Skip to content

nbPot

Module documentation for nbPot.

API Reference

AbstractNbDnaScheme

Bases: AbstractPotential

Source code in mrdna/model/nbPot.py
 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
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
class AbstractNbDnaScheme(AbstractPotential):

    def __init__(self, *args,**kwargs):
        AbstractPotential.__init__(self,*args,**kwargs)

        self.debye_length = self.debye_length0 # set by child class

        x,y = self.load_pmf()
        self.target_x = x
        self.target_y = y
        base = 4
        self.param_x = np.logspace(np.log(15)/np.log(base),np.log(120)/np.log(base),80,base=base)
        # print(self.param_x)

        self.target_x_interp = np.linspace(np.min(x),np.max(x),2*len(x)) # interpolate potential
        self.target_x_interp = np.arange(23.5,38,0.1) # interpolate potential
        self.target_y_interp = interp1d(x,y)(self.target_x_interp)

        self.bead_distribution_y = None

        """ Initialize caches """
        try:
            self.single_bp_pair_pot = np.loadtxt( self.get_package_cache_file() ).T
            self.param_x = self.single_bp_pair_pot[0,:]
            assert( len(self.param_x > 2) )
        except:
            pass

    def get_package_cache_file(self):
        raise NotImplementedError()

    def load_pmf(self):
        raise NotImplementedError()

    def load_bead_distributions(self):
        raise NotImplementedError()

    def potential(self, r, types):
        typeA, typeB = types
        """ Implements interface for NonbondedScheme """

        if typeA.name[0] == "O" or typeB.name[0] == "O":
            u = np.zeros( r.shape )
        else:
            u = self.nbPot(r, 0.5*typeA.nts, 0.5*typeB.nts)
        return u

    """ Remainder has to do with nbPot """
    def load_np(self,filename):
        return np.load(filename)['arr_0'].tolist()

    def parametric_potential(self,x,*parms):
        x0 = self.param_x
        x = np.array(x)
        u = interp1d(x0, np.array(parms),
                     bounds_error = False, fill_value="extrapolate",
                     assume_sorted=True)(x).T
        u[x<13] = u[x<13] + 0.5 * (x[x<13]-13)**2

        ## Debye correction
        if self.debye_length != self.debye_length0:
            ## units "e**2/(4 * pi * 80 epsilon0 AA)" kcal_mol
            A = 4.1507964
            with np.errstate(divide='ignore',invalid='ignore'):
                du = (A/x) * (np.exp(-x/self.debye_length) - np.exp(-x/self.debye_length0))

            du[x < 10] = du[x>=10][0]
            u = u + du

        return u-u[-1]

    def get_bead_distributions(self, interhelical_distances):
        if self.bead_distribution_y is None:
            self.load_bead_distributions()
        return self.bead_distribution_x, self.bead_distribution_y(interhelical_distances)

    def iterative_fit(self):
        try:
            import bead_dist_data as bdd
            x = bdd.bead_centers.x
        except:
            ## First iteration
            x = np.arange(0,200,0.2)
            f = self.get_target_force(x+2)
            f[f>0.5] = 0.5
            u = np.cumsum(f[::-1])[::-1]
            u = 0.5* u / (10*20)
            np.savetxt("pair-pot.dat", np.array((x,u)).T)
            return interp1d(x,u,
                            bounds_error = False, fill_value="extrapolate",
                            assume_sorted=True)(self.param_x).T

        x = x[x<50]
        data = np.loadtxt("last/pair-pot.dat")
        u_last = interp1d(data[:,0], data[:,1],
                          bounds_error = False, fill_value="extrapolate",
                          assume_sorted=True)(x).T

        particle_force = np.diff(u_last) / np.diff(x)

        for b in bdd.bead_dists:
            ids = bdd.bead_centers < 10
            b[:,ids] = 0

        R = bdd.interhelical_spacing
        R,y = self.load_rau_pressure()

