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# Line 2 | Line 2
2   mdl: Example model functions module for SPRI data.
3   Christopher Lausted, Institute for Systems Biology,
4   OSPRAI developers
5 < Last modified on 100421 (yymmdd)
5 > Last modified on 100511 (yymmdd)
6  
7 < Example:
7 > Examples:
8   #import mdl_module as mdl
9 < #params = {'Rate': {'value':1, 'min':-100.0, 'max':100.0, 'fixed':False} }
10 < #params = dict(Rate = dict(value=1, min=0, max=10, fixed=False))
11 < #times = range(100)
12 < #data1 = drift(time, data0, params)
13 < print data1
9 > #import numpy as np
10 > #times = np.arange(100)
11 > #data = np.zeros(100)
12 > #
13 > #params1 = dict(rate=dict(value=1.0, min=-100.0, max=100.0, fixed=True))
14 > #data1 = drift(time, data, param1)
15 > #
16 > #param2 = {'t1': {'value':30.0, 'min':30.0, 'max':30.0, 'fixed':True} }
17 > #param2['rmax'] =  {'value': 100.0}
18 > #param2['conc'] =  {'value': 1e-6}
19 > #param2['kon'] =   {'value': 2e4}
20 > #param2['t2'] =    {'value': 150.0}
21 > #param2['koff'] =  {'value': 1e-3}
22 > #param2['t3'] =    {'value': 270.0}
23 > #data2 = simple1to1(time, data, param2)
24   """
25 < __version__ = "100421"
25 > __version__ = "100511"
26  
27  
28   ## Import libraries
# Line 41 | Line 51
51          y[i] = y[i-1] + dy
52          
53      return y
54 +    ## End of drift() function.
55  
56  
57   def simple1to1(time, data, params):
58      """
59 <    This function simply models a 1:1 interaction
60 <    It requires numpy arrays of times and starting data values,
61 <    params['t1']['value']   is time of injection for binding
62 <    params['rmax']['value'] is maximum response.
63 <    params['conc']['value'] is time of concentration of analyte
64 <    params['kon']['value']  is on-rate of analyte
65 <    params['t2']['value']   is time of end binding / begin washing
66 <    params['koff']['value']  is off-rate of analyte
67 <    params['t3']['value']   is time end of washing / data fitting.
59 >    This function simply models a 1:1 interaction.
60 >    [A] + [L] --kon--> [AL]
61 >    [A] + [L] <-koff-- [AL]
62 >    
63 >    It requires numpy arrays of times and starting data values.
64 >    params['t1']['value']   is time of injection for binding, (s)
65 >    params['rmax']['value'] is maximum response, (RIU)
66 >    params['conc']['value'] is concentration of analyte [A], (M)
67 >    params['kon']['value']  is on-rate of analyte, (1/Ms)
68 >    params['t2']['value']   is time of end binding & begin washing, (s)
69 >    params['koff']['value']  is off-rate of analyte, (1/s)
70 >    params['t3']['value']   is time end of washing & data fitting, (s)
71      """
72      ## Skip parameter validation steps for now.
73      t1 = params['t1']['value']
# Line 62 | Line 76
76      kon = params['kon']['value']
77      t2 = params['t2']['value']
78      koff = params['koff']['value']
79 <    t3 = params['t3']['value']
79 >    t3 = params['t3']['value']
80 >    
81 >    """
82 >    Derivation:
83 >    d[AL]/dt = kon*[A]*[L] - koff*[AL]
84 >    y = [AL]
85 >    (rmax-y) = [L]
86 >    conc = [A]
87 >    rmax = [AL] + [L]
88 >    dy/dt = conc*kon*(rmax-y) - koff*y
89 >    """
90      
91      y = np.zeros(len(time), dtype=float)
92      base = y[0] = data[0]  ## Baseline SPR signal.
93      
94      ## Must iterate through data, numerical integration.
95      for i in range(1,len(time)):
96 +        dt = time[i] - time[i-1]
97 +        ## Treat function as having three separate phases.
98          if (time[i] <= t1):
99              ## Pre-binding phase.
