Modelling and analysis of an ensemble of eukaryotic translation initiation models

Inbuilt Tendency of the eIF2 Regulatory System to Counteract Uncertainties

Eukaryotic initiation factor 2 (eIF2) plays a fundamental role in the regulation of protein synthesis. Investigations have revealed that the regulation of eIF2 is robust against intrinsic uncertainties and is able to efficiently counteract them. The robustness properties of the eIF2 pathway against intrinsic disturbances is also well known. However the reasons for this ability to counteract stresses is less well understood. In this article, the robustness conferring properties of the eIF2 dependent regulatory system is explored with the help of a mathematical model. The novelty of the work presented in this article lies in articulating the possible reason behind the inbuilt robustness of the highly engineered eIF2 system against intrinsic perturbations. Our investigations reveal that the robust nature of the eIF2 pathway may originate from the existence of an attractive natural sliding surface within the system satisfying reaching and sliding conditions that are well established in the domain of control engineering.

From insulin to Akt: Time delays and dominant processes

Akt/PKB regulates numerous processes in the mammalian cell, including cell survival and proliferation, and glucose uptake in response to insulin. Abnormalities in Akt signalling are linked to the development of Type 2 diabetes, cardio-vascular disease, and cancer. In the absence of insulin, Akt is predominantly found in the inactive state in the cytosol. Following insulin stimulation, Akt translocates to the plasma membrane, docks, and is phosphorylated to take on the active conformation. In turn, the activated Akt travels to and phosphorylates its many downstream substrates. Although crucial to the activation process, the translocation of Akt from the cytosol to the plasma membrane is currently not well understood. Here we detail the parameter optimisation of a mathematical model of Akt translocation to experimental data. We have quantified the time delay between the application of insulin and the downstream Akt translocation response, indicating the constraints on the timing of the intermediate processes. A delay of approximately 0.4 min prior to the Akt response was determined for the application of 1 nM insulin to cells in the basal state, whereas it was found that a further transition from physiological insulin to higher stimuli did not incur a delay. Furthermore, our investigation indicates that the dominant processes regulating the appearance of Akt at the plasma membrane differ with the insulin level. For physiological insulin, the rate limiting step was the release of Akt to the plasma membrane in response to the insulin signal. In contrast, at high insulin levels, regulation of the recycling of Akt from the plasma membrane to the cytosol was also required.

Crosstalk in transition: the translocation of Akt

Akt/PKB is an important crosstalk node at the junction between a number of major signalling pathways in the mammalian cell. As a significant nutrient sensor, Akt plays a central role in many cellular processes, including cell growth, cell survival and glucose metabolism. The dysregulation of Akt signalling is implicated in the development of many diseases, from diabetes to cancer. The translocation of Akt from cytosol to plasma membrane is a crucial step in Akt activation. Akt is initially synthesized on the endoplasmic reticulum, but translocates to the plasma membrane (PM) in response to insulin stimulation, where it may be activated. The Akt is then recycled to the cytoplasm. The activated Akt may propagate signals to downstream substrates both at the PM and in the cytosol, hence understanding the translocation dynamics is an important step in dissecting the signalling system. At the present time, however, knowledge concerning the translocation of either activated and unactivated Akt is scant. Here we present a simple, deterministic, three-compartment ordinary differential equation model of Akt translocation in vitro. This model can reproduce the salient features of Akt translocation in a manner consistent with the experimental data. Furthermore, we demonstrate that this system is equivalent to a damped harmonic oscillator, and analyse the steady state and transient behaviour of the model over the entire parameter space.

JuPOETs: a constrained multiobjective optimization approach to estimate biochemical model ensembles in the Julia programming language

Background

Ensemble modeling is a promising approach for obtaining robust predictions and coarse grained population behavior in deterministic mathematical models. Ensemble approaches address model uncertainty by using parameter or model families instead of single best-fit parameters or fixed model structures. Parameter ensembles can be selected based upon simulation error, along with other criteria such as diversity or steady-state performance. Simulations using parameter ensembles can estimate confidence intervals on model variables, and robustly constrain model predictions, despite having many poorly constrained parameters.

