNA levels and lowers P-450cl17 mRNA levels (Auchus & Miller. 2000).

The 17 -Hydroxylase/17,2O-Desmolase (P-45Oc7f or CYP17A1 lTl) is a cytochrome P450 enzyme with 17-hydroxylase and 17,20-lyase activities that catalyzes two reactions: the hydroxylation of pregnenolone and progesterone at carbon 17, and the conversion of pregnenolone into C-19 steroids. P-450c17 is a key enzyme in the steroidogenic pathway producing all steroid hormones (progestins, mineralocorticoids, glucocorticoids, androgens, and estrogens). The theca cells of the follicle and the theca lutein cells of the corpus luteum, as well as the ovarian stroma, the adrenal gland, and Leydig cells express P-450c17. (Auchus

Aromatase cytochrome P-450 c17 is an enzyme found in the endoplasmic reticulum membrane that acts on aromatizable androgen. Aromatase P 450 catalyses the biosynthesis of all estrogens from androgens by transforming the A-ring of steroids to an aromatic state through the oxidation and elimination of the C19 methyl group (Ghosh et al., 2009; Straus & Hsueh, 2000). Aromatase expression is present in fetal and immature ovaries, and in rodents, aromatase expression/activity is restricted to the gonads and the brain. In humans, aromatase activity is expressed by the adrenal medulla (Belgorosky et al., 2008), adipose

FSH is the main factor inducing aromatase activity in mural granulosa cells located on the outer edge of healthy large antral follicles and luteal cells. Aromatase is not expressed in cumulus granulosa cells. The stimulatory effects of FSH are modulated in an inhibitory way by glucocorticoids, prolactin, progestins, inhibin, triiodothyronine and thyroxine (T3-T4) (Chen et

Bone morphogenetic protein 15 (BMP-15) and growth differentiating factor 9 (GDF9) produced by the oocytes also stimulate aromatase expression and the stimulatory effects of the tumor necrosis factor- (TNF-), epidermal growth factor (EGF), transferrin, nitric oxide (NO), and superoxide dismutase (Stocco 2008). Leptin has stimulatory or inhibitory effects on

Acting as an autocrine signal, estradiol enhances the stimulatory effects of FSH on aromatase activity in granulosa cells, and its effects are mediated by the activation of

Androgens enhance FSH effects on aromatase expression by increasing cAMP levels. Aromatizable androgens synthesized by theca-internal cells are the substrate for estrogen

al., 2010). Transforming growth factor-β (TGF-β) enhances FSH effects (Stocco, 2008).

aromatase expression depending on the animal studied (Sirotkin & Grossman, 2007).

hydroxyprogesterone, and dehydroepiandrosterone into A4.

tissue, breast, skin, and bone (Czajka-Oraniec & Simpson, 2010).

**4.3 17 -Hydroxylase/17,2O-Desmolase**

& Miller, 2000; Straus & Hsue, 2000).

**4.4 Aromatase cytochrome P-450c17**

estrogen receptor β (Wang et al., 2010).

The regulation of steroid hormones synthesis is mediated by hormones secreted by the pituitary, thyroid, adipose tissue, neuropeptides, adrenals, ovaries and testicles.


**5. Diagnosis**

*Hormone Therapy and Replacement in Cancer and Aging-Related Diseases*

expression is associated with shorter survival [10].

Ewing's sarcomas are associated with rearrangement of the *EWS* gene on chromosome 22q12 with an erythroblast transformation-specific (*ETS*) gene family member, resulting in formation of EWS-ETS fusion protein (EWS-FLI). FLI1 has been suggested as a useful marker particularly when hematolymphoid markers are negative. This translocation defines Ewing's sarcoma family of tumors (ESFT) and provides a major tool for their accurate diagnosis. The translocation results in different types of genetic abnormalities, e.g., five forms of EWSR1-FLI1, three forms of EWSR1-ERG, and one form of EWSR1-FEV. A high expression of BMI-1 in ESFT cells was found to significantly affect survival and proliferation. Expression of CXCR4 has been reported to increase the risk of tumor metastases, whereas CXCR7

Ewing's sarcoma has been reported to be associated with modulation of RANKL by VEGF-165, thus resulting in activation of osteoclast-mediated bone

On the basis of histological observations, chondrosarcomas are classified into

Grade I (low grade)—cytology similar to enchondroma and hyperchromatic

Grade III (high grade)—increased cellularity and nuclear atypia, occasional

Deletions in the loci of *CDKN2A*, *EXT1*, and *EXT2* genes, *p53* mutation as late event in tumor progression, and amplification of 12q13 and loss of 9p21 are genetic