100              base = y[i] = data[i]
# Line 77 | Line 103
103              yb = y[i-1] - base
104              dy = conc*kon*(rmax-yb) - koff*yb
105              if (abs(y[i-1]) > 999999999): dy = 0  ## Is this useful?
106 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
106 >            y[i] = y[i-1] + dy*dt
107          elif (t2 < time[i] <= t3):
108 <            ## Dissociation
108 >            ## Dissociation (conc=0)
109              yb = y[i-1]-base
110              dy = 0 - koff*yb
111 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
111 >            y[i] = y[i-1] + dy*dt
112              
113      return y
114 +    ## End of simple1to1() function
115 +
116 +
117 + def simple1to1_mtl(time, data, params):
118 +    """
119 +    This function simply models a 1:1 interaction with mass transport limitation.
120 +    [Abulk]  --km->  [Asurf] + [L]  --kon-->  [AL]
121 +    [Abulk]  <-km--  [Asurf] + [L]  <-koff--  [AL]
122 +    
123 +    It requires numpy arrays of times and starting data values,
124 +    params['t1']['value']   is time of injection for binding, (s)
125 +    params['rmax']['value'] is maximum response, (RIU)
126 +    params['conc']['value'] is concentration of analyte [Abulk], (M)
127 +    params['kon']['value']  is on-rate of analyte, (1/Ms)
128 +    params['t2']['value']   is time of end binding & begin washing, (s)
129 +    params['koff']['value'] is off-rate of analyte, (1/s)
130 +    params['t3']['value']   is time end of washing & data fitting, (s)
131 +    params['kmtl']['value'] is rate of diffusion,  (RIU/Ms)
132 +    """
133 +    ## Skip parameter validation steps for now.
134 +    t1 = params['t1']['value']
135 +    rmax = params['rmax']['value']
136 +    conc = params['conc']['value']
137 +    kon = params['kon']['value']
138 +    t2 = params['t2']['value']
139 +    koff = params['koff']['value']
140 +    t3 = params['t3']['value']
141 +    kmtl = params['kmtl']['value']
142 +    
143 +    """
144 +    Derivation:
145 +    d[AL]/dt = (kon*[A]*[L] - koff*[AL]) / (1 + kon*[L]/kmtl)
146 +    y = [AL]
147 +    (rmax-y) = [L]
148 +    conc = [Abulk]
149 +    rmax = [AL] + [L]
150 +    dy/dt  = (kon*conc*(rmax-y) - koff*y) / (1 + kon*(rmax-y)/kmtl)
151 +    """
152 +    
153 +    stat = {}  ## Error status dictionary.
154 +    y = np.zeros(len(time), dtype=float)
155 +    base = y[0] = data[0]  ## Baseline SPR signal.
156 +    
157 +    ## Error checks.
158 +    if (kmtl<=0):
159 +        ## Avoid div/0, assume user wants no mass transport limitation.
160 +        stat['kmtl must be > 0'] = True
161 +        kmtl = 1e40  ## An arbitrary very large number.
162 +    
163 +    ## Must iterate through data, numerical integration.
164 +    for i in range(1,len(time)):
165 +        dt = time[i] - time[i-1]
166 +        ## Treat function as having three separate phases.
167 +        if (time[i] <= t1):
168 +            ## Pre-binding phase.
169 +            base = y[i] = data[i]
170 +        elif (t1 < time[i] <= t2):
171 +            ## Binding phase
172 +            yb = y[i-1] - base
173 +            dy = (conc*kon*(rmax-yb) - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
174 +            ## Check for integration errors producing wild results.
175 +            if (abs(y[i-1]) > 9e9): dy = 0; stat['y>9e9'] = True
176 +            y[i] = y[i-1] + dy*dt
177 +        elif (t2 < time[i] <= t3):
178 +            ## Dissociation (conc=0)
179 +            yb = y[i-1] - base
180 +            dy = (0 - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
181 +            y[i] = y[i-1] + dy*dt
182 +    
183 +    if (len(stat.keys()) > 0): print "Errors in simple1to1:", stat.keys()
184 +    
185 +    return y
186 +    ## End of simple1to1_mtl() function
187 +
188 +
189  
190 + ################################# End of module #################################

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