The origins of time-delay in template biopolymerization processes.
ABSTRACT: Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models.
Project description:Genes with similar transcriptional activation kinetics can display very different temporal mRNA profiles because of differences in transcription time, degradation rate, and RNA-processing kinetics. Recent studies have shown that a splicing-associated RNA production delay can be significant. To investigate this issue more generally, it is useful to develop methods applicable to genome-wide datasets. We introduce a joint model of transcriptional activation and mRNA accumulation that can be used for inference of transcription rate, RNA production delay, and degradation rate given data from high-throughput sequencing time course experiments. We combine a mechanistic differential equation model with a nonparametric statistical modeling approach allowing us to capture a broad range of activation kinetics, and we use Bayesian parameter estimation to quantify the uncertainty in estimates of the kinetic parameters. We apply the model to data from estrogen receptor ? activation in the MCF-7 breast cancer cell line. We use RNA polymerase II ChIP-Seq time course data to characterize transcriptional activation and mRNA-Seq time course data to quantify mature transcripts. We find that 11% of genes with a good signal in the data display a delay of more than 20 min between completing transcription and mature mRNA production. The genes displaying these long delays are significantly more likely to be short. We also find a statistical association between high delay and late intron retention in pre-mRNA data, indicating significant splicing-associated production delays in many genes.
Project description:Time delays are known to play a crucial role in generating biological oscillations. The early embryonic cell cycle in the frog Xenopus laevis is one such example. Although various mathematical models of this oscillating system exist, it is not clear how to best model the required time delay. Here, we study a simple cell cycle model that produces oscillations due to the presence of an ultrasensitive, time-delayed negative feedback loop. We implement the time delay in three qualitatively different ways, using a fixed time delay, a distribution of time delays, and a delay that is state-dependent. We analyze the dynamics in all cases, and we use experimental observations to interpret our results and put constraints on unknown parameters. In doing so, we find that different implementations of the time delay can have a large impact on the resulting oscillations.
Project description:Designing genetic networks with desired functionalities requires an accurate mathematical framework that accounts for the essential mechanistic details of the system. Here, we formulate a time-delay model of protein translation and mRNA degradation by systematically reducing a detailed mechanistic model that explicitly accounts for the ribosomal dynamics and the cleaving of mRNA by endonucleases. We exploit various technical and conceptual advantages that our time-delay model offers over the mechanistic model to probe the behavior of a self-repressing gene over wide regions of parameter space. We show that a heuristic time-delay model of protein synthesis of a commonly used form yields a notably different prediction for the parameter region where sustained oscillations occur. This suggests that such heuristics can lead to erroneous results. The functional forms that arise from our systematic reduction can be used for every system that involves transcription and translation and they could replace the commonly used heuristic time-delay models for these processes. The results from our analysis have important implications for the design of synthetic gene networks and stress that such design must be guided by a combination of heuristic models and mechanistic models that include all relevant details of the process.
Project description:The reduction of protein translation is a common feature in senescent cells and aging organisms, yet the underlying mechanisms are not fully understood. Here we show that both global mRNA translation and mammalian/mechanistic target of rapamycin complex 1 (mTORC1) kinase activity are declined in a senescent model of mouse embryonic fibroblasts (MEFs). Furthermore, RNA-seq analyses from polysomal versus total mRNA fractions identify TOP-like mRNA of Rps15 whose translation is regulated by mTORC1 during MEF senescence. Overexpression of Rps15 delays MEF senescence, possibly through regulating ribosome maturation. Together, these findings indicate that the activation of mTORC1-Rps15 axis ameliorate senescence by regulating ribosome biogenesis, which may provide further insights into aging research.
Project description:Departure delays are a major cause of economic loss and inefficiency in the growing industry of passenger flights. A departure delay of a current flight is inevitably affected by the late arrival of the flight immediately preceding it with the same aircraft. We seek to understand the mechanisms of such propagated delays, and to obtain universal metrics by which to evaluate an airline's operational effectiveness in delay alleviation. Here we use big data collected by the American Bureau of Transportation Statistics to design models of flight delays. Offering two dynamic models of delay propagation, we divided all carriers into two groups exhibiting a shifted power law or an exponentially truncated shifted power law delay distribution, revealing two universal delay propagation classes. Three model parameters, extracted directly from dual data mining, help characterize each airline's operational efficiency in delay mitigation. Therefore, our modeling framework provides the crucially lacking evaluation indicators for airlines, potentially contributing to the mitigation of future departure delays.
Project description:Models of mRNA translation usually presume that transcripts are linear; upon reaching the end of a transcript each terminating ribosome returns to the cytoplasmic pool before initiating anew on a different transcript. A consequence of linear models is that faster translation of a given mRNA is unlikely to generate more of the encoded protein, particularly at low ribosome availability. Recent evidence indicates that eukaryotic mRNAs are circularized, potentially allowing terminating ribosomes to preferentially reinitiate on the same transcript. Here we model the effect of ribosome reinitiation on translation and show that, at high levels of reinitiation, protein synthesis rates are dominated by the time required to translate a given transcript. Our model provides a simple mechanistic explanation for many previously enigmatic features of eukaryotic translation, including the negative correlation of both ribosome densities and protein abundance on transcript length, the importance of codon usage in determining protein synthesis rates, and the negative correlation between transcript length and both codon adaptation and 5' mRNA folding energies. In contrast to linear models where translation is largely limited by initiation rates, our model reveals that all three stages of translation-initiation, elongation, and termination/reinitiation-determine protein synthesis rates even at low ribosome availability.
