The complexity of dynamics in small neural circuits

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of figures 8 and 9 fixed, results unchange

Nondiffusive suprathermal ion transport in simple magnetized toroidal plasmas

We investigate suprathermal ion dynamics in simple magnetized toroidal plasmas in the pres- ence of electrostatic turbulence driven by the ideal interchange instability. Turbulent fields from fluid simulations are used in the non-relativistic equation of ion motion to compute suprathermal tracer ion trajectories. Suprathermal ion dispersion starts with a brief ballistic phase, during which particles do not interact with the plasma, followed by a turbulence interaction phase. In this one simple system, we observe the entire spectrum of suprathermal ion dynamics, from subdiffusion to superdiffusion, depending on beam energy and turbulence amplitude. We estimate the duration of the ballistic phase and identify basic mechanisms during the interaction phase that determine the character of suprathermal ion dispersion upon the beam energy and turbulence fluctuation amplitude.Comment: 5 pages, 3 figures, accepted in PR

Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons

We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the Fitzhugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes places, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations, or non-local partial differential equations resembling the McKean-Vlasov-Fokker- Planck equations. We prove the well-posedness of these equations, i.e. the existence and uniqueness of a solution. We also show the results of some preliminary numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiment also indicate that the McKean-Vlasov-Fokker- Planck equations may be a good way to understand the mean-field dynamics through, e.g., a bifurcation analysis.Comment: 55 pages, 9 figure

Biophysical mechanisms of membrane perturbation and signal transduction produced by proteins and peptides

