Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation

Discrete stochastic simulations are a powerful tool for understanding the dynamics of chemical kinetics when there are small-to-moderate numbers of certain molecular species. In this paper we introduce delays into the stochastic simulation algorithm, thus mimicking delays associated with transcription and translation. We then show that this process may well explain more faithfully than continuous deterministic models the observed sustained oscillations in expression levels of hes1 mRNA and Hes1 protein

Receptor dimer stabilization By hierarchical plasma membrane microcompartments regulates cytokine signaling

The interaction dynamics of signaling complexes is emerging as a key determinant that regulates the specificity of cellular responses. We present a combined experimental and computational study that quantifies the consequences of plasma membrane microcompartmentalization for the dynamics of type I interferon receptor complexes. By using long-term dual-color quantum dot (QD) tracking, we found that the lifetime of individual ligand-induced receptor heterodimers depends on the integrity of the membrane skeleton (MSK), which also proved important for efficient downstream signaling. By pair correlation tracking and localization microscopy as well as by fast QD tracking, we identified a secondary confinement within ~300-nm-sized zones. A quantitative spatial stochastic diffusion-reaction model, entirely parameterized on the basis of experimental data, predicts that transient receptor confinement by the MSK meshwork allows for rapid reassociation of dissociated receptor dimers. Moreover, the experimentally observed apparent stabilization of receptor dimers in the plasma membrane was reproduced by simulations of a refined, hierarchical compartment model. Our simulations further revealed that the two-dimensional association rate constant is a key parameter for controlling the extent of MSK-mediated stabilization of protein complexes, thus ensuring the specificity of this effect. Together, experimental evidence and simulations support the hypothesis that passive receptor confinement by MSK-based microcompartmentalization promotes maintenance of signaling complexes in the plasma membrane

Probability distributed time delays: integrating spatial effects into temporal models

Background: In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive.Results: We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation.Conclusions: Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere

Exact Product Formation Rates for Stochastic Enzyme Kinetics

The rate of product formation is an important measure of the speed of enzyme reactions. Classical studies of enzyme reactions have been conducted in dilute solutions and under conditions that justified the substrate abundance assumption. However, such assumption is well-known to break down in the context of cellular biochemistry. Instead, the concentration of available substrate can become rate limiting. Here we use the chemical master equation to obtain expressions for the instantaneous and time averaged rate of product formation without invoking the conventional substrate abundance assumption. The expressions are derived for a broad range of enzyme reaction mechanisms, including those that involve one or many enzyme molecules, require multiple substrates, and exhibit cooperativity and substrate inhibition. Novel results include: (i) the relationship between the average rate of product formation (calculated over the time it takes for the reaction to finish) and the substrate concentration, for a Michaelis–Menten (MM) reaction with one enzyme molecule, is approximately given by a logarithmically corrected MM form; (ii) intrinsic noise decreases the sharpness of cooperative switches but enhances the filtering response of substrate inhibition; (iii) the relationship between the initial average rate of product formation and the initial substrate concentration for a MM reaction with no reversible reaction and with any number of enzyme and substrate molecules is a sum of Michaelis–Menten equations

