Roles of protein ubiquitination and degradation kinetics in biological oscillations

Targeted Protein Degradation: Principles and Applications of the Proteasome

The proteasome is a multi-catalytic protease complex that is involved in protein quality control via three proteolytic activities (i.e., caspase-, trypsin-, and chymotrypsin-like activities). Most cellular proteins are selectively degraded by the proteasome via ubiquitination. Moreover, the ubiquitin-proteasome system is a critical process for maintaining protein homeostasis. Here, we briefly summarize the structure of the proteasome, its regulatory mechanisms, proteins that regulate proteasome activity, and alterations to proteasome activity found in diverse diseases, chemoresistant cells, and cancer stem cells. Finally, we describe potential therapeutic modalities that use the ubiquitin-proteasome system.

The ups and downs of biological oscillators: a comparison of time-delayed negative feedback mechanisms

Many biochemical oscillators are driven by the periodic rise and fall of protein concentrations or activities. A negative feedback loop underlies such oscillations. The feedback can act on different parts of the biochemical network. Here, we mathematically compare time-delay models where the feedback affects production and degradation. We show a mathematical connection between the linear stability of the two models, and derive how both mechanisms impose different constraints on the production and degradation rates that allow oscillations. We show how oscillations are affected by the inclusion of a distributed delay, of double regulation (acting on production and degradation) and of enzymatic degradation.

Ubiquitination Flow Repressors: Enhancing Wound Healing of Infectious Diabetic Ulcers through Stabilization of Polyubiquitinated Hypoxia-Inducible Factor-1α by Theranostic Nitric Oxide Nanogenerators

Current treatments for diabetic ulcers (DUs) remain unsatisfactory due to the risk of bacterial infection and impaired angiogenesis during the healing process. The increased degradation of polyubiquitinated hypoxia-inducible factor-1α (HIF-1α) compromises wound healing efficacy. Therefore, the maintenance of HIF-1α protein stability might help treat DU. Nitric oxide (NO) is an intrinsic biological messenger that functions as a ubiquitination flow repressor and antibacterial agent; however, its clinical application in DU treatment is hindered by the difficulty in controlling NO release. Here, an intelligent near-infrared (NIR)-triggered NO nanogenerator (SNP@MOF-UCNP@ssPDA-Cy7/IR786s, abbreviated as SNP@UCM) is presented. SNP@UCM represses ubiquitination-mediated proteasomal degradation of HIF-1α by inhibiting its interaction with E3 ubiquitin ligases under NIR irradiation. Increased HIF-1α expression in endothelial cells by SNP@UCM enhances angiogenesis in wound sites, promoting vascular endothelial growth factor (VEGF) secretion and cell proliferation and migration. SNP@UCM also enables early detection of wound infections and ROS-mediated killing of bacteria. The potential clinical utility of SNP@UCM is further demonstrated in infected full-thickness DU model under NIR irradiation. SNP@UCM is the first reported HIF-1α-stabilizing advanced nanomaterial, and further materials engineering might offer a facile, mechanism-based method for clinical DU management.

A new ultradian rhythm in mammalian cell dry mass observed by holography

We have discovered a new 4 h ultradian rhythm that occurs during the interphase of the cell cycle in a wide range of individual mammalian cells, including both primary and transformed cells. The rhythm was detected by holographic lens-free microscopy that follows the histories of the dry mass of thousands of single live cells simultaneously, each at a resolution of five minutes. It was vital that the rhythm was observed in inherently heterogeneous cell populations, thus eliminating synchronization and labeling bias. The rhythm is independent of circadian rhythm, and is temperature-compensated. We show that the amplitude of the fundamental frequency provides a way to quantify the effects of, chemical reagents on cells, thus shedding light on its mechanism. The rhythm is suppressed by proteostasis disruptors and is detected only in proliferating cells, suggesting that it represents a massive degradation and re-synthesis of protein every 4 h in growing cells.