Project description:As part of its response to a perturbation, an animal often needs to reposition its body. Inertia acts to oppose the corrective motion, delaying the completion of the movement-we refer to this elapsed time as inertial delay. As animal size increases, muscle moment arms also increase, but muscles are proportionally weaker, and limb inertia is proportionally larger. Consequently, the scaling of inertial delays is complex. Our intent is to determine how quickly different sized animals can produce corrective movements when their muscles act at their force capacity, relative to the time within which those movements need to be performed. Here, we quantify inertial delay using two biomechanical models representing common scenarios in animal locomotion: a distributed mass pendulum approximating swing limb repositioning (swing task), and an inverted pendulum approximating whole body posture recovery (posture task). We parameterized the anatomical, muscular, and inertial properties of these models using literature scaling relationships, then determined inertial delay for each task across a large range of movement magnitudes and the full range of terrestrial mammal sizes. We found that inertial delays scaled with an average of M0.28 in the swing task and M0.35 in the posture task across movement magnitudes-larger animals require more absolute time to perform the same movement as small animals. The time available to complete a movement also increases with animal size, but less steeply. Consequently, inertial delays comprise a greater fraction of swing duration and other characteristic movement times in larger animals. We also compared inertial delays to the other component delays within the stimulus-response pathway. As movement magnitude increased, inertial delays exceeded these sensorimotor delays, and this occurred for smaller movements in larger animals. Inertial delays appear to be a challenge for motor control, particularly for bigger movements in larger animals.
Project description:Scalar Utility Theory (SUT) is a model used to predict animal and human choice behaviour in the context of reward amount, delay to reward, and variability in these quantities (risk preferences). This article reviews and extends SUT, deriving novel predictions. We show that, contrary to what has been implied in the literature, (1) SUT can predict both risk averse and risk prone behaviour for both reward amounts and delays to reward depending on experimental parameters, (2) SUT implies violations of several concepts of rational behaviour (e.g. it violates strong stochastic transitivity and its equivalents, and leads to probability matching) and (3) SUT can predict, but does not always predict, a linear relationship between risk sensitivity in choices and coefficient of variation in the decision-making experiment. SUT derives from Scalar Expectancy Theory which models uncertainty in behavioural timing using a normal distribution. We show that the above conclusions also hold for other distributions, such as the inverse Gaussian distribution derived from drift-diffusion models. A straightforward way to test the key assumptions of SUT is suggested and possible extensions, future prospects and mechanistic underpinnings are discussed.
Project description:Interactions between the ribosomal exit tunnel and the nascent peptide can affect translation elongation rates. While previous studies have already demonstrated the feasibility of such interactions, little is known about the nature of the stalling peptide sequences and their distribution in the proteome. Here we ask which peptide sequences tend to occupy the tunnel of stalled ribosomes and how they are distributed in the proteome. Using computational analysis of ribosome profiling data from S. cerevisiae, we identified for the first time dozens of short stalling peptide sequences and studied their statistical properties. We found that short peptide sequences associated with ribosome stalling tend significantly to be either over- or underrepresented in the proteome. We then showed that the stalling interactions may occur at different positions along the length of the tunnel, prominently close to the P-site. Our findings throw light on the determinants of nascent peptide-mediated ribosome stalling during translation elongation and support the novel conjecture that mRNA translation affects the proteomic distribution of short peptide sequences.
Project description:Within the framework of 'Network Physiology', we ask a fundamental question of how modulations in cardiac dynamics emerge from networked brain-heart interactions. We propose a generalized time-delay approach to identify and quantify dynamical interactions between physiologically relevant brain rhythms and the heart rate. We perform empirical analysis of synchronized continuous EEG and ECG recordings from 34 healthy subjects during night-time sleep. For each pair of brain rhythm and heart interaction, we construct a delay-correlation landscape (DCL) that characterizes how individual brain rhythms are coupled to the heart rate, and how modulations in brain and cardiac dynamics are coordinated in time. We uncover characteristic time delays and an ensemble of specific profiles for the probability distribution of time delays that underly brain-heart interactions. These profiles are consistently observed in all subjects, indicating a universal pattern. Tracking the evolution of DCL across different sleep stages, we find that the ensemble of time-delay profiles changes from one physiologic state to another, indicating a strong association with physiologic state and function. The reported observations provide new insights on neurophysiological regulation of cardiac dynamics, with potential for broad clinical applications. The presented approach allows one to simultaneously capture key elements of dynamic interactions, including characteristic time delays and their time evolution, and can be applied to a range of coupled dynamical systems.