polymers 0.3.7

Polymers Modeling Library
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305

#[cfg(feature = "extern")]
pub mod ex;

#[cfg(feature = "python")]
pub mod py;

mod test;

/// The worm-like chain (WLC) model thermodynamics in the isometric ensemble approximated using a Legendre transformation.
pub mod legendre;

use std::f64::consts::PI;
use crate::math::
{
    bessel_i,
    integrate_1d
};
use crate::physics::
{
    PLANCK_CONSTANT,
    BOLTZMANN_CONSTANT
};
use crate::physics::single_chain::
{
    ONE,
    ZERO,
    POINTS
};

/// The structure of the thermodynamics of the WLC model in the isometric ensemble.
pub struct WLC
{
    /// The mass of each hinge in the chain in units of kg/mol.
    pub hinge_mass: f64,

    /// The length of each link in the chain in units of nm.
    pub link_length: f64,

    /// The number of links in the chain.
    pub number_of_links: u8,

    /// The persistance length of the chain in units of nm.
    pub persistance_length: f64,

    nondimensional_persistance_length: f64,

    normalization_nondimensional_equilibrium_distribution: f64,

    /// The thermodynamic functions of the model in the isometric ensemble approximated using a Legendre transformation.
    pub legendre: self::legendre::WLC
}

/// The expected force as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, and persistance length.
pub fn force(number_of_links: &u8, link_length: &f64, persistance_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_force(number_of_links, &(persistance_length/contour_length), &(end_to_end_length/contour_length))*BOLTZMANN_CONSTANT*temperature/link_length
}

/// The expected nondimensional force as a function of the applied nondimensional end-to-end length per link, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_force(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    let g2 = nondimensional_end_to_end_length_per_link.powi(2);
    let a: f64 = 14.054;
    let b: f64 = 0.473;
    let c = vec![
        vec![-0.75, 0.359375, -0.109375],
        vec![-0.5, 1.0625, -0.5625]
    ];
    let c0: f64 = 1.0 - (1.0 + (0.38/nondimensional_persistance_length.powf(0.95)).powi(-5)).powf(-0.2);
    let d: f64 = if nondimensional_persistance_length < &0.125
    {
        1.0
    }
    else
    {
        1.0 - 1.0/(0.177/(nondimensional_persistance_length - 0.111) + 6.40*(nondimensional_persistance_length - 0.111).powf(0.783))
    };
    let f = (1.0 - c0*g2)/(1.0 - g2);
    let h = nondimensional_end_to_end_length_per_link/(1.0 - b.powi(2)*g2);
    let arg = -d*nondimensional_persistance_length*a*(1.0 + b)*h;
    let sum = (0..2).collect::<Vec<usize>>().iter().map(|i| (1..4).collect::<Vec<usize>>().iter().map(|j| c[*i][j - 1]*(nondimensional_persistance_length.powi(*i as i32 - 1)*g2.powi((*j).try_into().unwrap()))).sum::<f64>()).sum::<f64>();
    let d_sum_dg = (0..2).collect::<Vec<usize>>().iter().map(|i| (1..4).collect::<Vec<usize>>().iter().map(|j| (*j as f64)*c[*i][j - 1]*(nondimensional_persistance_length.powi(*i as i32 - 1)*g2.powi((*j).try_into().unwrap()))).sum::<f64>()).sum::<f64>()*2.0/nondimensional_end_to_end_length_per_link;
    -((5.0*nondimensional_end_to_end_length_per_link*(1.0 - c0/f) + d_sum_dg + 2.0*nondimensional_end_to_end_length_per_link*sum/(1.0 - g2))/(1.0 - g2) + 2.0*b*arg *(1.0 + nondimensional_end_to_end_length_per_link*b.powi(2)*h) + arg*bessel_i(&1, &arg)/bessel_i(&0, &arg)*(1.0/nondimensional_end_to_end_length_per_link + 2.0*b.powi(2)*h))/(*number_of_links as f64)
}

/// The Helmholtz free energy as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, hinge mass, and persistance length.
pub fn helmholtz_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, persistance_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, &(persistance_length/contour_length), &(end_to_end_length/contour_length), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The Helmholtz free energy per link as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, hinge mass, and persistance length.
pub fn helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, persistance_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_helmholtz_free_energy_per_link(number_of_links, link_length, hinge_mass, &(persistance_length/contour_length), &(end_to_end_length/contour_length), temperature)*BOLTZMANN_CONSTANT*temperature
}

