From de7ef52d7a4a2405cbf513bdca85c3922ed0cdb8 Mon Sep 17 00:00:00 2001 From: Chris Maffeo <cmaffeo2@illinois.edu> Date: Wed, 14 Nov 2018 16:55:25 -0600 Subject: [PATCH] Fit nb interactions directly against Rau and Parsegian data in 20 Mm Mg, 200 mM Na --- mrdna/model/nbPot.py | 476 +++++++++++++----- .../resources/nbPot.jj-nar-dna-pmf-100Mg.npz | Bin 7231114 -> 0 bytes .../nbPot.jj-nar-dna-pmf-20Mg-200Na.npz | Bin 7231114 -> 0 bytes .../nbPot.rau_refined_20Mg_200Na.dat | 250 +++++++++ 4 files changed, 597 insertions(+), 129 deletions(-) delete mode 100644 mrdna/resources/nbPot.jj-nar-dna-pmf-100Mg.npz delete mode 100644 mrdna/resources/nbPot.jj-nar-dna-pmf-20Mg-200Na.npz create mode 100644 mrdna/resources/nbPot.rau_refined_20Mg_200Na.dat diff --git a/mrdna/model/nbPot.py b/mrdna/model/nbPot.py index 6941f47..1ad9022 100644 --- a/mrdna/model/nbPot.py +++ b/mrdna/model/nbPot.py @@ -7,37 +7,13 @@ from mrdna.model.nonbonded import NonbondedScheme from mrdna import get_resource_path from mrdna.config import CACHE_DIR -## TODO: clean this file up a bit, make things protected - -_dxParam = -1 - -def _maxForce(x,u0,maxForce=40): - maxForce = maxForce * 0.014393265 # convert pN to kcal_mol/AA - dx = np.diff(x) - f = -np.diff(u0)/dx - f[ np.isnan(f) ] = 0 - - ids = np.where(f > maxForce)[0] - f[ids] = maxForce - ids = np.where(f < -maxForce)[0] - f[ids] = -maxForce - - u = np.hstack( ((0), np.cumsum(-f*dx)) ) - assert( np.any( x > 40 ) ) - ids = np.where(x > 40)[0] - - u = u - np.mean(u[ids]) - assert( np.isnan(u).sum() == 0 ) - return u +from scipy.optimize import curve_fit +from pathlib import Path -def integrate_potential(potfn,x,y,*parms): - u = np.zeros(np.shape(x)) - for h in y: - r = np.sqrt(x**2 + h**2) - r[r<1] = 1 - u = u + potfn(r,*parms) # * x/r - return u +## TODO: clean this file up a bit, make things protected +## units "291 k K" kcal_mol +kT = 0.57827709 def _round_bp(bp): return 10**(np.around(np.log10(bp)*100)/100.0) @@ -50,13 +26,21 @@ class AbstractNbDnaScheme(NonbondedScheme): x,y = self.load_pmf() self.target_x = x self.target_y = y - self.target_x_interp = np.linspace(np.min(x),np.max(x),1000) # interpolate potential + 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 """ - self._pot_dict = dict() # cache including only what has already been acessed try: - self._cached_params = np.load( self.get_package_cache_file() ) + 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 @@ -66,7 +50,7 @@ class AbstractNbDnaScheme(NonbondedScheme): def load_pmf(self): raise NotImplementedError() - def get_cache_file_for_pair(self,key): + def load_bead_distributions(self): raise NotImplementedError() def potential(self, r, typeA, typeB): @@ -82,40 +66,233 @@ class AbstractNbDnaScheme(NonbondedScheme): def load_np(self,filename): return np.load(filename)['arr_0'].tolist() - def set_cache_params(self,key): - if key not in self._pot_dict: - try: - self._pot_dict[key] = self._cached_params['{}:{}'.format(*key)] - except: - cache_file = self.get_cache_file_for_pair(key) - try: - self._pot_dict[key] = self.load_np(cache_file) - except: - self._pot_dict[key] = self.fit_potential(*key) - np.savez(cache_file, self._pot_dict[key]) - def parametric_potential(self,x,*parms): - x0 = self.target_x + 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>np.max(x0)] = 0 - return u - - def fit_potential(self,bp1,bp2): - assert(bp2 >= bp1) + return u-u[-1] - def fitFun(x,*parms): - ## 1-turn iteracting with at least 4 turns (more