A Multiscale Model to Investigate Circadian Rhythmicity of Pacemaker Neurons in the Suprachiasmatic Nucleus

The suprachiasmatic nucleus (SCN) of the hypothalamus is a multicellular system that drives daily rhythms in mammalian behavior and physiology. Although the gene regulatory network that produces daily oscillations within individual neurons is well characterized, less is known about the electrophysiology of the SCN cells and how firing rate correlates with circadian gene expression. We developed a firing rate code model to incorporate known electrophysiological properties of SCN pacemaker cells, including circadian dependent changes in membrane voltage and ion conductances. Calcium dynamics were included in the model as the putative link between electrical firing and gene expression. Individual ion currents exhibited oscillatory patterns matching experimental data both in current levels and phase relationships. VIP and GABA neurotransmitters, which encode synaptic signals across the SCN, were found to play critical roles in daily oscillations of membrane excitability and gene expression. Blocking various mechanisms of intracellular calcium accumulation by simulated pharmacological agents (nimodipine, IP3- and ryanodine-blockers) reproduced experimentally observed trends in firing rate dynamics and core-clock gene transcription. The intracellular calcium concentration was shown to regulate diverse circadian processes such as firing frequency, gene expression and system periodicity. The model predicted a direct relationship between firing frequency and gene expression amplitudes, demonstrated the importance of intracellular pathways for single cell behavior and provided a novel multiscale framework which captured characteristics of the SCN at both the electrophysiological and gene regulatory levels

Exact and Approximate Stochastic Simulation of Intracellular Calcium Dynamics

In simulations of chemical systems, the main task is to find an exact or approximate solution of the chemical master equation (CME) that satisfies certain constraints with respect to computation time and accuracy. While Brownian motion simulations of single molecules are often too time consuming to represent the mesoscopic level, the classical Gillespie algorithm is a stochastically exact algorithm that provides satisfying results in the representation of calcium microdomains. Gillespie's algorithm can be approximated via the tau-leap method and the chemical Langevin equation (CLE). Both methods lead to a substantial acceleration in computation time and a relatively small decrease in accuracy. Elimination of the noise terms leads to the classical, deterministic reaction rate equations (RRE). For complex multiscale systems, hybrid simulations are increasingly proposed to combine the advantages of stochastic and deterministic algorithms. An often used exemplary cell type in this context are striated muscle cells (e.g., cardiac and skeletal muscle cells). The properties of these cells are well described and they express many common calcium-dependent signaling pathways. The purpose of the present paper is to provide an overview of the aforementioned simulation approaches and their mutual relationships in the spectrum ranging from stochastic to deterministic algorithms

In silico evolution of signaling networks using rule-based models: bistable response dynamics

One of the ultimate goals in biology is to understand the design principles of biological systems. Such principles, if they exist, can help us better understand complex, natural biological systems and guide the engineering of de novo ones. Towards deciphering design principles, in silico evolution of biological systems with proper abstraction is a promising approach. Here, we demonstrate the application of in silico evolution combined with rule-based modelling for exploring design principles of cellular signaling networks. This application is based on a computational platform, called BioJazz, which allows in silico evolution of signaling networks with unbounded complexity. We provide a detailed introduction to BioJazz architecture and implementation and describe how it can be used to evolve and/or design signaling networks with defined dynamics. For the latter, we evolve signaling networks with switch-like response dynamics and demonstrate how BioJazz can result in new biological insights on network structures that can endow bistable response dynamics. This example also demonstrated both the power of BioJazz in evolving and designing signaling networks and its limitations at the current stage of development.Comment: 24 pages, 7 figure