Higher expression of PTHR1 and Bcl-2 was found to be associated with increasing histological grade in chondrosarcoma, suggesting its involvement in tumor progression. A higher expression of Aurora kinases A and B was relevant as prognosis marker for chondrosarcoma. Somatic heterozygous isocitrate dehydrogenase 1 (IDH1) hot spots (R132C and R132H) or IDH2 (R172S) mutations are specifically

qPCR analysis showed a high expression of COX-2 protein in solitary peripheral chondrosarcoma. Some of the studies reported a significant role of nitrotyrosine, COX-2, CD34, and lymphatic marker podoplanin with histological grades of chondrosarcoma. Molecules such as integrin-linked kinase α and β-parvin and Mig-2 allow attachment of cells to matrix and govern cell motility and growth, thus playing an important role in progression and prognosis of

Significantly high serum levels of receptor activator of nuclear factor-κB (RANK), OPG, IL-8, IL-6, and OPG/soluble RANKL ratio have been used to detect bone tumors. Osteosarcoma patients display a higher serum concentration of IL-16

Grade II (intermediate grade)—increased cellularity, hyperchromasia, distinct

**4.2 Ewing's sarcoma**

destruction [10].

three categories:

*4.3.1 Genetic markers*

**4.3 Chondrosarcoma**

plump nuclei of uniform size [10].

found in cartilaginous tumors [10].

*4.3.2 Biological and molecular markers*

as compared to chondrosarcoma patients [35].

chondrosarcomas [10].

nucleoli, and foci of myxoid alteration [10].

giant cells, abundant necrosis, and presence of mitosis [10].

aberrations found in conventional chondrosarcomas [10].

**22**

Bone scans, X-rays, and histologic evaluation of autopsy specimens are commonly used for radiologic and histologic assessment of tumor sites [5].


**4. Visualizing NCI using a charge density topology**

The topological features of the electronic charge density have played an important part in several schemes aiming to provide a route to understanding molecular structure from first principles, that is, without resorting to any form of empirical or approximate models (other than the physically justified approximations underlying the electronic structure methods employed). Methods such as the theory of Atoms in Molecules (AIM) [92] and the Electron Localisation Function (ELF) [93–95] can provide great insight into features of the density. Both AIM and the ELF are useful for studying strong interactions such as covalent or ionic bonding but are not as useful in the analysis of very weak interactions of the type that are important for subjects as diverse as protein structure, drug design, catalysis, materials selfassembly, and many more. To address this, Johnson et al. [91, 96] introduced the NCI analysis method. This approach is based on the electronic charge density, *ρ*, and its derivatives. The first derivative *ρ* enters into the expression for the reduced density gradient, *s*,

$$S = \frac{1}{(2(3\ \pi^2))^{4/3}} \frac{|\nabla \rho|}{\rho^{4/3}} \tag{4}$$

readily obtained with first principles electronic structure methods, such calculations remain too computationally expensive for the large systems of interest in biological or materials science applications. In such cases it is possible to approximate the charge density with a sum of atomic densities providing a pro-molecular density, *ρpro*. This approximate density does not include relaxation of the atomic densities as would happen in self-consistent calculations for bonded systems. Fortunately, the largest deviation of *ρ*pro from the fully relaxed density occurs in covalent bonding regions and has a minimal effect on the (low-density) NCI regions. Substituting *ρpro* into the equations above has been found to have have very little impact on the resulting NCI analysis. For purposes of interfacing with the results of molecular dynamics simulations, pro-molecular densities have the additional advantages that they are readily computed for both finite and extended/periodic systems and the fact that this approach requires orders of magnitude less computational time than the method based on first prin-

Modeling Soft Supramolecular Nanostructures by Molecular Simulations

http://dx.doi.org/10.5772/intechopen.74939

17

A recent development of the NCI method that makes use of the pro-molecular route to building the charge density of the system under study is the Independent Gradient Method (IGM) of Lefebvre et al. [90] As with the NCI method, IGM employs in addition to *ρ* quantities related to the first and second derivatives of the density. However, in IGM the reduced density gradient, *s*, is replaced with the descriptor *δginter*, defined as the difference between the

*ginter* = |∇*ρIGM*, *inter*|−|∇*ρ*| (6)

