Biological Networks

Networks of coordinated interactions among biological entities govern a myriad of biological functions that span a wide range of both length and time scales—from ecosystems to individual cells and from years to milliseconds. For these networks, the concept “the whole is greater than the sum of its parts” applies as a norm rather than an exception. Meanwhile, continued advances in molecular biology and high-throughput technology have enabled a broad and systematic interrogation of whole-cell networks, allowing the investigation of biological processes and functions at unprecedented breadth and resolution—even down to the single-cell level. The explosion of biological data, especially molecular-level intracellular data, necessitates new paradigms for unraveling the complexity of biological networks and for understanding how biological functions emerge from such networks. These paradigms introduce new challenges related to the analysis of networks in which quantitative approaches such as machine learning and mathematical modeling play an indispensable role. The Special Issue on “Biological Networks” showcases advances in the development and application of in silico network modeling and analysis of biological systems

REDEMPTION: reduced dimension ensemble modeling and parameter estimation

Summary: Here, we present REDEMPTION (Reduced Dimension Ensemble Modeling and Parameter estimation), a toolbox for parameter estimation and ensemble modeling of ordinary differential equations (ODEs) using time-series data. For models with more reactions than measured species, a common scenario in biological modeling, the parameter estimation is formulated as a nested optimization problem based on incremental parameter estimation strategy. REDEMPTION also includes a tool for the identification of an ensemble of parameter combinations that provide satisfactory goodness-of-fit to the data. The functionalities of REDEMPTION are accessible through a MATLAB user interface (UI), as well as through programming script. For computational speed-up, REDEMPTION provides a numerical parallelization option using MATLAB Parallel Computing toolbox. Availability and implementation: REDEMPTION can be downloaded from http://www.cabsel.ethz.ch/tools/redemption. Contact: [email protected]

Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method

Motivation: Time-series measurements of metabolite concentration have become increasingly more common, providing data for building kinetic models of metabolic networks using ordinary differential equations (ODEs). In practice, however, such time-course data are usually incomplete and noisy, and the estimation of kinetic parameters from these data is challenging. Practical limitations due to data and computational aspects, such as solving stiff ODEs and finding global optimal solution to the estimation problem, give motivations to develop a new estimation procedure that can circumvent some of these constraints. Results: In this work, an incremental and iterative parameter estimation method is proposed that combines and iterates between two estimation phases. One phase involves a decoupling method, in which a subset of model parameters that are associated with measured metabolites, are estimated using the minimization of slope errors. Another phase follows, in which the ODE model is solved one equation at a time and the remaining model parameters are obtained by minimizing concentration errors. The performance of this two-phase method was tested on a generic branched metabolic pathway and the glycolytic pathway of Lactococcus lactis. The results showed that the method is efficient in getting accurate parameter estimates, even when some information is missing. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Iterative approach to model identification of biological networks

BACKGROUND: Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements. RESULTS: The scheme includes a state regulator algorithm that provides estimates of all system unknowns (concentrations of the system components and the reaction rates of their inter-conversion). The full system information is used for estimation of the model parameters. An optimal experiment design using the parameter identifiability and D-optimality criteria is formulated to provide "rich" experimental data for maximizing the accuracy of the parameter estimates in subsequent iterations. The importance of model identifiability tests for optimal measurement selection is also considered. The iterative scheme is tested on a model for the caspase function in apoptosis where it is demonstrated that model accuracy improves with each iteration. Optimal experiment design was determined to be critical for model identification. CONCLUSION: The proposed algorithm has general application to modeling a wide range of cellular processes, which include gene regulation networks, signal transduction and metabolic networks

Are mutagenic non D-loop direct repeat motifs in mitochondrial DNA under a negative selection pressure?

Non D-loop direct repeats (DRs) in mitochondrial DNA (mtDNA) have been commonly implicated in the mutagenesis of mtDNA deletions associated with neuromuscular disease and ageing. Further, these DRs have been hypothesized to put a constraint on the lifespan of mammals and are under a negative selection pressure. Using a compendium of 294 mammalian mtDNA, we re-examined the relationship between species lifespan and the mutagenicity of such DRs. Contradicting the prevailing hypotheses, we found no significant evidence that long-lived mammals possess fewer mutagenic DRs than short-lived mammals. By comparing DR counts in human mtDNA with those in selectively randomized sequences, we also showed that the number of DRs in human mtDNA is primarily determined by global mtDNA properties, such as the bias in synonymous codon usage (SCU) and nucleotide composition. We found that SCU bias in mtDNA positively correlates with DR counts, where repeated usage of a subset of codons leads to more frequent DR occurrences. While bias in SCU and nucleotide composition has been attributed to nucleotide mutational bias, mammalian mtDNA still exhibit higher SCU bias and DR counts than expected from such mutational bias, suggesting a lack of negative selection against non D-loop DR

Role of Direct Repeat and Stem-Loop Motifs in mtDNA Deletions: Cause or Coincidence?

