Operating principles of circular toggle polygons

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states-(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad-three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C)-can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd-numbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

Quantitative Characteristic of ncRNA Regulation in Gene Regulatory Networks

RNA is mostly known for its role in protein synthesis, where it encodes information for protein sequence in its messenger RNA (mRNA) form (translation). Yet, RNA molecules regulate several cellular processes other than translation. Here, we present an overview of several mathematical models that help understanding and characterizing the role of noncoding RNA molecules (ncRNAs) in regulating gene expression and protein synthesis. First, we discuss relatively simple models where ncRNAs can modulate protein synthesis via targeting a mRNA. Then, we consider the case of feedback interactions between ncRNAs and their target proteins, and discuss several biological applications where these feedback architectures modulate a cellular phenotype and control the levels of intrinsic and extrinsic noise. Building from these simple circuit motifs, we examine feed-forward circuit motifs involving ncRNAs that generate precise spatial and temporal patterns of protein expression. Further, we investigate the competition between ncRNAs and other endogenous RNA molecules and show that the cross talk between coding and noncoding RNAs can form large genetic circuits that involve up to hundreds of chemical species. Finally, we discuss the role of ncRNAs in modulating cell-cell signaling pathways and therefore the dynamics of spatiotemporal pattern formation in a tissue.

Inflammaging and human longevity in the omics era

Inflammaging is a recent theory of aging originally proposed in 2000 where data and conceptualizations regarding the aging of the immune system (immunosenescence) and the evolution of immune responses from invertebrates to mammals converged. This theory has received an increasing number of citations and experimental confirmations. Here we present an updated version of inflammaging focused on omics data - particularly on glycomics - collected on centenarians, semi-supercentenarians and their offspring. Accordingly, we arrived to the following conclusions: i) inflammaging has a structure where specific combinations of pro- and anti-inflammatory mediators are involved; ii) inflammaging is systemic and more complex than we previously thought, as many organs, tissues and cell types participate in producing pro- and anti-inflammatory stimuli defined "molecular garbage"; iii) inflammaging is dynamic, can be propagated locally to neighboring cells and systemically from organ to organ by circulating products and microvesicles, and amplified by chronic age-related diseases constituting a "local fire", which in turn produces additional inflammatory stimuli and molecular garbage; iv) an integrated Systems Medicine approach is urgently needed to let emerge a robust and highly informative set/combination of omics markers able to better grasp the complex molecular core of inflammaging in elderly and centenarians.

Understanding microRNA-mediated gene regulatory networks through mathematical modelling

The discovery of microRNAs (miRNAs) has added a new player to the regulation of gene expression. With the increasing number of molecular species involved in gene regulatory networks, it is hard to obtain an intuitive understanding of network dynamics. Mathematical modelling can help dissecting the role of miRNAs in gene regulatory networks, and we shall here review the most recent developments that utilise different mathematical modelling approaches to provide quantitative insights into the function of miRNAs in the regulation of gene expression. Key miRNA regulation features that have been elucidated via modelling include: (i) the role of miRNA-mediated feedback and feedforward loops in fine-tuning of gene expression; (ii) the miRNA–target interaction properties determining the effectiveness of miRNA-mediated gene repression; and (iii) the competition for shared miRNAs leading to the cross-regulation of genes. However, there is still lack of mechanistic understanding of many other properties of miRNA regulation like unconventional miRNA–target interactions, miRNA regulation at different sub-cellular locations and functional miRNA variant, which will need future modelling efforts to deal with. This review provides an overview of recent developments and challenges in this field.

