A model checking approach to the parameter estimation of biochemical pathways

Model checking has historically been an important tool to verify models of a wide variety of systems. Typically a model has to exhibit certain properties to be classed ‘acceptable’. In this work we use model checking in a new setting; parameter estimation. We characterise the desired behaviour of a model in a temporal logic property and alter the model to make it conform to the property (determined through model checking). We have implemented a computational system called MC2(GA) which pairs a model checker with a genetic algorithm. To drive parameter estimation, the fitness of set of parameters in a model is the inverse of the distance between its actual behaviour and the desired behaviour. The model checker used is the simulation-based Monte Carlo Model Checker for Probabilistic Linear-time Temporal Logic with numerical constraints, MC2(PLTLc). Numerical constraints as well as the overall probability of the behaviour expressed in temporal logic are used to minimise the behavioural distance. We define the theory underlying our parameter estimation approach in both the stochastic and continuous worlds. We apply our approach to biochemical systems and present an illustrative example where we estimate the kinetic rate constants in a continuous model of a signalling pathway

Developmental appearance of factors that bind specifically to cis-regulatory sequences of a gene expressed in the sea urchin embryo

Previous gene-transfer experiments have identified a 2500-nucleotide 5' domain of the CyIIIa cytoskeletal actin gene, which contains cis-regulatory sequences that are necessary and sufficient for spatial and temporal control of CyIIIa gene expression during embryogenesis. This gene is activated in late cleavage, exclusively in aboral ectoderm cell lineages. In this study, we focus on interactions demonstrated in vitro between sequences of the regulatory domain and proteins present in crude extracts derived from sea urchin embryo nuclei and from unfertilized eggs. Quantitative gel-shift measurements are utilized to estimate minimum numbers of factor molecules per embryo at 24 hr postfertilization, when the CyIIIa gene is active, at 7 hr, when it is still silent, and in the unfertilized egg. We also estimate the binding affinity preferences (K_r) of the various factors for their respective sites, relative to their affinity for synthetic DNA competitors. At least 14 different specific interactions occur within the regulatory regions, some of which produce multiple DNA-protein complexes. Values of K_r range from approximately 2 x 10^4 to approximately 2 x 10^6 for these factors under the conditions applied. With one exception, the minimum factor prevalences that we measured in the 400-cell 24-hr embryo nuclear extracts fell within the range of 2 x 10^5 to 2 x 10^6 molecules per embryo, i.e., a few hundred to a few thousand molecules per nucleus. Three developmental patterns were observed with respect to factor prevalence: Factors reacting at one site were found in unfertilized egg cytoplasm at about the same level per egg or embryo as in 24-hr embryo nuclei; factors reacting with five other regions of the regulatory domain are not detectable in egg cytoplasm but in 7-hr mid-cleavage-stage embryo, nuclei are already at or close to their concentrations in the 24-hr embryo nuclei; and factors reacting with five additional regions are not detectable in egg cytoplasm and are low in 7-hr embryo nuclei, i.e., ⩽10% per embryo of the level they attain in 24-hr embryo nuclei. The rise in concentration of factors of the latter class could provide the proximal cause for the temporal activation of the CyIIIa gene at the early blastula stage

Disentangling the initiation from the response in joint attention: an eye-tracking study in toddlers with autism spectrum disorders

Joint attention (JA), whose deficit is an early risk marker for autism spectrum disorder (ASD), has two dimensions: (1) responding to JA and (2) initiating JA. Eye-tracking technology has largely been used to investigate responding JA, but rarely to study initiating JA especially in young children with ASD. The aim of this study was to describe the differences in the visual patterns of toddlers with ASD and those with typical development (TD) during both responding JA and initiating JA tasks. Eye-tracking technology was used to monitor the gaze of 17 children with ASD and 15 age-matched children with TD during the presentation of short video sequences involving one responding JA and two initiating JA tasks (initiating JA-1 and initiating JA-2). Gaze accuracy, transitions and fixations were analyzed. No differences were found in the responding JA task between children with ASD and those with TD, whereas, in the initiating JA tasks, different patterns of fixation and transitions were shown between the groups. These results suggest that children with ASD and those with TD show different visual patterns when they are expected to initiate joint attention but not when they respond to joint attention. We hypothesized that differences in transitions and fixations are linked to ASD impairments in visual disengagement from face, in global scanning of the scene and in the ability to anticipate object's action