        P = self.get_pressure(R)
        P_t = self.get_target_pressure(R)
        dP = P_t-P

        np.savetxt("raw_pressure.dat", self.get_raw_pressure())
        np.savetxt("pressure.dat", np.array((R,P)).T)
        np.savetxt("target_pressure.dat", np.array((R,P_t)).T)

        def fitFun(R,*uvals):
            df_interp = dfFun(*uvals)
            dP_local = self.get_virial_pressure(R, df_interp)
            print( np.std(dP_local-dP) )
            return dP_local

        def duFun(x,*popt):
            f = dfFun(*popt)(x)
            u = -np.cumsum(f) * np.mean( np.diff(x) )
            u = u - u[-1]
            return u

        def dfFun(x0,f0,x1_par,x2):
            x1 = (1-x1_par)*x0 + x1_par*x2
            t = np.linspace(0,1,100)
            x = x0*(1-t)**2 + 2*x1*(1-t)*t + x2*t**2
            f = f0*(1-t)**2
            return interp1d(x, f,
                            bounds_error = False,
                            fill_value=0,
                            assume_sorted=True)

        dP_sofar = np.zeros(dP.shape)
        popt_list = []
        for i in range(3):
            popt, pcov = opt.curve_fit(fitFun, R, dP-dP_sofar,
                                       bounds=((10,-0.1,0.1,35),
                                               (34,0.1,0.9,50)),
                                       p0=(20,0,0.25,50))
            popt_list.append(popt)
            dP_sofar += fitFun(R,*popt)

        du = np.zeros(x.shape)
        for popt in popt_list:
            du = du + duFun(x,*popt)

        du = savgol(du,int(2.5/(x[1]-x[0]))*2+1,3)
        u = u_last+0.75*du
        u = u-u[-1]

        np.savetxt("pair-pot.dat", np.array((x,u)).T)

        return interp1d(x,u,
                        bounds_error = False, fill_value="extrapolate",
                          assume_sorted=True)(self.param_x).T


    def get_virial_pressure(self, R, bead_force):
        """ Return pressure as fn of interhelical spacing """
        import bead_dist_data as bdd

        interhelical_spacing = bdd.interhelical_spacing
        volume = (np.pi*np.array(bdd.radii)**2) * bdd.height

        # units "kcal_mol/AA**3" atm
        # * 68568.409

        xy = bdd.bead_centers[np.newaxis,:]
        r = bdd.bead_centers[:,np.newaxis]
        force = bead_force(r)

        """ Pxy = 1/(4V) Sum_ij (xy_ij)**2 * bead_force(r_ij) / r_ij """
        ## 2*count because count only includes i < j
        pressure = [68568.409*np.sum( 2*count * (xy**2) * force / r ) / (4 * vol)
                    for vol,count in zip(volume,bdd.bead_dists)]
        return pchip_interpolate(interhelical_spacing, pressure, R)
        """
        return interp1d(interhelical_spacing, pressure,
                        bounds_error = False,
                        kind='cubic',
                        fill_value="extrapolate",
                        assume_sorted=True)(R)

        ## Fit double exponential

        try:
            def fitfn(x,A,a,b):
                return A*a**(-b**x)
            def fit_wrap(x,*popt):
                print("pressure:",pressure)
                print("  ",fitfn(interhelical_spacing, *popt) - pressure)
                return fitfn(x,*popt)
            popt, pcov = opt.curve_fit(fit_wrap, interhelical_spacing, pressure,
                                       bounds=((-np.inf,0,0),
                                               (np.inf,np.inf,np.inf)),
                                       p0=(0,1,1))
            return fitfn(R,*popt)
        except:
            return interp1d(interhelical_spacing, pressure,
                            bounds_error = False, 
                            fill_value="extrapolate",
                            assume_sorted=True)(R)
        """


    def get_interhelical_density(self,R):
        data = np.loadtxt("last/density.dat")
        r,rho = data.T 
        rho = rho / r**2
        rho = rho/np.trapz(rho,r)
        filter_points = int(2.5/(r[1]-r[0]))*2 + 1
        rho = savgol(rho, filter_points, 3) # smooth density
        return interp1d(r,rho,
                          bounds_error = False, fill_value=0,
                          assume_sorted=True)(R).T

    def get_raw_pressure(self):
        from bead_dist_data import interhelical_spacing, pressure
        distance = interhelical_spacing
        assert( len(distance) > 2 )
        return distance,pressure

    def get_pressure(self,R):
        distance,pressure = self.get_raw_pressure()
        # distance,pressure = np.loadtxt("last/pressure.dat")
        return pchip_interpolate(distance, pressure, R)
        return interp1d(distance, pressure,
                        bounds_error = False,
                        kind='cubic',
                        fill_value="extrapolate",
                        assume_sorted=True)(R)
        def fitfn(x,a,b):
            return a**(-b**x)

