Python Programming for Biology: Bioinformatics and Beyond

Figure 25.5.  A simple graphical representation of the chemical structure of paracetamol,

with atom coordinates determined by the particle dynamics algorithm. Python code for the

ChemView class used to generate such graphics is available in the on-line material,

http://www.cambridge.org/pythonforbiology

.

Graphical  inspection  of  the  atomic  coordinates  reveals  a  bent  aromatic  ring  and  thus

reaffirms that the force field used is very simple and naïve. However, the result shows that

the  approach  is  working  and  we  have  a  reasonable  extended  conformation,  given  the

specified rules.

1

The name Monte Carlo is from the Monte Carlo Casino in Monaco, and the name was

given by the physicist John von Neuman for the idea that Stanis

ław Ulam had for a way to

estimate neutron collisions. Both were working at Los Alamos at the time, developing the

atomic  bomb.  Monte  Carlo  was  a  secret  code  phrase  and  had  notions  of  probability  and

chance, albeit related to gambling.

2

 Metropolis,  N.,  Rosenbluth,  A.W.,  Rosenbluth,  M.N.,  Teller,  A.H.,  and  Teller,  E.

(1953).  Equation  of  state  calculations  by  fast  computing  machines.  Journal  of  Chemical

Physics 21(6): 1087.

3

Hastings, W.K. (1970). Monte Carlo sampling methods using Markov chains and their

applications. Biometrika 57(1): 97–109.

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4

It can be shown that the standard deviation of this estimate for π is

, where n

is the number of samples, so with 100000 samples this gives 0.013.

5

http://en.wikipedia.org/wiki/Rosenbrock_function

.  Rosenbrock,  H.H.  (1960).  An

automatic method for finding the greatest or least value of a function. Computer Journal

3: 175–184.

6

 Kirkpatrick,  S.,  Gelatt  Jr.,  C.D.,  and  Vecchi,  M.P.  (1983).  Optimization  by  simulated

annealing. Science 220(4598): 671–680.

7

Černý,  V.  (1985).  Thermodynamical  approach  to  the  traveling  salesman  problem:  an

efficient simulation algorithm. Journal of Optimization Theory and Applications  45:  41–

51.

8

When the force is proportional to distance the term is described as ‘harmonic’.

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