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"""
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mdl: Example model functions module for SPRI data.
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Christopher Lausted, Institute for Systems Biology,
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OSPRAI developers
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Last modified on 100511 (yymmdd)
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Examples:
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#import mdl_module as mdl
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#import numpy as np
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#times = np.arange(100)
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#data = np.zeros(100)
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#
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#params1 = dict(rate=dict(value=1.0, min=-100.0, max=100.0, fixed=True))
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#data1 = drift(time, data, param1)
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#
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#param2 = {'t1': {'value':30.0, 'min':30.0, 'max':30.0, 'fixed':True} }
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#param2['rmax'] = {'value': 100.0}
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#param2['conc'] = {'value': 1e-6}
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#param2['kon'] = {'value': 2e4}
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#param2['t2'] = {'value': 150.0}
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#param2['koff'] = {'value': 1e-3}
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#param2['t3'] = {'value': 270.0}
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#data2 = simple1to1(time, data, param2)
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"""
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__version__ = "100511"
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## Import libraries
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import numpy as np
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from copy import deepcopy
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def drift(time, data, params):
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"""
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This function simply models a constant signal drift in units/second.
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It requires numpy arrays of times and starting data values,
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It only requires one parameter in the params list.
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params['rate']['value']
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"""
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y = np.zeros(len(time), dtype=float)
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try:
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rate = params['rate']['value']
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except KeyError:
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print "Error: Rate parameter not supplied to drift() model."
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return y
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## Numerical integration.
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y[0] = data[0]
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for i in range(1,len(time)):
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dy = rate * (time[i]-time[i-1])
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y[i] = y[i-1] + dy
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return y
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## End of drift() function.
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def simple1to1(time, data, params):
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"""
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This function simply models a 1:1 interaction.
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[A] + [L] --kon--> [AL]
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[A] + [L] <-koff-- [AL]
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It requires numpy arrays of times and starting data values.
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params['t1']['value'] is time of injection for binding, (s)
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params['rmax']['value'] is maximum response, (RIU)
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params['conc']['value'] is concentration of analyte [A], (M)
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params['kon']['value'] is on-rate of analyte, (1/Ms)
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params['t2']['value'] is time of end binding & begin washing, (s)
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params['koff']['value'] is off-rate of analyte, (1/s)
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params['t3']['value'] is time end of washing & data fitting, (s)
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"""
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## Skip parameter validation steps for now.
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t1 = params['t1']['value']
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rmax = params['rmax']['value']
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conc = params['conc']['value']
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kon = params['kon']['value']
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t2 = params['t2']['value']
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koff = params['koff']['value']
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t3 = params['t3']['value']
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"""
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Derivation:
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d[AL]/dt = kon*[A]*[L] - koff*[AL]
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y = [AL]
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(rmax-y) = [L]
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conc = [A]
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rmax = [AL] + [L]
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dy/dt = conc*kon*(rmax-y) - koff*y
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"""
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y = np.zeros(len(time), dtype=float)
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base = y[0] = data[0] ## Baseline SPR signal.
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## Must iterate through data, numerical integration.
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for i in range(1,len(time)):
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dt = time[i] - time[i-1]
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## Treat function as having three separate phases.
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if (time[i] <= t1):
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## Pre-binding phase.
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base = y[i] = data[i]
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elif (t1 < time[i] <= t2):
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## Binding phase
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yb = y[i-1] - base
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dy = conc*kon*(rmax-yb) - koff*yb
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if (abs(y[i-1]) > 999999999): dy = 0 ## Is this useful?
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y[i] = y[i-1] + dy*dt
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elif (t2 < time[i] <= t3):
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## Dissociation (conc=0)
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yb = y[i-1]-base
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dy = 0 - koff*yb
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y[i] = y[i-1] + dy*dt
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return y
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## End of simple1to1() function
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def simple1to1_mtl(time, data, params):
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"""
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This function simply models a 1:1 interaction with mass transport limitation.
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[Abulk] --km-> [Asurf] + [L] --kon--> [AL]
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[Abulk] <-km-- [Asurf] + [L] <-koff-- [AL]
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It requires numpy arrays of times and starting data values,
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params['t1']['value'] is time of injection for binding, (s)
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params['rmax']['value'] is maximum response, (RIU)
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params['conc']['value'] is concentration of analyte [Abulk], (M)
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params['kon']['value'] is on-rate of analyte, (1/Ms)
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params['t2']['value'] is time of end binding & begin washing, (s)
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params['koff']['value'] is off-rate of analyte, (1/s)
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params['t3']['value'] is time end of washing & data fitting, (s)
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params['kmtl']['value'] is rate of diffusion, (RIU/Ms)
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"""
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## Skip parameter validation steps for now.
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t1 = params['t1']['value']
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rmax = params['rmax']['value']
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conc = params['conc']['value']
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kon = params['kon']['value']
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t2 = params['t2']['value']
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koff = params['koff']['value']
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t3 = params['t3']['value']
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kmtl = params['kmtl']['value']
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"""
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Derivation:
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d[AL]/dt = (kon*[A]*[L] - koff*[AL]) / (1 + kon*[L]/kmtl)
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y = [AL]
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(rmax-y) = [L]
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conc = [Abulk]
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rmax = [AL] + [L]
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dy/dt = (kon*conc*(rmax-y) - koff*y) / (1 + kon*(rmax-y)/kmtl)
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"""
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stat = {} ## Error status dictionary.
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y = np.zeros(len(time), dtype=float)
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base = y[0] = data[0] ## Baseline SPR signal.
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## Error checks.
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if (kmtl<=0):
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## Avoid div/0, assume user wants no mass transport limitation.
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stat['kmtl must be > 0'] = True
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kmtl = 1e40 ## An arbitrary very large number.
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## Must iterate through data, numerical integration.
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for i in range(1,len(time)):
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dt = time[i] - time[i-1]
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## Treat function as having three separate phases.
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if (time[i] <= t1):
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## Pre-binding phase.
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base = y[i] = data[i]
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elif (t1 < time[i] <= t2):
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## Binding phase
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yb = y[i-1] - base
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dy = (conc*kon*(rmax-yb) - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
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## Check for integration errors producing wild results.
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if (abs(y[i-1]) > 9e9): dy = 0; stat['y>9e9'] = True
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y[i] = y[i-1] + dy*dt
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elif (t2 < time[i] <= t3):
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## Dissociation (conc=0)
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yb = y[i-1] - base
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dy = (0 - koff*yb) / (1 + kon*(rmax-yb)/kmtl)
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y[i] = y[i-1] + dy*dt
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if (len(stat.keys()) > 0): print "Errors in simple1to1:", stat.keys()
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return y
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## End of simple1to1_mtl() function
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################################# End of module ################################# |
