Project: s41467-024-50114-5 | Function: riekeModel (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Implements the biophysical photoreceptor model using six differential equations that mimic the enzymatic reactions of the phototransduction cascade, incorporating dynamic adaptation mechanisms for converting light stimuli into photocurrents

**KEY TERMS:** {
  "sigma": "photopigment decay rate σ",
  "phi": "PDE decay rate φ",
  "eta": "PDE activation rate η",
  "cgmp2cur": "cGMP to current conversion",
  "gamma": "sensitivity parameter γ",
  "TimeStep": "temporal integration step"
}

**CONTEXT CODE:** #!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Mar 18 14:53:08 2022

@author: Saad Idrees, Joel Zylberberg's Lab, York University
idrees.sa@gmail.com

This is a custom keras layer that converts light stimulus (R*/rod/s) into photoreceptor currents by using a biophysical model
of the photoreceptor by Rieke's lab "Predicting and Manipulating Cone Responses to Naturalistic Inputs. Juan M. Angueyra, Jacob Baudin, Gregory W. Schwartz, Fred Rieke
Journal of Neuroscience 16 February 2022, 42 (7) 1254-1274; DOI: 10.1523/JNEUROSCI.0793-21.2021


"""

import tensorflow as tf
from tensorflow.keras import Model
from tensorflow.keras.layers import Conv2D, Dense, Activation, Flatten, Reshape, MaxPool2D, BatchNormalization, GaussianNoise,LayerNormalization
from tensorflow.keras.regularizers import l1, l2


# Photoreceptor-CNN model
# Solve the differential equations using Euler method
@tf.function(autograph=True,experimental_relax_shapes=True)
def riekeModel(X_fun,TimeStep,sigma,phi,eta,cgmp2cur,cgmphill,cdark,beta,betaSlow,hillcoef,hillaffinity,gamma,gdark):
    raise NotImplementedError("Function has been masked for testing purposes")


class photoreceptor_REIKE(tf.keras.layers.Layer):
    def __init__(self,pr_params,units=1,dtype='foat16'):
        super(photoreceptor_REIKE,self).__init__()
        self.units = units
        self.pr_params = pr_params
        # self.dtype='float16'
        

    def get_config(self):
        config = super().get_config()
        config.update({
            'units': self.units,
        })
        return config

    def build(self,input_shape):
        dtype = self.dtype
        
        sigma_init = tf.keras.initializers.Constant(self.pr_params['sigma'])
        self.sigma = tf.Variable(name='sigma',initial_value=sigma_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['sigma_trainable'])
        sigma_scaleFac = tf.keras.initializers.Constant(self.pr_params['sigma_scaleFac'])
        self.sigma_scaleFac = tf.Variable(name='sigma_scaleFac',initial_value=sigma_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        phi_init = tf.keras.initializers.Constant(self.pr_params['phi'])
        self.phi = tf.Variable(name='phi',initial_value=phi_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['phi_trainable'])
        phi_scaleFac = tf.keras.initializers.Constant(self.pr_params['phi_scaleFac'])
        self.phi_scaleFac = tf.Variable(name='phi_scaleFac',initial_value=phi_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
       
        eta_init = tf.keras.initializers.Constant(self.pr_params['eta'])
        self.eta = tf.Variable(name='eta',initial_value=eta_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['eta_trainable'])
        eta_scaleFac = tf.keras.initializers.Constant(self.pr_params['eta_scaleFac'])
        self.eta_scaleFac = tf.Variable(name='eta_scaleFac',initial_value=eta_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        beta_init = tf.keras.initializers.Constant(self.pr_params['beta'])
        self.beta = tf.Variable(name='beta',initial_value=beta_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['beta_trainable'])
        beta_scaleFac = tf.keras.initializers.Constant(self.pr_params['beta_scaleFac'])
        self.beta_scaleFac = tf.Variable(name='beta_scaleFac',initial_value=beta_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)

        cgmp2cur_init = tf.keras.initializers.Constant(self.pr_params['cgmp2cur'])
        self.cgmp2cur = tf.Variable(name='cgmp2cur',initial_value=cgmp2cur_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['cgmp2cur_trainable'])
        