My primary research interest is focused on the field of cellular electrical activity, ranging from the ion channels that generates it, up to the study of intracellular processes regulating it, and new generation of drugs. For this purpose, during my Ph.D. I have learnt and improved different cutting-edge techniques, i.e. the patch-clamp technique, the fluorescence imaging, and the synthesis and use of model membranes. Moreover, to explore particular aspects of these molecular mechanisms and to overcome the issues raised during the investigations, non-conventional strategies were employed, even requiring the development of specific devices not commercially available. In summary, my Ph.D. thesis is focused on two projects: the biophysical characterization of a particular class of membrane active peptides, and the modulation of visual phototransduction in vertebrate cones. In the first project, I investigated the mechanism of membrane perturbation of cell-penetrating and antimicrobial peptides using the patch-clamp technique. Cell-penetrating peptides (CPPs) are short peptides that are able to cross the cell membrane via energy-dependent and/or independent mechanisms, with low toxicity and without the use of specific receptors. This ability is preserved even when CPPs are conjugated with a large cargo, thus representing an innovative pharmacological tool for the diffusion of large and hydrophilic drugs into the cells. Despite the mechanism of cellular uptake is still debated in literature, it has been proved that it can occur by either direct translocation or endocytosis. In the latter case, though, the cargo-peptide complex often remains trapped inside the endocytic vesicles and is not able to reach its therapeutic target. A possible solution to this problem could be found in another class of small peptides, similar to CPPs, i.e. the antimicrobial peptides (AMPs). AMPs are 12-50 amino acids long peptides, which represent an essential part in the innate immune system in most organisms. Indeed, they are among the first defensive molecules released during infections and their activity is direct thorough the membrane of bacteria, causing its destruction and consequently the death of the pathogen. Therefore, the ability of AMPs to disrupt biological membranes could be exploited to improve the CPPs escape from the endocytic vesicles in addition to, of course, their application as a novel class of antibiotics. The idea is to conjugate the CPP with a molecule that possess an antimicrobial activity, which can destroy the vesicle membrane, and help the complex to reach its target once it has been internalized in the cell. On this ground, the first project I carried out regards the study of a novel chimeric peptide, CM18-Tat11, composed of the antimicrobial peptide CM18 (a cecropin-mellitin hybrid peptide) linked to the cell-penetrating peptide Tat11 (derived from the basic domain of HIV-1 Tat protein). In particular, I investigated the membrane perturbing activity of this peptide (and of its elements) using the patch-clamp technique and operating under strictly physiological conditions. This study has been carried out by recording the ion current flowing through the channels formed by these peptides (if any), once inserted in the membrane of Chinese hamster ovary (CHO) cells. In these experiments, the peptides were applied to (and removed from) the extracellular CHO membrane in ~50 ms with a computer-controlled microperfusion system. Therefore, besides assessing ion channel characteristics, the dynamics of pore formation and disaggregation could be precisely evaluated as well. I found that CM18-Tat11 produces a large and irreversible plasma membrane lysis, at concentration where CM18 and Tat11 give instead a nearly reversible membrane permeabilization and no perturbation, respectively. Furthermore, using the same method, I studied the biophysical characteristic of another antimicrobial peptide, called CM12, which sequence was obtained from the optimization of CM18. When applied on CHO, CM12 and CM18 produce voltage-independent membrane permeabilization, and no single-channel events were detected at low peptides concentration. These results indicate that both peptides form pores according to a toroidal model, in which the lipid layer bends continuously through the pore so that the core is formed by both lipid head groups and the peptides. Finally, I have studied the single-channels properties generated by the pore-forming peptide alamethicin (Alm) F50/5 and its [L-Glu(OMe)7,18,19] analog inserted in a natural membrane and in giant unilamellar vesicles (GUVs). The possibility to compare the channel activity in the precisely controlled lipid environment of GUVs, with the one recorded in a natural membrane, will open new possibilities in the biophysical characterization of the pores. The second project of this thesis is focused on the study of the physiological role of the calcium sensor GCAP3 (guanylate cyclase activated protein 3) in the phototransduction cascade in zebrafish. I pursued this study simulating the over expressions and the knockdown of this protein, through the delivery of zGCAP3, or of its monoclonal antibody, into zebrafish cone cytoplasm, while recording their photorensponses with the patch-clamp technique. The proteins were administered inside the cone via the patch pipette thanks to an intracellular perfusion system developed in this thesis. This system allows the delivery of exogenous molecules inside the cell with a controlled timing, by expelling them with a small teflon tube inserted into the pipette lumen controlled by a microperfusion apparatus. Results indicated that the increase in the concentration in zGCAP3 did not altered significantly the light response, while the perfusion with the antibody anti-zGCAP3 caused the progressive fall of the dark current, together with the progressive slowing down of the flash response kinetics. The surprising lack of an effect of zGCAP3 incorporation, suggests that the endogenous number of zGCAP3 is saturating, therefore any further increase of this sensor is ineffective. However, the effects of the antibody can be explained as an inhibition of the target enzyme of zGCAP3, which is the guanylate cyclase (GC). Finally, no experiments mentioned above would have been accomplished without the development of a “pressure-polishing” system, which makes it possible to modify the geometry of the patch-clamp pipette. The pipette shank (the final part of the pipette) is, in fact, very long and tapered, thus generating a high resistance to the passage of ions and molecules, and making very difficult to perfuse efficiently the cell with the internal perfusion. The pressure polishing setup I developed enlarged the patch pipette shank, using a calibrated combination of heat and air pressure. These pipettes minimized errors in membrane potential control and allowed the insertion of teflon tubes in the pipette lumen very close to its tip

Master of Science

thesisThe Stochastic Time-Inverted Lagrangian Transport (STILT) model is comprised of a compiled Fortran executable that carries out advection and dispersion calculations as well as a higher level code layer for simulation control and user interaction, written in the open source data analysis language R. We introduce modifications to the STILT-R codebase with the aim to improve the model's applicability to fine-scale trace gas measurement approaches. The changes facilitate placement of spatially distributed receptors and provide high level methods for single and multinode parallelism. We present a kernel density estimator to calculate influence footprints and demonstrate improvements over previous methods. This framework provides a central source repository to reduce code fragmentation between STILT user groups as well as a systematic, well-documented workflow for users. We apply the modified STILT to lightrail measurements in Salt Lake City, UT and discuss how results from our analyses can inform future fine-scale measurement approaches and modeling efforts