Rule-based cell systems model of aging using feedback loop motifs mediated by stress responses

Abstract

Investigating the complex systems dynamics of the aging process requires integration of a broad range of cellular processes describing damage and functional decline co-existing with adaptive and protective regulatory mechanisms. We evolve an integrated generic cell network to represent the connectivity of key cellular mechanisms structured into positive and negative feedback loop motifs centrally important for aging. The conceptual network is casted into a fuzzy-logic, hybrid-intelligent framework based on interaction rules assembled from a priori knowledge. Based upon a classical homeostatic representation of cellular energy metabolism, we first demonstrate how positive-feedback loops accelerate damage and decline consistent with a vicious cycle. This model is iteratively extended towards an adaptive response model by incorporating protective negative-feedback loop circuits. Time-lapse simulations of the adaptive response model uncover how transcriptional and translational changes, mediated by stress sensors NF-kappaB and mTOR, counteract accumulating damage and dysfunction by modulating mitochondrial respiration, metabolic fluxes, biosynthesis, and autophagy, crucial for cellular survival. The model allows consideration of lifespan optimization scenarios with respect to fitness criteria using a sensitivity analysis. Our work establishes a novel extendable and scalable computational approach capable to connect tractable molecular mechanisms with cellular network dynamics underlying the emerging aging phenotype.

Figure 1. Iterative model development.

Overview of the steps taken to assemble a generic cell aging model. The model is instantiated with a combined energy producing (mitochondria) and consuming (biosynthesis) complex and a parameter setting that provides homeostasis in metabolic fluxes, which is disturbed by reactive oxygen species (ROS) as a byproduct of mitochondrial respiration, damaging proteins and organelle function. In the next iterations stress response pathways are assembled into the network topology providing adaptive and regulatory systems feedback. This includes NF-κB, a sensor of oxidative stress, and mTOR, an energy sensor. The resulting model is investigated by a sensitivity analysis. The model can be extended and scaled.

Figure 2. Graph of a positive feedback-loop motif.

Several key processes related to biological aging can be described by positive feedback-loop motifs, as shown by this “vicious cycle” model. Metabolic fluxes (marked by blue lines) are initially in homeostasis. Reactive oxygen species (ROS) damage intracellular proteins including mitochondrial structures (red lines). This leads to impairment of ATP generation and biosynthesis, further increasing ROS levels. A portion of oxidized proteins is removed by autophagy, which constitutes a sink in this model.

Figure 3. Simulations of a positive feedback-loop motif.

A rule-based fuzzy-logic computation shows dynamical changes of age-related alterations in the Vicious Cycle (VC) model as shown in Figure 2. The main characteristic of the simulation outcome is a steep increase in free radicals (ROS) and oxidized proteins due to an amplifying positive feedback, since ROS damages mitochondrial DNA and mitochondrial proteins, impairing the ability to produce ATP, which leads to an increase in ADP levels. Accordingly, mitochondrial respiration and biosynthesis decline exponentially with age. Also provided is the total accumulated energy turnover, which is leveling off with age due to reduced metabolism. High levels of free radical concentrations and protein oxidation are not viable and may lead to cell apoptosis. The end of cellular lifespan is defined here and in all subsequent simulations when oxidized proteins exceeds a 0.4 level, data beyond this point are still shown in shaded areas until ATP consumption reaches zero.

Figure 4. Circuitry of the Adaptive Response model.

The Adaptive Response (AR) model represents an interaction network topology with both positive-destructive and negative-protective feedback mechanisms co-existing in cellular aging. Dysfunctional mitochondria and a decrease in protein turnover are positive feedbacks and contribute to the accumulation of oxidized proteins. Increased levels of ROS and oxidized proteins activate the redox-sensitive stress response transcription factor NF-κB, while declining ATP levels inhibit the energy sensor mTOR, which supports negative feedbacks through changes in transcription and translation (dotted green lines indicate flow of information and arrow endstyles the suggested function in aging). This includes downregulation of protein biosynthesis and genes coding for mitochondrial proteins. In addition, the activity of scavengers and autophagy is enhanced. A compensatory mechanism to mitochondrial dysfunction is upregulation of aerobic glycolysis. Secondary positive feedback-loops incorporate the production of cytokines as a byproduct of the cell-autonomous response of NF-κB, activating the NADPH oxidase system in an autocrine fashion, as well as reduced protein turnover rates. The beneficial role of mTOR inhibition in aging may be blunted by high ROS concentrations (see Results for details).