Toward Multiscale Models of Cyanobacterial Growth

Oxygenic photosynthesis dominates global primary productivity ever since its evolution more than three billion years ago. While many aspects of phototrophic growth are well understood, it remains a considerable challenge to elucidate the manifold dependencies and interconnections between the diverse cellular processes that together facilitate the synthesis of new cells. Phototrophic growth involves the coordinated action of several layers of cellular functioning, ranging from the photosynthetic light reactions and the electron transport chain, to carbon-concentrating mechanisms and the assimilation of inorganic carbon. It requires the synthesis of new building blocks by cellular metabolism, protection against excessive light, as well as diurnal regulation by a circadian clock and the orchestration of gene expression and cell division. Computational modeling allows us to quantitatively describe these cellular functions and processes relevant for phototrophic growth. As yet, however, computational models are mostly confined to the inner workings of individual cellular processes, rather than describing the manifold interactions between them in the context of a living cell. Using cyanobacteria as model organisms, this contribution seeks to summarize existing computational models that are relevant to describe phototrophic growth and seeks to outline their interactions and dependencies. Our ultimate aim is to understand cellular functioning and growth as the outcome of a coordinated operation of diverse yet interconnected cellular processes.Peer Reviewe

Neuronal oscillations on an ultra-slow timescale: daily rhythms in electrical activity and gene expression in the mammalian master circadian clockwork

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Neuronal oscillations of the brain, such as those observed in the cortices and hippocampi of behaving animals and humans, span across wide frequency bands, from slow delta waves (0.1 Hz) to ultra-fast ripples (600 Hz). Here, we focus on ultra-slow neuronal oscillators in the hypothalamic suprachiasmatic nuclei (SCN), the master daily clock that operates on interlocking transcription-translation feedback loops to produce circadian rhythms in clock gene expression with a period of near 24 h (< 0.001 Hz). This intracellular molecular clock interacts with the cell's membrane through poorly understood mechanisms to drive the daily pattern in the electrical excitability of SCN neurons, exhibiting an up-state during the day and a down-state at night. In turn, the membrane activity feeds back to regulate the oscillatory activity of clock gene programs. In this review, we emphasise the circadian processes that drive daily electrical oscillations in SCN neurons, and highlight how mathematical modelling contributes to our increasing understanding of circadian rhythm generation, synchronisation and communication within this hypothalamic region and across other brain circuits.M.D.C.B is supported by the University ofExeter Medical School (UEMS). C.O.D’s work was partially supported bythe National Science Foundation under grant nos. DMS-1412877 and DMS-155237, and the U.S. Army Research Laboratory and the U.S. ArmyResearch Office under Grant No. W911NF-16-1-0584

Formal reasoning on qualitative models of coinfection of HIV and Tuberculosis and HAART therapy.

BACKGROUND: Several diseases, many of which nowadays pandemic, consist of multifactorial pathologies. Paradigmatic examples come from the immune response to pathogens, in which cases the effects of different infections combine together, yielding complex mutual feedback, often a positive one that boosts infection progression in a scenario that can easily become lethal. HIV is one such infection, which weakens the immune system favouring the insurgence of opportunistic infections, amongst which Tuberculosis (TB). The treatment with antiretroviral therapies has shown effective in reducing mortality. An in-depth understanding of complex systems, like the one consisting of HIV, TB and related therapies, is an open great challenge, on the boundaries of bioinformatics, computational and systems biology. RESULTS: We present a simplified formalisation of the highly dynamic system consisting of HIV, TB and related therapies, at the cellular level. The progression of the disease (AIDS) depends hence on interactions between viruses, cells, chemokines, the high mutation rate of viruses, the immune response of individuals and the interaction between drugs and infection dynamics. We first discuss a deterministic model of dual infection (HIV and TB) which is able to capture the long-term dynamics of CD4 T cells, viruses and Tumour Necrosis Factor (TNF). We contrast this model with a stochastic approach which captures intrinsic fluctuations of the biological processes. Furthermore, we also integrate automated reasoning techniques, i.e. probabilistic model checking, in our formal analysis. Beyond numerical simulations, model checking allows general properties (effectiveness of anti-HIV therapies) to be verified against the models by means of an automated procedure. Our work stresses the growing importance and flexibility of model checking techniques in bioinformatics. In this paper we i) describe HIV as a complex case of infectious diseases; ii) provide a number of different formal descriptions that suitably account for aspects of interests; iii) suggest that the integration of different models together with automated reasoning techniques can improve the understanding of infections and therapies through formal analysis methodologies. CONCLUSION: We argue that the described methodology suitably supports the study of viral infections in a formal, automated and expressive manner. We envisage a long-term contribution of this kind of approaches to clinical Bioinformatics and Translational Medicine.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are