is not needed) - y = np.arange(-20,21)*(bp2*3.4) + 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) - return (10.0/bp1) * integrate_potential(self.parametric_potential, x,y,*parms) + 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 - popt, pcov = opt.curve_fit(fitFun, self.target_x_interp, - self.target_y_interp, - p0=self.target_y/10**2 ) # find fit to interpolated potential - return popt + 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]) @@ -126,45 +303,11 @@ class AbstractNbDnaScheme(NonbondedScheme): return smaller,larger,smaller_shift,larger_shift def nbPot(self, x, bps1, bps2): - smaller,larger,smaller_shift,larger_shift = self.get_rounded_bp(bps1,bps2) - key = (smaller_shift,larger_shift) - self.set_cache_params(key) - - u = self.parametric_potential(x,*self._pot_dict[key]) - u = u * ( (smaller/smaller_shift)*(larger/larger_shift) ) - - # u1 = _maxForce(x,u, 100) - # u2 = savgol(u1, int(5.0/(self.x0[1]-self.x0[0])), 3) - u2 = u - assert(np.sum(np.isnan(u2)) == 0) - return u2 - - """ Creating package cache """ - - def _write_cache(self): - keys = [] - for i in np.arange(0.4,5.5,0.01): - ir = _round_bp(i) - for j in np.arange(0.4,5.5,0.01): - if j < i: continue - keys.append( (ir,_round_bp(j)) ) - - keys = sorted(list(set(keys))) - print(len(keys)) - - new_cache_dict = dict() - - args = [(self, new_cache_dict, key) for key in keys] - - from multiprocessing import Pool - p = Pool(15) - print("Starting pool") - for arg in args: - _add_parameter_to_cache_dict(arg) - - p.map( _add_parameter_to_cache_dict, args ) - print("done with pool") - np.savez( self.get_package_cache_file(), **new_cache_dict) + 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 def _add_parameter_to_cache_dict( args ): @@ -175,58 +318,133 @@ def _add_parameter_to_cache_dict( args ): class nbDnaScheme100Mg(AbstractNbDnaScheme): - def get_package_cache_file(self): - return get_resource_path("nbPot.jj-nar-dna-pmf-100Mg.npz") + def get_package_cache_file(self): + return get_resource_path("nbPot.rau_refined_100Mg.dat") + + def load_rau_pressure(self): + data = np.loadtxt("rau-data-100Mg.dat") + x = data[:,0] + y0 = data[:,1] + y = (10**y0) * 9.8692327e-07 # convert dyne/cm^2 to atm + return x,y + def load_pmf(self): d = np.loadtxt(get_resource_path("jj-nar-dna-pmf-100Mg.dat")) - x0 = d[:,1] + _dxParam + x0 = d[:,1] y0 = d[:,0] # kcal/mol for 10bp with 10bp, according to JY - y0 = y0 - np.mean(y0[x0>(38.5 + _dxParam)]) # set 0 to tail of potential - y0 = savgol(y0, int(5.0/(x0[1]-x0[0])), 3) # smooth potential + y0 = y0 - np.mean(y0[x0 > 38.5]) # set 0 to tail of potential + filter_points = int(2.5/(x0[1]-x0[0]))*2 + 1 + y0 = savgol(y0, filter_points, 3) # smooth potential return x0,y0 - def get_cache_file_for_pair(self,key): - filename = "nbPot-100Mg-{}-{}.npz".format(*key) - return CACHE_DIR / filename + def load_bead_distributions(self): + from bead_dist_data import helix_bins, bead_bins + from bead_dist_data import helix_centers, bead_centers + import bead_dist_data as bdd + + self.bead_distribution_x = x = bdd.bead_centers + + all_x = [] + all_y = [] + for i in range(0,len(bdd.helix_centers),1): + y = bdd.bead_dists_for_helix_dist[i] + + # if y.sum() == 0: continue + if bdd.helix_centers[i] < 20: continue + all_x.append( bdd.helix_centers[i] ) + filter_points = int(5/(x[1]-x[0]))*2 + 1 + y = savgol( y, filter_points, 3) # smooth and normalize data + y[y<0] = 0 # ensure positive + y = 10*20 * y/np.trapz(y,x) # normalize + all_y.append( y ) + + self.bead_distribution_y = interp1d( np.array(all_x), np.array(all_y), + axis=0, + kind='linear', + bounds_error = False, fill_value="extrapolate", + assume_sorted=True) + class nbDnaScheme20Mg(AbstractNbDnaScheme): - def get_package_cache_file(self): - return get_resource_path("nbPot.jj-nar-dna-pmf-20Mg-200Na.npz") + def get_package_cache_file(self): + return get_resource_path("nbPot.rau_refined_20Mg_200Na.dat") + + def load_rau_pressure(self): + data = np.loadtxt("rau-data-20Mg.dat") + x = data[:,0] + y0 = data[:,1] + y = (10**y0) * 9.8692327e-07 # convert dyne/cm^2 to atm + return x,y + def load_pmf(self): d = np.loadtxt(get_resource_path("jj-nar-dna-pmf-20Mg-200Na.dat")) - x0 = d[:,1] + _dxParam + x0 = d[:,1] y0 = d[:,0] # kcal/mol for 10bp with 10bp, according to JY - y0 = y0 - np.mean(y0[x0>(38.5 + _dxParam)]) # set 0 to tail of potential - y0 = savgol(y0, int(5.0/(x0[1]-x0[0])), 3) # smooth potential + y0 = y0 - np.mean(y0[x0 > 38.5]) # set 0 to tail of potential + filter_points = int(2.5/(x0[1]-x0[0]))*2 + 1 + y0 = savgol(y0, filter_points, 3) # smooth potential return x0,y0 - def get_cache_file_for_pair(self,key): - filename = "nbPot-20Mg-200Na-{}-{}.npz".format(*key) - return CACHE_DIR / filename + def load_bead_distributions(self): + import bead_dist_data as bdd -nbDnaScheme = nbDnaScheme100Mg() + self.bead_distribution_centers = bdd.bead_centers + self.bead_distribution_radii = bdd.radii + self.bead_distribution_counts = bdd.bead_dists + ... + + + for i in range(0,len(bdd.helix_centers),1): + y = bdd.bead_dists_for_helix_dist[i] + + # if y.sum() == 0: continue + if bdd.helix_centers[i] < 20: continue + all_x.append( bdd.helix_centers[i] ) + filter_points = int(5/(x[1]-x[0]))*2 + 1 + y = savgol( y, filter_points, 3) # smooth and normalize data + y[y<0] = 0 # ensure positive + y = 10*20 * y/np.trapz(y,x) # normalize + all_y.append( y ) -def _plot_things(): - np.savetxt("jj-filtered.dat", np.array((x0,y0)).T) - x = np.arange(0, 50, 0.1) - ## run some tests - for i in (0.5,1,1.05,2,3.333,5): - for j in (1,1.05,1.1,2,3.333, 4,5): - if i > j: continue - - # y = (10.0/i)*integrate_potential(nbPot_full, x, np.arange(-20,20)*(3.4*j) , i, j) - # np.savetxt("test1-{}-{}.dat".format(i,j), np.array((x,y)).T), + self.bead_distribution_y = interp1d( np.array(all_x), np.array(all_y), + axis=0, + bounds_error = False, fill_value="extrapolate", + assume_sorted=True) - y = (10.0/i)*integrate_potential(nbPot, x, np.arange(-20,20)*(3.4*j) , i, j) - np.savetxt("test2-{}-{}.dat".format(i,j), np.array((x,y)).T), + +# nbDnaScheme100MgObj = nbDnaScheme100Mg() +nbDnaScheme = nbDnaScheme20MgObj = nbDnaScheme20Mg() if __name__ == "__main__": # import cProfile # cProfile.run("_run()") # _generate_cache() + # tmp = nbDnaScheme20Mg() + # tmp._write_cache() + # pass + tmp = nbDnaScheme20Mg() - tmp._write_cache() - pass + + # dR = 1 + # for R in np.arange(22,35,2): + # x,ys = tmp.get_bead_distributions(np.array([R-0.5*dR,R+0.5*dR])) + # y1,y2 = ys + # d_rho_dR = (y2-y1)/dR + # # plt.plot(x,d_rho_dR) + + # x = np.arange(20,50,1) + # tmp.nbPot(x,1,1) + + + # plt.gca().set_xlim((10,40)) + # plt.savefig("test.pdf") + + # x = np.arange(20,50,1) + # tmp.nbPot(x,1,1) + + nb = nbDnaScheme20MgObj + x = np.arange(10,50,1) + u = nb.nbPot(x,1,1) diff --git a/mrdna/resources/nbPot.jj-nar-dna-pmf-100Mg.npz b/mrdna/resources/nbPot.jj-nar-dna-pmf-100Mg.npz deleted file mode 100644 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