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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 > **Parameters:**
11 >  * *time* (numpy array) -- Time points, usually in seconds.
12 >  * *data* (numpy array) -- Initial SPR signal values.
13 >  * *params* (dictionary of dictionaries) -- Model parameter description.  
14 >  
15 > **Returns:** numpy array of calculated SPR signal values.
16 >
17 > The dictionary keys are the names of model parameters
18 > (e.g. 'rmax' for maximal response, or 'kon' for kinetic on-rate).
19 > Each model parameter is described by a subdictionary containing four entries.
20 >
21 >  * ``'value'``  The current value of the parameter.
22 >  * ``'min'``    The minimum allowable value.
23 >  * ``'max'``    The maximum allowable value.
24 >  * ``'fixed'``  Either 'float', 'fixed', or a reference to another ROI.
25 >
26 > The ``min``, ``max``, and ``fixed`` keys are used during automatic curve-fitting.
27 > A fixed parameter is not allowed to change, while a float parameter is adjusted
28 > until the least-squares algorithm has minimized the sum-squared error.
29 > The *fixed* parameter may also be an integer, in which case it is fixed to
30 > the value of a parameter of the same name in another ROI.  
31 >
32 > The model function returns an array of values obtained by numerical integration.
33 > The model is represented by differential equations and integrated using the
34 > rectangle rule or, preferentially, using the trapezoidal rule.
35 >
36 > .. moduleauthor:: Christopher Lausted,
37 >                  Institute for Systems Biology,
38 >                  OSPRAI developers.
39 >                  
40 > Examples::
41 >
42 >  >>> import mdl_module as mdl
43 >  >>> import numpy as np
44 >  >>> times = np.arange(100)
45 >  >>> data = np.zeros(100)
46 >  >>>
47 >  >>> param1 = dict(rate=dict(value=1.0, min=-100.0, max=100.0, fixed=True))
48 >  >>> data1 = drift(time, data, param1)
49 >  >>>
50 >  >>> param2 = {'t1': {'value':30.0, 'min':30.0, 'max':30.0, 'fixed':True} }
51 >  >>> param2['rmax'] =  {'value': 100.0}
52 >  >>> param2['conc'] =  {'value': 1e-6}
53 >  >>> param2['kon'] =   {'value': 2e4}
54 >  >>> param2['t2'] =    {'value': 150.0}
55 >  >>> param2['koff'] =  {'value': 1e-3}
56 >  >>> param2['t3'] =    {'value': 270.0}
57 >  >>> data2 = simple1to1(time, data, param2)
58   """
59 < __version__ = "100421"
59 > __version__ = "110216"
60  
61  
62   ## Import libraries
# Line 25 | Line 69
69      This function simply models a constant signal drift in units/second.
70      It requires numpy arrays of times and starting data values,
71      It only requires one parameter in the params list.
72 <    params['rate']['value']
72 >    
73 >    ``params['rate']['value']``
74      """
75      y = np.zeros(len(time), dtype=float)
76      try:
# Line 41 | Line 86
86          y[i] = y[i-1] + dy
87          
88      return y
89 +    ## End of drift() function.
90  
91  
92   def simple1to1(time, data, params):
93      """
94 <    This function simply models a 1:1 interaction
95 <    It requires numpy arrays of times and starting data values,
96 <    params['t1']['value']   is time of injection for binding
97 <    params['rmax']['value'] is maximum response.
98 <    params['conc']['value'] is time of concentration of analyte
99 <    params['kon']['value']  is on-rate of analyte
100 <    params['t2']['value']   is time of end binding / begin washing
101 <    params['koff']['value']  is off-rate of analyte
102 <    params['t3']['value']   is time end of washing / data fitting.
94 >    This function simply models a 1:1 interaction.
95 >    The model parameters are described in the table below.
96 >    
97 >    Model::
98 >    
99 >      [A] + [L] --kon--> [AL]
100 >      [A] + [L] <-koff-- [AL]
101 >    
102 >    Derivation::
103 >    
104 >      d[AL]/dt = kon*[A]*[L] - koff*[AL]
105 >      y = [AL]
106 >      (rmax-y) = [L]
107 >      conc = [A]
108 >      rmax = [AL] + [L]
109 >      dy/dt = conc*kon*(rmax-y) - koff*y
110 >    
111 >    ======================= ============================================
112 >    Model Parameter         Description
113 >    ======================= ============================================
114 >    params['t1']['value']   time of injection for binding, (s)
115 >    params['rmax']['value'] maximum response, (RIU)
116 >    params['conc']['value'] concentration of analyte [A], (M)
117 >    params['kon']['value']  on-rate of analyte, (1/Ms)
118 >    params['t2']['value']   time of end binding & begin washing, (s)
119 >    params['koff']['value'] off-rate of analyte, (1/s)
120 >    params['t3']['value']   time end of washing & data fitting, (s)
121 >    ----------------------- --------------------------------------------
122 >    *Optional*            
123 >    params['cofa']['value'] concentration factor, (1/dilution factor)
124 >    ======================= ============================================
125 >    
126      """
127 +    
128      ## Skip parameter validation steps for now.
