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# Line 1 | Line 1
1   """
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)
6 <
7 < Example:
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
2 > mdl_module
3 > -------------------------------------------------------------------------------
4 >
5 > **Example model functions module for SPRI data.**
6 > Just a few simple, common interaction models will go here.
7 > In the future, each new model will go in its own module/file.
8 > Each model is a function taking three parameters
9 >
10 > 1. *time*    An array of time values, usually in seconds.
11 > 2. *data*    An array of initial SPR signal values.
12 > 3. *params*  A dictionary of dictionaries.  
13 >
14 > The dictionary keys are the names of model parameters
15 > (e.g. 'rmax' for maximal response, or 'kon' for kinetic on-rate).
16 > Each model parameter is described by a subdictionary containing four entries.
17 >
18 > 1. *'value'*  The current value of the parameter.
19 > 2. *'min'*    The minimum allowable value.
20 > 3. *'max'*    The maximum allowable value.
21 > 4. *'fixed'*  Either 'float', 'fixed', or a reference to another ROI.
22 >
23 > The *min*, *max*, and *fixed* keys are used during automatic curve-fitting.
24 > A fixed parameter is not allowed to change, while a float parameter is adjusted
25 > until the least-squares algorithm has minimized the sum-squared error.
26 > The *fixed* parameter may also be an integer, in which case it is fixed to
27 > the value of a parameter of the same name in another ROI.  
28 >
29 > The model function returns an array of values obtained by numerical integration.
30 > The model is represented by differential equations and integrated using the
31 > rectangle rule or, preferentially, using the trapezoidal rule.
32 >
33 > .. moduleauthor:: Christopher Lausted,
34 >                  Institute for Systems Biology,
35 >                  OSPRAI developers.
36 >                  
37 > Examples::
38 >
39 >  >>> import mdl_module as mdl
40 >  >>> import numpy as np
41 >  >>> times = np.arange(100)
42 >  >>> data = np.zeros(100)
43 >  >>>
44 >  >>> params1 = dict(rate=dict(value=1.0, min=-100.0, max=100.0, fixed=True))
45 >  >>> data1 = drift(time, data, param1)
46 >  >>>
47 >  >>> param2 = {'t1': {'value':30.0, 'min':30.0, 'max':30.0, 'fixed':True} }
48 >  >>> param2['rmax'] =  {'value': 100.0}
49 >  >>> param2['conc'] =  {'value': 1e-6}
50 >  >>> param2['kon'] =   {'value': 2e4}
51 >  >>> param2['t2'] =    {'value': 150.0}
52 >  >>> param2['koff'] =  {'value': 1e-3}
53 >  >>> param2['t3'] =    {'value': 270.0}
54 >  >>> data2 = simple1to1(time, data, param2)
55   """
56 < __version__ = "100421"
56 > __version__ = "110215"
57  
58  
59   ## Import libraries
# Line 25 | Line 66
66      This function simply models a constant signal drift in units/second.
67      It requires numpy arrays of times and starting data values,
68      It only requires one parameter in the params list.
69 +    
70      params['rate']['value']
71 +    
72 +    :param time: Time points.
73 +    :type time: numpy array
74 +    :param data: SPR signal values.
75 +    :type data: numpy array
76 +    :param params: Binding model parameter description.
77 +    :type params: dictionary of dictionaries
78 +    :returns: numpy array
79      """
80      y = np.zeros(len(time), dtype=float)
81      try:
# Line 41 | Line 91
91          y[i] = y[i-1] + dy
92          
93      return y
94 +    ## End of drift() function.
95  
96  
97   def simple1to1(time, data, params):
98      """
99 <    This function simply models a 1:1 interaction
100 <    It requires numpy arrays of times and starting data values,
101 <    params['t1']['value']   is time of injection for binding
102 <    params['rmax']['value'] is maximum response.
103 <    params['conc']['value'] is time of concentration of analyte
104 <    params['kon']['value']  is on-rate of analyte
105 <    params['t2']['value']   is time of end binding / begin washing
106 <    params['koff']['value']  is off-rate of analyte
107 <    params['t3']['value']   is time end of washing / data fitting.
99 >    This function simply models a 1:1 interaction.
100 >    
101 >    Model::
102 >    
103 >      [A] + [L] --kon--> [AL]
104 >      [A] + [L] <-koff-- [AL]
105 >    
106 >    Derivation::
107 >    
108 >      d[AL]/dt = kon*[A]*[L] - koff*[AL]
109 >      y = [AL]
110 >      (rmax-y) = [L]
111 >      conc = [A]
112 >      rmax = [AL] + [L]
113 >      dy/dt = conc*kon*(rmax-y) - koff*y
114 >    
115 >    ======================= ============================================
116 >    Model Parameter         Description
117 >    ======================= ============================================
118 >    params['t1']['value']   time of injection for binding, (s)
119 >    params['rmax']['value'] maximum response, (RIU)
120 >    params['conc']['value'] concentration of analyte [A], (M)
121 >    params['kon']['value']  on-rate of analyte, (1/Ms)
122 >    params['t2']['value']   time of end binding & begin washing, (s)
123 >    params['koff']['value'] off-rate of analyte, (1/s)
124 >    params['t3']['value']   time end of washing & data fitting, (s)
125 >    ----------------------- --------------------------------------------
126 >    *Optional*            
127 >    params['cofa']['value'] concentration factor, (1/dilution factor)
128 >    ======================= ============================================
129 >    
130      """
131 +    
132      ## Skip parameter validation steps for now.
