Model Reconstruction for Moment-based Stochastic Chemical Kinetics

Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is, however, computationally expensive and sophisticated numerical methods are required. Here, we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a very efficient simulation of the time evolution of the process. In order to regain the state probabilities from the moment representation, we combine the fast moment-based simulation with a maximum entropy approach for the reconstruction of the underlying probability distribution. We investigate the usefulness of this combined approach in the setting of stochastic chemical kinetics and present numerical results for three reaction networks showing its efficiency and accuracy. Besides a simple dimerization system, we study a bistable switch system and a multi-attractor network with complex dynamics.Comment: 20 pages,5 figure

Model reconstruction for moment-based stochastic chemical kinetics

Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains, where each chemical reaction corresponds to a state transition of the process. However, the analysis of such processes is computationally expensive and sophisticated numerical methods are required. The main complication comes due to the largeness problem of the state space, so that analysis techniques based on an exploration of the state space are often not feasible and the integration of the moments of the underlying probability distribution has become a very popular alternative. In this thesis we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a more timeefficient simulation of the time evolution of the process. In order to regain the state probabilities from the moment representation, we combine the moment-based simulation (MM) with a maximum entropy approach: the maximum entropy principle is applied to derive a distribution that fits best to a given sequence of moments. We further extend this approach by incorporating the conditional moments (MCM) which allows not only to reconstruct the distribution of the species present in high amount in the system, but also to approximate the probabilities of species with low molecular counts. For the given distribution reconstruction framework, we investigate the numerical accuracy and stability using case studies from systems biology, compare two different moment approximation methods (MM and MCM), examine if it can be used for the reaction rates estimation problem and describe the possible future applications. In this thesis we propose an analysis framework in which we integrate a number of moments of the process instead of the state probabilities. This results in a more time-efficient simulation of the time evolution of the process. In order to regain the state probabilities from the moment representation, we combine the moment-based simulation (MM) with a maximum entropy approach: the maximum entropy principle is applied to derive a distribution that fits best to a given sequence of moments. We further extend this approach by incorporating the conditional moments (MCM) which allows not only to reconstruct the distribution of the species present in high amount in the system, but also to approximate the probabilities of species with low molecular counts. For the given distribution reconstruction framework, we investigate the numerical accuracy and stability using case studies from systems biology, compare two different moment approximation methods (MM and MCM), examine if it can be used for the reaction rates estimation problem and describe the possible future applications.Basierend auf der Theorie der stochastischen chemischen Kinetiken können die inhärente Zufälligkeit und Stochastizität von biochemischen Reaktionsnetzwerken durch diskrete zeitkontinuierliche Markow-Ketten genau beschrieben werden, wobei jede chemische Reaktion einem Zustandsübergang des Prozesses entspricht. Die Analyse solcher Prozesse ist jedoch rechenaufwendig und komplexe numerische Verfahren sind erforderlich. Analysetechniken, die auf dem Abtasten des Zustandsraums basieren, sind durch dessen Größe oft nicht anwendbar. Als populäre Alternative wird heute häufig die Integration der Momente der zugrundeliegenden Wahrscheinlichkeitsverteilung genutzt. In dieser Arbeit schlagen wir einen Analyserahmen vor, in dem wir, anstatt der Zustandswahrscheinlichkeiten, zugrundeliegende Momente des Prozesses integrieren. Dies führt zu einer zeiteffizienteren Simulation der zeitlichen Entwicklung des Prozesses. Um die Zustandswahrscheinlichkeiten aus der Momentreprsentation wiederzugewinnen, kombinieren wir die momentbasierte Simulation (MM) mit Entropiemaximierung: Die Maximum- Entropie-Methode wird angewendet, um eine Verteilung abzuleiten, die am besten zu einer bestimmten Sequenz von Momenten passt. Wir erweitern diesen Ansatz durch das Einbeziehen bedingter Momente (MCM), die es nicht nur erlauben, die Verteilung der in großer Menge im System enthaltenen Spezies zu rekonstruieren, sondern es ebenso ermöglicht, sich den Wahrscheinlichkeiten von Spezies mit niedrigen Molekulargewichten anzunähern. Für das gegebene System zur Verteilungsrekonstruktion untersuchen wir die numerische Genauigkeit und Stabilität anhand von Fallstudien aus der Systembiologie, vergleichen zwei unterschiedliche Verfahren der Momentapproximation (MM und MCM), untersuchen, ob es für das Problem der Abschätzung von Reaktionsraten verwendet werden kann und beschreiben die mögliche zukünftige Anwendungen