Results

In this software note, we present a multiobjective based technique to estimate parameter or models ensembles, the Pareto Optimal Ensemble Technique in the Julia programming language (JuPOETs). JuPOETs integrates simulated annealing with Pareto optimality to estimate ensembles on or near the optimal tradeoff surface between competing training objectives. We demonstrate JuPOETs on a suite of multiobjective problems, including test functions with parameter bounds and system constraints as well as for the identification of a proof-of-concept biochemical model with four conflicting training objectives. JuPOETs identified optimal or near optimal solutions approximately six-fold faster than a corresponding implementation in Octave for the suite of test functions. For the proof-of-concept biochemical model, JuPOETs produced an ensemble of parameters that gave both the mean of the training data for conflicting data sets, while simultaneously estimating parameter sets that performed well on each of the individual objective functions.

Conclusions

JuPOETs is a promising approach for the estimation of parameter and model ensembles using multiobjective optimization. JuPOETs can be adapted to solve many problem types, including mixed binary and continuous variable types, bilevel optimization problems and constrained problems without altering the base algorithm. JuPOETs is open source, available under an MIT license, and can be installed using the Julia package manager from the JuPOETs GitHub repository

The Akt switch model: Is location sufficient?

Akt/PKB is a biochemical regulator that functions as an important cross-talk node between several signalling pathways in the mammalian cell. In particular, Akt is a key mediator of glucose transport in response to insulin. The phosphorylation (activation) of only a small percentage of the Akt pool of insulin-sensitive cells results in maximal translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM). This enables the diffusion of glucose into the cell. The dysregulation of Akt signalling is associated with the development of diabetes, cancer and cardiovascular disease. Akt is synthesised in the cytoplasm in the inactive state. Under the influence of insulin, it moves to the PM, where it is phosphorylated to form pAkt. Although phosphorylation occurs only at the PM, pAkt is found in many cellular locations, including the PM, the cytoplasm, and the nucleus. Indeed, the spatial distribution of pAkt within the cell appears to be an important determinant of downstream regulation. Here we present a simple, linear, four-compartment ordinary differential equation (ODE) model of Akt activation that tracks both the biochemical state and the physical location of Akt. This model embodies the main features of the activation of this important cross-talk node and is consistent with the experimental data. In particular, it allows different downstream signalling motifs without invoking separate feedback pathways. Moreover, the model is computationally tractable, readily analysed, and elucidates some of the apparent anomalies in insulin signalling via Akt.

Dynamic Modeling and Analysis of the Cross-Talk between Insulin/AKT and MAPK/ERK Signaling Pathways

Feedback loops play a key role in the regulation of the complex interactions in signal transduction networks. By studying the network of interactions among the biomolecules present in signaling pathways at the systems level, it is possible to understand how the biological functions are regulated and how the diseases emerge from their deregulations. This paper identifies the key feedback loops involved in the cross-talk among the insulin-AKT and MAPK/ERK signaling pathways. We developed a mathematical model that can be used to study the steady-state and dynamic behavior of the interactions among these two important signaling pathways. Modeling analysis and simulation case studies identify the key interaction parameters and the feedback loops that determine the normal and disease phenotypes.

mRNA translation and protein synthesis: an analysis of different modelling methodologies and a new PBN based approach

Background

mRNA translation involves simultaneous movement of multiple ribosomes on the mRNA and is also subject to regulatory mechanisms at different stages. Translation can be described by various codon-based models, including ODE, TASEP, and Petri net models. Although such models have been extensively used, the overlap and differences between these models and the implications of the assumptions of each model has not been systematically elucidated. The selection of the most appropriate modelling framework, and the most appropriate way to develop coarse-grained/fine-grained models in different contexts is not clear.

