Filtering a Pythons Pandas DataFrame based on values from dictionary

I have some data that I have read into Python as a pandas dataframe:

             Unnamed: 0  Initial_guess  Lower_bound  Upper_bound Estimated_or_Fixed  
      0          Ka              5     0.000001        10000          Estimated   
      2          Kd              5     0.000001        10000          Estimated   
      3          Ki              5     0.000001        10000          Estimated   
      5          Kr              5     0.000001        10000          Estimated   
      6        R1_I              5     0.000001        10000          Estimated   
      7         PR1              5     0.000001        10000          Estimated   
      8         PR2              5     0.000001        10000          Estimated   
      9       alpha              5     0.000001        10000          Estimated   
      10        Kcd              5     0.000001        10000          Estimated   
      12       Klid              5     0.000001        10000          Estimated   
      18    LR1R2_I              5     1.000000        10000          Estimated   

        Variable_type  
0   Kinetic parameter  
2   Kinetic parameter  
3   Kinetic parameter  
5   Kinetic parameter  
6   Kinetic parameter  
7   Kinetic parameter  
8   Kinetic parameter  
9   Kinetic parameter  
10  Kinetic parameter  
12  Kinetic parameter  
18         Species IC  

The first column unnamed: 0 are parameters. I have many models each containing different combinations of these parameters. My task is to filter this table for each model by removing any row who's parameter is not present in the model. I have dictionaries for each model with the parameters they contain. Parameters can be of two types, species IC or kinetic parameter. Here is an example of these dictionaries for the first model:

Species_IC:
{'R1': '2.7109e+02', 'R2': '1.2709e+02', 'R1_I': '2.7109e+03', 'R2_I': '1.2709e+03', 'LR1R2': '1.6913e+00', 'LR1R2_I': '1.6913e+01'}

Kinetic_parameter:
{'Ka': '1.0000e+00', 'TGFb': '1.0000e-01', 'Synth': '1.0000e+00', 'PR1': '8.0000e+00', 'Sink': '0.0000e+00', 'PR2': '4.0000e+00', 'alpha': '1.0000e+00'}

My Code:

def write_parameter_bounds_file(self):
    model1=self.all_models_dirs[0] #get first model from a list of model. I'll do it on the first model then generalize to the rest. 
    species=self.get_model_species(model1+'.xml') #get the species dct from this model
    parameters=self.get_model_parameters(model1+'.xml')#get parameter dct from this model
    param_info=self.read_parameter_bounds_template() #get all parameters from template. This is the pandas dataframe at the top. 
    estimated_species=[]
    estimated_params=[]
    for i in species.keys():
        print '\n'
        for j in param_info[param_info.columns[0]]:
            if i==j:
                estimated_species.append(i)
    for i in parameters.keys():
        print '\n'
        for j in param_info[param_info.columns[0]]:
            if i==j:
                estimated_params.append(i)
    param_list=estimated_params+estimated_species #This is a list of the parameters that need to be included in the output df

Does anybody know how I can use param_list to filter the original pandas df?

Thanks