Deep learning-based fully automatic segmentation of wrist cartilage in MR images

The study objective was to investigate the performance of a dedicated convolutional neural network (CNN) optimized for wrist cartilage segmentation from 2D MR images. CNN utilized a planar architecture and patch-based (PB) training approach that ensured optimal performance in the presence of a limited amount of training data. The CNN was trained and validated in twenty multi-slice MRI datasets acquired with two different coils in eleven subjects (healthy volunteers and patients). The validation included a comparison with the alternative state-of-the-art CNN methods for the segmentation of joints from MR images and the ground-truth manual segmentation. When trained on the limited training data, the CNN outperformed significantly image-based and patch-based U-Net networks. Our PB-CNN also demonstrated a good agreement with manual segmentation (Sorensen-Dice similarity coefficient (DSC) = 0.81) in the representative (central coronal) slices with large amount of cartilage tissue. Reduced performance of the network for slices with a very limited amount of cartilage tissue suggests the need for fully 3D convolutional networks to provide uniform performance across the joint. The study also assessed inter- and intra-observer variability of the manual wrist cartilage segmentation (DSC=0.78-0.88 and 0.9, respectively). The proposed deep-learning-based segmentation of the wrist cartilage from MRI could facilitate research of novel imaging markers of wrist osteoarthritis to characterize its progression and response to therapy

State of Renal Blood Flow in Premature Children with Hemodynamically Significant Patent Ductus Arteriosus

Introduction: Hemodynamically significant patent ductus arteriosus (HSPDA) lowers the renal circulation because of the "ductal stealing phenomenon," which can change the renal blood flow. The aim: To study the state of blood flow in the main renal artery and interlobar renal artery in premature infants with HSPDA. Materials and methods: 74 preterm newborns (gestational age 29-36 weeks) were divided into three groups: І - 40 children with HSPDA, ІІ - 17 children with patent ductus arteriosus (PDA) without hemodynamic disorders, ІІІ - 17 children with closed ductus arteriosus. Color ultrasound Doppler scan of the vascular bed of the kidneys was performed using a microconvex sensor with a frequency of 5-8 MHz ("TOSHIBA" Nemso XG model SSA-580A (Japan) from the main renal artery to the interlobar renal arteries of the right kidney. The following parameters of renal blood flow were studied: peak systolic velocity (PSV), end-diastolic velocity (EDV), resistance index (RI). Results: Peak systolic velocity (PSV) in the main renal artery and interlobar renal arteries did not differ significantly between groups. On the first, third, and tenth days of life, there was a significant decrease in the EDV of blood flow and increased RI in the main renal artery. The EDV of blood flow and RI in the interlobar renal artery on the first day of life did not differ depending on PDA's presence and its hemodynamic significance. On the third and tenth days of life and in the interlobar renal artery, a significant decrease in EDV of blood flow and increased RI were noted. These renal blood flow characteristics were closely related to the size of the PDA on the first day of life. Conclusion: A feature of renal hemodynamics in HSPDA in premature infants is a decrease in the EDV of blood flow in the main renal artery and interlobar renal artery, as well as an increase in the RI of these vessels, directly correlating with the size of the PDA in the first day of life. During the first ten days of life, dynamic control revealed a slowed process of restoration of renal blood flow in babies with HSPDA, despite the PDA's closure

Experimental Biological Protocols with Formal Semantics

Both experimental and computational biology is becoming increasingly automated. Laboratory experiments are now performed automatically on high-throughput machinery, while computational models are synthesized or inferred automatically from data. However, integration between automated tasks in the process of biological discovery is still lacking, largely due to incompatible or missing formal representations. While theories are expressed formally as computational models, existing languages for encoding and automating experimental protocols often lack formal semantics. This makes it challenging to extract novel understanding by identifying when theory and experimental evidence disagree due to errors in the models or the protocols used to validate them. To address this, we formalize the syntax of a core protocol language, which provides a unified description for the models of biochemical systems being experimented on, together with the discrete events representing the liquid-handling steps of biological protocols. We present both a deterministic and a stochastic semantics to this language, both defined in terms of hybrid processes. In particular, the stochastic semantics captures uncertainties in equipment tolerances, making it a suitable tool for both experimental and computational biologists. We illustrate how the proposed protocol language can be used for automated verification and synthesis of laboratory experiments on case studies from the fields of chemistry and molecular programming