133 <    t1 = params['t1']['value']
134 <    rmax = params['rmax']['value']
135 <    conc = params['conc']['value']
136 <    kon = params['kon']['value']
137 <    t2 = params['t2']['value']
138 <    koff = params['koff']['value']
139 <    t3 = params['t3']['value']
133 >    t1 = float(params['t1']['value'])
134 >    rmax = float(params['rmax']['value'])
135 >    conc = float(params['conc']['value'])
136 >    kon = float(params['kon']['value'])
137 >    t2 = float(params['t2']['value'])
138 >    koff = float(params['koff']['value'])
139 >    t3 = float(params['t3']['value'])
140 >    if ('cofa' in params.keys()):
141 >        conc *= float(params['cofa']['value'])
142      
143      y = np.zeros(len(time), dtype=float)
144      base = y[0] = data[0]  ## Baseline SPR signal.
145      
146      ## Must iterate through data, numerical integration.
147      for i in range(1,len(time)):
148 +        dt = time[i] - time[i-1]
149 +        ## Treat function as having three separate phases.
150          if (time[i] <= t1):
151              ## Pre-binding phase.
152              base = y[i] = data[i]
# Line 77 | Line 155
155              yb = y[i-1] - base
156              dy = conc*kon*(rmax-yb) - koff*yb
157              if (abs(y[i-1]) > 999999999): dy = 0  ## Is this useful?
158 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
158 >            y[i] = y[i-1] + dy*dt
159          elif (t2 < time[i] <= t3):
160 <            ## Dissociation
160 >            ## Dissociation (conc=0)
161              yb = y[i-1]-base
162              dy = 0 - koff*yb
163 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
163 >            y[i] = y[i-1] + dy*dt
164              
165      return y
166 +    """End of simple1to1() function"""
167 +
168 +
169 + def simple1to1_mtl(time, data, params):
170 +    """
171 +    This function simply models a 1:1 interaction with mass transport limitation.
172 +    
173 +    Model::
174 +    
175 +      [Abulk]  --km->  [Asurf] + [L]  --kon-->  [AL]
176 +      [Abulk]  <-km--  [Asurf] + [L]  <-koff--  [AL]
177 +    
178 +    Derivation::
179 +    
180 +      d[AL]/dt = (kon*[A]*[L] - koff*[AL]) / (1 + kon*[L]/kmtl)
181 +      y = [AL]
182 +      (rmax-y) = [L]
183 +      conc = [Abulk]
184 +      rmax = [AL] + [L]
185 +      dy/dt  = (kon*conc*(rmax-y) - koff*y) / (1 + kon*(rmax-y)/kmtl)
186 +    
187 +    ======================= ============================================
188 +    Model Parameter         Description
189 +    ======================= ============================================
190 +    params['t1']['value']   time of injection for binding, (s)
191 +    params['rmax']['value'] maximum response, (RIU)
192 +    params['conc']['value'] concentration of analyte [Abulk], (M)
193 +    params['kon']['value']  on-rate of analyte, (1/Ms)
194 +    params['t2']['value']   time of end binding & begin washing, (s)
195 +    params['koff']['value'] off-rate of analyte, (1/s)
196 +    params['t3']['value']   time end of washing & data fitting, (s)
197 +    params['kmtl']['value'] rate of diffusion,  (RIU/Ms)
198 +    ----------------------- --------------------------------------------
199 +    *Optional*            
200 +    params['cofa']['value'] concentration factor, (1/dilution factor)
201 +    ======================= ============================================
202 +    
203 +    """
204 +    
205 +    ## Skip parameter validation steps for now.
206 +    t1 = params['t1']['value']
207 +    rmax = params['rmax']['value']
208 +    conc = params['conc']['value']
209 +    kon = params['kon']['value']
210 +    t2 = params['t2']['value']
211 +    koff = params['koff']['value']
212 +    t3 = params['t3']['value']
213 +    kmtl = params['kmtl']['value']
214 +    if ('cofa' in params.keys()):
215 +        conc *= float(params['cofa']['value'])
216 +        
217 +    ## Initialize variables.
218 +    stat = {}  ## Error status dictionary.
219 +    y = np.zeros(len(time), dtype=float)
220 +    base = y[0] = data[0]  ## Baseline SPR signal.
221 +    
222 +    ## Error checks.
223 +    if (kmtl<=0):
224 +        ## Avoid div/0, assume user wants no mass transport limitation.
225 +        stat['kmtl must be > 0'] = True
226 +        kmtl = 1e40  ## An arbitrary very large number.
227 +    
228 +    ## Must iterate through data, numerical integration.
229 +    for i in range(1,len(time)):
230 +        dt = time[i] - time[i-1]
231 +        ## Treat function as having three separate phases.
232 +        if (time[i] <= t1):
233 +            ## Pre-binding phase.
234 +            base = y[i] = data[i]
235 +        elif (t1 < time[i] <= t2):
236 +            ## Binding phase
237 +            yb = y[i-1] - base
238 +            dy = (conc*kon*(rmax-yb) - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
239 +            ## Check for integration errors producing wild results.
240 +            if (abs(y[i-1]) > 9e9): dy = 0; stat['y>9e9'] = True
241 +            y[i] = y[i-1] + dy*dt
242 +        elif (t2 < time[i] <= t3):
243 +            ## Dissociation (conc=0)
244 +            yb = y[i-1] - base
245 +            dy = (0 - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
246 +            y[i] = y[i-1] + dy*dt
247 +    
248 +    if (len(stat.keys()) > 0): print "Errors in simple1to1:", stat.keys()
249 +    
250 +    return y
251 +    """End of simple1to1_mtl() function"""
252 +
253 +
254  
255 + ################################# End of module ###############################

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