Deletion mutations within mitochondrial DNA (mtDNA) have been implicated in degenerative and aging related conditions, such as sarcopenia and neuro-degeneration. While the precise molecular mechanism of deletion formation in mtDNA is still not completely understood, genome motifs such as direct repeat (DR) and stem-loop (SL) have been observed in the neighborhood of deletion breakpoints and thus have been postulated to take part in mutagenesis. In this study, we have analyzed the mitochondrial genomes from four different mammals: human, rhesus monkey, mouse and rat, and compared them to randomly generated sequences to further elucidate the role of direct repeat and stem-loop motifs in aging associated mtDNA deletions. Our analysis revealed that in the four species, DR and SL structures are abundant and that their distributions in mtDNA are not statistically different from randomized sequences. However, the average distance between the reported age associated mtDNA breakpoints and their respective nearest DR motifs is significantly shorter than what is expected of random chance in human (p<10−4) and rhesus monkey (p = 0.0034), but not in mouse (p = 0.0719) and rat (p = 0.0437), indicating the existence of species specific difference in the relationship between DR motifs and deletion breakpoints. In addition, the frequencies of large DRs (>10 bp) tend to decrease with increasing lifespan among the four mammals studied here, further suggesting an evolutionary selection against stable mtDNA misalignments associated with long DRs in long-living animals. In contrast to the results on DR, the probability of finding SL motifs near a deletion breakpoint does not differ from random in any of the four mtDNA sequences considered. Taken together, the findings in this study give support for the importance of stable mtDNA misalignments, aided by long DRs, as a major mechanism of deletion formation in long-living, but not in short-living mammals

Is mitochondrial DNA turnover slower than commonly assumed?

Mutations arise during DNA replication due to oxidative lesions and intrinsic polymerase errors. Mitochondrial DNA (mtDNA) mutation rate is therefore closely linked to the mitochondrial DNA turnover process, especially in post mitotic cells. This makes the mitochondrial DNA turnover rate critical for understanding the origin and dynamics of mtDNA mutagenesis in post mitotic cells. Experimental mitochondrial turnover quantification has been based on different mitochondrial macromolecules, such as mitochondrial proteins, lipids and DNA, and the experimental data suggested highly divergent turnover rates, ranging from over 2days to about 1year. In this article we argue that mtDNA turnover rate cannot be as fast as is often envisaged. Using a stochastic model based on the chemical master equation, we show that a turnover rate corresponding to mtDNA half-life in the order of months is the most consistent with published mtDNA mutation level

Effects of Lithium on Age-related Decline in Mitochondrial Turnover and Function in Caenorhabditis elegans

Aging has been associated with the accumulation of damages in molecules and organelles in cells, particularly mitochondria. The rate of damage accumulation is closely tied to the turnover of the affected cellular components. Perturbing mitochondrial turnover has been shown to significantly affect the rate of deterioration of mitochondrial function with age and to alter lifespan of model organisms. In this study, we investigated the effects of upregulating autophagy using lithium in Caenorhabditis elegans. We found that lithium treatment increased both the lifespan and healthspan of C. elegans without any significant change in the mortality rate and oxidative damages to proteins. The increase in healthspan was accompanied by improved mitochondrial energetic function. In contrast, mitochondrial DNA copy number decreased faster with age under lithium. To better understand the interactions among mitochondrial turnover, damage, and function, we created a mathematical model that described the dynamics of functional and dysfunctional mitochondria population. The combined analysis of model and experimental observations showed how preferential (selective) autophagy of dysfunctional mitochondria could lead to better mitochondrial functionality with age, despite a lower population size. However, the results of model analysis suggest that the benefit of increasing autophagy for mitochondrial function is expected to diminish at higher levels of upregulation due to a shrinking mitochondrial populatio

Maximizing signal-to-noise ratio in the random mutation capture assay

The ‘Random Mutation Capture' assay allows for the sensitive quantitation of DNA mutations at extremely low mutation frequencies. This method is based on PCR detection of mutations that render the mutated target sequence resistant to restriction enzyme digestion. The original protocol prescribes an end-point dilution to about 0.1 mutant DNA molecules per PCR well, such that the mutation burden can be simply calculated by counting the number of amplified PCR wells. However, the statistical aspects associated with the single molecular nature of this protocol and several other molecular approaches relying on binary (on/off) output can significantly affect the quantification accuracy, and this issue has so far been ignored. The present work proposes a design of experiment (DoE) using statistical modeling and Monte Carlo simulations to obtain a statistically optimal sampling protocol, one that minimizes the coefficient of variance in the measurement estimates. Here, the DoE prescribed a dilution factor at about 1.6 mutant molecules per well. Theoretical results and experimental validation revealed an up to 10-fold improvement in the information obtained per PCR well, i.e. the optimal protocol achieves the same coefficient of variation using one-tenth the number of wells used in the original assay. Additionally, this optimization equally applies to any method that relies on binary detection of a small number of template

Single-cell transcriptional uncertainty landscape of cell differentiation [version 2; peer review: 2 approved]

Background: Single-cell studies have demonstrated the presence of significant cell-to-cell heterogeneity in gene expression. Whether such heterogeneity is only a bystander or has a functional role in the cell differentiation process is still hotly debated. Methods: In this study, we quantified and followed single-cell transcriptional uncertainty – a measure of gene transcriptional stochasticity in single cells – in 10 cell differentiation systems of varying cell lineage progressions, from single to multi-branching trajectories, using the stochastic two-state gene transcription model. Results: By visualizing the transcriptional uncertainty as a landscape over a two-dimensional representation of the single-cell gene expression data, we observed universal features in the cell differentiation trajectories that include: (i) a peak in single-cell uncertainty during transition states, and in systems with bifurcating differentiation trajectories, each branching point represents a state of high transcriptional uncertainty; (ii) a positive correlation of transcriptional uncertainty with transcriptional burst size and frequency; (iii) an increase in RNA velocity preceding the increase in the cell transcriptional uncertainty. Conclusions: Our findings suggest a possible universal mechanism during the cell differentiation process, in which stem cells engage stochastic exploratory dynamics of gene expression at the start of the cell differentiation by increasing gene transcriptional bursts, and disengage such dynamics once cells have decided on a particular terminal cell identity. Notably, the peak of single-cell transcriptional uncertainty signifies the decision-making point in the cell differentiation process