Efficient exploration of discrete energy landscapes

A Boolean network model of hypoxia, mechanosensing and TGF-β signaling captures the role of phenotypic plasticity and mutations in tumor metastasis

The tumor microenvironment aids cancer progression by promoting several cancer hallmarks, independent of cancer-related mutations. Biophysical properties of this environment, such as the stiffness of the matrix cells adhere to and local cell density, impact proliferation, apoptosis, and the epithelial to mesenchymal transition (EMT). The latter is a rate-limiting step for invasion and metastasis, enhanced in hypoxic tumor environments but hindered by soft matrices and/or high cell densities. As these influences are often studied in isolation, the crosstalk between hypoxia, biomechanical signals, and the classic EMT driver TGF-β is not well mapped, limiting our ability to predict and anticipate cancer cell behaviors in changing tumor environments. To address this, we built a Boolean regulatory network model that integrates hypoxic signaling with a mechanosensitive model of EMT, which includes the EMT-promoting crosstalk of mitogens and biomechanical signals, cell cycle control, and apoptosis. Our model reproduces the requirement of Hif-1α for proliferation, the anti-proliferative effects of strong Hif-1α stabilization during hypoxia, hypoxic protection from anoikis, and hypoxia-driven mechanosensitive EMT. We offer experimentally testable predictions about the effect of VHL loss on cancer hallmarks, with or without secondary oncogene activation. Taken together, our model serves as a predictive framework to synthesize the signaling responses associated with tumor progression and metastasis in healthy vs. mutant cells. Our single-cell model is a key step towards more extensive regulatory network models that cover damage-response and senescence, integrating most cell-autonomous cancer hallmarks into a single model that can, in turn, control the behavior of in silico cells within a tissue model of epithelial homeostasis and carcinoma.

Unlocking Mitochondrial Dysfunction-Associated Senescence (MiDAS) with NAD + - a Boolean Model of Mitochondrial Dynamics and Cell Cycle Control

The steady accumulation of senescent cells with aging creates tissue environments that aid cancer evolution. Aging cell states are highly heterogeneous. 'Deep senescent' cells rely on healthy mitochondria to fuel a strong proinflammatory secretome, including cytokines, growth and transforming signals. Yet, the physiological triggers of senescence such as the reactive oxygen species (ROS) can also trigger mitochondrial dysfunction, and sufficient energy deficit to alter their secretome and cause chronic oxidative stress - a state termed Mitochondrial Dysfunction-Associated Senescence (MiDAS). Here, we offer a mechanistic hypothesis for the molecular processes leading to MiDAS, along with testable predictions. To do this we have built a Boolean regulatory network model that qualitatively captures key aspects of mitochondrial dynamics during cell cycle progression (hyper-fusion at the G1/S boundary, fission in mitosis), apoptosis (fission and dysfunction) and glucose starvation (reversible hyper-fusion), as well as MiDAS in response to SIRT3 knockdown or oxidative stress. Our model reaffirms the protective role of NAD + and external pyruvate. We offer testable predictions about the growth factor- and glucose-dependence of MiDAS and its reversibility at different stages of reactive oxygen species (ROS)-induced senescence. Our model provides mechanistic insights into the distinct stages of DNA-damage induced senescence, the relationship between senescence and epithelial-to-mesenchymal transition in cancer and offers a foundation for building multiscale models of tissue aging.

Highlights

Boolean regulatory network model reproduces mitochondrial dynamics during cell cycle progression, apoptosis, and glucose starvation. Model offers a mechanistic explanation for the positive feedback loop that locks in Mitochondrial Dysfunction-Associated Senescence (MiDAS), involving autophagy-resistant, hyperfused, dysfunctional mitochondria. Model reproduces ROS-mediated mitochondrial dysfunction and suggests that MiDAS is part of the early phase of damage-induced senescence. Model predicts that cancer-driving mutations that bypass the G1/S checkpoint generally increase the incidence of MiDAS, except for p53 loss.

pourRNA-a time- and memory-efficient approach for the guided exploration of RNA energy landscapes

MOTIVATION

The folding dynamics of ribonucleic acids (RNAs) are typically studied via coarse-grained models of the underlying energy landscape to face the exponential growths of the RNA secondary structure space. Still, studies of exact folding kinetics based on gradient basin abstractions are currently limited to short sequence lengths due to vast memory requirements. In order to compute exact transition rates between gradient basins, state-of-the-art approaches apply global flooding schemes that require to memorize the whole structure space at once. pourRNA tackles this problem via local flooding techniques where memorization is limited to the structure ensembles of individual gradient basins.

