|
|
1 | (6) |
|
1.1 Simulation Approaches for Biochemical Reactions |
|
|
3 | (2) |
|
|
5 | (2) |
|
2 Stochastic Simulation of Biochemical Reaction Systems |
|
|
7 | (22) |
|
2.1 Stochastic Chemical Kinetics |
|
|
7 | (9) |
|
2.1.1 Biochemical Reactions |
|
|
7 | (4) |
|
2.1.2 Reaction Propensity |
|
|
11 | (2) |
|
2.1.3 Chemical Master Equation |
|
|
13 | (3) |
|
2.2 Stochastic Simulation |
|
|
16 | (4) |
|
2.3 Simulation Output Analysis |
|
|
20 | (7) |
|
2.3.1 Confidence Interval Estimation |
|
|
20 | (2) |
|
2.3.2 Probability Distribution Estimation |
|
|
22 | (1) |
|
2.3.3 Illustrative Examples |
|
|
22 | (5) |
|
|
27 | (1) |
|
|
27 | (2) |
|
3 Implementations of the Stochastic Simulation Algorithm |
|
|
29 | (84) |
|
|
31 | (6) |
|
3.1.1 Enhanced Direct Method |
|
|
34 | (3) |
|
3.2 Improvements for Direct Method |
|
|
37 | (21) |
|
3.2.1 Direct Method with Sorted Reactions |
|
|
38 | (5) |
|
3.2.2 Direct Method with Multi-level Search |
|
|
43 | (2) |
|
3.2.3 Direct Method with Tree-Based Search |
|
|
45 | (10) |
|
3.2.4 Direct Method with Composition-Rejection Search |
|
|
55 | (3) |
|
3.3 Partial-Propensity Direct Method |
|
|
58 | (10) |
|
3.3.1 PDM with Composition-Rejection Search |
|
|
66 | (2) |
|
3.4 Benchmark of DM and Its Derived Algorithms |
|
|
68 | (3) |
|
3.5 First Reaction Method |
|
|
71 | (4) |
|
3.5.1 First Family Method |
|
|
74 | (1) |
|
|
75 | (10) |
|
3.6.1 Modified Next Reaction Method |
|
|
81 | (4) |
|
3.7 Benchmark of FRM and Its Derived Algorithms |
|
|
85 | (2) |
|
|
87 | (9) |
|
|
95 | (1) |
|
3.9 Improvements for RSSA |
|
|
96 | (8) |
|
3.9.1 RSSA with Tree-Based Search |
|
|
96 | (3) |
|
3.9.2 RSSA with Composition-Rejection Search |
|
|
99 | (2) |
|
3.9.3 RSSA with Table-Lookup Search |
|
|
101 | (3) |
|
3.10 Benchmark of RSSA and Its Derived Algorithms |
|
|
104 | (4) |
|
|
108 | (3) |
|
|
111 | (2) |
|
4 Approximate Simulation of Biochemical Reaction Systems |
|
|
113 | (68) |
|
4.1 Probability-Weighted Dynamic Monte Carlo Method |
|
|
115 | (3) |
|
4.2 Bounded Acceptance Probability RSSA |
|
|
118 | (4) |
|
|
122 | (11) |
|
|
125 | (6) |
|
4.3.2 Avoiding the Negative Population Problem |
|
|
131 | (1) |
|
4.3.3 Switching to Exact Simulation |
|
|
131 | (1) |
|
4.3.4 The T-Leaping Algorithm |
|
|
132 | (1) |
|
4.4 Improvements for T-Leaping |
|
|
133 | (7) |
|
|
133 | (4) |
|
|
137 | (1) |
|
|
138 | (2) |
|
|
140 | (4) |
|
|
142 | (2) |
|
4.6 Benchmark of Approximate Stochastic Algorithms |
|
|
144 | (3) |
|
4.7 Chemical Langevin Method |
|
|
147 | (1) |
|
4.8 Deterministic Simulation |
|
|
148 | (30) |
|
4.8.1 From Biochemical Reactions to ODEs |
|
|
150 | (5) |
|
4.8.2 Numerical Solution of ODEs |
|
|
155 | (3) |
|
4.8.3 Improving the Accuracy of Numerical Methods |
|
|
158 | (6) |
|
|
164 | (4) |
|
|
168 | (6) |
|
4.8.6 Issues of Deterministic Simulation |
|
|
174 | (4) |
|
|
178 | (1) |
|
|
178 | (3) |
|
5 Hybrid Simulation Algorithms |
|
|
181 | (26) |
|
|
181 | (3) |
|
5.2 Reaction-Based System Partitioning |
|
|
184 | (3) |
|
5.3 Synchronization of Exact and Approximate Simulations |
|
|
187 | (4) |
|
5.4 Hybrid Rejection-Based SSA (HRSSA) |
|
|
191 | (6) |
|
5.4.1 Correctness of the Simulation of Slow Reactions |
|
|
195 | (2) |
|
5.5 Hybrid Simulation with Stiffness |
|
|
197 | (7) |
|
5.5.1 Formulation of Reactions with Stiffness |
|
|
198 | (4) |
|
5.5.2 Slow-Scale Stochastic Simulation Algorithm |
|
|
202 | (2) |
|
5.5.3 Nested Stochastic Simulation Algorithm |
|
|
204 | (1) |
|
|
204 | (1) |
|
|
205 | (2) |
|
|
207 | (10) |
|
|
207 | (1) |
|
A.2 Fast Isomerization Model |
|
|
207 | (1) |
|
|
208 | (1) |
|
|
208 | (1) |
|
|
209 | (1) |
|
A.6 Gene Expression Model |
|
|
210 | (1) |
|
|
211 | (1) |
|
|
212 | (1) |
|
|
213 | (1) |
|
A.10 B Cell Antigen Receptor Signaling Model |
|
|
214 | (1) |
|
|
214 | (3) |
|
B Random Number Generation |
|
|
217 | (8) |
|
B.1 Uniform Random Number Generator |
|
|
217 | (1) |
|
B.2 Non-uniform Random Number Generator |
|
|
218 | (7) |
|
|
218 | (2) |
|
B.2.2 Exponential Distribution |
|
|
220 | (1) |
|
B.2.3 Erlang Distribution |
|
|
220 | (1) |
|
B.2.4 Normal Distribution |
|
|
221 | (1) |
|
B.2.5 Discrete Distribution with Given Probability Vector |
|
|
222 | (1) |
|
B.2.6 Poisson Distribution |
|
|
222 | (1) |
|
B.2.7 Binomial Distribution |
|
|
223 | (1) |
|
B.2.8 Multinomial Distribution |
|
|
224 | (1) |
References |
|
225 | |