/// The relative Helmholtz free energy as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, and persistance length.
pub fn relative_helmholtz_free_energy(number_of_links: &u8, link_length: &f64, persistance_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_relative_helmholtz_free_energy(&(persistance_length/contour_length), &(end_to_end_length/contour_length))*BOLTZMANN_CONSTANT*temperature
}

/// The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature, parameterized by the number of links, link length, and persistance length.
pub fn relative_helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, persistance_length: &f64, end_to_end_length: &f64, temperature: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_relative_helmholtz_free_energy_per_link(number_of_links, &(persistance_length/contour_length), &(end_to_end_length/contour_length))*BOLTZMANN_CONSTANT*temperature
}

/// The nondimensional Helmholtz free energy as a function of the applied nondimensional end-to-end length per link and temperature, parameterized by the number of links, link length, hinge mass, and nondimensional persistance length.
pub fn nondimensional_helmholtz_free_energy(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_persistance_length: &f64, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
{
    //
    // Note: not exactly correct unless P_eq is already normalized.
    //
    let g2 = nondimensional_end_to_end_length_per_link.powi(2);
    let a: f64 = 14.054;
    let b: f64 = 0.473;
    let c = vec![
        vec![-0.75, 0.359375, -0.109375],
        vec![-0.5, 1.0625, -0.5625]
    ];
    let c0: f64 = 1.0 - (1.0 + (0.38/nondimensional_persistance_length.powf(0.95)).powi(-5)).powf(-0.2);
    let d: f64;
    let e: f64;
    if nondimensional_persistance_length < &0.125
    {
        d = 1.0;
        e = (0.75/PI/nondimensional_persistance_length).powf(1.5)*(1.0 - 1.25*nondimensional_persistance_length);
    }
    else
    {
        d = 1.0 - 1.0/(0.177/(nondimensional_persistance_length - 0.111) + 6.40*(nondimensional_persistance_length - 0.111).powf(0.783));
        e = 112.04*nondimensional_persistance_length.powi(2)*(0.246/nondimensional_persistance_length - a*nondimensional_persistance_length).exp();
    }
    let f = (1.0 - c0*g2)/(1.0 - g2);
    let h = nondimensional_end_to_end_length_per_link/(1.0 - b.powi(2)*g2);
    let arg = -d*nondimensional_persistance_length*a*(1.0 + b)*h;
    let sum = (0..2).collect::<Vec<usize>>().iter().map(|i| (1..4).collect::<Vec<usize>>().iter().map(|j| c[*i][j - 1]*(nondimensional_persistance_length.powi(*i as i32 - 1)*g2.powi((*j).try_into().unwrap()))).sum::<f64>()).sum::<f64>();
    -e.ln() - 2.5*f.ln() - sum/(1.0 - g2) - arg*b*nondimensional_end_to_end_length_per_link - bessel_i(&0, &arg).ln() - ((*number_of_links as f64) - 1.0)*(4.0*(-1.0/nondimensional_persistance_length).exp().acos().sin()*PI.powi(2)*hinge_mass*link_length.powi(2)*BOLTZMANN_CONSTANT*temperature/PLANCK_CONSTANT.powi(2)).ln()
}

/// The nondimensional Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link and temperature, parameterized by the number of links, link length, and hinge mass, and nondimensional persistance length.
pub fn nondimensional_helmholtz_free_energy_per_link(number_of_links: &u8, link_length: &f64, hinge_mass: &f64, nondimensional_persistance_length: &f64, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
{
    nondimensional_helmholtz_free_energy(number_of_links, link_length, hinge_mass, nondimensional_persistance_length, nondimensional_end_to_end_length_per_link, temperature)/(*number_of_links as f64)
}

/// The nondimensional relative Helmholtz free energy as a function of the applied nondimensional end-to-end length per link, parameterized by the nondimensional persistance length.
pub fn nondimensional_relative_helmholtz_free_energy(nondimensional_persistance_length: &f64, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    nondimensional_helmholtz_free_energy(&8, &1.0, &1.0, nondimensional_persistance_length, nondimensional_end_to_end_length_per_link, &300.0) - nondimensional_helmholtz_free_energy(&8, &1.0, &1.0, nondimensional_persistance_length, &ZERO, &300.0)
}

/// The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link, parameterized by the number of links and nondimensional persistance length.
pub fn nondimensional_relative_helmholtz_free_energy_per_link(number_of_links: &u8, nondimensional_persistance_length: &f64, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    nondimensional_relative_helmholtz_free_energy(nondimensional_persistance_length, nondimensional_end_to_end_length_per_link)/(*number_of_links as f64)
}