Figure 5. Fuzzy-logic simulation of a model including NF-κB.

In this simulation the VC-model is extended towards an adaptive response (AR) model by introducing the NF-κB pathway that protectively upregulates ROS scavengers and downregulates mitochondrial function. Compensatory upregulation of aerobic glycolysis diverts ATP consumption from mitochondrial respiration. Model lifespan is only slightly extended and the model still shows an accelerated decline.

Figure 6. Fuzzy-logic simulation of the Adaptive Response model.

In this simulation of the complete AR-model (see graph in Figure 4) concentration of reactive molecules stay constant at low levels and oxidized proteins accumulate slower increasing lifespan, different to the model predictions shown in Figures 3 and 5. In this setting, oxidized proteins become the main mechanism for activation of the stress response sensor NF-κB. Low ATP values decrease mTOR, downregulate ribosomal functions, but enhance autophagy as protecting mechanisms. The underlying alterations in gene transcription and translation decrease mitochondrial respiration but upregulate aerobic glycolysis, which becomes a major contributing factor to energy supply towards the end of lifespan. The overall accumulated energy turnover is higher compared to all other models. The AR model demonstrates an earlier onset and more linear rates of decline for energy related parameters if compared to the aging phenotype predicted by the Vicious Cycle model.

Figure 7. Simulation of NF-κB blockade.

In this version of the AR model NF-κB is inhibited from a mid-point time on. The scavenging role of NF-κB and its role in mitochondrial regulation, along with increased biosynthesis by ROS activation of mTOR, cause an instant improvement of metabolic functions moving the cell to a “younger state”, consistent with NF-kB blockade experiments. However, the model prediction after this point in time has the characteristic of a vicious cycle with accelerated decline not improving lifespan.

Figure 8. Simulation of decreased mTOR sensitivity.

In this version of the AR model mTOR sensitivity to lower ATP levels is decreased by 20% and lifespan is compared to the simulation in Figure 6. An initial decline in mTOR becomes reversed by increasing ROS levels, enhanced by mTOR mediated activation of biosynthesis and mitochondrial activities. This is an example of “unsuccessful aging”, demonstrating the critical role of mTOR in the regulation of the aging process.

Figure 9. Sensitivity analysis of NF-κB.

In this analysis the sensitivity of NF-κB is modified between +/−5 and +/−20%, and by +100% and −50%. The NF-κB activity is plotted over the course of lifespan as recorded by simulation runs compared to a baseline (black) from model predictions shown in Figure 6. End of lifespan is reached when the level of oxidized proteins reaches 0.4 as indicated. A second fitness criterion indicates ATP consumption levels at a 0.4 threshold (dotted magenta line). Substantial differences in NF-κB activity are observed around midlife but converge later without affecting overall lifespan. Substantial reduction in lifespan is only seen at very low NF-κB values along with damage related low levels of ATP consumption.

Figure 10. Sensitivity analysis of mTOR.

Alteration in mTOR sensitivity to low ATP levels introduced in steps of +/−5% have a significant effect on lifespan, as indicated by the length of simulations runs carried out until oxidized protein concentrations reach a critical level. Changes do not increase in proportion to higher degrees of perturbations. It is noted that mTOR activities at positive changes from the baseline (black line) can initially decline, but increase later. Stronger inhibition of mTOR slows accumulation of oxidized proteins, but reduces other fitness parameters such as ATP consumption (dotted magenta line) that may negatively impact physiological functions.