RESULTS

Compared to the only available tool for exact gradient basin-based macro-state transition rates (namely barriers), pourRNA computes the same exact transition rates up to 10 times faster and requires two orders of magnitude less memory for sequences that are still computationally accessible for exhaustive enumeration. Parallelized computation as well as additional heuristics further speed up computations while still producing high-quality transition model approximations. The introduced heuristics enable a guided trade-off between model quality and required computational resources. We introduce and evaluate a macroscopic direct path heuristics to efficiently compute refolding energy barrier estimations for the co-transcriptionally trapped RNA sv11 of length 115 nt. Finally, we also show how pourRNA can be used to identify folding funnels and their respective energetically lowest minima.

AVAILABILITY AND IMPLEMENTATION

pourRNA is freely available at https://github.com/ViennaRNA/pourRNA.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Studying O2 pathways in [NiFe]- and [NiFeSe]-hydrogenases

Hydrogenases are efficient biocatalysts for H₂ production and oxidation with various potential biotechnological applications.[NiFe]-class hydrogenases are highly active in both production and oxidation processes—albeit primarily biased to the latter—but suffer from being sensitive to O₂.[NiFeSe] hydrogenases are a subclass of [NiFe] hydrogenases with, usually, an increased insensitivity to aerobic environments. In this study we aim to understand the structural causes of the low sensitivity of a [NiFeSe]-hydrogenase, when compared with a [NiFe] class enzyme, by studying the diffusion of O₂. To unravel the differences between the two enzymes, we used computational methods comprising Molecular Dynamics simulations with explicit O₂ and Implicit Ligand Sampling methodologies. With the latter, we were able to map the free energy landscapes for O₂ permeation in both enzymes. We derived pathways from these energy landscapes and selected the kinetically more relevant ones with reactive flux analysis using transition path theory. These studies evidence the existence of quite different pathways in both enzymes and predict a lower permeation efficiency for O₂ in the case of the [NiFeSe]-hydrogenase when compared with the [NiFe] enzyme. These differences can explain the experimentally observed lower inhibition by O₂ on [NiFeSe]-hydrogenases, when compared with [NiFe]-hydrogenases. A comprehensive map of the residues lining the most important O₂ pathways in both enzymes is also presented.

Boolean model of growth signaling, cell cycle and apoptosis predicts the molecular mechanism of aberrant cell cycle progression driven by hyperactive PI3K

The PI3K/AKT signaling pathway plays a role in most cellular functions linked to cancer progression, including cell growth, proliferation, cell survival, tissue invasion and angiogenesis. It is generally recognized that hyperactive PI3K/AKT1 are oncogenic due to their boost to cell survival, cell cycle entry and growth-promoting metabolism. That said, the dynamics of PI3K and AKT1 during cell cycle progression are highly nonlinear. In addition to negative feedback that curtails their activity, protein expression of PI3K subunits has been shown to oscillate in dividing cells. The low-PI3K/low-AKT1 phase of these oscillations is required for cytokinesis, indicating that oncogenic PI3K may directly contribute to genome duplication. To explore this, we construct a Boolean model of growth factor signaling that can reproduce PI3K oscillations and link them to cell cycle progression and apoptosis. The resulting modular model reproduces hyperactive PI3K-driven cytokinesis failure and genome duplication and predicts the molecular drivers responsible for these failures by linking hyperactive PI3K to mis-regulation of Polo-like kinase 1 (Plk1) expression late in G2. To do this, our model captures the role of Plk1 in cell cycle progression and accurately reproduces multiple effects of its loss: G2 arrest, mitotic catastrophe, chromosome mis-segregation / aneuploidy due to premature anaphase, and cytokinesis failure leading to genome duplication, depending on the timing of Plk1 inhibition along the cell cycle. Finally, we offer testable predictions on the molecular drivers of PI3K oscillations, the timing of these oscillations with respect to division, and the role of altered Plk1 and FoxO activity in genome-level defects caused by hyperactive PI3K. Our model is an important starting point for the predictive modeling of cell fate decisions that include AKT1-driven senescence, as well as the non-intuitive effects of drugs that interfere with mitosis.

