A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

A new approach for the dynamic modelling of the human knee

Mathematical models of the knee joint are important tools which have both theoretical and practical applications. They are used by researchers to fully understand the stabilizing role of the components of the joint, by engineers as an aid for prosthetic design, by surgeons during the planning of an operation or during the operation itself, and by orthopedists for diagnosis and rehabilitation purposes. The principal aims of knee models are to reproduce the restraining function of each structure of the joint and to replicate the relative motion of the bones which constitute the joint itself. It is clear that the first point is functional to the second one. However, the standard procedures for the dynamic modelling of the knee tend to be more focused on the second aspect: the motion of the joint is correctly replicated, but the stabilizing role of the articular components is somehow lost. A first contribution of this dissertation is the definition of a novel approach — called sequential approach — for the dynamic modelling of the knee. The procedure makes it possible to develop more and more sophisticated models of the joint by a succession of steps, starting from a first simple model of its passive motion. The fundamental characteristic of the proposed procedure is that the results obtained at each step do not worsen those already obtained at previous steps, thus preserving the restraining function of the knee structures. The models which stem from the first two steps of the sequential approach are then presented. The result of the first step is a model of the passive motion of the knee, comprehensive of the patello-femoral joint. Kinematical and anatomical considerations lead to define a one degree of freedom rigid link mechanism, whose members represent determinate components of the joint. The result of the second step is a stiffness model of the knee. This model is obtained from the first one, by following the rules of the proposed procedure. Both models have been identified from experimental data by means of an optimization procedure. The simulated motions of the models then have been compared to the experimental ones. Both models accurately reproduce the motion of the joint under the corresponding loading conditions. Moreover, the sequential approach makes sure the results obtained at the first step are not worsened at the second step: the stiffness model can also reproduce the passive motion of the knee with the same accuracy than the previous simpler model. The procedure proved to be successful and thus promising for the definition of more complex models which could also involve the effect of muscular forces.

Quality and safety of oils and fats obtained as co-products or by-products of the food chain and destined to animal production

The aim of the first part of this thesis was to evaluate the effect of trans fatty acid- (TFA), contaminant, polycyclic aromatic hydrocarbon (PAH)- and oxidation productenriched diets on the content of TFA and conjugated linoleic acid (CLA) isomers in meat and liver of both poultry and rabbit. The enriched feedings were prepared with preselected fatty co-and by-products that contained low and high levels of TFA (low, palm fatty acid distillate; high, hydrogenated palm fatty acid distillate), environmental contaminants (dioxins and PCBs) (two different fish oils), PAH (olive oil acid oils and pomace olive oil from chemical refining, for low and high levels) and oxidation products (sunflower-olive oil blend before and after frying), so as to obtain single feedings with three enrichment degrees (high, medium and low) of the compound of interest. This experimental set-up is a part of a large, collaborative European project (http://www.ub.edu/feedfat/), where other chemical and health parameters are assessed. Lipids were extracted, methylated with diazomethane, then transmethylated with 2N KOH/methanol and analyzed by GC and silver-ion TLC-GC. TFA and CLA were determined in the fats, the feedings, meat and liver of both poultry and rabbit. In general, the level of TFA and CLA in meat and liver mainly varied according to those originally found in the feeding fats. It must be pointed out, though, that TFA and CLA accumulation was different for the two animal species, as well as for the two types of tissues. The TFA composition of meat and liver changes according to the composition of the oils added to the feeds with some differences between species. Chicken meat with skin shows higher TFA content (2.6–5.4 fold) than rabbit meat, except for the “PAH” trial. Chicken liver shows higher TFA content (1.2–2.1 fold) than rabbit liver, except for the “TRANS” and “PAH” trials. In both chicken and rabbit meats, the TFA content was higher for the “TRANS” trial, followed by the “DIOXIN” trial. Slight differences were found on the “OXIDATION” and “PAH” trends in both types of meats. In both chicken and rabbit livers, the TFA content was higher for the “TRANS” trial, followed by those of the “PAH”, “DIOXIN” and “OXIDATION” trials. This trend, however, was not identical to that of feeds, where the TFA content varied as follows: “TRANS” > “DIOXIN” >“PAH” > “OXIDATION”. In chicken and rabbit meat samples, C18:1 TFA were the most abundant, followed by C18:2 TFA and C18:3 TFA, except for the “DIOXIN” trial where C18:3 TFA > C18:2 TFA. In chicken and rabbit liver samples of the “TRANS” and “OXIDATION” trials, C18:1 TFA were the most abundant, followed by C18:2 TFA and C18:3 TFA, whereas C18:3 TFA > C18:2 in the “DIOXIN” trial. Slight differences were found on the “PAH” trend in livers from both species. The second part of the thesis dealt with the study of lipid oxidation in washed turkey muscle added with different antioxidants. The evaluation on the oxidative stability of muscle foods found that oxidation could be measured by headspace solid phase microestraction (SPME) of hexanal and propanal. To make this method effective, an antioxidant system was added to stored muscle to stop the oxidative processes. An increase in ionic strength of the sample was also implemented to increase the concentration of aldehydes in the headspace. This method was found to be more sensitive than the commonly used thiobarbituric acid reactive substances (TBARs) method. However, after antioxidants were added and oxidation was stopped, the concentration of aldehydes decreased. It was found that the decrease in aldehyde concentration was due to the binding of the aldehydes to muscle proteins, thus decreasing the volatility and making them less detectable.

