Ilya Potapov

Effects of codon sequence on the dynamics of genetic networks

In prokaryotes, the rate at which codons are translated varies from one codon to the next. Using a stochastic model of transcription and translation at the nucleotide and codon levels, we investigate the effects of the codon sequence on the dynamics of protein numbers. For sequences generated according to the codon frequencies in Escherichia coli, we find that mean protein numbers at near equilibrium differ with the codon sequence, due to the mean codon translation efficiencies, in particular of the codons at the ribosome binding site region. We find close agreement between these predictions and measurements of protein expression levels as a function of the codon sequence. Next, we investigate the effects of short codon sequences at the start/end of the RNA sequence with linearly increasing/decreasing translation efficiencies, known as slow ramps. The ramps affect the mean, but not the fluctuations, in proteins numbers by affecting the rate of translation initiation. Finally, we show that slow ramps affect the dynamics of small genetic circuits, namely, switches and clocks. In switches, ramps affect the frequency of switching and bias the robustness of the noisy attractors. In repressilators, ramps alter the robustness of periodicity. We conclude that codon sequences affect the dynamics of gene expression and genetic circuits and, thus, are likely to be under selection regarding both mean codon frequency as well as spatial arrangement along the sequence.

Multi-stable dynamics of the non-adiabatic repressilator.

The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.

Information transfer in QT-RR dynamics: Towards a model-free QT correction method

The relation between the electrical properties of the heart and the beating rate is essential for the heart functioning. This relation is central when calculating the “corrected QT interval” — an important measure of the risk of potentially lethal arrhythmias. We use the transfer entropy method from information theory to quantitatively study the mutual dynamics of the ventricular action potential duration (the QT interval) and the length of the beat-to-beat (RR) interval. We show that for healthy individuals there is a strong asymmetry in the information transfer: the information flow from RR to QT dominates over the opposite flow (from QT to RR), i.e. QT depends on RR to a larger extent than RR on QT. Moreover, the history of the intervals has a strong effect on the information transfer: at sufficiently long QT history length the information flow asymmetry inverts and the RR influence on QT dynamics weakens. Finally, we demonstrate that the widely used QT correction methods cannot properly capture the changes in the information flows between QT and RR. We conclude that our results obtained through a model-free informational perspective can be utilised to improve and test the QT correction schemes in clinics.Abstract Background Heart dynamics is complex and results from interactions between various processes. The relation between the electrical properties of the heart and the beating rate is essential for the heart functioning. This relation is central when determining the corrected QT interval — an important measure of the risk for potentially lethal arrhythmias. Methods We use the transfer entropy method from information theory to quantitatively study the mutual dynamics of the ventricular action potential duration (the QT interval) and the length of the beat-to-beat (RR) interval. This method allows for quantifying unidirectional information flows between the coupled processes and, thus, for assessing the degree of inter-dependence in an empirical data-driven manner. Results We show that the QT and RR intervals are coupled in a dynamical fashion. In particular, for healthy individuals there is a strong asymmetry in the information transfer: the information flow from RR to QT dominates over the opposite flow (from QT to RR), i.e. QT depends on RR to a larger extent than RR on QT. Moreover, the history of the intervals has a strong effect on the information transfer. For example, at sufficiently long QT history length the information flow asymmetry inverts, that is, the QT-to-RR transfer becomes larger than RR-to-QT and the RR influence on QT dynamics weakens. Additionally, we observe a critical history length of RR (about 25 heart beats), after which the RR-to-QT transfer no longer changes. Finally, we examine how the QT correction affects the information flows between QT and RR. We demonstrate that the current QT correction methods cannot properly capture the changes in the information flows between the coupled QT and RR time series. Conclusions We conclude that our results obtained through a model-free information theory perspective can be directly utilized to significantly improve the present QT correction schemes in clinics.

Information transfer in QT-RR dynamics: Application to QT-correction

The relation between the electrical properties of the heart and the beating rate is essential for the heart functioning. This relation is central when calculating the “corrected QT interval” — an important measure of the risk of potentially lethal arrhythmias. We use the transfer entropy method from information theory to quantitatively study the mutual dynamics of the ventricular action potential duration (the QT interval) and the length of the beat-to-beat (RR) interval. We show that for healthy individuals there is a strong asymmetry in the information transfer: the information flow from RR to QT dominates over the opposite flow (from QT to RR), i.e. QT depends on RR to a larger extent than RR on QT. Moreover, the history of the intervals has a strong effect on the information transfer: at sufficiently long QT history length the information flow asymmetry inverts and the RR influence on QT dynamics weakens. Finally, we demonstrate that the widely used QT correction methods cannot properly capture the changes in the information flows between QT and RR. We conclude that our results obtained through a model-free informational perspective can be utilised to improve and test the QT correction schemes in clinics.