Evolution of Quantum Algorithms using Genetic Programming

Automatic quantum circuit design is motivated by the difficulties in manual design, because quantum algorithms are highly non-intuitive and practical quantum computer hardware is not yet available. Thus, quantum computers have to be simulated on classical hardware which naturally entails an exponential growth of computational costs and allows only to simulate small quantum systems, i. e., with only few qubits. Huge search spaces render evolutionary approaches nearly unable to achieve breakthrough solutions in the development of new quantum algorithms. Consequently, at present we must be content to evolve essentially already existing (black-box) quantum algorithms. This thesis presents empirical results on the evolution of quantum circuits using genetic programming. For that purpose, a linear and a linear-tree GP system (allowing intermediate measurements) with integrated quantum computer simulator were implemented. Their practicality in evolving quantum circuits is shown in different experiments for 1-SAT (solutions act like Hogg's algorithm) and the Deutsch-Jozsa problem. These experiments confirm that the evolution of quantum circuits is practically feasible only for sufficiently small problem instances. In this context, scalability and the detection of scalability becomes very important. It is shown that scalable quantum circuits are evolvable to a certain degree: a general quantum circuit can be inferred manually from the evolved solutions for small instances of the given problem. Besides, further experiments indicate that 're-evolution' is effective for the evolution of scalable quantum circuits. With this method the start population of a problem instance is inoculated with evolved solutions for a smaller problem instance. Furthermore, investigations of fitness landscapes and selection strategies are made, with the aim of improving the efficiency of evolutionary search. A notable result is that using the crossover operator damages rather than benefits evolution of quantum circuits.Quantenalgorithmen sind hochgradig unintuitiv und einsetzbare Quantenrechner sind (noch) nicht verfügbar. Dies erschwert den manuellen Entwurf von Quantenalgorithmen und motiviert die Suche nach Techniken zum computerunterstützten bzw. automatischen Entwurf. Simulationen von Quantenschaltkreisen (QS) auf konventionellen Rechnern sind aber leider sehr rechenintensiv. Aufgrund der (in der Anzahl der Qubits) exponentiell anwachsenden Kosten ist nur eine Simulation kleiner Quantensysteme (mit wenig Qubits) akzeptabel. Zudem sind die Suchräume quasi beliebig groß,worin wohl auch begründet liegt, warum der evolutionäre Ansatz bislang nicht zu einem Durchbruch in der Entwicklung neuer Quantenalgorithmen führte. Zum gegenwärtigen Zeitpunkt muss man sich daher mit der Evolution bekannter (black-box) Quantenalgorithmen begnügen. Die vorliegende Arbeit präsentiert empirische Ergebnisse zur Evolution von QS mit Hilfe des Genetischen Programmierens. Für die Experimente wurde ein effizienter Quantensimulator entwickelt, der in einem umgebenden GP-System zum Einsatz kommt. Dabei wurden zunächst linear-tree (erlaubt Zwischenmessungen), später auch rein lineare Genom-Strukturen für die Programmrepräsentation verwendet. Die Evolvierbarkeit von QS wird an Hand von Experimenten für kleine Probleminstanzen des 1-SAT Problems und des Deutsch-Jozsa Problems gezeigt. Die Experimente bestätigen, dass die Evolution von QS nur für genügend kleine Probleminstanzen praktisch machbar ist. Vor diesem Hintergrund ist gerade die Skalierbarkeit von QS besonders wichtig. Es wird gezeigt, dass skalierbare QS bis zu einem gewissen Grad evolviert werden können. Dabei wird ein allgemeiner Schaltkreis von den evolvierten Lösungen für sehr kleine Probleminstanzen abgeleitet.Die Methode der 'Vorevolution', so belegen weitere Experimente, ist für die Evolution skalierbarer QS wirksam einsetzbar. Bei dieser Methode werden der Startpopulation einer Probleminstanz bereits evolvierte Lösungen einer kleineren Probleminstanz 'eingeimpft'. Ferner werden Fitnesslandschaften untersucht und ein Vergleich von Selektionsstrategien angestellt, mit dem Ziel, durch diese Erkenntnisse zu einer Effizienzsteigerung der evolutionären Suche zu gelangen. Dabei ist ein beachtenswertes Resultat, dass die Verwendung eines Crossover Operators der Evolution von QS eher schadet, als ihr nützt

Comparison of Selection Strategies for Evolutionary Quantum Circuit Design

Abstract. Evolution of quantum circuits faces two major challenges: complex and huge search spaces and the high costs of simulating quantum circuits on conventional computers. In this paper we analyze different selection strategies, which are applied to the Deutsch-Jozsa problem and the 1-SAT problem using our GP system. Furthermore, we show the effects of adding randomness to the selection mechanism of a (1,10) selection strategy. It can be demonstrated that this boosts the evolution of quantum algorithms on particular problems

Stochastic adaptation and fold-change detection: from single-cell to population behavior

<p>Abstract</p> <p>Background</p> <p>In cell signaling terminology, adaptation refers to a system's capability of returning to its equilibrium upon a transient response. To achieve this, a network has to be both sensitive and precise. Namely, the system must display a significant output response upon stimulation, and later on return to pre-stimulation levels. If the system settles at the exact same equilibrium, adaptation is said to be 'perfect'. Examples of adaptation mechanisms include temperature regulation, calcium regulation and bacterial chemotaxis.</p> <p>Results</p> <p>We present models of the simplest adaptation architecture, a two-state protein system, in a stochastic setting. Furthermore, we consider differences between individual and collective adaptive behavior, and show how our system displays fold-change detection properties. Our analysis and simulations highlight why adaptation needs to be understood in terms of probability, and not in strict numbers of molecules. Most importantly, selection of appropriate parameters in this simple linear setting may yield populations of cells displaying adaptation, while single cells do not.</p> <p>Conclusions</p> <p>Single cell behavior cannot be inferred from population measurements and, sometimes, collective behavior cannot be determined from the individuals. By consequence, adaptation can many times be considered a purely emergent property of the collective system. This is a clear example where biological ergodicity cannot be assumed, just as is also the case when cell replication rates are not homogeneous, or depend on the cell state. Our analysis shows, for the first time, how ergodicity cannot be taken for granted in simple linear examples either. The latter holds even when cells are considered isolated and devoid of replication capabilities (cell-cycle arrested). We also show how a simple linear adaptation scheme displays fold-change detection properties, and how rupture of ergodicity prevails in scenarios where transitions between protein states are mediated by other molecular species in the system, such as phosphatases and kinases.</p