The Integrated European Project "GEHA - GEnetics of Healthy Aging": recruitment, health status assessment and survival of the Italian 90+ sibpairs

The present study is part of the EU Integrated Project “GEHA – Genetics of Healthy Aging” (Franceschi C et al., Ann N Y Acad Sci. 1100: 21-45, 2007), whose aim is to identify genes involved in healthy aging and longevity, which allow individuals to survive to advanced age in good cognitive and physical function and in the absence of major age-related diseases. Aims The major aims of this thesis were the following: 1. to outline the recruitment procedure of 90+ Italian siblings performed by the recruiting units of the University of Bologna (UNIBO) and Rome (ISS). The procedures related to the following items necessary to perform the study were described and commented: identification of the eligible area for recruitment, demographic aspects related to the need of getting census lists of 90+siblings, mail and phone contact with 90+ subjects and their families, bioethics aspects of the whole procedure, standardization of the recruitment methodology and set-up of a detailed flow chart to be followed by the European recruitment centres (obtainment of the informed consent form, anonimization of data by using a special code, how to perform the interview, how to collect the blood, how to enter data in the GEHA Phenotypic Data Base hosted at Odense). 2. to provide an overview of the phenotypic characteristics of 90+ Italian siblings recruited by the recruiting units of the University of Bologna (UNIBO) and Rome (ISS). The following items were addressed: socio-demographic characteristics, health status, cognitive assessment, physical conditions (handgrip strength test, chair-stand test, physical ability including ADL, vision and hearing ability, movement ability and doing light housework), life-style information (smoking and drinking habits) and subjective well-being (attitude towards life). Moreover, haematological parameters collected in the 90+ sibpairs as optional parameters by the Bologna and Rome recruiting units were used for a more comprehensive evaluation of the results obtained using the above mentioned phenotypic characteristics reported in the GEHA questionnaire. 3. to assess 90+ Italian siblings as far as their health/functional status is concerned on the basis of three classification methods proposed in previous studies on centenarians, which are based on: • actual functional capabilities (ADL, SMMSE, visual and hearing abilities) (Gondo et al., J Gerontol. 61A (3): 305-310, 2006); • actual functional capabilities and morbidity (ADL, ability to walk, SMMSE, presence of cancer, ictus, renal failure, anaemia, and liver diseases) (Franceschi et al., Aging Clin Exp Res, 12:77-84, 2000); • retrospectively collected data about past history of morbidity and age of disease onset (hypertension, heart disease, diabetes, stroke, cancer, osteopororis, neurological diseases, chronic obstructive pulmonary disease and ocular diseases) (Evert et al., J Gerontol A Biol Sci Med Sci. 58A (3): 232-237, 2003). Firstly these available models to define the health status of long-living subjects were applied to the sample and, since the classifications by Gondo and Franceschi are both based on the present functional status, they were compared in order to better recognize the healthy aging phenotype and to identify the best group of 90+ subjects out of the entire studied population. 4. to investigate the concordance of health and functional status among 90+ siblings in order to divide sibpairs in three categories: the best (both sibs are in good shape), the worst (both sibs are in bad shape) and an intermediate group (one sib is in good shape and the other is in bad shape). Moreover, the evaluation wanted to discover which variables are concordant among siblings; thus, concordant variables could be considered as familiar variables (determined by the environment or by genetics). 