code: def linear_reaction_coefficients(model, reactions=None):
      
      linear_coefficients = {}
      reactions = model.reactions if not reactions else reactions
      try:
          objective_expression = model.solver.objective.expression
          coefficients = objective_expression.as_coefficients_dict()
      except AttributeError:
          return linear_coefficients
      for rxn in reactions:
          forward_coefficient = coefficients.get(rxn.forward_variable, 0)
          reverse_coefficient = coefficients.get(rxn.reverse_variable, 0)
          if forward_coefficient != 0:
              if forward_coefficient == -reverse_coefficient:
                  linear_coefficients[rxn] = float(forward_coefficient)
      return linear_coefficients
docs: Coefficient for the reactions in a linear objective.
  
      Parameters
      ----------
      model : cobra model
          the model object that defined the objective
      reactions : list
          an optional list for the reactions to get the coefficients for. All
          reactions if left missing.
  
      Returns
      -------
      dict
          A dictionary where the key is the reaction object and the value is
          the corresponding coefficient. Empty dictionary if there are no
          linear terms in the objective.