Proteasome Biology: Chemistry and Bioengineering Insights

Proteasomal degradation provides the crucial machinery for maintaining cellular proteostasis. The biological origins of modulation or impairment of the function of proteasomal complexes may include changes in gene expression of their subunits, ubiquitin mutation, or indirect mechanisms arising from the overall impairment of proteostasis. However, changes in the physico-chemical characteristics of the cellular environment might also meaningfully contribute to altered performance. This review summarizes the effects of physicochemical factors in the cell, such as pH, temperature fluctuations, and reactions with the products of oxidative metabolism, on the function of the proteasome. Furthermore, evidence of the direct interaction of proteasomal complexes with protein aggregates is compared against the knowledge obtained from immobilization biotechnologies. In this regard, factors such as the structures of the natural polymeric scaffolds in the cells, their content of reactive groups or the sequestration of metal ions, and processes at the interface, are discussed here with regard to their influences on proteasomal function.

Robustness of a biomolecular oscillator to pulse perturbations

Biomolecular oscillators can function robustly in the presence of environmental perturbations, which can either be static or dynamic. While the effect of different circuit parameters and mechanisms on the robustness to steady perturbations has been investigated, the scenario for dynamic perturbations is relatively unclear. To address this, the authors use a benchmark three protein oscillator design - the repressilator - and investigate its robustness to pulse perturbations, computationally as well as use analytical tools of Floquet theory. They found that the metric provided by direct computations of the time it takes for the oscillator to settle after pulse perturbation is applied, correlates well with the metric provided by Floquet theory. They investigated the parametric dependence of the Floquet metric, finding that the parameters that increase the effective delay enhance robustness to pulse perturbation. They found that the structural changes such as increasing the number of proteins in a ring oscillator as well as adding positive feedback, both of which increase effective delay, facilitates such robustness. These results highlight such design principles, especially the role of delay, for designing an oscillator that is robust to pulse perturbation.

In silico modeling of phosphorylation dependent and independent c-Myc degradation

Background

c-Myc plays an important role in cell proliferation, cell growth and in differentiation, making it a key regulator for carcinogenesis and pluripotency. Tight control of c-myc turnover is required by ubiquitin-mediated degradation. This is achieved in the system by two F-box proteins Skp2 and FBXW7.

Results

Dynamic modelling technique was used to build two exclusive models for phosphorylation dependent degradation of Myc by FBXW7 (Model 1) and phosphorylation independent degradation by Skp2 (Model 2). Sensitivity analysis performed on these two models revealed that these models were corroborating experimental studies. It was also seen that Model 1 was more robust and perhaps more efficient in degrading c-Myc. These results questioned the existence of the two models in the system and to answer the question a combined model was hypothesised which had a decision making switch. The combined model had both Skp2 and FBXW7 mediated degradation where again the latter played a more important role. This model was able to achieve the lowest levels of ubiquitylated Myc and therefore functioned most efficiently in degradation of Myc.

Conclusion

In this report, c-Myc degradation by two F-box proteins was mathematically evaluated based on the importance of c-Myc turnover. The study was performed in a homeostatic system and therefore, prompts the exploration of c-Myc degradation in cancer state and in pluripotent state.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2846-x) contains supplementary material, which is available to authorized users.

Stability of Wake-Sleep Cycles Requires Robust Degradation of the PERIOD Protein

Robustness in biology is the stability of phenotype under diverse genetic and/or environmental perturbations. The circadian clock has remarkable stability of period and phase that-unlike other biological oscillators-is maintained over a wide range of conditions. Here, we show that the high fidelity of the circadian system stems from robust degradation of the clock protein PERIOD. We show that PERIOD degradation is regulated by a balance between ubiquitination and deubiquitination, and that disruption of this balance can destabilize the clock. In mice with a loss-of-function mutation of the E3 ligase gene β-Trcp2, the balance of PERIOD degradation is perturbed and the clock becomes dramatically unstable, presenting a unique behavioral phenotype unlike other circadian mutant animal models. We believe that our data provide a molecular explanation for how circadian phases, such as wake-sleep onset times, can become unstable in humans, and we present a unique mouse model to study human circadian disorders with unstable circadian rhythm phases.