5. to perform a survival analysis by using mortality data at 1st January 2009 from the follow-up as the main outcome and selected functional and clinical parameters as explanatory variables. Methods A total of 765 90+ Italian subjects recruited by UNIBO (549 90+ siblings, belonging to 258 families) and ISS (216 90+ siblings, belonging to 106 families) recruiting units are included in the analysis. Each subject was interviewed according to a standardized questionnaire, comprising extensively utilized questions that have been validated in previous European studies on elderly subjects and covering demographic information, life style, living conditions, cognitive status (SMMSE), mood, health status and anthropometric measurements. Moreover, subjects were asked to perform some physical tests (Hand Grip Strength test and Chair Standing test) and a sample of about 24 mL of blood was collected and then processed according to a common protocol for the preparation and storage of DNA aliquots. Results From the analysis the main findings are the following: - a standardized protocol to assess cognitive status, physical performances and health status of European nonagenarian subjects was set up, in respect to ethical requirements, and it is available as a reference for other studies in this field; - GEHA families are enriched in long-living members and extreme survival, and represent an appropriate model for the identification of genes involved in healthy aging and longevity; - two simplified sets of criteria to classify 90+ sibling according to their health status were proposed, as operational tools for distinguishing healthy from non healthy subjects; - cognitive and functional parameters have a major role in categorizing 90+ siblings for the health status; - parameters such as education and good physical abilities (500 metres walking ability, going up and down the stairs ability, high scores at hand grip and chair stand tests) are associated with a good health status (defined as “cognitive unimpairment and absence of disability”); - male nonagenarians show a more homogeneous phenotype than females, and, though far fewer in number, tend to be healthier than females; - in males the good health status is not protective for survival, confirming the male-female health survival paradox; - survival after age 90 was dependent mainly on intact cognitive status and absence of functional disabilities; - haemoglobin and creatinine levels are both associated with longevity; - the most concordant items among 90+ siblings are related to the functional status, indicating that they contain a familiar component. It is still to be investigated at what level this familiar component is determined by genetics or by environment or by the interaction between genetics, environment and chance (and at what level). Conclusions In conclusion, we could state that this study, in accordance with the main objectives of the whole GEHA project, represents one of the first attempt to identify the biological and non biological determinants of successful/unsuccessful aging and longevity. Here, the analysis was performed on 90+ siblings recruited in Northern and Central Italy and it could be used as a reference for others studies in this field on Italian population. Moreover, it contributed to the definition of “successful” and “unsuccessful” aging and categorising a very large cohort of our most elderly subjects into “successful” and “unsuccessful” groups provided an unrivalled opportunity to detect some of the basic genetic/molecular mechanisms which underpin good health as opposed to chronic disability. Discoveries in the topic of the biological determinants of healthy aging represent a real possibility to identify new markers to be utilized for the identification of subgroups of old European citizens having a higher risk to develop age-related diseases and disabilities and to direct major preventive medicine strategies for the new epidemic of chronic disease in the 21st century.

Technical innovations for the diagnosis and the rehabilitation of motor and perceptive impairments of the child with Cerebral Palsy