/// The equilibrium probability density of end-to-end vectors as a function of the end-to-end length, parameterized by the number of links, link length, and persistance length.
pub fn equilibrium_distribution(number_of_links: &u8, link_length: &f64, persistance_length: &f64, normalization_nondimensional_equilibrium_distribution: &f64, end_to_end_length: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_equilibrium_distribution(&(persistance_length/contour_length), normalization_nondimensional_equilibrium_distribution, &(end_to_end_length/contour_length))/contour_length.powi(3)
}

/// The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link as a function of the applied nondimensional end-to-end length per link, parameterized by the nondimensional persistance length.
pub fn nondimensional_equilibrium_distribution(nondimensional_persistance_length: &f64, normalization_nondimensional_equilibrium_distribution: &f64, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    let g2 = nondimensional_end_to_end_length_per_link.powi(2);
    let a: f64 = 14.054;
    let b: f64 = 0.473;
    let c = vec![
        vec![-0.75, 0.359375, -0.109375],
        vec![-0.5, 1.0625, -0.5625]
    ];
    let c0: f64 = 1.0 - (1.0 + (0.38/nondimensional_persistance_length.powf(0.95)).powi(-5)).powf(-0.2);
    let d: f64;
    let e: f64;
    if nondimensional_persistance_length < &0.125
    {
        d = 1.0;
        e = (0.75/PI/nondimensional_persistance_length).powf(1.5)*(1.0 - 1.25*nondimensional_persistance_length);
    }
    else
    {
        d = 1.0 - 1.0/(0.177/(nondimensional_persistance_length - 0.111) + 6.40*(nondimensional_persistance_length - 0.111).powf(0.783));
        e = 112.04*nondimensional_persistance_length.powi(2)*(0.246/nondimensional_persistance_length - a*nondimensional_persistance_length).exp();
    }
    let f = (1.0 - c0*g2)/(1.0 - g2);
    let h = nondimensional_end_to_end_length_per_link/(1.0 - b.powi(2)*g2);
    let arg = -d*nondimensional_persistance_length*a*(1.0 + b)*h;
    let sum = (0..2).collect::<Vec<usize>>().iter().map(|i| (1..4).collect::<Vec<usize>>().iter().map(|j| c[*i][j - 1]*(nondimensional_persistance_length.powi(*i as i32 - 1)*g2.powi((*j).try_into().unwrap()))).sum::<f64>()).sum::<f64>();
    e*f.powf(2.5)*(sum/(1.0 - g2) + arg*b*nondimensional_end_to_end_length_per_link).exp()*bessel_i(&0, &arg)/normalization_nondimensional_equilibrium_distribution
}

/// The equilibrium probability density of end-to-end lengths as a function of the end-to-end length, parameterized by the number of links, link length, and persistance length.
pub fn equilibrium_radial_distribution(number_of_links: &u8, link_length: &f64, persistance_length: &f64, normalization_nondimensional_equilibrium_distribution: &f64, end_to_end_length: &f64) -> f64
{
    let contour_length = (*number_of_links as f64)*link_length;
    nondimensional_equilibrium_radial_distribution(&(persistance_length/contour_length), normalization_nondimensional_equilibrium_distribution, &(end_to_end_length/contour_length))/contour_length
}

/// The nondimensional equilibrium probability density of nondimensional end-to-end lengths per link as a function of the nondimensional end-to-end length per link, parameterized by the nondimensional persistance length.
pub fn nondimensional_equilibrium_radial_distribution(nondimensional_persistance_length: &f64, normalization_nondimensional_equilibrium_distribution: &f64, nondimensional_end_to_end_length_per_link: &f64) -> f64
{
    4.0*PI*nondimensional_end_to_end_length_per_link.powi(2)*nondimensional_equilibrium_distribution(nondimensional_persistance_length, normalization_nondimensional_equilibrium_distribution, nondimensional_end_to_end_length_per_link)
}

