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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diff --git a/mrdna/resources/nbPot.rau_refined_20Mg_200Na.dat b/mrdna/resources/nbPot.rau_refined_20Mg_200Na.dat
new file mode 100644
index 0000000..0bfb24d
--- /dev/null
+++ b/mrdna/resources/nbPot.rau_refined_20Mg_200Na.dat
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GitLab