The treatment of the Cerebral Palsy (CP) is considered as the “core problem” for the whole field of the pediatric rehabilitation. The reason why this pathology has such a primary role, can be ascribed to two main aspects. First of all CP is the form of disability most frequent in childhood (one new case per 500 birth alive, (1)), secondarily the functional recovery of the “spastic” child is, historically, the clinical field in which the majority of the therapeutic methods and techniques (physiotherapy, orthotic, pharmacologic, orthopedic-surgical, neurosurgical) were first applied and tested. The currently accepted definition of CP – Group of disorders of the development of movement and posture causing activity limitation (2) – is the result of a recent update by the World Health Organization to the language of the International Classification of Functioning Disability and Health, from the original proposal of Ingram – A persistent but not unchangeable disorder of posture and movement – dated 1955 (3). This definition considers CP as a permanent ailment, i.e. a “fixed” condition, that however can be modified both functionally and structurally by means of child spontaneous evolution and treatments carried out during childhood. The lesion that causes the palsy, happens in a structurally immature brain in the pre-, peri- or post-birth period (but only during the firsts months of life). The most frequent causes of CP are: prematurity, insufficient cerebral perfusion, arterial haemorrhage, venous infarction, hypoxia caused by various origin (for example from the ingestion of amniotic liquid), malnutrition, infection and maternal or fetal poisoning. In addition to these causes, traumas and malformations have to be included. The lesion, whether focused or spread over the nervous system, impairs the whole functioning of the Central Nervous System (CNS). As a consequence, they affect the construction of the adaptive functions (4), first of all posture control, locomotion and manipulation. The palsy itself does not vary over time, however it assumes an unavoidable “evolutionary” feature when during growth the child is requested to meet new and different needs through the construction of new and different functions. It is essential to consider that clinically CP is not only a direct expression of structural impairment, that is of etiology, pathogenesis and lesion timing, but it is mainly the manifestation of the path followed by the CNS to “re”-construct the adaptive functions “despite” the presence of the damage. “Palsy” is “the form of the function that is implemented by an individual whose CNS has been damaged in order to satisfy the demands coming from the environment” (4). Therefore it is only possible to establish general relations between lesion site, nature and size, and palsy and recovery processes. It is quite common to observe that children with very similar neuroimaging can have very different clinical manifestations of CP and, on the other hand, children with very similar motor behaviors can have completely different lesion histories. A very clear example of this is represented by hemiplegic forms, which show bilateral hemispheric lesions in a high percentage of cases. The first section of this thesis is aimed at guiding the interpretation of CP. First of all the issue of the detection of the palsy is treated from historical viewpoint. Consequently, an extended analysis of the current definition of CP, as internationally accepted, is provided. The definition is then outlined in terms of a space dimension and then of a time dimension, hence it is highlighted where this definition is unacceptably lacking. The last part of the first section further stresses the importance of shifting from the traditional concept of CP as a palsy of development (defect analysis) towards the notion of development of palsy, i.e., as the product of the relationship that the individual however tries to dynamically build with the surrounding environment (resource semeiotics) starting and growing from a different availability of resources, needs, dreams, rights and duties (4). In the scientific and clinic community no common classification system of CP has so far been universally accepted. Besides, no standard operative method or technique have been acknowledged to effectively assess the different disabilities and impairments exhibited by children with CP. CP is still “an artificial concept, comprising several causes and clinical syndromes that have been grouped together for a convenience of management” (5). The lack of standard and common protocols able to effectively diagnose the palsy, and as a consequence to establish specific treatments and prognosis, is mainly because of the difficulty to elevate this field to a level based on scientific evidence. A solution aimed at overcoming the current incomplete treatment of CP children is represented by the clinical systematic adoption of objective tools able to measure motor defects and movement impairments. A widespread application of reliable instruments and techniques able to objectively evaluate both the form of the palsy (diagnosis) and the efficacy of the treatments provided (prognosis), constitutes a valuable method able to validate care protocols, establish the efficacy of classification systems and assess the validity of definitions. Since the ‘80s, instruments specifically oriented to the analysis of the human movement have been advantageously designed and applied in the context of CP with the aim of measuring motor deficits and, especially, gait deviations. The gait analysis (GA) technique has been increasingly used over the years to assess, analyze, classify, and support the process of clinical decisions making, allowing for a complete investigation of gait with an increased temporal and spatial resolution. GA has provided a basis for improving the outcome of surgical and nonsurgical treatments and for introducing a new modus operandi in the identification of defects and functional adaptations to the musculoskeletal disorders. Historically, the first laboratories set up for gait analysis developed their own protocol (set of procedures for data collection and for data reduction) independently, according to performances of the technologies available at that time. In particular, the stereophotogrammetric systems mainly based on optoelectronic technology, soon became a gold-standard for motion analysis. They have been successfully applied especially for scientific purposes. Nowadays