/// The implemented functionality of the thermodynamics of the WLC model in the isometric ensemble.
impl WLC
{
    /// Initializes and returns an instance of the thermodynamics of the WLC model in the isometric ensemble.
    pub fn init(number_of_links: u8, link_length: f64, hinge_mass: f64, persistance_length: f64) -> Self
    {
        let nondimensional_persistance_length = persistance_length/(number_of_links as f64)/link_length;
        let normalization_nondimensional_equilibrium_distribution = integrate_1d(&|nondimensional_end_to_end_length_per_link: &f64| nondimensional_equilibrium_radial_distribution(&nondimensional_persistance_length, &1.0, nondimensional_end_to_end_length_per_link), &ZERO, &ONE, &POINTS);
        WLC
        {
            hinge_mass,
            link_length,
            number_of_links,
            persistance_length,
            nondimensional_persistance_length,
            normalization_nondimensional_equilibrium_distribution,
            legendre: self::legendre::WLC::init(number_of_links, link_length, hinge_mass, persistance_length)
        }
    }
    /// The expected force as a function of the applied end-to-end length and temperature.
    pub fn force(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        force(&self.number_of_links, &self.link_length, &self.persistance_length, end_to_end_length, temperature)
    }
    /// The expected nondimensional force as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_force(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_force(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_end_to_end_length_per_link)
    }
    /// The Helmholtz free energy as a function of the applied end-to-end length and temperature.
    pub fn helmholtz_free_energy(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, end_to_end_length, temperature)
    }
    /// The Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
    pub fn helmholtz_free_energy_per_link(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.persistance_length, end_to_end_length, temperature)
    }
    /// The relative Helmholtz free energy as a function of the applied end-to-end length and temperature.
    pub fn relative_helmholtz_free_energy(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        relative_helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.persistance_length, end_to_end_length, temperature)
    }
    /// The relative Helmholtz free energy per link as a function of the applied end-to-end length and temperature.
    pub fn relative_helmholtz_free_energy_per_link(&self, end_to_end_length: &f64, temperature: &f64) -> f64
    {
        relative_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.persistance_length, end_to_end_length, temperature)
    }
    /// The nondimensional Helmholtz free energy as a function of the applied nondimensional end-to-end length per link and temperature.
    pub fn nondimensional_helmholtz_free_energy(&self, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
    {
        nondimensional_helmholtz_free_energy(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, nondimensional_end_to_end_length_per_link, temperature)
    }
    /// The nondimensional Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link and temperature.
    pub fn nondimensional_helmholtz_free_energy_per_link(&self, nondimensional_end_to_end_length_per_link: &f64, temperature: &f64) -> f64
    {
        nondimensional_helmholtz_free_energy_per_link(&self.number_of_links, &self.link_length, &self.hinge_mass, &self.nondimensional_persistance_length, nondimensional_end_to_end_length_per_link, temperature)
    }
    /// The nondimensional relative Helmholtz free energy as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_relative_helmholtz_free_energy(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_relative_helmholtz_free_energy(&self.nondimensional_persistance_length, nondimensional_end_to_end_length_per_link)
    }
    /// The nondimensional relative Helmholtz free energy per link as a function of the applied nondimensional end-to-end length per link.
    pub fn nondimensional_relative_helmholtz_free_energy_per_link(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_relative_helmholtz_free_energy_per_link(&self.number_of_links, &self.nondimensional_persistance_length, nondimensional_end_to_end_length_per_link)
    }
    /// The equilibrium probability density of end-to-end vectors as a function of the end-to-end length.
    pub fn equilibrium_distribution(&self, end_to_end_length: &f64) -> f64
    {
        equilibrium_distribution(&self.number_of_links, &self.link_length, &self.persistance_length, &self.normalization_nondimensional_equilibrium_distribution, end_to_end_length)
    }
    /// The nondimensional equilibrium probability density of nondimensional end-to-end vectors per link as a function of the nondimensional end-to-end length per link.
    pub fn nondimensional_equilibrium_distribution(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_equilibrium_distribution(&self.nondimensional_persistance_length, &self.normalization_nondimensional_equilibrium_distribution, nondimensional_end_to_end_length_per_link)
    }
    /// The equilibrium probability density of end-to-end lengths as a function of the end-to-end length.
    pub fn equilibrium_radial_distribution(&self, end_to_end_length: &f64) -> f64
    {
        equilibrium_radial_distribution(&self.number_of_links, &self.link_length, &self.persistance_length, &self.normalization_nondimensional_equilibrium_distribution, end_to_end_length)
    }
    /// The nondimensional equilibrium probability density of nondimensional end-to-end lengths per link as a function of the nondimensional end-to-end length per link.
    pub fn nondimensional_equilibrium_radial_distribution(&self, nondimensional_end_to_end_length_per_link: &f64) -> f64
    {
        nondimensional_equilibrium_radial_distribution(&self.nondimensional_persistance_length, &self.normalization_nondimensional_equilibrium_distribution, nondimensional_end_to_end_length_per_link)
    }
}