Rule-based modeling with BioNetGen has been widely used to study the dynamics of complex biochemical systems. Rule-based models can be analyzed by carrying out deterministic or stochastic simulations. However, they are often difficult to calibrate due to many unknown parameters and limited experimental training data. Here we present a generic parameter estimation framework for calibrating rule-based models. The experimental data as well as qualitative properties of the system are encoded as a specification formula in a bounded linear temporal logic. Given a candidate set of parameter values we apply the statistical model checking procedure to evaluate the quality of this candidate set. Based on the outcome, a new set of parameters is chosen using a standard global search strategy. We have tested our method on a p53-induced apoptosis model. The results show that our method scales well and efficiently obtains good parameter estimates.

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ δ-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for prostate cancer therapy.

We present a novel code generation scheme for GPUs. Its key feature is the platform-aware generation of a heterogeneous pool of threads. This exposes more data-sharing opportunities among the concurrent threads and reduces the memory requirements that would otherwise exceed the capacity of the on-chip memory. Instead of the conventional strategy of focusing on exposing as much parallelism as possible, our scheme leverages on the phased nature of memory access patterns found in many applications that exhibit massive parallelism. We demonstrate the effectiveness of our code generation strategy on a computational systems biology application. This application consists of computing a Dynamic Bayesian Network (DBN) approximation of the dynamics of signalling pathways described as a system of Ordinary Differential Equations (ODEs). The approximation algorithm involves (i) sampling many (of the order of a few million) times from the set of initial states, (ii) generating trajectories through numerical integration, and (iii) storing the statistical properties of this set of trajectories in Conditional Probability Tables (CPTs) of a DBN via a prespecified discretization of the time and value domains. The trajectories can be computed in parallel. However, the intermediate data needed for computing them, as well as the entries for the CPTs, are too large to be stored locally. Our experiments show that the proposed code generation scheme scales well, achieving significant performance improvements on three realistic signalling pathways models. These results suggest how our scheme could be extended to deal with other applications involving systems of ODEs.

MOTIVATION: Biopathways are often modeled as systems of ordinary differential equations (ODEs). Such systems will usually have many unknown parameters and hence will be difficult to calibrate. Since the data available for calibration will have limited precision, an approximate representation of the ODEs dynamics should suffice. One must, however, be able to efficiently construct such approximations for large models and perform model calibration and subsequent analysis. RESULTS: We present a graphical processing unit (GPU) based scheme by which a system of ODEs is approximated as a dynamic Bayesian network (DBN). We then construct a model checking procedure for DBNs based on a simple probabilistic linear time temporal logic. The GPU implementation considerably extends the reach of our previous PC-cluster-based implementation (Liu et al., 2011b). Further, the key components of our algorithm can serve as the GPU kernel for other Monte Carlo simulations-based analysis of biopathway dynamics. Similarly, our model checking framework is a generic one and can be applied in other systems biology settings. We have tested our methods on three ODE models of bio-pathways: the epidermal growth factor-nerve growth factor pathway, the segmentation clock network and the MLC-phosphorylation pathway models. The GPU implementation shows significant gains in performance and scalability whereas the model checking framework turns out to be convenient and efficient for specifying and verifying interesting pathways properties. AVAILABILITY: The source code is freely available at http://www.comp.nus.edu.sg/~rpsysbio/pada-gpu/

Dynamic Bayesian Networks (DBNs) can serve as succinct probabilistic dynamic models of biochemical networks. To analyze these models, one must compute the probability distribution over system states at a given time point. Doing this exactly is infeasible for large models; hence one must use approximate algorithms. The Factored Frontier algorithm (FF) is one such algorithm. However FF as well as the earlier Boyen-Koller (BK) algorithm can incur large errors. To address this, we present a new approximate algorithm called the Hybrid Factored Frontier (HFF) algorithm. At each time slice, in addition to maintaining probability distributions over local states-as FF does-HFF explicitly maintains the probabilities of a number of global states called spikes. When the number of spikes is 0, we get FF and with all global states as spikes, we get the exact inference algorithm. We show that by increasing the number of spikes one can reduce errors while the additional computational effort required is only quadratic in the number of spikes. We validated the performance of HFF on large DBN models of biopathways. Each pathway has more than 30 species and the corresponding DBN has more than 3,000 nodes. Comparisons with FF and BK show that HFF is a useful and powerful approximate inferencing algorithm for DBNs.

The complement system is key to innate immunity and its activation is necessary for the clearance of bacteria and apoptotic cells. However, insufficient or excessive complement activation will lead to immune-related diseases. It is so far unknown how the complement activity is up- or down- regulated and what the associated pathophysiological mechanisms are. To quantitatively understand the modulatory mechanisms of the complement system, we built a computational model involving the enhancement and suppression mechanisms that regulate complement activity. Our model consists of a large system of Ordinary Differential Equations (ODEs) accompanied by a dynamic Bayesian network as a probabilistic approximation of the ODE dynamics. Applying Bayesian inference techniques, this approximation was used to perform parameter estimation and sensitivity analysis. Our combined computational and experimental study showed that the antimicrobial response is sensitive to changes in pH and calcium levels, which determines the strength of the crosstalk between CRP and L-ficolin. Our study also revealed differential regulatory effects of C4BP. While C4BP delays but does not decrease the classical complement activation, it attenuates but does not significantly delay the lectin pathway activation. We also found that the major inhibitory role of C4BP is to facilitate the decay of C3 convertase. In summary, the present work elucidates the regulatory mechanisms of the complement system and demonstrates how the bio-pathway machinery maintains the balance between activation and inhibition. The insights we have gained could contribute to the development of therapies targeting the complement system.