Results

We systematically analyze and compare how different modelling methodologies can be used to describe translation. We define various statistically equivalent codon-based simulation algorithms and analyze the importance of the update rule in determining the steady state, an aspect often neglected. Then a novel probabilistic Boolean network (PBN) model is proposed for modelling translation, which enjoys an exact numerical solution. This solution matches those of numerical simulation from other methods and acts as a complementary tool to analytical approximations and simulations. The advantages and limitations of various codon-based models are compared, and illustrated by examples with real biological complexities such as slow codons, premature termination and feedback regulation. Our studies reveal that while different models gives broadly similiar trends in many cases, important differences also arise and can be clearly seen, in the dependence of the translation rate on different parameters. Furthermore, the update rule affects the steady state solution.

Conclusions

The codon-based models are based on different levels of abstraction. Our analysis suggests that a multiple model approach to understanding translation allows one to ascertain which aspects of the conclusions are robust with respect to the choice of modelling methodology, and when (and why) important differences may arise. This approach also allows for an optimal use of analysis tools, which is especially important when additional complexities or regulatory mechanisms are included. This approach can provide a robust platform for dissecting translation, and results in an improved predictive framework for applications in systems and synthetic biology.

The translational machinery is an optimized molecular network that affects cellular homoeostasis and disease

Translation involves interactions between mRNAs, ribosomes, tRNAs and a host of translation factors. Emerging evidence on the eukaryotic translational machinery indicates that these factors are organized in a highly optimized network, in which the levels of the different factors are finely matched to each other. This optimal factor network is essential for producing proteomes that result in optimal fitness, and perturbations to the optimal network that significantly affect translational activity therefore result in non-optimal proteomes, fitness losses and disease. On the other hand, experimental evidence indicates that translation and cell growth are relatively robust to perturbations, and viability can be maintained even upon significant damage to individual translation factors. How the eukaryotic translational machinery is optimized, and how it can maintain optimization in the face of changing internal parameters, are open questions relevant to the interaction between translation and cellular disease states.

Regulatory networks and complex interactions between the insulin and angiotensin II signalling systems: models and implications for hypertension and diabetes

The cross-talk between insulin and angiotensin II signalling pathways plays a significant role in the co-occurrence of diabetes and hypertension. We developed a mathematical model of the system of interactions among the biomolecules that are involved in the cross-talk between the insulin and angiotensin II signalling pathways. We have identified several feedback structures that regulate the dynamic behavior of the individual signalling pathways and their interactions. Different scenarios are simulated and dominant steady-state, dynamic and stability characteristics are revealed. The proposed mechanistic model describes how angiotensin II inhibits the actions of insulin and impairs the insulin-mediated vasodilation. The model also predicts that poor glycaemic control induced by diabetes contributes to hypertension by activating the renin angiotensin aystem.

Solving the lost in translation problem: improving the effectiveness of translational research

Translational research frequently fails to replicate in the clinic what has been demonstrated in the laboratory. This has been true for neuroprotection in the central nervous system, neuroprotection in glaucoma, as well as many other areas of medicine. Two fundamental reasons for this 'Lost in Translation' problem are the 'Butterfly Effect' (chaotic behavior of many animal models) and the 'Two Cultures' problem (differences between the methodologies for preclinical and clinical research). We propose several strategies to deal with these issues, including the use of ensembles of animal models, adding intraocular pressure lowering to preclinical neuroprotection studies, changing the way in which preclinical research is done, and increasing interactions between the preclinical and clinical teams.