Memory-efficient RNA energy landscape exploration

MOTIVATION

Energy landscapes provide a valuable means for studying the folding dynamics of short RNA molecules in detail by modeling all possible structures and their transitions. Higher abstraction levels based on a macro-state decomposition of the landscape enable the study of larger systems; however, they are still restricted by huge memory requirements of exact approaches.

RESULTS

We present a highly parallelizable local enumeration scheme that enables the computation of exact macro-state transition models with highly reduced memory requirements. The approach is evaluated on RNA secondary structure landscapes using a gradient basin definition for macro-states. Furthermore, we demonstrate the need for exact transition models by comparing two barrier-based approaches, and perform a detailed investigation of gradient basins in RNA energy landscapes.

AVAILABILITY AND IMPLEMENTATION

Source code is part of the C++ Energy Landscape Library available at http://www.bioinf.uni-freiburg.de/Software/.

Phylogeny and evolution of RNA structure

Darwin's conviction that all living beings on Earth are related and the graph of relatedness is tree-shaped has been essentially confirmed by phylogenetic reconstruction first from morphology and later from data obtained by molecular sequencing. Limitations of the phylogenetic tree concept were recognized as more and more sequence information became available. The other path-breaking idea of Darwin, natural selection of fitter variants in populations, is cast into simple mathematical form and extended to mutation-selection dynamics. In this form the theory is directly applicable to RNA evolution in vitro and to virus evolution. Phylogeny and population dynamics of RNA provide complementary insights into evolution and the interplay between the two concepts will be pursued throughout this chapter. The two strategies for understanding evolution are ultimately related through the central paradigm of structural biology: sequence ⇒ structure ⇒ function. We elaborate on the state of the art in modeling both phylogeny and evolution of RNA driven by reproduction and mutation. Thereby the focus will be laid on models for phylogenetic sequence evolution as well as evolution and design of RNA structures with selected examples and notes on simulation methods. In the perspectives an attempt is made to combine molecular structure, population dynamics, and phylogeny in modeling evolution.

Efficient procedures for the numerical simulation of mid-size RNA kinetics

Motivation

Methods for simulating the kinetic folding of RNAs by numerically solving the chemical master equation have been developed since the late 90's, notably the programs Kinfold and Treekin with Barriers that are available in the Vienna RNA package. Our goal is to formulate extensions to the algorithms used, starting from the Gillespie algorithm, that will allow numerical simulations of mid-size (~ 60–150 nt) RNA kinetics in some practical cases where numerous distributions of folding times are desired. These extensions can contribute to analyses and predictions of RNA folding in biologically significant problems.

Results

By describing in a particular way the reduction of numerical simulations of RNA folding kinetics into the Gillespie stochastic simulation algorithm for chemical reactions, it is possible to formulate extensions to the basic algorithm that will exploit memoization and parallelism for efficient computations. These can be used to advance forward from the small examples demonstrated to larger examples of biological interest.

Software

The implementation that is described and used for the Gillespie algorithm is freely available by contacting the authors, noting that the efficient procedures suggested may also be applicable along with Vienna's Kinfold.

Approximating the set of local minima in partial RNA folding landscapes

MOTIVATION

We study a stochastic method for approximating the set of local minima in partial RNA folding landscapes associated with a bounded-distance neighbourhood of folding conformations. The conformations are limited to RNA secondary structures without pseudoknots. The method aims at exploring partial energy landscapes pL induced by folding simulations and their underlying neighbourhood relations. It combines an approximation of the number of local optima devised by Garnier and Kallel (2002) with a run-time estimation for identifying sets of local optima established by Reeves and Eremeev (2004).

RESULTS

The method is tested on nine sequences of length between 50 nt and 400 nt, which allows us to compare the results with data generated by RNAsubopt and subsequent barrier tree calculations. On the nine sequences, the method captures on average 92% of local minima with settings designed for a target of 95%. The run-time of the heuristic can be estimated by O(n(2)Dνlnν), where n is the sequence length, ν is the number of local minima in the partial landscape pL under consideration and D is the maximum number of steepest descent steps in attraction basins associated with pL.