*δginter > 0* indicates the presence of NCI and the magnitude of the descriptor at a point in space gives an indication of the strength of the interaction. *ρIGM, inter* is obtained from sums over all the atomic densities in the different fragments (here for two fragments A and B in the

> = |∑ *i*=1 *NA* \_\_\_*i x*|+ |∑ *i*=1 *NB* \_\_\_*i*

The IGM approach has the attractive feature that *δginter* allows for a more facile comparison of the strength of the weak interactions than the quantity *s* in the original NCI [90]. This is due to the fact that the presence of significant non-covalent interactions is indicated when *s* → *0* making interpretation difficult whereas the magnitude of the IGM quantity *δginter* increases in

An illustrative example of the use of the NCI and IGM methods is given in **Figures 3** and **4**. The host-guest complex shown is between curcurbit[7]uril and the dodecyl serine-based monomeric cationic surfactant 12SerTFAc [97] (to make the example more accessible to the reader only a single configuration is shown). Calculation of the NCI and IGM descriptors was

As can be seen from the molecular structure images, both the *s* and *δginter* surfaces provide qualitatively similar information and display the general distribution of the most significant

*x*| (7)

first derivatives of the charge densities for the total system and the fragments

\_\_\_ *x*) *IGM*,*inter*

performed using IGMPlot version 1.0 (http://kisthelp.univ-reims.fr/IGMPLOT/).

ciples electronic structure calculations.

x-direction)

(

proportion to the strength of the interaction.

In regions of low *ρ* such as the density tails far from a molecule the gradient remains large and so *s* displays high values. However, in regions of low *ρ* between atoms where weak NCI occur the gradient (and therefore *s*) drop to zero.

In order to differentiate between stabilizing attractive interactions and those that are unfavorable and destabilize the system it is necessary to analyze the second derivative (Laplacian) of the charge density *2 ρ*. Decomposition of *2 ρ* into the three eigenvalues representing the axes of maximal variation

$$
\nabla^2 \rho = \lambda\_1 + \lambda\_2 + \lambda\_{\mathcal{Y}} \text{ ( $\lambda\_1 \le \lambda\_2 \le \lambda\_3$ )}\tag{5}
$$

provides information on the nature of the interactions at a given point in space. *λ2* displays negative values in stabilizing/bonding regions (charge is flowing into this region indicating a local build-up of *ρ*) while in destabilizing/repulsive regions it is positive (charge flowing out, indicating a local depletion of *ρ*). Plotting *s* against *sign(λ2 )ρ* will therefore permit the identification of NCI in regions where s and *sign(λ2 )ρ* → *0*. Although these quantities can be readily obtained with first principles electronic structure methods, such calculations remain too computationally expensive for the large systems of interest in biological or materials science applications. In such cases it is possible to approximate the charge density with a sum of atomic densities providing a pro-molecular density, *ρpro*. This approximate density does not include relaxation of the atomic densities as would happen in self-consistent calculations for bonded systems. Fortunately, the largest deviation of *ρ*pro from the fully relaxed density occurs in covalent bonding regions and has a minimal effect on the (low-density) NCI regions.

of regions of low charge density corresponding to stabilizing/destabilizing NCI, based on the analysis of the electronic charge density of the interacting molecules and the respective gradients. Although the original NCI method of Johnson and co-workers [91] provide a very similar qualitative analysis of NCI, the reduced density gradient, s, used to identify the interaction types is a dimensionless quantity and therefore difficults the evaluation of the respective strengths. The new IGM allows for a quantitative comparison of the strength of NCI

The topological features of the electronic charge density have played an important part in several schemes aiming to provide a route to understanding molecular structure from first principles, that is, without resorting to any form of empirical or approximate models (other than the physically justified approximations underlying the electronic structure methods employed). Methods such as the theory of Atoms in Molecules (AIM) [92] and the Electron Localisation Function (ELF) [93–95] can provide great insight into features of the density. Both AIM and the ELF are useful for studying strong interactions such as covalent or ionic bonding but are not as useful in the analysis of very weak interactions of the type that are important for subjects as diverse as protein structure, drug design, catalysis, materials selfassembly, and many more. To address this, Johnson et al. [91, 96] introduced the NCI analysis method. This approach is based on the electronic charge density, *ρ*, and its derivatives. The

first derivative *ρ* enters into the expression for the reduced density gradient, *s*,