        popt, pcov = opt.curve_fit(fitfn, distance, pressure,
                                   bounds=(0,np.inf),
                                   p0=(1,1))
        return fitfn(R,*popt)


    def get_interhelical_force(self,R):
        y = pressure = self.get_pressure(R)
        x = R
        force = (x*y / np.sqrt(3)) * 34 * 1.4583976e-05 # convert atm AA**2 to kcal/mol AA
        return force

    def get_target_interhelical_density(self,R):
        r,u = self.load_pmf()
        rho = np.exp( -u/kT )  
        rho = rho / np.trapz(rho,r)
        return interp1d(r,rho,
                          bounds_error = False, fill_value=0,
                          assume_sorted=True)(R).T

    def get_target_force(self,R):
        x,y = self.load_rau_force()
        # return pchip_interpolate(x, y, R)
        # return interp1d(x,y,
        #                 bounds_error = False,
        #                 # kind='cubic',
        #                 fill_value="extrapolate",
        #                 assume_sorted=True)(R)

        def fitfn(x,A,a):
            return A * np.exp(-(x-18)/a)
        popt,pcov = curve_fit(fitfn, x,y, p0=(10,20))
        return fitfn(R,*popt)

    def get_target_pressure(self,R):
        x,y = self.load_rau_pressure()
        return pchip_interpolate(x, y, R)
        return interp1d(x,y,
                        bounds_error = False,
                        kind='cubic',
                        fill_value="extrapolate",
                        assume_sorted=True)(R)
        def fitfn(x,A,a):
            return A * np.exp(-(x-18)/a)
        popt,pcov = curve_fit(fitfn, x,y, p0=(10,20))
        return fitfn(R,*popt)

    def load_rau_force(self):
        x,y = self.load_rau_pressure()
        y = (x*y / np.sqrt(3)) * 34 * 1.4583976e-05 # convert atm AA**2 to kcal/mol AA
        return x,y

    def get_rounded_bp(self,bps1,bps2):
        larger  = np.max([bps1,bps2])
        smaller = np.min([bps1,bps2])
        smaller_shift, larger_shift = [_round_bp(bp) for bp in (smaller,larger)]

        key = (smaller_shift,larger_shift)
        return smaller,larger,smaller_shift,larger_shift

    def nbPot(self, x, bps1, bps2):
        x0,u0 = self.single_bp_pair_pot
        u = self.parametric_potential(x,*u0)
        u = u * bps1 * bps2
        assert(np.sum(np.isnan(u)) == 0)
        return u

bead_distribution_y = None instance-attribute

Initialize caches

get_virial_pressure(R, bead_force)

Return pressure as fn of interhelical spacing

Source code in mrdna/model/nbPot.py
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
def get_virial_pressure(self, R, bead_force):
    """ Return pressure as fn of interhelical spacing """
    import bead_dist_data as bdd

    interhelical_spacing = bdd.interhelical_spacing
    volume = (np.pi*np.array(bdd.radii)**2) * bdd.height

    # units "kcal_mol/AA**3" atm
    # * 68568.409

    xy = bdd.bead_centers[np.newaxis,:]
    r = bdd.bead_centers[:,np.newaxis]
    force = bead_force(r)

    """ Pxy = 1/(4V) Sum_ij (xy_ij)**2 * bead_force(r_ij) / r_ij """
    ## 2*count because count only includes i < j
    pressure = [68568.409*np.sum( 2*count * (xy**2) * force / r ) / (4 * vol)
                for vol,count in zip(volume,bdd.bead_dists)]
    return pchip_interpolate(interhelical_spacing, pressure, R)
    """
    return interp1d(interhelical_spacing, pressure,
                    bounds_error = False,
                    kind='cubic',
                    fill_value="extrapolate",
                    assume_sorted=True)(R)

    ## Fit double exponential

    try:
        def fitfn(x,A,a,b):
            return A*a**(-b**x)
        def fit_wrap(x,*popt):
            print("pressure:",pressure)
            print("  ",fitfn(interhelical_spacing, *popt) - pressure)
            return fitfn(x,*popt)
        popt, pcov = opt.curve_fit(fit_wrap, interhelical_spacing, pressure,
                                   bounds=((-np.inf,0,0),
                                           (np.inf,np.inf,np.inf)),
                                   p0=(0,1,1))
        return fitfn(R,*popt)
    except:
        return interp1d(interhelical_spacing, pressure,
                        bounds_error = False, 
                        fill_value="extrapolate",
                        assume_sorted=True)(R)
    """