Dynamical modeling of syncytial mitotic cycles in Drosophila embryos

Immediately following fertilization, the fruit fly embryo undergoes 13 rapid, synchronous, syncytial nuclear division cycles driven by maternal genes and proteins. During these mitotic cycles, there are barely detectable oscillations in the total level of B-type cyclins. In this paper, we propose a dynamical model for the molecular events underlying these early nuclear division cycles in Drosophila. The model distinguishes nuclear and cytoplasmic compartments of the embryo and permits exploration of a variety of rules for protein transport between the compartments. Numerical simulations reproduce the main features of wild-type mitotic cycles: patterns of protein accumulation and degradation, lengthening of later cycles, and arrest in interphase 14. The model is consistent with mutations that introduce subtle changes in the number of mitotic cycles before interphase arrest. Bifurcation analysis of the differential equations reveals the dependence of mitotic oscillations on cycle number, and how this dependence is altered by mutations. The model can be used to predict the phenotypes of novel mutations and effective ranges of the unmeasured rate constants and transport coefficients in the proposed mechanism

BioDiVinE: A Framework for Parallel Analysis of Biological Models

In this paper a novel tool BioDiVinEfor parallel analysis of biological models is presented. The tool allows analysis of biological models specified in terms of a set of chemical reactions. Chemical reactions are transformed into a system of multi-affine differential equations. BioDiVinE employs techniques for finite discrete abstraction of the continuous state space. At that level, parallel analysis algorithms based on model checking are provided. In the paper, the key tool features are described and their application is demonstrated by means of a case study

Model Revision from Temporal Logic Properties in Computational Systems Biology

International audienceSystems biologists build models of bio-molecular processes from knowledge acquired both at the gene and protein levels, and at the phenotype level through experiments done in wildlife and mutated organisms. In this chapter, we present qualitative and quantitative logic learning tools, and illustrate how they can be useful to the modeler. We focus on biochemical reaction models written in the Systems Biology Markup Language SBML, and interpreted in the Biochemical Abstract Machine BIOCHAM. We first present a model revision algorithm for inferring reaction rules from biological properties expressed in temporal logic. Then we discuss the representations of kinetic models with ordinary differential equations (ODEs) and with stochastic logic programs (SLPs), and describe a parameter search algorithm for finding parameter values satisfying quantitative temporal properties. These methods are illustrated by a simple model of the cell cycle control, and by an application to the modelling of the conditions of synchronization in period of the cell cycle by the circadian cycle

Modelling the Dynamics of an Aedes albopictus Population

We present a methodology for modelling population dynamics with formal means of computer science. This allows unambiguous description of systems and application of analysis tools such as simulators and model checkers. In particular, the dynamics of a population of Aedes albopictus (a species of mosquito) and its modelling with the Stochastic Calculus of Looping Sequences (Stochastic CLS) are considered. The use of Stochastic CLS to model population dynamics requires an extension which allows environmental events (such as changes in the temperature and rainfalls) to be taken into account. A simulator for the constructed model is developed via translation into the specification language Maude, and used to compare the dynamics obtained from the model with real data.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314

Developmental appearance of factors that bind specifically to cis-regulatory sequences of a gene expressed in the sea urchin embryo

Previous gene-transfer experiments have identified a 2500-nucleotide 5' domain of the CyIIIa cytoskeletal actin gene, which contains cis-regulatory sequences that are necessary and sufficient for spatial and temporal control of CyIIIa gene expression during embryogenesis. This gene is activated in late cleavage, exclusively in aboral ectoderm cell lineages. In this study, we focus on interactions demonstrated in vitro between sequences of the regulatory domain and proteins present in crude extracts derived from sea urchin embryo nuclei and from unfertilized eggs. Quantitative gel-shift measurements are utilized to estimate minimum numbers of factor molecules per embryo at 24 hr postfertilization, when the CyIIIa gene is active, at 7 hr, when it is still silent, and in the unfertilized egg. We also estimate the binding affinity preferences (K_r) of the various factors for their respective sites, relative to their affinity for synthetic DNA competitors. At least 14 different specific interactions occur within the regulatory regions, some of which produce multiple DNA-protein complexes. Values of K_r range from approximately 2 x 10^4 to approximately 2 x 10^6 for these factors under the conditions applied. With one exception, the minimum factor prevalences that we measured in the 400-cell 24-hr embryo nuclear extracts fell within the range of 2 x 10^5 to 2 x 10^6 molecules per embryo, i.e., a few hundred to a few thousand molecules per nucleus. Three developmental patterns were observed with respect to factor prevalence: Factors reacting at one site were found in unfertilized egg cytoplasm at about the same level per egg or embryo as in 24-hr embryo nuclei; factors reacting with five other regions of the regulatory domain are not detectable in egg cytoplasm but in 7-hr mid-cleavage-stage embryo, nuclei are already at or close to their concentrations in the 24-hr embryo nuclei; and factors reacting with five additional regions are not detectable in egg cytoplasm and are low in 7-hr embryo nuclei, i.e., ⩽10% per embryo of the level they attain in 24-hr embryo nuclei. The rise in concentration of factors of the latter class could provide the proximal cause for the temporal activation of the CyIIIa gene at the early blastula stage