Difference between revisions of "Integrated model description"

Revision as of 16:38, 6 March 2021

Model construction

BioUML platform for model reconstruction

BioUML (Biological Universal Modeling Language) (Kolpakov et al., 2019) [1] is an integrated platform for modeling of biological systems and developed in Java. The tool is applicable to solve the wide range of tasks including access to diverse biological databases, mathematical description and visual representation of biological systems, numerical calculations and parametric and other types of model analysis. The main features of the BioUML are: an ability to use both standalone version of the tool and web-services remotely; a support of generally accepted standards for model description of biological systems (SBML) and their graphical notation (SBGN) [Hucka et al., 2018; Le Novere et al., 2009]; visual modeling of biological systems and processes: an user has an opportunity to graphically construct and edit the developed model; a support of different mathematical representations (ordinary differential equations, algebraic equations, discrete events and stochastic modeling) a modular platform architecture that facilitates extension and/or addition of new types of models, methods of numerical calculations etc.

Visual modeling

Representation of investigating systems as graphical diagrams by means of a software supporting visual modeling can significantly facilitate procedure of the model reconstruction. We consider visual modeling as a formal graphical representation of the system and/or modeling processes as a diagram and consequent dynamic simulation based on the representation. Graphical notation is a crucial component of visual modeling which allows one to formally and completely build a model. A visual model can be presented by some types of diagrams enabling description of diverse aspects of the structure and function of a complex system with different levels of details. This formal graphical representation is a basis for automatic code generation by specialized tools to simulate the model. We have made an extension of well-known SBGN notation [Le Novere, 2009] in order to simulate physiological processes which require not only description between metabolites, but also ability to use algebraic, differential equations and instant transition of the system from one state to another. In addition, connections between equations indicate signal transduction in the model while interface ports of modules (or submodels) have also a direction (input, output or contact). A meta-model is a basis of the visual modeling in BioUML which ensures a formalism for complex description, graphical representation and numerical simulation of biological systems on different levels of their hierarchical organization. A meta-model consists of three interrelated levels of complex systems description: graphical representation - system’s structure is described as compartmentalized graph; database - each element of the graph can include reference on a certain object in the database; runned model - an element of the model (variables, mathematical equations, discrete events, states and transitions) can be associated with an element of the graph (vertices, arcs and compartments). As an example, vertices of the graph can be represented by variables or states of the system, while arcs of the graph correspond to equations describing changes of these variables or transitions between two states. The description of the biological system as a meta-model is used to generate a Java code reflecting the model as a system of algebraic and/or differential equations, considering delay components, piecewise functions, discrete events and transitions. To generate a code the specific simulation engine is employed which defines the model type and corresponding simulation method.

A multi-compartmental complex model

A BioUML diagram describing a modular multi-compartmental model contains interconnected elements or modules (submodels) each of which is referred to another diagram (also may be modular). A directed connection between input and output nodes determines the signal transduction from a module to another one, while undirected relation between contacts reflects signals exchange between modules (Figure 1). According to this methodology, an integrated mathematical model describing energy metabolism of the human skeletal muscle [11, 14][2] considering (Ca²⁺)-dependent signaling pathway and downstream regulatory processes of early and late response genes expression has been built. A complex mathematical model [14] developed by Li and coathours in MATLAB has been rebuilt in BioUML as an initial model of the energy metabolism of the human skeletal muscle taking into account quantitative differences between fiber I and II types (Figure 2). An activation mechanism that enhances energy metabolism via transport and reaction fluxes due to physical exercise was harnessed as the stress function depending on general work rate parameter. The work rate parameter defines intensity of the physical exercise and variates depending on the mode of the exercise.

Upgrade of the model (metabolic level)

It is worth to note that values of activation coefficients associated with ATPase [Stienen 1996, He 2000, Szentesi 2001, Barclay 2017] and pyruvate dehydrogenase reaction fluxes for type I and type II fibers [Parolin 1999, Kiilerich 2008, Albers 2015] as well as time constant of ATPase flux rate coefficient in response to exercise were modified (Table X) according to recent published data and estimations [Broxterman 2017, Bartlett 2020]. Despite overall net glycogen breakdowns during muscle contraction, exercise also increases the activity of glycogen synthase (GS) [Wojtaszewski 2001, Nielsen 2003, Jensen 2009, Jensen 2012]. The GS reaction results in ATP consumption, therefore GS reaction fluxes were modified according to [Wojtaszewski 2001, Jensen 2009, Jensen 2012b]. The rates of muscle glycogen synthesis during exercise assumed to be equal in type I and type II fibres and were estimated from average post-exercise glycogen synthesis data [Casey 1995]. To consider the allosteric regulation of AMPK activity (in corresponding modules, Fig. X, Table X)) concentrations of free ADP and AMP in the cytosol were calculated using intracellular Cr, PCr, ATP and H+ concentrations as well as the equilibrium constants for creatine phosphokinase and adenylate kinases in each fiber type as described previously [Lawson 1979, Dudley 1985, Mannion 1993] (Figure 3).

The diagram of the modular model describing metabolism of human skeletal muscle is presented on Figure 2. The cytosol includes metabolic reactions of the glycolysis, glycogenolysis and lipids metabolism, while tricarboxylic acid (TCA) cycle, ß-oxidation and oxidative phosphorylation reactions are presented in the mitochondria. The intermediate compartment between those is a transport module which contains passive and facilitated transport reactions for model intracellular species. Kinetic laws presenting metabolic and transport flux expressions exactly match the initial model developed by Li and coathors [14].

