Modelling molecular processes in weight loss:Regulation of metabolic flexibility

The World Health Organisation has estimated a three-fold increase in global obesity from 1975 to 2018. This is alarming as obesity is associated with several chronic illnesses including cardiovascular diseases, type 2 diabetes, metabolic syndrome, and several forms of cancer. This research utilises multiple types of data from a weight loss study to identify key cellular processes in the cells of the adipose tissue involved in weight loss. The objective is to highlight cellular pathways and genes, which can be targeted to counter obesity and associated illnesses. It was observed that metabolic flexibility, the ability of organisms to switch between metabolic nutrients, was impaired in obese individuals along with an increase in inflammation, indicating possible interactions between the two leading to the development of chronic illnesses in obesity

Modelling and Analysis of the Feeding Regimen Induced Entrainment of Hepatocyte Circadian Oscillators Using Petri Nets

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Parametric linear hybrid automata for complex environmental systems modeling

Environmental systems, whether they be weather patterns or predator-prey relationships, are dependent on a number of different variables, each directly or indirectly affecting the system at large. Since not all of these factors are known, these systems take on non-linear dynamics, making it difficult to accurately predict meaningful behavioral trends far into the future. However, such dynamics do not warrant complete ignorance of different efforts to understand and model close approximations of these systems. Towards this end, we have applied a logical modeling approach to model and analyze the behavioral trends and systematic trajectories that these systems exhibit without delving into their quantification. This approach, formalized by René Thomas for discrete logical modeling of Biological Regulatory Networks (BRNs) and further extended in our previous studies as parametric biological linear hybrid automata (Bio-LHA), has been previously employed for the analyses of different molecular regulatory interactions occurring across various cells and microbial species. As relationships between different interacting components of a system can be simplified as positive or negative influences, we can employ the Bio-LHA framework to represent different components of the environmental system as positive or negative feedbacks. In the present study, we highlight the benefits of hybrid (discrete/continuous) modeling which lead to refinements among the fore-casted behaviors in order to find out which ones are actually possible. We have taken two case studies: an interaction of three microbial species in a freshwater pond, and a more complex atmospheric system, to show the applications of the Bio-LHA methodology for the timed hybrid modeling of environmental systems. Results show that the approach using the Bio-LHA is a viable method for behavioral modeling of complex environmental systems by finding timing constraints while keeping the complexity of the model at a minimum

Simulation results depicting the over feeding scenario with 5 meals/day.

<p>The meals were simulated on 0800 hrs, 1100 hrs, 1400 hrs, 1700 hrs, and 2000 hrs, along with the 12 hour overnight fast. The results indicate an over expression of PARP1, with suppressed expressions of almost all entities, other than HSF1.</p

The generated reachability graph of the complete discrete Petri Net model.

<p>The order of the tuple in each marking is ⟨CB, SIRT1, PC, Feed, HSF1, PARP1⟩. The graph was generated from the initial marking <i>m</i>₀ = (0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1), shown at the top. It consists of 64 unique markings and 224 marking transitions, and is itself a single strongly connected component.</p

Schematic diagram of the entities and pathways linking feeding-fasting signals to Circadian Clock and Oscillators.

<p>The core circadian clock comprises of the entities CLOCK, BMAL1, CLOCK-BMAL1, RORs, PERIOD, CRYPTOCHROME, and PER-CRY. The metabolic arm of the circadian system comprises of the enzymes NAMPT, NMNAT, and SIRT1 with the metabolites Nic, NMN, and NAD⁺. Finally, the entities PARP1, HSF1, CREB, and ChREBP link the feeding and fasting signals to the rest of the circadian system via their interactions.</p

Example of a standard Petri Net.

<p>(A) A simple Petri Net model using the standard Petri Net framework. The set <i>P</i> = {<i>p</i>1, <i>p</i>2} is the set of places, <i>T</i> = {<i>t</i>1, <i>t</i>2} is the set of transitions, <i>f</i> = {<i>p</i>1<i>t</i>1, <i>p</i>2<i>t</i>2, <i>t</i>1<i>p</i>2, <i>t</i>2<i>p</i>1} is the set of directed arcs all of which have an arc weight of 1, and <i>m</i>₀ = (2, 0) being the initial marking for the ordered tuple (<i>p</i>1, <i>p</i>2). (B) The Reachability Graph obtained from the PN from the initial marking <i>m</i>₀. The graph shows three cycles: (2, 0) → (1, 1) → (0, 2) → (1, 1) → (2, 0), (2, 0) → (1, 1) → (2, 0), <i>and</i>(1, 1) → (0, 2) → (1, 1); and contains no deadlocks.</p

Simulation results of the 3 meals/day entrainment base scenario.

<p>Each grid box shows 1 complete day on the x-axis, and a complete level on the y-axis. The graph shows the oscillations of the entities in accordance with the 0800 hrs breakfast, 1400 hrs lunch, and 2000 hrs dinner, with an overnight fast of 12 hours, for a duration of 10 days. The entities were able to entrain on the third day, and continued the periodic behaviour from then on. All entities are utilising their respective rate values given in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0117519#pone.0117519.t002" target="_blank">Table 2</a>, except for the Feeding signal which is modelled as a periodic discrete signal, shown as the vertical black pillars. The number of meals, and their timings was assumed to be the prevalent regimen, and were thus used as the base scenario to model other differing regimen scenarios.</p

Table showing the rates used for the continuous transitions of each entity. The concentration increase rate specifies the rate for the transitons <i>t</i> ∈ °<i>p</i>, and the concentration decrease rate specifies for <i>t</i> ∈ <i>p</i>°, for place <i>p</i> representing the entity in the system.

<p>Table showing the rates used for the continuous transitions of each entity. The concentration increase rate specifies the rate for the transitons <i>t</i> ∈ °<i>p</i>, and the concentration decrease rate specifies for <i>t</i> ∈ <i>p</i>°, for place <i>p</i> representing the entity in the system.</p