Designing attractive models via automated identification of chaotic and oscillatory dynamical regimes

Chaos and oscillations continue to capture the interest of both the scientific and public domains. Yet despite the importance of these qualitative features, most attempts at constructing mathematical models of such phenomena have taken an indirect, quantitative approach, for example, by fitting models to a finite number of data points. Here we develop a qualitative inference framework that allows us to both reverse-engineer and design systems exhibiting these and other dynamical behaviours by directly specifying the desired characteristics of the underlying dynamical attractor. This change in perspective from quantitative to qualitative dynamics, provides fundamental and new insights into the properties of dynamical systems

Thermodynamic State Ensemble Models of cis-Regulation

A major goal in computational biology is to develop models that accurately predict a gene's expression from its surrounding regulatory DNA. Here we present one class of such models, thermodynamic state ensemble models. We describe the biochemical derivation of the thermodynamic framework in simple terms, and lay out the mathematical components that comprise each model. These components include (1) the possible states of a promoter, where a state is defined as a particular arrangement of transcription factors bound to a DNA promoter, (2) the binding constants that describe the affinity of the protein–protein and protein–DNA interactions that occur in each state, and (3) whether each state is capable of transcribing. Using these components, we demonstrate how to compute a cis-regulatory function that encodes the probability of a promoter being active. Our intention is to provide enough detail so that readers with little background in thermodynamics can compose their own cis-regulatory functions. To facilitate this goal, we also describe a matrix form of the model that can be easily coded in any programming language. This formalism has great flexibility, which we show by illustrating how phenomena such as competition between transcription factors and cooperativity are readily incorporated into these models. Using this framework, we also demonstrate that Michaelis-like functions, another class of cis-regulatory models, are a subset of the thermodynamic framework with specific assumptions. By recasting Michaelis-like functions as thermodynamic functions, we emphasize the relationship between these models and delineate the specific circumstances representable by each approach. Application of thermodynamic state ensemble models is likely to be an important tool in unraveling the physical basis of combinatorial cis-regulation and in generating formalisms that accurately predict gene expression from DNA sequence

Non-destructive detection of cross-sectional strain and defect structure in an individual Ag five-fold twinned nanowire by 3D electron diffraction mapping

Coherent x-ray diffraction investigations on Ag five-fold twinned nanowires (FTNWs) have drawn controversial conclusions concerning whether the intrinsic 7.35° angular gap could be compensated homogeneously through phase transformation or inhomogeneously by forming disclination strain field. In those studies, the x-ray techniques only provided an ensemble average of the structural information from all the Ag nanowires. Here, using three-dimensional (3D) electron diffraction mapping approach, we non-destructively explore the cross-sectional strain and the related strain-relief defect structures of an individual Ag FTNW with diameter about 30 nm. The quantitative analysis of the fine structure of intensity distribution combining with kinematic electron diffraction simulation confirms that for such a Ag FTNW, the intrinsic 7.35° angular deficiency results in an inhomogeneous strain field within each single crystalline segment consistent with the disclination model of stress-relief. Moreover, the five crystalline segments are found to be strained differently. Modeling analysis in combination with system energy calculation further indicates that the elastic strain energy within some crystalline segments, could be partially relieved by the creation of stacking fault layers near the twin boundaries. Our study demonstrates that 3D electron diffraction mapping is a powerful tool for the cross-sectional strain analysis of complex 1D nanostructures

Somitogenesis Clock-Wave Initiation Requires Differential Decay and Multiple Binding Sites for Clock Protein

Somitogenesis is a process common to all vertebrate embryos in which repeated blocks of cells arise from the presomitic mesoderm (PSM) to lay a foundational pattern for trunk and tail development. Somites form in the wake of passing waves of periodic gene expression that originate in the tailbud and sweep posteriorly across the PSM. Previous work has suggested that the waves result from a spatiotemporally graded control protein that affects the oscillation rate of clock-gene expression. With a minimally constructed mathematical model, we study the contribution of two control mechanisms to the initial formation of this gene-expression wave. We test four biologically motivated model scenarios with either one or two clock protein transcription binding sites, and with or without differential decay rates for clock protein monomers and dimers. We examine the sensitivity of wave formation with respect to multiple model parameters and robustness to heterogeneity in cell population. We find that only a model with both multiple binding sites and differential decay rates is able to reproduce experimentally observed waveforms. Our results show that the experimentally observed characteristics of somitogenesis wave initiation constrain the underlying genetic control mechanisms

Noise Amplification in Human Tumor Suppression following Gamma Irradiation

The influence of noise on oscillatory motion is a subject of permanent interest, both for fundamental and practical reasons. Cells respond properly to external stimuli by using noisy systems. We have clarified the effect of intrinsic noise on the dynamics in the human cancer cells following gamma irradiation. It is shown that the large amplification and increasing mutual information with delay are due to coherence resonance. Furthermore, frequency domain analysis is used to study the mechanisms

Uncovering a Macrophage Transcriptional Program by Integrating Evidence from Motif Scanning and Expression Dynamics

Macrophages are versatile immune cells that can detect a variety of pathogen-associated molecular patterns through their Toll-like receptors (TLRs). In response to microbial challenge, the TLR-stimulated macrophage undergoes an activation program controlled by a dynamically inducible transcriptional regulatory network. Mapping a complex mammalian transcriptional network poses significant challenges and requires the integration of multiple experimental data types. In this work, we inferred a transcriptional network underlying TLR-stimulated murine macrophage activation. Microarray-based expression profiling and transcription factor binding site motif scanning were used to infer a network of associations between transcription factor genes and clusters of co-expressed target genes. The time-lagged correlation was used to analyze temporal expression data in order to identify potential causal influences in the network. A novel statistical test was developed to assess the significance of the time-lagged correlation. Several associations in the resulting inferred network were validated using targeted ChIP-on-chip experiments. The network incorporates known regulators and gives insight into the transcriptional control of macrophage activation. Our analysis identified a novel regulator (TGIF1) that may have a role in macrophage activation

From Dynamic Expression Patterns to Boundary Formation in the Presomitic Mesoderm

The segmentation of the vertebrate body is laid down during early embryogenesis. The formation of signaling gradients, the periodic expression of genes of the Notch-, Fgf- and Wnt-pathways and their interplay in the unsegmented presomitic mesoderm (PSM) precedes the rhythmic budding of nascent somites at its anterior end, which later develops into epithelialized structures, the somites. Although many in silico models describing partial aspects of somitogenesis already exist, simulations of a complete causal chain from gene expression in the growth zone via the interaction of multiple cells to segmentation are rare. Here, we present an enhanced gene regulatory network (GRN) for mice in a simulation program that models the growing PSM by many virtual cells and integrates WNT3A and FGF8 gradient formation, periodic gene expression and Delta/Notch signaling. Assuming Hes7 as core of the somitogenesis clock and LFNG as modulator, we postulate a negative feedback of HES7 on Dll1 leading to an oscillating Dll1 expression as seen in vivo. Furthermore, we are able to simulate the experimentally observed wave of activated NOTCH (NICD) as a result of the interactions in the GRN. We esteem our model as robust for a wide range of parameter values with the Hes7 mRNA and protein decays exerting a strong influence on the core oscillator. Moreover, our model predicts interference between Hes1 and HES7 oscillators when their intrinsic frequencies differ. In conclusion, we have built a comprehensive model of somitogenesis with HES7 as core oscillator that is able to reproduce many experimentally observed data in mice