Ghrelin suppresses inflammation in HUVECs by inhibiting ubiquitin-mediated uncoupling protein 2 degradation

Atherosclerosis is considered the major cause of heart attack, stroke and gangrene of the extremities, which is responsible for 50% of all mortality in Western countries. The pathogenesis and causes of atherosclerosis remain elusive. Recent studies highlight inflammation as a contributing factor for atherosclerosis in all stages of the disease process. In this study, we demonstrate that the treatment of human umbilical vein endothelial cells (HUVECs) with ghrelin inhibits the oxidized low-density lipoprotein (oxLDL)-induced inflammatory response, In addition, treatment with ghrelin led to the accumulation of uncoupling protein 2 (UCP2) in the cells, thus decreasing reactive oxygen species (ROS) generation. Moreover, the siRNA-mediated knockdown of UCP2 expression suggested that the inhibitory effects of ghrelin on the inflammatory response relied on its ability to induce the accumulation of cellular UCP2 levels. Further analysis indicated that the accumulation of UCP2 in the ghrelin-treated cells was due to the ability of ghrelin to inhibit the ubiquitination of UCP2 and prevent UCP2 degradation, resulting in the extended protein half-life of UCP2. On the whole, our data indicate that ghrelin inhibits the oxLDL-induced inflammatory response in HUVECs, and may thus have potential for use as an anti-atherosclerotic agent. Our data may also provide valuable insight into the pathogenesis of atherosclerosis.

Irreversible APC(Cdh1) Inactivation Underlies the Point of No Return for Cell-Cycle Entry

Proliferating cells must cross a point of no return before they replicate their DNA and divide. This commitment decision plays a fundamental role in cancer and degenerative diseases and has been proposed to be mediated by phosphorylation of retinoblastoma (Rb) protein. Here, we show that inactivation of the anaphase-promoting complex/cyclosome (APC(Cdh1)) has the necessary characteristics to be the point of no return for cell-cycle entry. Our study shows that APC(Cdh1) inactivation is a rapid, bistable switch initiated shortly before the start of DNA replication by cyclin E/Cdk2 and made irreversible by Emi1. Exposure to stress between Rb phosphorylation and APC(Cdh1) inactivation, but not after APC(Cdh1) inactivation, reverted cells to a mitogen-sensitive quiescent state, from which they can later re-enter the cell cycle. Thus, APC(Cdh1) inactivation is the commitment point when cells lose the ability to return to quiescence and decide to progress through the cell cycle.

Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations

Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.

Rhythmic behavior is omnipresent in biology and has many crucial functions. In cells the activation levels and abundances of signaling molecules such as NF-κB, p53, EGFR or calcium repeatedly increase and decrease in response to stimuli. Such a dynamic behavior can also be observed monitoring the concentrations of mRNAs and proteins in the circadian clock and the cell cycle. Period and amplitude which are the time span between peaks and the peak height, respectively, as well as their variabilities are important features of oscillations. The circadian period is very stable allowing for proper time keeping, whereas in calcium signaling the period is very variable encoding different stimulation strengths. Our goal is to examine the origin of differences in sensitivities of periods and amplitudes using a computational approach. We use prototype oscillators and demonstrate that they can be used to derive general principles that explain the degree of robustness in period and amplitude for a set of commonly used models of cellular oscillators. Our findings imply that the robustness of oscillating systems can be influenced by feedback type and kinetic properties to which special attention should be paid when designing mathematical models of cellular rhythms.

Identification of Unintuitive Features of Sumoylation through Mathematical Modeling

Sumoylation is a multistep, multienzymatic post-translational modification in which a small ubiquitin-like modifier protein (SUMO) is attached to the target. We present the first mathematical model for sumoylation including enzyme mechanism details such as autosumoylation of E2 and multifunctional nature of SENP. Simulations and analysis reveal three nonobvious properties for the long term response, modeled as an open system: (i) the steady state sumoylation level is robust to variation in several enzyme properties; (ii) even when autosumoylation of E2 results in equal or higher activity, the target sumoylation levels are lower; and (iii) there is an optimal SENP concentration at which steady state target sumoylation level is maximum. These results are qualitatively different for a short term response modeled as a closed system, where e.g. sumoylation always decreases with increasing SENP levels. Simulations with multiple targets suggest that the available SUMO is limiting, indicating a possible explanation for the experimentally observed low fractional sumoylation. We predict qualitative differences in system responses at short post-translational and longer transcriptional time scales. We thus use this mechanism-based model to explain system properties and generate testable hypotheses for existence and mechanism of unexpected responses.