        cgmphill_init = tf.keras.initializers.Constant(self.pr_params['cgmphill'])
        self.cgmphill = tf.Variable(name='cgmphill',initial_value=cgmphill_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['cgmphill_trainable'])
        cgmphill_scaleFac = tf.keras.initializers.Constant(self.pr_params['cgmphill_scaleFac'])
        self.cgmphill_scaleFac = tf.Variable(name='cgmphill_scaleFac',initial_value=cgmphill_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        cdark_init = tf.keras.initializers.Constant(self.pr_params['cdark'])
        self.cdark = tf.Variable(name='cdark',initial_value=cdark_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['cdark_trainable'])
        
        betaSlow_init = tf.keras.initializers.Constant(self.pr_params['betaSlow'])
        self.betaSlow = tf.Variable(name='betaSlow',initial_value=betaSlow_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['betaSlow_trainable'])
        betaSlow_scaleFac = tf.keras.initializers.Constant(self.pr_params['betaSlow_scaleFac'])
        self.betaSlow_scaleFac = tf.Variable(name='betaSlow_scaleFac',initial_value=betaSlow_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        hillcoef_init = tf.keras.initializers.Constant(self.pr_params['hillcoef'])
        self.hillcoef = tf.Variable(name='hillcoef',initial_value=hillcoef_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['hillcoef_trainable'])
        hillcoef_scaleFac = tf.keras.initializers.Constant(self.pr_params['hillcoef_scaleFac'])
        self.hillcoef_scaleFac = tf.Variable(name='hillcoef_scaleFac',initial_value=hillcoef_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        hillaffinity_init = tf.keras.initializers.Constant(self.pr_params['hillaffinity'])
        self.hillaffinity = tf.Variable(name='hillaffinity',initial_value=hillaffinity_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['hillaffinity_trainable'])
        hillaffinity_scaleFac = tf.keras.initializers.Constant(self.pr_params['hillaffinity_scaleFac'])
        self.hillaffinity_scaleFac = tf.Variable(name='hillaffinity_scaleFac',initial_value=hillaffinity_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
        
        gamma_init = tf.keras.initializers.Constant(self.pr_params['gamma'])
        self.gamma = tf.Variable(name='gamma',initial_value=gamma_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['gamma_trainable'])
        gamma_scaleFac = tf.keras.initializers.Constant(self.pr_params['gamma_scaleFac'])
        self.gamma_scaleFac = tf.Variable(name='gamma_scaleFac',initial_value=gamma_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)
                
        gdark_init = tf.keras.initializers.Constant(self.pr_params['gdark'])
        self.gdark = tf.Variable(name='gdark',initial_value=gdark_init(shape=(1,self.units),dtype=dtype),trainable=self.pr_params['gdark_trainable'])
        gdark_scaleFac = tf.keras.initializers.Constant(self.pr_params['gdark_scaleFac'])
        self.gdark_scaleFac = tf.Variable(name='gdark_scaleFac',initial_value=gdark_scaleFac(shape=(1,self.units),dtype=dtype),trainable=False)


 
    def call(self,inputs):
        X_fun = inputs

        timeBin = float(self.pr_params['timeBin']) # ms
        frameTime = timeBin # ms
        upSamp_fac = int(frameTime/timeBin)
        TimeStep = 1e-3*timeBin
        
        if upSamp_fac>1:
            X_fun = tf.keras.backend.repeat_elements(X_fun,upSamp_fac,axis=1) 
            X_fun = X_fun/upSamp_fac     # appropriate scaling for photons/ms

        sigma = self.sigma * self.sigma_scaleFac
        phi = self.phi * self.phi_scaleFac
        eta = self.eta * self.eta_scaleFac
        cgmp2cur = self.cgmp2cur
        cgmphill = self.cgmphill * self.cgmphill_scaleFac
        cdark = self.cdark
        beta = self.beta * self.beta_scaleFac
        betaSlow = self.betaSlow * self.betaSlow_scaleFac


Complete the function implementation replacing "raise NotImplementedError".