129 <    t1 = params['t1']['value']
130 <    rmax = params['rmax']['value']
131 <    conc = params['conc']['value']
132 <    kon = params['kon']['value']
133 <    t2 = params['t2']['value']
134 <    koff = params['koff']['value']
135 <    t3 = params['t3']['value']
129 >    t1 = float(params['t1']['value'])
130 >    rmax = float(params['rmax']['value'])
131 >    conc = float(params['conc']['value'])
132 >    kon = float(params['kon']['value'])
133 >    t2 = float(params['t2']['value'])
134 >    koff = float(params['koff']['value'])
135 >    t3 = float(params['t3']['value'])
136 >    if ('cofa' in params.keys()):
137 >        conc *= float(params['cofa']['value'])
138      
139      y = np.zeros(len(time), dtype=float)
140      base = y[0] = data[0]  ## Baseline SPR signal.
141      
142      ## Must iterate through data, numerical integration.
143      for i in range(1,len(time)):
144 +        dt = time[i] - time[i-1]
145 +        ## Treat function as having three separate phases.
146          if (time[i] <= t1):
147              ## Pre-binding phase.
148              base = y[i] = data[i]
# Line 77 | Line 151
151              yb = y[i-1] - base
152              dy = conc*kon*(rmax-yb) - koff*yb
153              if (abs(y[i-1]) > 999999999): dy = 0  ## Is this useful?
154 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
154 >            y[i] = y[i-1] + dy*dt
155          elif (t2 < time[i] <= t3):
156 <            ## Dissociation
156 >            ## Dissociation (conc=0)
157              yb = y[i-1]-base
158              dy = 0 - koff*yb
159 <            y[i] = y[i-1] + dy * (time[i] - time[i-1])
159 >            y[i] = y[i-1] + dy*dt
160              
161      return y
162 +    """End of simple1to1() function"""
163 +
164 +
165 + def simple1to1_mtl(time, data, params):
166 +    """
167 +    This function simply models a 1:1 interaction with mass transport limitation.
168 +    The model parameters are described in the table below.
169 +    
170 +    Model::
171 +    
172 +      [Abulk]  --km->  [Asurf] + [L]  --kon-->  [AL]
173 +      [Abulk]  <-km--  [Asurf] + [L]  <-koff--  [AL]
174 +    
175 +    Derivation::
176 +    
177 +      d[AL]/dt = (kon*[A]*[L] - koff*[AL]) / (1 + kon*[L]/kmtl)
178 +      y = [AL]
179 +      (rmax-y) = [L]
180 +      conc = [Abulk]
181 +      rmax = [AL] + [L]
182 +      dy/dt  = (kon*conc*(rmax-y) - koff*y) / (1 + kon*(rmax-y)/kmtl)
183 +    
184 +    ======================= ============================================
185 +    Model Parameter         Description
186 +    ======================= ============================================
187 +    params['t1']['value']   time of injection for binding, (s)
188 +    params['rmax']['value'] maximum response, (RIU)
189 +    params['conc']['value'] concentration of analyte [Abulk], (M)
190 +    params['kon']['value']  on-rate of analyte, (1/Ms)
191 +    params['t2']['value']   time of end binding & begin washing, (s)
192 +    params['koff']['value'] off-rate of analyte, (1/s)
193 +    params['t3']['value']   time end of washing & data fitting, (s)
194 +    params['kmtl']['value'] rate of diffusion,  (RIU/Ms)
195 +    ----------------------- --------------------------------------------
196 +    *Optional*            
197 +    params['cofa']['value'] concentration factor, (1/dilution factor)
198 +    ======================= ============================================
199 +    
200 +    """
201 +    
202 +    ## Skip parameter validation steps for now.
203 +    t1 = params['t1']['value']
204 +    rmax = params['rmax']['value']
205 +    conc = params['conc']['value']
206 +    kon = params['kon']['value']
207 +    t2 = params['t2']['value']
208 +    koff = params['koff']['value']
209 +    t3 = params['t3']['value']
210 +    kmtl = params['kmtl']['value']
211 +    if ('cofa' in params.keys()):
212 +        conc *= float(params['cofa']['value'])
213 +        
214 +    ## Initialize variables.
215 +    stat = {}  ## Error status dictionary.
216 +    y = np.zeros(len(time), dtype=float)
217 +    base = y[0] = data[0]  ## Baseline SPR signal.
218 +    
219 +    ## Error checks.
220 +    if (kmtl<=0):
221 +        ## Avoid div/0, assume user wants no mass transport limitation.
222 +        stat['kmtl must be > 0'] = True
223 +        kmtl = 1e40  ## An arbitrary very large number.
224 +    
225 +    ## Must iterate through data, numerical integration.
226 +    for i in range(1,len(time)):
227 +        dt = time[i] - time[i-1]
228 +        ## Treat function as having three separate phases.
229 +        if (time[i] <= t1):
230 +            ## Pre-binding phase.
231 +            base = y[i] = data[i]
232 +        elif (t1 < time[i] <= t2):
233 +            ## Binding phase
234 +            yb = y[i-1] - base
235 +            dy = (conc*kon*(rmax-yb) - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
236 +            ## Check for integration errors producing wild results.
237 +            if (abs(y[i-1]) > 9e9): dy = 0; stat['y>9e9'] = True
238 +            y[i] = y[i-1] + dy*dt
239 +        elif (t2 < time[i] <= t3):
240 +            ## Dissociation (conc=0)
241 +            yb = y[i-1] - base
242 +            dy = (0 - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
243 +            y[i] = y[i-1] + dy*dt
244 +    
245 +    if (len(stat.keys()) > 0): print "Errors in simple1to1:", stat.keys()
246 +    
247 +    return y
248 +    """End of simple1to1_mtl() function"""
249 +
250 +
251  
252 + ################################# End of module ###############################

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