Abstract
The purpose of this book is to introduce researchers and practitioners to recent advances and applications of Monte Carlo Simulation (MCS). Random sampling is the key of the MCS technique. The 11 chapters of this book collectively illustrates how such a sampling technique is exploited to solve difficult problems or analyze complex systems in various engineering and science domains. Issues related to the use of MCS including goodness-of-fit, uncertainty evaluation, variance reduction, optimization, and statistical estimation are discussed and examples of solutions are given. Novel applications of MCS are demonstrated in financial systems modeling, estimation of transition behavior of organic molecules, chemical reaction, particle diffusion, kinetic simulation of biophysics and biological data, and healthcare practices. To enlarge the accessibility of this book, both field-specific background materials and field-specific usages of MCS are introduced in most chapters. The aim of this book is to unify knowledge of MCS from different fields to facilitate research and new applications of MCS.
Figures
![Figure 1. Histogram plots of the number of BCR molecules with at least one ITAM phosphorylated by Lyn (figure re-pro‐ duced from our earlier published article in Journal of Theoretical Biology 2012;307: 174-182; reference [46]). Data from one thousand single cell runs were used (at t =, 105 MC step); simulation parameters are listed in Table 2 of [46]. The num‐ ber of Lyn-phosphorylated BCRs, a measure of early-time membrane proximal signaling, increases with affinity.](https://s3-eu-west-1.amazonaws.com/com.mendeley.prod.article-extracted-content/images/2489f886-b415-377a-899f-ba77caff926a/thumbnail-1e25a282-c23a-4f4d-902a-709e4098077c-0.png)
![Figure 2. (A) Schematic of the BCR-lipid raft formation simulation. (B) Time-course of BCR-lipid raft formation is simu‐ lated for two affinity values, low affinity (top): KA = 107 M-1 (Pon = 10-3 and Poff=10-6) and high affinity (bottom): KA = 109 M-1 (Pon = 10-2 and Poff=10-7). Affinity discrimination has been studied experimentally for similar affinity values: KA = 9.9 x 106 M-1 (B1-8-Low antibody) and KA = 5.2 x 108 M-1 (B1-8-High antibody) for the antigen hapten NIP [42]. We use the following energy-based parameter values in our simulation: BB = 3.0, BL = 2.0 and LL = 2.0 (in KBT); BB and BL values are for antigen bound BCRs. Both unbound (blue) and bound BCRs (red) are shown at the cell-cell contact region. Raft forming lipids (not shown) are co-clustered with the B cell receptors. Significantly larger amount of BCRs are clustered in the high affinity case.](https://s3-eu-west-1.amazonaws.com/com.mendeley.prod.article-extracted-content/images/2489f886-b415-377a-899f-ba77caff926a/thumbnail-e2e9b742-d06e-41db-b3ed-dc073a90065a-1.png)
![Figure 4. Time course of caspase 3 activation, as readout for apoptotic activation, is shown for single cells. Data is shown for simulation of the pure type 1 activation (4A) and the pure type 2 activation (4B). 1 Monte Carlo step = 10-4 sec. Normalized data is shown for caspase-8 = 1 (left) and caspase-8 = 10 (right). Nano-molar concentration is ob‐ tained by multiplying the number of molecules with 1.67. Data is shown for 10 individual single cell runs. Data is simi‐ lar to our earlier published result (Figure 2) in Biophysical Journal 2008;95: 3559-3562 [65].](https://s3-eu-west-1.amazonaws.com/com.mendeley.prod.article-extracted-content/images/2489f886-b415-377a-899f-ba77caff926a/thumbnail-412f58d0-7a38-43b6-872c-db3ea300af4d-3.png)
![Figure 5. Apoptotic activation, under the action of 3 μm HA14-1 (a BH3 mimetic Bcl-2 protein inhibitor [77-78]) is shown for normal (left) and cancer (right) cells. Time course of caspase 3 activation, as readout for downstream apop‐ totic activation, is shown for single cells. 1 Monte Carlo step = 10-4 sec. Nano-molar concentration is obtained by multi‐ plying the number of molecules with 1.67. Data is shown for 10 individual single cell runs (only a fraction of cells show activation within the given simulation time).](https://s3-eu-west-1.amazonaws.com/com.mendeley.prod.article-extracted-content/images/2489f886-b415-377a-899f-ba77caff926a/thumbnail-dc8748c1-407a-4920-aa33-436d8f3db59f-4.png)
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CITATION STYLE
Raychaudhuri, S. (2013). Kinetic Monte Carlo Simulation in Biophysics and Systems Biology. In Theory and Applications of Monte Carlo Simulations. InTech. https://doi.org/10.5772/53709
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