Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

ATG based combination therapy - a novel clinically relevant approach to promote regulation and induce long-term allograft survival

Regulatory T cells (Treg) actively regulate alloimmune responses and promote transplantation tolerance. Polyclonal anti-thymocyte globulin (ATG), a widely used induction therapy in clinical organ transplantation, depletes peripheral T cells. However, resistance to tolerance induction is seen with certain T cell depleting strategies and is attributed to alterations in the balance of naïve, memory and regulatory T cells. Here we report a novel reagent, murine ATG (mATG), depletes T cells but preferentially spares CD25+ natural Tregs which limit skewing of T cell repertoire toward T-effector-memory (Tem) phenotype among the recovering T cells. T-cell depletion with mATG combined with CTLA4Ig and Sirolimus synergize to prolong graft survival by tipping the Treg/Tem balance further in favor of Tregs by preserving Tregs, facilitating generation of new Tregs by a conversion mechanism and limiting Tem expansion in response to alloantigen and homeostatic proliferation. These results provide the rationale for translating such novel combination therapies to promote tolerance in primate and human organ transplantation.

Role of nitric oxide and endocannabinoids in synaptic plasticity in the perirhinal cortex and in visual recognition memory

Introduction and aims of the research Nitric oxide (NO) and endocannabinoids (eCBs) are major retrograde messengers, involved in synaptic plasticity (long-term potentiation, LTP, and long-term depression, LTD) in many brain areas (including hippocampus and neocortex), as well as in learning and memory processes. NO is synthesized by NO synthase (NOS) in response to increased cytosolic Ca2+ and mainly exerts its functions through soluble guanylate cyclase (sGC) and cGMP production. The main target of cGMP is the cGMP-dependent protein kinase (PKG). Activity-dependent release of eCBs in the CNS leads to the activation of the Gαi/o-coupled cannabinoid receptor 1 (CB1) at both glutamatergic and inhibitory synapses. The perirhinal cortex (Prh) is a multimodal associative cortex of the temporal lobe, critically involved in visual recognition memory. LTD is proposed to be the cellular correlate underlying this form of memory. Cholinergic neurotransmission has been shown to play a critical role in both visual recognition memory and LTD in Prh. Moreover, visual recognition memory is one of the main cognitive functions impaired in the early stages of Alzheimer’s disease. The main aim of my research was to investigate the role of NO and ECBs in synaptic plasticity in rat Prh and in visual recognition memory. Part of this research was dedicated to the study of synaptic transmission and plasticity in a murine model (Tg2576) of Alzheimer’s disease. Methods Field potential recordings. Extracellular field potential recordings were carried out in horizontal Prh slices from Sprague-Dawley or Dark Agouti juvenile (p21-35) rats. LTD was induced with a single train of 3000 pulses delivered at 5 Hz (10 min), or via bath application of carbachol (Cch; 50 μM) for 10 min. LTP was induced by theta-burst stimulation (TBS). In addition, input/output curves and 5Hz-LTD were carried out in Prh slices from 3 month-old Tg2576 mice and littermate controls. Behavioural experiments. The spontaneous novel object exploration task was performed in intra-Prh bilaterally cannulated adult Dark Agouti rats. Drugs or vehicle (saline) were directly infused into the Prh 15 min before training to verify the role of nNOS and CB1 in visual recognition memory acquisition. Object recognition memory was tested at 20 min and 24h after the end of the training phase. Results Electrophysiological experiments in Prh slices from juvenile rats showed that 5Hz-LTD is due to the activation of the NOS/sGC/PKG pathway, whereas Cch-LTD relies on NOS/sGC but not PKG activation. By contrast, NO does not appear to be involved in LTP in this preparation. Furthermore, I found that eCBs are involved in LTP induction, but not in basal synaptic transmission, 5Hz-LTD and Cch-LTD. Behavioural experiments demonstrated that the blockade of nNOS impairs rat visual recognition memory tested at 24 hours, but not at 20 min; however, the blockade of CB1 did not affect visual recognition memory acquisition tested at both time points specified. In three month-old Tg2576 mice, deficits in basal synaptic transmission and 5Hz-LTD were observed compared to littermate controls. Conclusions The results obtained in Prh slices from juvenile rats indicate that NO and CB1 play a role in the induction of LTD and LTP, respectively. These results are confirmed by the observation that nNOS, but not CB1, is involved in visual recognition memory acquisition. The preliminary results obtained in the murine model of Alzheimer’s disease indicate that deficits in synaptic transmission and plasticity occur very early in Prh; further investigations are required to characterize the molecular mechanisms underlying these deficits.

Analysis of the memory B cell response against glycoconjugate vaccines

The development of vaccines directed against polysaccharide capsules of S. pneumoniae, H. influenzae and N. meningitidis have been of great importance in preventing potentially fatal infections. Bacterial capsular polysaccharides are T-cell-independent antigens that induce specific antibody response characterized by IgM immunoglobulins, with a very low IgG class switched response and lack of capability of inducing a booster response. The inability of pure polysaccharides to induce sustained immune responses has required the development of vaccines containing polysaccharides conjugated to a carrier protein, with the aim to generate T cell help. It is clear that the immunogenicity of glycoconjugate vaccines can vary depending on different factors, e.g. chemical nature of the linked polysaccharide, carrier protein, age of the target population, adjuvant used. The present study analyzes the memory B cell (MBC) response to the polysaccharide and to the carrier protein following vaccination with a glycoconjugate vaccine for the prevention of Group B streptococcus (GBS) infection. Not much is known about the role of adjuvants in the development of immunological memory raised against GBS polysaccharides, as well as about the influence of having a pre-existing immunity against the carrier protein on the B cell response raised against the polysaccharide component of the vaccine. We demonstrate in the mouse model that adjuvants can increase the antibody and memory B cell response to the carrier protein and to the conjugated polysaccharide. We also demonstrate that a pre-existing immunity to the carrier protein favors the development of the antibody and memory B cell response to subsequent vaccinations with a glycoconjugate, even in absence of adjuvants. These data provide a useful insight for a better understanding of the mechanism of action of this class of vaccines and for designing the best vaccine that could result in a productive and long lasting memory response.