Protein turnover during in vitro tissue engineering

Repopulating acellular biological scaffolds with phenotypically appropriate cells is a promising approach for regenerating functional tissues and organs. Under this tissue engineering paradigm, reseeded cells are expected to remodel the scaffold by active protein synthesis and degradation; however, the rate and extent of this remodeling remain largely unknown. Here, we present a technique to measure dynamic proteome changes during in vitro remodeling of decellularized tissue by reseeded cells, using vocal fold mucosa as the model system. Decellularization and recellularization were optimized, and a stable isotope labeling strategy was developed to differentiate remnant proteins constituting the original scaffold from proteins newly synthesized by reseeded cells. Turnover of matrix and cellular proteins and the effects of cell-scaffold interaction were elucidated. This technique sheds new light on in vitro tissue remodeling and the process of tissue regeneration, and is readily applicable to other tissue and organ systems.

Robustness and period sensitivity analysis of minimal models for biochemical oscillators

Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.

Anomalous fluctuation scaling laws in stochastic enzyme kinetics: increase of noise strength with the mean concentration

It is commonly thought that if a rate constant is perturbed such that the intracellular concentration of a certain species increases, then the fluctuations in the concentration will correspondingly decrease in strength. We here test whether this conventional wisdom generally holds true. We study the dependence of the noise strength (the coefficient of variation) in protein concentrations as a function of the mean protein concentration for a system in which protein is transported in and out of an intracellular compartment and it is catalyzed into a product by a multisubunit enzyme inside the compartment. The mean protein concentration is varied through perturbation of one of the rate constants. For low protein concentrations, the noise strength scales as [P]-1/2, where [P] is the mean concentration; this is the conventional fluctuation scaling law. However, we show that over a wide range of physiological concentrations, there are manifest anomalous fluctuation scaling laws proportional to [P]0 and [P](N-1)/2, where N is the number of binding sites of the multisubunit enzyme. These laws are particularly conspicuous when the rate of protein import into the compartment is much larger than its export rate out of the compartment and when the enzyme exhibits positive cooperativity. The results imply that over a certain range of physiological concentrations, noise strength remains the same or increases with the mean protein concentration. This contradicts the popularly held notion that noise strength decreases with increasing concentration and suggests that noise can be important even when the number of molecules is large.

Post-translational regulation enables robust p53 regulation

Background

The tumor suppressor protein p53 plays important roles in DNA damage repair, cell cycle arrest and apoptosis. Due to its critical functions, the level of p53 is tightly regulated by a negative feedback mechanism to increase its tolerance towards fluctuations and disturbances. Interestingly, the p53 level is controlled by post-translational regulation rather than transcriptional regulation in this feedback mechanism.

Results

We analyzed the dynamics of this feedback to understand whether post-translational regulation provides any advantages over transcriptional regulation in regard to disturbance rejection. When a disturbance happens, even though negative feedback reduces the steady-state error, it can cause a system to become less stable and transiently overshoots, which may erroneously trigger downstream reactions. Therefore, the system needs to balance the trade-off between steady-state and transient errors. Feedback control and adaptive estimation theories revealed that post-translational regulation achieves a better trade-off than transcriptional regulation, contributing to a more steady level of p53 under the influence of noise and disturbances. Furthermore, post-translational regulation enables cells to respond more promptly to stress conditions with consistent amplitude. However, for better disturbance rejection, the p53- Mdm2 negative feedback has to pay a price of higher stochastic noise.

Conclusions

Our analyses suggest that the p53-Mdm2 feedback favors regulatory mechanisms that provide the optimal trade-offs for dynamic control.

Oscillatory enzyme reactions and Michaelis-Menten kinetics

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase.