Finite-size and correlation-induced effects in Mean-field Dynamics

The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system

Gestational trophoblastic disease: does central nervous system chemoprophylaxis have a role?

In the UK there are standardized surveillance procedures for gestational trophoblastic disease. However, there are differences in practice between the two treatment centres in terms of definition of persistent gestational trophoblastic disease, prognostic risk assessment and chemotherapeutic regimens. The role of prophylactic chemotherapy for cerebral micrometastatic disease in persistent gestational trophoblastic disease is unclear. We have analysed the outcome of 69 patients with lung metastases who elsewhere might have received prophylactic intrathecal chemotherapy. Of the 69 patients, 67 received intravenous chemotherapy only. The other two patients had cerebral metastases at presentation. One patient who received only intravenous chemotherapy subsequently developed a cerebral metastasis, but this patient's initial treatment was compromised by non-compliance. This experience supports our current policy of not treating patients with pulmonary metastases, without clinical evidence of central nervous system (CNS) involvement, with prophylactic intrathecal therapy. © 1999 Cancer Research Campaig

Stochastic models for the in silico simulation of synaptic processes

Background: Research in life sciences is benefiting from a large availability of formal description techniques and analysis methodologies. These allow both the phenomena investigated to be precisely modeled and virtual experiments to be performed in silico. Such experiments may result in easier, faster, and satisfying approximations of their in vitro/vivo counterparts. A promising approach is represented by the study of biological phenomena as a collection of interactive entities through process calculi equipped with stochastic semantics. These exploit formal grounds developed in the theory of concurrency in computer science, account for the not continuous, nor discrete, nature of many phenomena, enjoy nice compositional properties and allow for simulations that have been demonstrated to be coherent with data in literature. Results: Motivated by the need to address some aspects of the functioning of neural synapses, we have developed one such model for synaptic processes in the calyx of Held, which is a glutamatergic synapse in the auditory pathway of the mammalia. We have developed such a stochastic model starting from existing kinetic models based on ODEs of some sub-components of the synapse, integrating other data from literature and making some assumptions about non-fully understood processes. Experiments have confirmed the coherence of our model with known biological data, also validating the assumptions made. Our model overcomes some limitations of the kinetic ones and, to our knowledge, represents the first model of synaptic processes based on process calculi. The compositionality of the approach has permitted us to independently focus on tuning the models of the pre- and post- synaptic traits, and then to naturally connect them, by dealing with “interface” issues. Furthermore, we have improved the expressiveness of the model, e.g. by embedding easy control of element concentration time courses. Sensitivity analysis over several parameters of the model has provided results that may help clarify the dynamics of synaptic transmission, while experiments with the model of the complete synapse seem worth explaining short-term plasticity mechanisms. Conclusions: Specific presynaptic and postsynaptic mechanisms can be further analysed under various conditions, for instance by studying the presynaptic behaviour under repeated activations. The level of details of the description can be refined, for instance by further specifying the neurotransmitter generation and release steps. Taking advantage of the compositionality of the approach, an enhanced model could then be composed with other neural models, designed within the same framework, in order to obtain a more detailed and comprehensive model. In the long term, we are interested, in particular, in addressing models of synaptic plasticity, i.e. activity dependent mechanisms, which are the bases of memory and learning processes. More on the computer science side, we plan to follow some directions to improve the underlying computational model and the linguistic primitives it provides as suggested by the experiments carried out, e.g. by introducing a suitable notion of (spatial) locality

The use of a physiologically based pharmacokinetic model to evaluate deconvolution measurements of systemic absorption

BACKGROUND: An unknown input function can be determined by deconvolution using the systemic bolus input function (r) determined using an experimental input of duration ranging from a few seconds to many minutes. The quantitative relation between the duration of the input and the accuracy of r is unknown. Although a large number of deconvolution procedures have been described, these routines are not available in a convenient software package. METHODS: Four deconvolution methods are implemented in a new, user-friendly software program (PKQuest, ). Three of these methods are characterized by input parameters that are adjusted by the user to provide the "best" fit. A new approach is used to determine these parameters, based on the assumption that the input can be approximated by a gamma distribution. Deconvolution methodologies are evaluated using data generated from a physiologically based pharmacokinetic model (PBPK). RESULTS AND CONCLUSIONS: The 11-compartment PBPK model is accurately described by either a 2 or 3-exponential function, depending on whether or not there is significant tissue binding. For an accurate estimate of r the first venous sample should be at or before the end of the constant infusion and a long (10 minute) constant infusion is preferable to a bolus injection. For noisy data, a gamma distribution deconvolution provides the best result if the input has the form of a gamma distribution. For other input functions, good results are obtained using deconvolution methods based on modeling the input with either a B-spline or uniform dense set of time points

Functional Refinement in the Projection from Ventral Cochlear Nucleus to Lateral Superior Olive Precedes Hearing Onset in Rat

Principal neurons of the lateral superior olive (LSO) compute the interaural intensity differences necessary for localizing high-frequency sounds. To perform this computation, the LSO requires precisely tuned, converging excitatory and inhibitory inputs that are driven by the two ears and that are matched for stimulus frequency. In rodents, the inhibitory inputs, which arise from the medial nucleus of the trapezoid body (MNTB), undergo extensive functional refinement during the first postnatal week. Similar functional refinement of the ascending excitatory pathway, which arises in the anteroventral cochlear nucleus (AVCN), has been assumed but has not been well studied. Using whole-cell voltage clamp in acute brainstem slices of neonatal rats, we examined developmental changes in input strength and pre- and post-synaptic properties of the VCN-LSO pathway. A key question was whether functional refinement in one of the two major input pathways might precede and then guide refinement in the opposite pathway. We find that elimination and strengthening of VCN inputs to the LSO occurs over a similar period to that seen for the ascending inhibitory (MNTB-LSO) pathway. During this period, the fractional contribution provided by NMDA receptors (NMDARs) declines while the contribution from AMPA receptors (AMPARs) increases. In the NMDAR-mediated response, GluN2B-containing NMDARs predominate in the first postnatal week and decline sharply thereafter. Finally, the progressive decrease in paired-pulse depression between birth and hearing onset allows these synapses to follow progressively higher frequencies. Our data are consistent with a model in which the excitatory and inhibitory projections to LSO are functionally refined in parallel during the first postnatal week, and they further suggest that GluN2B-containing NMDARs may mediate early refinement in the VCN-LSO pathway

Search for Gravitational Waves from Primordial Black Hole Binary Coalescences in the Galactic Halo

We use data from the second science run of the LIGO gravitational-wave detectors to search for the gravitational waves from primordial black hole (PBH) binary coalescence with component masses in the range 0.2--$1.0 M_\odot$. The analysis requires a signal to be found in the data from both LIGO observatories, according to a set of coincidence criteria. No inspiral signals were found. Assuming a spherical halo with core radius 5 kpc extending to 50 kpc containing non-spinning black holes with masses in the range 0.2--$1.0 M_\odot$, we place an observational upper limit on the rate of PBH coalescence of 63 per year per Milky Way halo (MWH) with 90% confidence.Comment: 7 pages, 4 figures, to be submitted to Phys. Rev.

Temperature Control of Fimbriation Circuit Switch in Uropathogenic Escherichia coli: Quantitative Analysis via Automated Model Abstraction

Uropathogenic Escherichia coli (UPEC) represent the predominant cause of urinary tract infections (UTIs). A key UPEC molecular virulence mechanism is type 1 fimbriae, whose expression is controlled by the orientation of an invertible chromosomal DNA element—the fim switch. Temperature has been shown to act as a major regulator of fim switching behavior and is overall an important indicator as well as functional feature of many urologic diseases, including UPEC host-pathogen interaction dynamics. Given this panoptic physiological role of temperature during UTI progression and notable empirical challenges to its direct in vivo studies, in silico modeling of corresponding biochemical and biophysical mechanisms essential to UPEC pathogenicity may significantly aid our understanding of the underlying disease processes. However, rigorous computational analysis of biological systems, such as fim switch temperature control circuit, has hereto presented a notoriously demanding problem due to both the substantial complexity of the gene regulatory networks involved as well as their often characteristically discrete and stochastic dynamics. To address these issues, we have developed an approach that enables automated multiscale abstraction of biological system descriptions based on reaction kinetics. Implemented as a computational tool, this method has allowed us to efficiently analyze the modular organization and behavior of the E. coli fimbriation switch circuit at different temperature settings, thus facilitating new insights into this mode of UPEC molecular virulence regulation. In particular, our results suggest that, with respect to its role in shutting down fimbriae expression, the primary function of FimB recombinase may be to effect a controlled down-regulation (rather than increase) of the ON-to-OFF fim switching rate via temperature-dependent suppression of competing dynamics mediated by recombinase FimE. Our computational analysis further implies that this down-regulation mechanism could be particularly significant inside the host environment, thus potentially contributing further understanding toward the development of novel therapeutic approaches to UPEC-caused UTIs

The Generation of Promoter-Mediated Transcriptional Noise in Bacteria

Noise in the expression of a gene produces fluctuations in the concentration of the gene product. These fluctuations can interfere with optimal function or can be exploited to generate beneficial diversity between cells; gene expression noise is therefore expected to be subject to evolutionary pressure. Shifts between modes of high and low rates of transcription initiation at a promoter appear to contribute to this noise both in eukaryotes and prokaryotes. However, models invoked for eukaryotic promoter noise such as stable activation scaffolds or persistent nucleosome alterations seem unlikely to apply to prokaryotic promoters. We consider the relative importance of the steps required for transcription initiation. The 3-step transcription initiation model of McClure is extended into a mathematical model that can be used to predict consequences of additional promoter properties. We show in principle that the transcriptional bursting observed at an E. coli promoter by Golding et al. (2005) can be explained by stimulation of initiation by the negative supercoiling behind a transcribing RNA polymerase (RNAP) or by the formation of moribund or dead-end RNAP-promoter complexes. Both mechanisms are tunable by the alteration of promoter kinetics and therefore allow the optimization of promoter mediated noise.Comment: 4 figures, 1 table. Supplemental materials are also include