the optoelectronic systems have significantly improved their performances in term of spatial and temporal resolution, however many laboratories continue to use the protocols designed on the technology available in the ‘70s and now out-of-date. Furthermore, these protocols are not coherent both for the biomechanical models and for the adopted collection procedures. In spite of these differences, GA data are shared, exchanged and interpreted irrespectively to the adopted protocol without a full awareness to what extent these protocols are compatible and comparable with each other. Following the extraordinary advances in computer science and electronics, new systems for GA no longer based on optoelectronic technology, are now becoming available. They are the Inertial and Magnetic Measurement Systems (IMMSs), based on miniature MEMS (Microelectromechanical systems) inertial sensor technology. These systems are cost effective, wearable and fully portable motion analysis systems, these features gives IMMSs the potential to be used both outside specialized laboratories and to consecutive collect series of tens of gait cycles. The recognition and selection of the most representative gait cycle is then easier and more reliable especially in CP children, considering their relevant gait cycle variability. The second section of this thesis is focused on GA. In particular, it is firstly aimed at examining the differences among five most representative GA protocols in order to assess the state of the art with respect to the inter-protocol variability. The design of a new protocol is then proposed and presented with the aim of achieving gait analysis on CP children by means of IMMS. The protocol, named ‘Outwalk’, contains original and innovative solutions oriented at obtaining joint kinematic with calibration procedures extremely comfortable for the patients. The results of a first in-vivo validation of Outwalk on healthy subjects are then provided. In particular, this study was carried out by comparing Outwalk used in combination with an IMMS with respect to a reference protocol and an optoelectronic system. In order to set a more accurate and precise comparison of the systems and the protocols, ad hoc methods were designed and an original formulation of the statistical parameter coefficient of multiple correlation was developed and effectively applied. On the basis of the experimental design proposed for the validation on healthy subjects, a first assessment of Outwalk, together with an IMMS, was also carried out on CP children. The third section of this thesis is dedicated to the treatment of walking in CP children. Commonly prescribed treatments in addressing gait abnormalities in CP children include physical therapy, surgery (orthopedic and rhizotomy), and orthoses. The orthotic approach is conservative, being reversible, and widespread in many therapeutic regimes. Orthoses are used to improve the gait of children with CP, by preventing deformities, controlling joint position, and offering an effective lever for the ankle joint. Orthoses are prescribed for the additional aims of increasing walking speed, improving stability, preventing stumbling, and decreasing muscular fatigue. The ankle-foot orthosis (AFO), with a rigid ankle, are primarily designed to prevent equinus and other foot deformities with a positive effect also on more proximal joints. However, AFOs prevent the natural excursion of the tibio-tarsic joint during the second rocker, hence hampering the natural leaning progression of the whole body under the effect of the inertia (6). A new modular (submalleolar) astragalus-calcanear orthosis, named OMAC, has recently been proposed with the intention of substituting the prescription of AFOs in those CP children exhibiting a flat and valgus-pronated foot. The aim of this section is thus to present the mechanical and technical features of the OMAC by means of an accurate description of the device. In particular, the integral document of the deposited Italian patent, is provided. A preliminary validation of OMAC with respect to AFO is also reported as resulted from an experimental campaign on diplegic CP children, during a three month period, aimed at quantitatively assessing the benefit provided by the two orthoses on walking and at qualitatively evaluating the changes in the quality of life and motor abilities. As already stated, CP is universally considered as a persistent but not unchangeable disorder of posture and movement. Conversely to this definition, some clinicians (4) have recently pointed out that movement disorders may be primarily caused by the presence of perceptive disorders, where perception is not merely the acquisition of sensory information, but an active process aimed at guiding the execution of movements through the integration of sensory information properly representing the state of one’s body and of the environment. Children with perceptive impairments show an overall fear of moving and the onset of strongly unnatural walking schemes directly caused by the presence of perceptive system disorders. The fourth section of the thesis thus deals with accurately defining the perceptive impairment exhibited by diplegic CP children. A detailed description of the clinical signs revealing the presence of the perceptive impairment, and a classification scheme of the clinical aspects of perceptual disorders is provided. In the end, a functional reaching test is proposed as an instrumental test able to disclosure the perceptive impairment. References 1. Prevalence and characteristics of children with cerebral palsy in Europe. Dev Med Child Neurol. 2002 Set;44(9):633-640. 2. Bax M, Goldstein M, Rosenbaum P, Leviton A, Paneth N, Dan B, et al. Proposed definition and classification of cerebral palsy, April 2005. Dev Med Child Neurol. 2005 Ago;47(8):571-576. 3. Ingram TT. A study of cerebral palsy in the childhood population of Edinburgh. Arch. Dis. Child. 1955 Apr;30(150):85-98. 4. Ferrari A, Cioni G. The spastic forms of cerebral palsy : a guide to the assessment of adaptive functions. Milan: Springer; 2009. 5. Olney SJ, Wright MJ. Cerebral Palsy. Campbell S et al. Physical Therapy for Children. 2nd Ed. Philadelphia: Saunders. 2000;:533-570. 6. Desloovere K, Molenaers G, Van Gestel L, Huenaerts C, Van Campenhout A, Callewaert B, et al. How can push-off be preserved during use of an ankle foot orthosis in children with hemiplegia? A prospective controlled study. Gait Posture. 2006 Ott;24(2):142-151.

