<｜begin▁of▁sentence｜>### Instruction:
Certainly! Let's rephrase this scenario in the context of a molecular biology research scenario:

Imagine we are conducting a study on the molecular pathways within a cellular system, where we need to analyze the flow of a signaling molecule 'X' as it interacts with various receptors and enzymes represented by 'a', 'b', 'c', 'd', and 'e', eventually resulting in an outcome 'Y'. The interactions are quantified by the affinity constants, which are analogous to network capacity in our model, given by the following connections: 'X' to 'a' (3.0), 'X' to 'b' (1.0), 'a' to 'c' (3.0), 'b' to 'c' (5.0), 'b' to 'd' (4.0), 'd' to 'e' (2.0), 'c' to 'Y' (2.0), and 'e' to 'Y' (3.0).

How would we calculate the maximum signaling capacity from molecule 'X' (source) to outcome 'Y' (sink) throughout this cellular network using the Edmonds-Karp algorithm to ensure that signal transduction is optimized?
### Response:
import networkx as nx
from networkx.algorithms.flow import edmonds_karp

# Create a directed graph
G = nx.DiGraph()

# Add edges with capacity
G.add_edge('x', 'a', capacity=3.0)
G.add_edge('x', 'b', capacity=1.0)
G.add_edge('a', 'c', capacity=3.0)
G.add_edge('b', 'c', capacity=5.0)
G.add_edge('b', 'd', capacity=4.0)
G.add_edge('d', 'e', capacity=2.0)
G.add_edge('c', 'y', capacity=2.0)
G.add_edge('e', 'y', capacity=3.0)

# Compute maximum flow
R = edmonds_karp(G, 'x', 'y')
flow_value = R.graph['flow_value']

print('The maximum flow from node x to node y is:', flow_value)
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