*ρ*. Decomposition of *2*

out, indicating a local depletion of *ρ*). Plotting *s* against *sign(λ2*

provides information on the nature of the interactions at a given point in space. *λ2*

(2(3 *π*2))1/3

In regions of low *ρ* such as the density tails far from a molecule the gradient remains large and so *s* displays high values. However, in regions of low *ρ* between atoms where weak NCI occur

In order to differentiate between stabilizing attractive interactions and those that are unfavorable and destabilize the system it is necessary to analyze the second derivative (Laplacian)

negative values in stabilizing/bonding regions (charge is flowing into this region indicating a local build-up of *ρ*) while in destabilizing/repulsive regions it is positive (charge flowing

\_\_\_\_ |∇*ρ*|

, which corresponds directly to the charge

*ρ*4/3 (4)

*ρ* into the three eigenvalues representing the

, (*λ*1 ≤ *λ*2 ≤ *λ*3) (5)

*)ρ* → *0*. Although these quantities can be

displays

*)ρ* will therefore permit the

through the calculation of the IGM descriptor, δg

*s* = \_\_\_\_\_\_\_\_ 1

the gradient (and therefore *s*) drop to zero.

∇2 *ρ* = *λ*1 + *λ*2 + *λ*3

identification of NCI in regions where s and *sign(λ2*

of the charge density *2*

axes of maximal variation

**4. Visualizing NCI using a charge density topology**

density gradient(s) in real-space.

16 Molecular Dynamics

Substituting *ρpro* into the equations above has been found to have have very little impact on the resulting NCI analysis. For purposes of interfacing with the results of molecular dynamics simulations, pro-molecular densities have the additional advantages that they are readily computed for both finite and extended/periodic systems and the fact that this approach requires orders of magnitude less computational time than the method based on first principles electronic structure calculations.

A recent development of the NCI method that makes use of the pro-molecular route to building the charge density of the system under study is the Independent Gradient Method (IGM) of Lefebvre et al. [90] As with the NCI method, IGM employs in addition to *ρ* quantities related to the first and second derivatives of the density. However, in IGM the reduced density gradient, *s*, is replaced with the descriptor *δginter*, defined as the difference between the first derivatives of the charge densities for the total system and the fragments

$$\delta \mathbf{g}^{\text{inter}} = \left| \nabla \rho^{\text{IGM}, \text{ inter}} \right| - \left| \nabla \rho \right| \tag{6}$$

*δginter > 0* indicates the presence of NCI and the magnitude of the descriptor at a point in space gives an indication of the strength of the interaction. *ρIGM, inter* is obtained from sums over all the atomic densities in the different fragments (here for two fragments A and B in the x-direction)

$$\left(\frac{\delta\rho}{\delta x}\right)^{\text{IGM},\text{totr}} = \left| \sum\_{i=1}^{N\_e} \frac{\delta\rho\_i}{\delta x} \right| + \left| \sum\_{i=1}^{N\_e} \frac{\delta\rho\_i}{\delta x} \right| \tag{7}$$

The IGM approach has the attractive feature that *δginter* allows for a more facile comparison of the strength of the weak interactions than the quantity *s* in the original NCI [90]. This is due to the fact that the presence of significant non-covalent interactions is indicated when *s* → *0* making interpretation difficult whereas the magnitude of the IGM quantity *δginter* increases in proportion to the strength of the interaction.

An illustrative example of the use of the NCI and IGM methods is given in **Figures 3** and **4**. The host-guest complex shown is between curcurbit[7]uril and the dodecyl serine-based monomeric cationic surfactant 12SerTFAc [97] (to make the example more accessible to the reader only a single configuration is shown). Calculation of the NCI and IGM descriptors was performed using IGMPlot version 1.0 (http://kisthelp.univ-reims.fr/IGMPLOT/).

As can be seen from the molecular structure images, both the *s* and *δginter* surfaces provide qualitatively similar information and display the general distribution of the most significant

of) systems such as those arising from MD simulations it is likely that the future will see the

Modeling Soft Supramolecular Nanostructures by Molecular Simulations

http://dx.doi.org/10.5772/intechopen.74939

19

This section presents some examples in which MD or MC simulations are used for establishing the contributions of NCI (e.g. electrostatic, hydrophobic and hydrogen-bond interactions) to the free energy, in systems in which these are the main source of recognition, assembly, and stability. These include, for instance, host-guest complexes, polyelectrolytes

