To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints based on the problem statement.

Let's define:
- $x_1$ as the number of paintings.
- $x_2$ as the number of photo prints.

The objective is to maximize profit. The profit per painting sold is $330, and the profit per photo print sold is $170. Thus, the objective function can be represented as:
\[ \text{Maximize} \quad 330x_1 + 170x_2 \]

The constraints are based on the available wall space and budget, as well as the requirement that at least 20% of items in stock must be photo prints.

1. Wall Space Constraint: Each painting takes 7 sq ft, and each photo print takes 4 sq ft. The total available wall space is 200 sq ft.
\[ 7x_1 + 4x_2 \leq 200 \]

2. Budget Constraint: A painting costs $400, and a photo print costs $200. The total budget is $7000.
\[ 400x_1 + 200x_2 \leq 7000 \]

3. Photo Prints Percentage Constraint: At least 20% of the items must be photo prints.
\[ x_2 \geq 0.20(x_1 + x_2) \]
This can be simplified to:
\[ 0.80x_2 \geq 0.20x_1 \]
Or:
\[ 4x_2 \geq x_1 \]

All variables are non-negative since they represent quantities of items.

Now, let's express this in the requested JSON format:

```json
{
    'sym_variables': [('x1', 'number of paintings'), ('x2', 'number of photo prints')],
    'objective_function': '330*x1 + 170*x2',
    'constraints': [
        '7*x1 + 4*x2 <= 200',
        '400*x1 + 200*x2 <= 7000',
        '4*x2 >= x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

And here is the Gurobi code in Python to solve this problem:

```python
from gurobipy import *

# Create a new model
m = Model("Art Gallery Optimization")

# Define variables
x1 = m.addVar(vtype=GRB.INTEGER, name="number_of_paintings")
x2 = m.addVar(vtype=GRB.INTEGER, name="number_of_photo_prints")

# Set the objective function
m.setObjective(330*x1 + 170*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(7*x1 + 4*x2 <= 200, "wall_space_constraint")
m.addConstr(400*x1 + 200*x2 <= 7000, "budget_constraint")
m.addConstr(4*x2 >= x1, "photo_prints_percentage_constraint")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found: {m.objVal} profit")
    print(f"Number of paintings: {x1.x}")
    print(f"Number of photo prints: {x2.x}")
else:
    print("No optimal solution found")
```