Reactivity of activated electrophiles and nucleophiles: labile intermediates and properties of the reaction products

The main topic of my Ph.D. thesis is the study of nucleophilic and electrophilic aromatic substitution reaction, in particular from a mechanistic point of view. The research was mainly focused on the reactivity of superactivated aromatic systems. In spite of their high reactivity (hence the high reaction’s rate), we were able to identify and in some case to isolate -complexes until now only hypothesized. For example, interesting results comes from the study of the protonation of the supernucleophiles tris(dialkylamino)benzenes. However, the best result obtained in this field was the isolation and structural characterization of the first stables zwitterionic Wheland-Meisenheimer complexes by using 2,4-dipyrrolidine-1,3-thiazole as supernucleophile and 4,6-dinitrobenzofuroxan or 4,6-dinitrotetrazolepyridine as superelectrophile. These reactions were also studied by means of computational chemistry, which allowed us to better investigate on the energetic and properties of the reactions and reactants studied. We also discovered, in some case fortuitously, some relevant properties and application of the compounds we synthesized, such as fluorescence in solid state and nanoparticles, or textile dyeing. We decided to investigate all these findings also by collaborating with other research groups. During a period in the “Laboratoire de Structure et Réactivité des Systèmes Moléculaires Complexes-SRSMC, Université de Lorraine et CNRS, France, I carried out computational studies on new iron complexes for the use as dyes in Dye Sensitized Solar Cells (DSSC). Furthermore, thanks to this new expertise, I was involved in a collaboration for the study of the ligands’ interaction in biological systems. A collaboration with University of Urbino allowed us to investigate on the reactivity of 1,2-diaza-1,3-dienes toward nucleophiles such as amino and phosphine derivatives, which led to the synthesis of new products some of which are 6 or 7 member heterocycles containing both phosphorus and nitrogen atoms.

Characterization of the Caspr2 and NLGN2 ligands: a proteomic and biochemical approach

Autism Spectrum Disorder (ASD) is a range of early-onset conditions classified as neurodevelopmental disorders, characterized by deficits in social interactions and communication, as well as by restricted interest and repetitive behaviors. Among the proteins associated with this spectrum of disease there are Caspr2, α-NRXN1, NLGN1-4. Caspr2 is involved in the clustering of K+ channels at the juxtaparanodes, where it is proposed to bind TAG-1. Recent works reported a synaptic localization of Caspr2, but little is know on its role in this compartment. NRXNs and their ligand NLGNs, instead, have a well-defined role in the formation and maintenance of synapses. Among the neuroligins, NLGN2 binds NRXNs with the lowest affinity, suggesting that it could have other not yet characterized ligands. The aim of this work was to better characterize the binding of Caspr2 to TAG-1 and to identify new potential binding partner for Caspr2 and NLGN2. Unexpectedly, using Isothermal Titration Calorimetry and co-immunoprecipitation experiments the direct association of the first two proteins could not be verified and the results indicate that the first evidences reporting it were biased by false-positive artifacts. These findings, together with the uncharacterized synaptic localization of Caspr2, made the identification of new potential binding partners for this protein necessary. To find new proteins that associate with Caspr2 and NLGN2, affinity chromatography in tandem with mass spectrometry experiments were performed. Interestingly, about 25 new potential partners were found for these two proteins and NLGN1, that was originally included as a control: 5 of those, namely SFRP1, CLU, APOE, CNTN1 and TNR, were selected for further investigations. Only the association of CLU to NLGN2 was confirmed. In the future, screenings of the remaining candidates have to be carried out and the functional role for the proposed NLGN2-CLU complex has to be studied.