Mathematical and Computational Modelling of Ribosomal Movement and Protein Synthesis: an overview

Translation or protein synthesis consists of a complex system of chemical reactions, which ultimately result in decoding of the mRNA and the production of a protein. The complexity of this reaction system makes it difficult to quantitatively connect its input parameters (such as translation factor or ribosome concentrations, codon composition of the mRNA, or energy availability) to output parameters (such as protein synthesis rates or ribosome densities on mRNAs). Mathematical and computational models of translation have now been used for nearly five decades to investigate translation, and to shed light on the relationship between the different reactions in the system. This review gives an overview over the principal approaches used in the modelling efforts, and summarises some of the major findings that were made.

Computational modeling and analysis of insulin induced eukaryotic translation initiation

Insulin, the primary hormone regulating the level of glucose in the bloodstream, modulates a variety of cellular and enzymatic processes in normal and diseased cells. Insulin signals are processed by a complex network of biochemical interactions which ultimately induce gene expression programs or other processes such as translation initiation. Surprisingly, despite the wealth of literature on insulin signaling, the relative importance of the components linking insulin with translation initiation remains unclear. We addressed this question by developing and interrogating a family of mathematical models of insulin induced translation initiation. The insulin network was modeled using mass-action kinetics within an ordinary differential equation (ODE) framework. A family of model parameters was estimated, starting from an initial best fit parameter set, using 24 experimental data sets taken from literature. The residual between model simulations and each of the experimental constraints were simultaneously minimized using multiobjective optimization. Interrogation of the model population, using sensitivity and robustness analysis, identified an insulin-dependent switch that controlled translation initiation. Our analysis suggested that without insulin, a balance between the pro-initiation activity of the GTP-binding protein Rheb and anti-initiation activity of PTEN controlled basal initiation. On the other hand, in the presence of insulin a combination of PI3K and Rheb activity controlled inducible initiation, where PI3K was only critical in the presence of insulin. Other well known regulatory mechanisms governing insulin action, for example IRS-1 negative feedback, modulated the relative importance of PI3K and Rheb but did not fundamentally change the signal flow.

A systems view of the protein expression process

Many biological processes are regulated by changing the concentration and activity of proteins. The presence of a protein at a given subcellular location at a given time with a certain conformation is the result of an apparently sequential process. The rate of protein formation is influenced by chromatin state, and the rates of transcription, translation, and degradation. There is an exquisite control system where each stage of the process is controlled both by seemingly unregulated proteins as well as through feedbacks mediated by RNA and protein products. Here we review the biological facts and mathematical models for each stage of the protein production process. We conclude that advances in experimental techniques leading to a detailed description of the process have not been matched by mathematical models that represent the details of the process and facilitate analysis. Such an exercise is the first step towards development of a framework for a systems biology analysis of the protein production process.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1007/s11693-011-9088-1) contains supplementary material, which is available to authorized users.

Modeling and analysis of retinoic acid induced differentiation of uncommitted precursor cells

Manipulation of differentiation programs has therapeutic potential in a spectrum of human cancers and neurodegenerative disorders. In this study, we integrated computational and experimental methods to unravel the response of a lineage uncommitted precursor cell-line, HL-60, to Retinoic Acid (RA). HL-60 is a human myeloblastic leukemia cell-line used extensively to study human differentiation programs. Initially, we focused on the role of the BLR1 receptor in RA-induced differentiation and G1/0-arrest in HL-60. BLR1, a putative G protein-coupled receptor expressed following RA exposure, is required for RA-induced cell-cycle arrest and differentiation and causes persistent MAPK signaling. A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell-lines with and without RA. The current model described the dynamics of 729 proteins and protein complexes interconnected by 1356 interactions. An ensemble strategy was used to compensate for uncertain model parameters. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. The ensemble of models also correctly predicted Rb and p47phox regulation and the correlation between p21-CDK4-cyclin D formation and G1/0-arrest following exposure to RA. Finally, we investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. Taken together, the model presented here was a first step toward a systematic framework for analysis of programmed differentiation. These studies also demonstrated that mechanistic network modeling can help prioritize experimental directions by generating falsifiable hypotheses despite uncertainty.