# Stratified RE-SWHAM

## Table of Contents

- 1. how to install
- 2. list of options:
- 2.1. options and descriptions
- 2.1.1. -d observation_data_file
- 2.1.2. -f state_information_file
- 2.1.3. -a number_of_macrostate
- 2.1.4. -t temperature
- 2.1.5. -u potential_function_type
- 2.1.6. -i input_unit -o output_unit
- 2.1.7. -q equilibrium_length
- 2.1.8. -n number_of_cycles
- 2.1.9. -x number_of_exchange_attempts
- 2.1.10. -s print_list_of_states
- 2.1.11. -p print_list_of_properties
- 2.1.12. -k -m

- 2.1. options and descriptions

## 1 how to install

compile:

g++ sreswham.cpp -lm -o sreswham.o

## 2 list of options:

simple description | default | |
---|---|---|

h | print out help information | - |

d | input file contains information of observations | - |

f | input file contains information of states | - |

a | number of disconnected macrostate clusters | |

u | type of the potential function | - |

t | temperature | -1.0 |

i | unit of potential energies in the input file | 0 |

o | unit of free energies of the output | 0 |

q | length of the equilibrium period | - |

n | number of the RE cycles | - |

x | number of exchange attempts in RE | - |

s | list of states to print out | - |

p | list of properties of each observation to print out | 0 |

k | input numbers are in units of one thousand | - |

m | input numbers are in units of one million | - |

### 2.1 options and descriptions

#### 2.1.1 -d observation_data_file

The "observation_data_file" contains information of observations. Like the input file for UWHAM, this file contains \(M\) blocks. Each block corresponds to a \(\lambda\)-state. At the beginning of each block, there is a comment line or multiple comment lines starting with "@" or "#". Do not leave blank lines between blocks. After comments lines, there is a \(N_i \times K\) matrix, where \(N_i\) is the total number of observations observed at the \(i^{th}\) state and \(K\) is the total number of properties of each observation. To apply Stratified RE-SWHAM, the last property of each observation is the index of the macrostate cluster that this observation belongs to. The index of macrostate clusters starts from one (not zero).

#### 2.1.2 -f state_information_file

This file contains \(M\) lines. Each line represents a \(\lambda\)-state. If the value of temperature defined by "-t" option is negative, the first item of each line is the temperature of that \(\lambda\)-state. Usually, the next item of each line can be the lambda value of that \(\lambda\)-state. To apply Stratified RE-SWHAM, the last item of each line is the tag that marks whether this \(\lambda\)-state is fully connected ("1" means true; "0" means false).

#### 2.1.3 -a number_of_macrostate

How many macrostates or macrostate clusters defined in this system.

#### 2.1.4 -t temperature

The temperature of all the simulations. This option is only useful when the simulations are run at a single temperature. The default value of this option is \(-1\). If "temperature" is negative, the temperature of each state is defined be the first float number of each line in the "state_information_file", see option "-f".

#### 2.1.5 -u potential_function_type

The potential energy (biasing potential energy) can be calculated for each observation at any \(\lambda\)-state. As shown in the following table, four different potential functions have been implemented in the SWHAM code. The potential function \(U[i][j][k]\) is the potential energy of the \(j^{th}\) observation observed at the \(i^{th}\) \(\lambda\)-state calculated by the Hamiltonian function of the \(k^{th}\) \(\lambda\)-state in units of \(k_B T\).

type | description | potential function \(U[i][j][k]\) |
---|---|---|

0 | UWHAM-like input | \(D[i][j][k]/(K_B S[k][1])\) |

1 | Temperature replica exchange | \(D[i][j][1]/(K_B S[k][1])\) |

2 | Hamiltonian replica exchange | \(D[i][j][1] \times S[k][2]/(K_B S[k][1])\) |

3 | Temperature and Hamiltonian replica exchange | \((D[i][j][1]+D[i][j][2] \times S[k][2])/(K_B S[k][1])\) |

In this table, \(D[i][j][k]\) is the \(k^{th}\) property of the \(j^{th}\) observation observed at the \(i^{th}\) \(\lambda\)-state. \(S[k][1]\) is the first property, namely the temperature, of the \(k^{th}\) \(\lambda\)-state.