Computational Model of MicroRNA Control of HIF-VEGF Pathway: Insights into the Pathophysiology of Ischemic Vascular Disease and Cancer

HRMs (hypoxia-responsive miRNAs) are a specific group of microRNAs that are regulated by hypoxia. Recent studies revealed that several HRMs including let-7 family miRNAs were highly induced in response to HIF (hypoxia-inducible factor) stabilization in hypoxia, and they potently participated in angiogenesis by targeting AGO1 (argonaute 1) and upregulating VEGF (vascular endothelial growth factor). Here we constructed a novel computational model of microRNA control of HIF-VEGF pathway in endothelial cells to quantitatively investigate the role of HRMs in modulating the cellular adaptation to hypoxia. The model parameters were optimized and the simulations based on these parameters were validated against several published in vitro experimental data. To advance the mechanistic understanding of oxygen sensing in hypoxia, we demonstrated that the rate of HIF-1α nuclear import substantially influences its stabilization and the formation of HIF-1 transcription factor complex. We described the biological feedback loops involving let-7 and AGO1 in which the impact of external perturbations were minimized; as a pair of master regulators when low oxygen tension was sensed, they coordinated the critical process of VEGF desuppression in a controlled manner. Prompted by the model-motivated discoveries, we proposed and assessed novel pathway-specific therapeutics that modulate angiogenesis by adjusting VEGF synthesis in tumor and ischemic cardiovascular disease. Through simulations that capture the complex interactions between miRNAs and miRNA-processing molecules, this model explores an innovative perspective about the distinctive yet integrated roles of different miRNAs in angiogenesis, and it will help future research to elucidate the dysregulated miRNA profiles found in cancer and various cardiovascular diseases.

Cells living in a hypoxic environment secrete signals to stimulate new blood vessel growth, a process termed angiogenesis, to acquire more oxygen and nutrients. Hypoxia-inducible factor 1 (HIF-1) accumulates in hypoxia and expedites the release of pro-angiogenic cytokines such as vascular endothelial growth factor (VEGF), a prime inducer of angiogenesis. The intermediate signaling events connecting HIF-1 and VEGF are tightly controlled by microRNAs (miRs), which are endogenous, non-coding RNA molecules and powerful regulators in cancer and cardiovascular disease. Given the importance of angiogenesis in tumor development and post-ischemia reperfusion, it holds great basic research and therapeutic value to investigate how miRs modulate intracellular VEGF synthesis to control angiogenesis in hypoxia. We present a computational model that details the interactions between miRs and other key molecules which make up different hierarchies in HIF-miR-VEGF pathway. Based on simulation analysis, new potential therapies are introduced and tested in silico, from which the strategies that most effectively reduce VEGF synthesis in cancer, or enhance VEGF release in ischemic vascular disease are identified. We conclude that in hypoxia different miRs work consonantly to fine-tune the cellular adaptations; when a master miR alters its expression, dynamics of other miRs vary accordingly which together contribute to aberrant RNA/protein profiles observed in the pathophysiology of multiple diseases.

A simple stochastic model for the feedback circuit between p16INK4a and p53 mediated by p38MAPK: implications for senescence and apoptosis

The mechanisms leading to the cell fate decision between apoptosis and senescence upon DNA damage are still unclear and have stochastic features. Cellular oxidative stress can generate DNA damage and activate the important mitogen-activated protein kinase 14 (p38MAPK) that is involved in pathologies like Alzheimer's disease. Based on experimental evidence we propose a simple network that might operate at the core of the cell control machinery for the choice between apoptosis and senescence involving the cross-talk between p38MAPK, the tumor suppressor protein p53 and the cyclin-dependent kinase inhibitor (p16INK4a). We have performed two types of analyses, deterministic and stochastic, exploring the system's parameter space, in the first, we calculated the fixed points of the deterministic model and, in the second, we numerically integrated the master equation for the stochastic version. The model shows a variety of behaviors dependent on the parameters including states of high expression levels of p53 or p16INK4a that can be associated with an apoptotic or senescent phenotype, respectively, in agreement with experimental data. In addition, we observe both monostable and bistable behavior (where bistability is a phenomenon in which two stable steady states coexist for a fixed set of control parameter values) which here we suggest to be involved in the cell fate decision problem.

