Table 1.
Space and time complexities for network-based (SSA) and network-free (NF) stochastic simulation algorithms.
Table 2.
Summary of example models used to test the performance of the HPP method.
Figure 1.
Basic workflow of the HPP simulation method.
Given a rule-based model and a user-specified set of population-mapping rules (which define the population species), partial network expansion (PNE) is performed to generate a hybrid version of the original model. The hybrid model is then passed to a population-adapted network-free simulator (e.g., NFsim 1.11), which generates the time-evolution trajectories for all observable quantities specified in the original model.
Figure 2.
Simple illustration of ambiguity in the products of reaction rules.
(A) A simple rule encodes the reversible binding of two molecule types, A and B. (B)–(D) If both molecules have multiple binding sites then they may be present within arbitrarily complex complexes. Breaking the bond between A and B thus produces a variety of product species, some of which may correspond to population species and others not. Dashed line represents a bond addition/deletion operation.
Figure 3.
Simple receptor activation model in BNGL format.
Abridged; see Text S2 of the supporting material for the complete model and Text S3 for the population-mapping rules.
Figure 4.
Partial network expansion (PNE) applied to Rule 11f of Fig. 3.
See Text S4 of the supporting material for the complete, partially-expanded model.
Figure 5.
HPP performance analysis for the TLBR model.
(A) peak memory usage (left: absolute, right: relative to NFsim); (B) CPU run time (left: absolute, right: relative to NFsim); (C) number of reaction events fired during a simulation (); (D) equilibrium distribution of number of clusters (
). The slight deviation from linearity for ‘NF’ in (A) is an artifact of how memory is allocated in NFsim.
Figure 6.
HPP performance analysis for the actin polymerization model.
(A) peak memory usage (left: absolute, right: relative to NFsim); (B) CPU run time (left: absolute, right: relative to NFsim); (C) number of reaction events fired during a simulation (); (D) equilibrium distribution of actin polymer lengths (
). The slight deviation from linearity for ‘NF’ in (A) is an artifact of how memory is allocated in NFsim.
Figure 7.
HPP performance analysis for the signaling model.
(A) peak memory usage (left: absolute, right: relative to NFsim); (B) CPU run time (left: absolute, right: relative to NFsim); (C) number of reaction events fired during a simulation (); (D) timecourses (means and
frequency envelopes;
) for
receptor (top) and receptor-recruited,
Syk (bottom). The slight deviation from linearity for ‘NF’ in (A) is an artifact of how memory is allocated in NFsim. SSA timecourses are virtually indistinguishable from those in (D) and have been omitted for clarity.
Figure 8.
HPP performance analysis for the EGFR signaling model.
(A) peak memory usage (left: absolute, right: relative to NFsim); (B) CPU run time (left: absolute, right: relative to NFsim); (C) number of reaction events fired during a simulation (); (D) timecourses (means and 5–95% frequency envelopes;
) for activated Sos (top) and nuclear phosphorylated ERK (bottom). The slight deviation from linearity for ‘NF’ in (A) is an artifact of how memory is allocated in NFsim. Due to high computational expense, SSA statistics were not collected in (C) and (D).
Figure 9.
HPP performance analyses for various lumping thresholds at cell fraction .
(A) TLBR; (B) Actin; (C) ; (D) EGFR. In all plots, threshold values for different lumping sets are shown on the x-axis. For TLBR and Actin, some thresholds yield the same set of population species as larger thresholds and are thus omitted from the figures. For TLBR, results for thresholds
are omitted due to impractically large partial networks in those cases. Results for NFsim (‘NF’) and the hand-picked lumping sets from Figs. 5–8 (‘HPP’) are shown in all plots for comparison. Error bars show standard error (three samples).
Figure 10.
Memory use vs. simulated volume for different simulation methods, including a hypothetical automated HPP (aHPP).
For finite networks, aHPP memory use plateaus once the entire reaction network has been generated. For infinite networks, the scaling at large volumes should fall somewhere between constant and linear (no worse than HPP) depending on the model (see Sec. S2 of Text S1 for an analysis).
Figure 11.
Cost of running simulations on the Amazon Elastic Compute Cloud (EC2).
The minimum cost as a function of memory requirement was calculated based on January 2012 pricing (http://aws.amazon.com/ec2/) of all Standard, High-CPU, and High-Memory EC2 instances (see Sec. S1 of Text S1 for details of the calculation). Also included are values for NFsim, HPP, and SSA simulations of the EGFR model at cell fraction .