- UWHAM-like input (-u 0)

This option allows the SWHAM program to use the UWHAM-format input, where \(D[i][j][k]\) is the potential energy of the \(j^{th}\) observation observed at the \(i^{th}\) \(\lambda\)-state calculated by the Hamiltonian function of the \(k^{th}\) \(\lambda\)-state. Note that the last property of each observation is the index of the macrostate cluster that this observation belongs to. Therefore, each observation has at least \(M+1\) properties, where \(M\) is the total number of \(\lambda\)-states.

- Temperature replica exchange (-u 1)

This potential function is implemented to analyze the data generated by temperature replica exchange (RE) simulations. In the "observation_data_file", the first property of each observation \(D[i][j][1]\) is the potential energy of that observation. Note in temperature RE simulations, the Hamiltonian functions of all \(\lambda\)-state are the same. More properties can be appended after the potential energy. In the "state_information_file", the first property of each state \(S[k][1]\) is the temperature of that state.

- Hamiltonian replica exchange (-u 2)

This potential function is implemented to analyze the data generated by Hamiltonian replica exchange simulations. To use this type of potential function, the first property of each observation in the "observation_data_file" \(D[i][j][1]\) is the Hamiltonian energy part linearly controlled by the parameter \(\lambda\). In Hamiltonian RE simulations, all the simulations are run at the same temperature. Therefore, the temperature (\(S[k][1]\)) can be inputted by using the '-t' option. The first property of each state in the "state_information_file" (\(S[k][2]\)) is the \(\lambda\) value of that \(\lambda\)-state.

- Temperature and Hamiltonian replica exchange (-u 3)

This potential function is implemented to analyze the data generated by Temperature and Hamiltonian replica exchange simulations. The first property of each observation in the "observation_data_file" \(D[[i][j][1]\) is the Hamiltonian energy part which is not controlled by the parameter \(\lambda\), and the second property of each observation \(D[i][j][2]\) is the Hamiltonian energy part which is linearly controlled by the parameter \(\lambda\). The first property of each state in the "state_information_file" \(S[k][1]\) is the temperature of that state, and the second property $S[k][2]$is the \(\lambda\) value of that state.

#### 2.1.6 -i input_unit -o output_unit

The unit of energies in the input and output. The default unit for potential energies used in UWHAM is \(k_B T\). However, if the data are generated by simulations running at a single temperature, UWHAM program can read and output energies in a different unit. For these two options, "0" represents \(k_B T\); "1" represents \(kcal/mol\); and "2" represents "kJ/mol".

#### 2.1.7 -q equilibrium_length

How many cycles to run to equilibrate the system. Stratified RE-SWHAM is run by cycles. No results are printed out during the equilibrium.

#### 2.1.8 -n number_of_cycles

This option specifies how many cycles to be run after equilibrium.

#### 2.1.9 -x number_of_exchange_attempts

This option specifies how many exchange attempts should be in the exchange procedure of RE-SWHAM cycle. To reach the infinite exchange limit, a number between \(M^2\) and \(M^3\) is recommended, where \(M\) is the total number of \(\lambda\)-states of the system.

#### 2.1.10 -s print_list_of_states

"print_list_of_states" is a list of \(\lambda\)-state indexes. For example, "1,3,5" means the first, the third and the fifth \(\lambda\)-states; "2-4" represents the second, the third and the fourth \(\lambda\)-states; and "1,3-5,9" represents the first, the third, the fourth, the fifth and the ninth \(\lambda\)-states. Note the index of \(\lambda\)-state starts from one, not zero. When the data are analyzed by Stratified RE-SWHAM, the properties of the observation (see option "-p") sampled at those states listed in "print_list_of_states" will be printed out every RE cycle.

#### 2.1.11 -p print_list_of_properties

"print_list_of_properties" is a list of properties indexes. During the Stratified RE-SWHAM analysis, the properties listed in "print_list_of_properties" of the observation sampled at those states listed in "print_list_of_states" (see option "-s") will be printed out every RE cycle. Note the index starts from one, not zero. If "print_list_of_properties" contains one single value zero (-p 0), the index of the observation will be printed out.

#### 2.1.12 -k -m

These two options are used to reduce the zeros for the input of option "-q" and "-n". If the "-k" switch is turned on, the input numbers of option "-q" and "-n" are in unit of one thousand. If the "-m" switch is turned on, the input numbers of option "-q" and "-n" are in unit of one million. If both are used, the input numbers of those options are in unit of one billion.