Active Degradation Explains the Distribution of Nuclear Proteins during Cellular Senescence

The amount of cellular proteins is a crucial parameter that is known to vary between cells as a function of the replicative passages, and can be important during physiological aging. The process of protein degradation is known to be performed by a series of enzymatic reactions, ranging from an initial step of protein ubiquitination to their final fragmentation by the proteasome. In this paper we propose a stochastic dynamical model of nuclear proteins concentration resulting from a balance between a constant production of proteins and their degradation by a cooperative enzymatic reaction. The predictions of this model are compared with experimental data obtained by fluorescence measurements of the amount of nuclear proteins in murine tail fibroblast (MTF) undergoing cellular senescence. Our model provides a three-parameter stationary distribution that is in good agreement with the experimental data even during the transition to the senescent state, where the nuclear protein concentration changes abruptly. The estimation of three parameters (cooperativity, saturation threshold, and maximal velocity of the reaction), and their evolution during replicative passages shows that only the maximal velocity varies significantly. Based on our modeling we speculate the reduction of functionality of the protein degradation mechanism as a possible competitive inhibition of the proteasome.

Small molecules, big effects: the role of microRNAs in regulation of cardiomyocyte death

MicroRNAs (miRNAs) are a class of small non-coding RNAs involved in posttranscriptional regulation of gene expression, and exerting regulatory roles in plethora of biological processes. In recent years, miRNAs have received increased attention for their crucial role in health and disease, including in cardiovascular disease. This review summarizes the role of miRNAs in regulation of cardiac cell death/cell survival pathways, including apoptosis, autophagy and necrosis. It is envisaged that these miRNAs may explain the mechanisms behind the pathogenesis of many cardiac diseases, and, most importantly, may provide new avenues for therapeutic intervention that will limit cardiomyocyte cell death before it irreversibly affects cardiac function. Through an in-depth literature analysis coupled with integrative bioinformatics (pathway and synergy analysis), we dissect here the landscape of complex relationships between the apoptosis-regulating miRNAs in the context of cardiomyocyte cell death (including regulation of autophagy–apoptosis cross talk), and examine the gaps in our current understanding that will guide future investigations.

Bistability in the chemical master equation for dual phosphorylation cycles

Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory, and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed at elucidating the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional chemical master equation for a well-known model of a two step phospho/dephosphorylation cycle using the quasi-steady state approximation of enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the external field derived from the generation and recombination transition rates, can be decomposed by the Helmholtz theorem, into a conservative and a rotational (irreversible) part. Moreover, this decomposition allows to compute the stationary distribution via a perturbative approach. For a finite number of molecules there exists diffusion dynamics in a macroscopic region of the state space where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.

The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions

BACKGROUND

It is well known that the deterministic dynamics of biochemical reaction networks can be more easily studied if timescale separation conditions are invoked (the quasi-steady-state assumption). In this case the deterministic dynamics of a large network of elementary reactions are well described by the dynamics of a smaller network of effective reactions. Each of the latter represents a group of elementary reactions in the large network and has associated with it an effective macroscopic rate law. A popular method to achieve model reduction in the presence of intrinsic noise consists of using the effective macroscopic rate laws to heuristically deduce effective probabilities for the effective reactions which then enables simulation via the stochastic simulation algorithm (SSA). The validity of this heuristic SSA method is a priori doubtful because the reaction probabilities for the SSA have only been rigorously derived from microscopic physics arguments for elementary reactions.

RESULTS

We here obtain, by rigorous means and in closed-form, a reduced linear Langevin equation description of the stochastic dynamics of monostable biochemical networks in conditions characterized by small intrinsic noise and timescale separation. The slow-scale linear noise approximation (ssLNA), as the new method is called, is used to calculate the intrinsic noise statistics of enzyme and gene networks. The results agree very well with SSA simulations of the non-reduced network of elementary reactions. In contrast the conventional heuristic SSA is shown to overestimate the size of noise for Michaelis-Menten kinetics, considerably under-estimate the size of noise for Hill-type kinetics and in some cases even miss the prediction of noise-induced oscillations.

CONCLUSIONS

A new general method, the ssLNA, is derived and shown to correctly describe the statistics of intrinsic noise about the macroscopic concentrations under timescale separation conditions. The ssLNA provides a simple and accurate means of performing stochastic model reduction and hence it is expected to be of widespread utility in studying the dynamics of large noisy reaction networks, as is common in computational and systems biology.