MD and free-energy calculations have provided insight on relevant aspects including the effect of substituents, the role of solvation, and rationales for the conformation and thermodynamic characterization of the systems under investigation. Among several studies on the topic, available in the literature, only a few are briefly reviewed. For instance, MD simulations in water, with PMF estimation based on both TI and constraint force methods, have been used for inspecting the thermodynamic properties of binding of some inorganic ions,

confined β-cyclodextrins [14, 98]. In general, the association process between the host and guest molecules is analyzed along the reaction coordinate defined by the distance between the centers of mass of both host and guest, along a reference coordinate (e.g. z-axis). In these particular systems, electrostatic interactions and hydrogen bonding have played a major role on the binding process. For instance, simulations have elucidated the association mode of sulfate anion with free and grafted β-cyclodextrin (see **Figure 5**). For the latter system, a small minimum in the PMF profile (**Figure 5**, top), positioned at a larger distance relative to the cavity of surface-grafted cyclodextrin, suggested the formation of a noninclusion complex. The ion binds to the host by forming hydrogen bonds with the free-cyclodextrin portal. Also relevant is the individual energy contributions to the cyclodextrin-ion interaction, which is governed by electrostatic interactions. However, this favorable electrostaction contribution is not sufficient to compensate desolvation of the anion, considering the respective hydration energy [14].

The release and transport of drugs mediated by cyclodextrin-based carriers, have also been investigated [99] systematically using MD and free-energy calculations, showing the preferred inclusion modes of such drugs for cyclodextrins. One example (see **Figure 6**), refers to the binding of amphotericin B (AmB), which possesses two sites, within the respective prolonged macrolide, with higher binding affinity to γ-cyclodextrin. The decomposition of the PMFs into free-energy contributions have suggested that van der Waals and electrostatic interactions are

Recently, some of the authors [5] have demonstrated the relevance of non-included moieties in the stability constants of several cyclodextrin-based complexes. The binding constants for naphtalene derivatives forming complexes with β-cyclodextrin were calculated (ranging from

naphthalene promoted an increase in the binding constant (up to 100-fold), irrespective of the

kJ.mol−1), pointing out the important effects of the substituents. Substitution of

the main driving forces responsible for the formation of this type of complexes [99].

2− (**Figure 5**), and ferrocenyl alkanethiols with both free and gold-surface

newer IGM method being used much more extensively than the original NCI one.

**5. Applications**

and proteins.

such as ClO4

128 to 2.1×104

− and SO4

**Figure 3.** Host-guest complexation between curcurbit[7]uril and the dodecyl serine-based monomeric cationic surfactant 12SerTFAc. (left) reduced density gradient, *s* = 0.4, isosurface colored by value of *sign(λ2 )ρ* (−0.03 ≤ *sign(λ2 )ρ* ≤ 0.03 a.U.). Blue = stabilizing, red = destabilizing and green = weak interactions. (right) scatter plot of *s* and *sign(λ2 )ρ* values.

**Figure 4.** Host-guest complexation between curcurbit[7]uril and 12serTFAc sufactant. (left) IGM *δginter* = 0.01 a.U.Isosurface colored by value of *sign(λ2 )ρ* (−0.03 ≤ *sign(λ2 )ρ* ≤ 0.03 a.U.). Blue = stabilizing, red = destabilizing and green = weak interactions. (right) scatter plot of *δginter* and *sign(λ2 )ρ* values.

host-guest interactions. Similarly, the color-coding provided by the value of *sign(λ2 )ρ* can be seen to predict that the interactions are largely of the weak van der Waals type with the exception of a single blue region denoting the hydrogen bond between the serine hydroxyl group and the host. A significant difference between the *s* and *δginter* surfaces is that the latter also contains information on the strength of the interactions through the volumes of the isosurface regions at a given point. The IGM approach therefore provides an important extra source of information on the nature of the interactions. The intrinsic difference between the two methods is even more clearly seen in the adjacent scatter plots. In the IGM plot (**Figure 4**, right) peaks of different magnitude corresponding to different strengths of interaction can be seen which give rise to the differing isosurface volumes. The NCI plot (**Figure 3**, right), however, displays all spikes in the non-covalent interaction region −0.025 ≤ *sign(λ2 )ρ* ≤ 0.025 in a very similar manner and makes interpretation much less easy. For this reason, despite very similar computational requirements for both methods making them equally suitable for analysis of large (ensembles of) systems such as those arising from MD simulations it is likely that the future will see the newer IGM method being used much more extensively than the original NCI one.