A generator of morphological clones for plant species

Detailed and realistic tree form generators have numerous applications in ecology and forestry. Here, we present an algorithm for generating morphological tree “clones” based on the detailed reconstruction of the laser scanning data, statistical measure of similarity, and a plant growth algorithm with simple stochastic rules. The algorithm is designed to produce tree forms, i.e. morphological clones, similar as a whole (coarse-grain scale), but varying in minute details of organization (fine-grain scale). We present a general procedure for obtaining these morphological clones. Although we opted for certain choices in our algorithm, its various parts may vary depending on the application. Namely, we have shown that specific multi-purpose procedural stochastic growth model can be algorithmically adjusted to produce the morphological clones replicated from the target experimentally measured tree. For this, we have developed a statistical measure of similarity (structural distance) between any given pair of trees, which allows for the comprehensive comparing of the tree morphologies in question by means of empirical distributions describing geometrical and topological features of a tree. Our algorithm can be used in variety of applications and contexts for exploration of the morphological potential of the growth models, arising in all sectors of plant science research. Summary Statement We present an algorithmic framework, based on the Bayesian inference, for generating morphological tree clones using a combination of stochastic growth models and experimentally derived tree structures.

Bayes Forest: a data-intensive generator of morphological tree clones

Abstract Detailed and realistic tree form generators have numerous applications in ecology and forestry. For example, the varying morphology of trees contributes differently to formation of landscapes, natural habitats of species, and eco-physiological characteristics of the biosphere. Here, we present an algorithm for generating morphological tree “clones” based on the detailed reconstruction of the laser scanning data, statistical measure of similarity, and a plant growth model with simple stochastic rules. The algorithm is designed to produce tree forms, i.e., morphological clones, similar (and not identical) in respect to tree-level structure, but varying in fine-scale structural detail. Although we opted for certain choices in our algorithm, individual parts may vary depending on the application, making it a general adaptable pipeline. Namely, we showed that a specific multipurpose procedural stochastic growth model can be algorithmically adjusted to produce the morphological clones replicated from the target experimentally measured tree. For this, we developed a statistical measure of similarity (structural distance) between any given pair of trees, which allows for the comprehensive comparing of the tree morphologies by means of empirical distributions describing the geometrical and topological features of a tree. Finally, we developed a programmable interface to manipulate data required by the algorithm. Our algorithm can be used in a variety of applications for exploration of the morphological potential of the growth models (both theoretical and experimental), arising in all sectors of plant science research.

Effects of molecular noise on the multistability in a synthetic genetic oscillator

We used 3-genes genetic oscillator as a model of oscillators coupled with quorum sensing, implemented as the production of a diffusive molecule, autoinducer. The autoinducer stimulates expression of the target gene within the oscillators core, providing a positive feedback. Previous studies suggest that there is a hysteresis in the system between oscillatory (OS) and stationary (SS) dynamical solutions. We question the robustness of these attractors in presence of molecular noise, existing due to small number of molecules in the characteristic processes of gene expression. We showed distributions of return times of OS near and within the hysteresis region. The SS is revealed by the return times duration increase as the system approaches hysteresis. Moreover, the amplitude of stochastic oscillations is larger because of sensitivity of the system to the steady state even outside of the hysteresis. The sensitivity is caused by the stochastic drift in the parameter space.

Sequence Dependent Properties of the Expression Dynamics of Genes and Gene Networks

The sequence of a gene determines the protein sequence and structure, but to some extent also the kinetics of protein production. Namely, the DNA and the codon sequence affect the kinetics of transcription and translation elongation, respectively. Here, using a stochastic model of transcription and translation at the nucleotide and codon levels, we investigate the effects of the codon sequence on the dynamics of single gene expression and of a genetic switch. We find that the ribosome binding site region sequence affects mean expression rates. In the genetic toggle switch, the sequence is shown to affect the switching frequency.