Signaling level

The concentration of Ca2+ ions in the myoplasm increases in proportion to intensity of exercise. Ca2+ binds to calmodulin, thereby activating CaMKs and phosphatase calcineurin (Gehlert 2015). CaMKII is the most abundant isoform in the human skeletal muscle, whereas CaMKI and CaMKIV are not expressed at detectable levels (Rose 2006). An increase in CaMKII activity results in CREB1 Ser133 phosphorylation leading to activation of the transcription factor (Johannessen&Moens 2007, Olesen 2010). Calcineurin can dephosphorylate (and activate) CRTCs at Ser171 (CREB-regulated transcription coactivators) playing a key role in regulating transcriptional activity of CREB1 (Altarejos 2011). Another target of calmodulin is calcium/calmodulin-dependent protein kinase kinase 2 (CAMKK2) that phosphorylates AMPK Thr172 thereby activating the kinase (Abbott 2009). In turn, activated AMPK can phosphorylate CREB1 Ser133 [Thomson 2008]. Collectively, these findings drove us to include in our model the Ca2+-dependent regulation of calmodulin, CREB1 (via CaMKII), CRTC (via calcineurin), and AMPK (via CaMKK2) (Figure 3). The amount of these proteins in human skeletal muscle was estimated using published proteomics and transcriptomics data [Murgia 2017, Popov 2019] (see Supplementary data in Akberdin 2020). There are three different heterotrimeric complexes in the human skeletal muscles: α2β2γ1, α2β2γ3, and α1β2γ1 [Wojtaszewski 2005]. Distinct kinetic properties (an intrinsic enzyme activity, binding affinities of AMP, ADP and ATP to the specific isoform, sensitivity to de- and phosphorylation of AMPK heterotrimers) [Rajamohan 2016, Ross 2016] and their subcellular localization [Pinter 2013] cause a differential regulation of the AMPK heterotrimers in vivo. The α2β2γ3 complex is phosphorylated and activated during moderate- to high-intensity exercise, while the activity associated with the other two AMPK heterotrimers is almost unchanged [Birk 2006]. However, the basal activity of α2β2γ3 complex is significantly lower than others. Taking into account the general AMPK basal and exercise-induced activity is considered as a sum of isoforms activities, all isoforms in the corresponding module was considered to quantitatively fit an experimental data obtained at baseline and after an exercise [Birk 2006, Willows 2017]. AMPK is regulated by various ways: an up-stream kinase LKB1 can phosphorylate AMPK at Thr172 [Lizcano 2004, Jansen et al. 2009]. On the other hand, both ATP and AMP allosterically regulate AMPK: an exercise-induced decrease in intramuscular ATP increases its activity, while an increase in AMP activates it [Hardie 2016, Li 2017]. Hence, in our model the AMPK is regulated via AMP, ATP, and LKB1, as well as CaMKK2 (as mentioned above).

Gene expression level

An aerobic exercise induces expression of several hundreds of genes regulating many cell functions: energy metabolism, transport of various substances, angiogenesis, mitochondrial biogenesis. Regulation of the transcriptomic response to acute exercise includes dozens of transcription regulators [Popov et al. 2019] and seems to be extremely complex. Therefore to consider the response on gene expression level we exemplify the regulation of some genes encoding a transcription co-activator PGC-1α (encoded by PPARGC1A gene) and nuclear receptors NR4As - key exercise-induced regulators of the angiogenesis, mitochondrial biogenesis, fat and carbohydrate metabolism in skeletal muscle [Lira 2010, Pearen&Muscat 2018]. Expression of NR4A2, NR4A3 mRNA rapidly increases during the first hour after an aerobic exercise (early response genes) due activation of Ca2+\calcineurin-dependent signaling [8, 19, 46–48, Pearen&Muscat 2018]. We included in our model the Ca2+-dependent regulation (Ca2+\calcineurin-CaMKII-CREB1) of NR4As genes using data of contractile activity-specific mRNA response of these genes [8]. Expression of PPARGC1A mRNA rises 3 to 4 h after an exercise (late response gene МОЖЕТ БЫТЬ ЛУЧШЕ ВЕЗДЕ (и на рисунках) ЗАМЕНИТЬ НА gene with delay response Т.К. 4 ЧАСА СЛОЖНО НАЗВАТЬ ПОЗДНИМ ОТВЕТОМ) [8]. The transcription regulation of PPARGC1A via the canonical (proximal) and inducible (distal) promoters is very complicated, and includes Ca2+- and AMPK-dependent signaling, as well as CREB1 and its co-activator CRTC [Popov et al. 2015, Popov 2018]. The phosphorylation level of many signaling kinases drops to basal levels within the first hour after an aerobic exercise. Moreover, in a genome-wide study on various human tissues, it was shown that the phosphorylation level of CREB Ser133 does not always correlate with its transcriptional activity [53]. Therefore, we suggested the expression of late response genes (including PPARGC1A) is regulated by increasing the expression of one of the early response genes encoding transcription factors leading to a rapid increase corresponding protein (see Fig. 5 in Akberdin 2020). Analysis of contractile activity-specific transcriptomic data [8] showed that a rapid increase in the expression of genes encoding various TFs is observed already in the first hour after an exercise. It turned out that the binding motifs of some TFs (CREB-like proteins, as well as proteins of the AP-1 family: FOS and JUN) are located and intersected with each other both in the alternative and in the canonical promoters of the PPARGC1A gene [Akberdin 2020], i.e. these TFs can act as a potential regulators of this gene. This is consistent with the fact that these TFs can bind to DNA and regulate the expression of target genes as homo- and heterodimers [49, 50]. Based on these considerations, we included in the model the regulation of gene expression of early (NR4A2, NR4A3) and delayed (PPARGC1A) genes: early response genes are regulated via the activation of existent TFs (e.g. CREB1) and their co-activators (e.g. CRTC), while delayed response genes - via an increase in the expression of early response genes encoding transcription factors (transcription factor X in our model, Fig. N).

References

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