1 Introduction to biological modelling |
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1 | (18) |
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1 | (1) |
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2 | (1) |
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1.3 Why is stochastic modelling necessary? |
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2 | (4) |
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6 | (2) |
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1.5 Modelling genetic and biochemical networks |
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8 | (8) |
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1.6 Modelling higher-level systems |
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16 | (1) |
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17 | (1) |
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17 | (2) |
2 Representation of biochemical networks |
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19 | (26) |
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2.1 Coupled chemical reactions |
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19 | (1) |
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2.2 Graphical representations |
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19 | (2) |
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21 | (10) |
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2.4 Systems Biology Markup Language (SBML) |
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31 | (5) |
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36 | (6) |
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42 | (1) |
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43 | (2) |
3 Probability models |
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45 | (46) |
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45 | (11) |
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3.2 Discrete probability models |
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56 | (8) |
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3.3 The discrete uniform distribution |
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64 | (1) |
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3.4 The binomial distribution |
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64 | (1) |
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3.5 The geometric distribution |
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65 | (2) |
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3.6 The Poisson distribution |
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67 | (3) |
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3.7 Continuous probability models |
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70 | (5) |
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3.8 The uniform distribution |
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75 | (2) |
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3.9 The exponential distribution |
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77 | (5) |
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3.10 The normal/Gaussian distribution |
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82 | (4) |
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3.11 The gamma distribution |
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86 | (2) |
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88 | (1) |
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89 | (2) |
4 Stochastic simulation |
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91 | (18) |
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91 | (1) |
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4.2 Monte-Carlo integration |
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91 | (1) |
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4.3 Uniform random number generation |
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92 | (1) |
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4.4 Transformation methods |
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93 | (4) |
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97 | (1) |
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98 | (3) |
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101 | (1) |
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4.8 Using the statistical programming language, R |
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101 | (5) |
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4.9 Analysis of simulation output |
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106 | (1) |
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107 | (1) |
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108 | (1) |
5 Markov processes |
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109 | (30) |
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109 | (1) |
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5.2 Finite discrete time Markov chains |
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109 | (6) |
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5.3 Markov chains with continuous state space |
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115 | (6) |
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5.4 Markov chains in continuous time |
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121 | (12) |
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133 | (2) |
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135 | (2) |
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137 | (2) |
6 Chemical and biochemical kinetics |
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139 | (80) |
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6.1 Classical continuous deterministic chemical kinetics |
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139 | (6) |
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6.2 Molecular approach to kinetics |
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145 | (2) |
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6.3 Mass-action stochastic kinetics |
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147 | (2) |
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6.4 The Gillespie algorithm |
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149 | (1) |
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6.5 Stochastic Petri nets (SPNs) |
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150 | (3) |
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6.6 Rate constant conversion |
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153 | (4) |
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157 | (3) |
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6.8 Software for simulating stochastic kinetic networks |
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160 | (1) |
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161 | (1) |
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161 | (2) |
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163 | (18) |
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163 | (1) |
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7.2 Dimerisation kinetics |
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163 | (5) |
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7.3 Michaelis-Menten enzyme kinetics |
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168 | (4) |
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7.4 An auto-regulatory genetic network |
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172 | (4) |
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176 | (2) |
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178 | (1) |
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179 | (2) |
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8 Beyond the Gillespie algorithm |
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181 | (16) |
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181 | (1) |
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8.2 Exact simulation methods |
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181 | (5) |
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8.3 Approximate simulation strategies |
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186 | (4) |
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8.4 Hybrid simulation strategies |
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190 | (6) |
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196 | (1) |
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196 | (1) |
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9 Bayesian inference and MCMC |
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197 | (22) |
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9.1 Likelihood and Bayesian inference |
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197 | (5) |
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202 | (10) |
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9.3 The Metropolis-Hastings algorithm |
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212 | (4) |
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216 | (1) |
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216 | (1) |
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217 | (2) |
10 Inference for stochastic kinetic models |
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219 | (18) |
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219 | (1) |
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10.2 Inference given complete data |
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220 | (3) |
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10.3 Discrete-time observations of the system state |
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223 | (7) |
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10.4 Diffusion approximations for inference |
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230 | (4) |
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234 | (1) |
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234 | (1) |
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235 | (2) |
11 Conclusions |
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237 | (2) |
A SBML Models |
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239 | (8) |
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A.1 Auto-regulatory network |
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239 | (3) |
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A.2 Lotka-Volterra reaction system |
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242 | (1) |
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A.3 Dimerisation-kinetics model |
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243 | (4) |
References |
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247 | (4) |
Index |
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251 | |