  Experiments and theories have shown that when steric interactions between
crowding particles and proteins are dominant, which give rise to Asakura-Oosawa
depletion forces, then the stabilities of the proteins increase compared to the
infinite dilution case. We show using theoretical arguments that the crowder
volume fraction ($\Phi_C$) dependent increase in the melting temperature of
globular proteins, $\Delta T_m(\Phi_C) \approx \Phi_C^{\alpha}$ where $\alpha =
\frac{1}{(3 \nu_{eff} - 1)}$. The effective Flory exponent, $\nu_{eff}$,
relates the radius of gyration in the unfolded state to the number of amino
acid residues in the protein. We derive the bound 1.25 $\le \alpha \le$ 2.0.
The theoretical predictions are confirmed using molecular simulations of
$\lambda$ repressor in the presence of spherical crowding particles. Analyses
of previous simulations and experiments confirm the predicted theoretical bound
for $\alpha$. We show that the non-specific attractions between crowding
particles and amino acid residues have to be substantial to fully negate the
enhanced protein stabilities due to intra protein attractive Asakura-Oosawa
(AO) depletion potential. Using the findings, we provide an alternate
explanation for the very modest (often less than 0.5 Kcal/mol) destabilization
in certain proteins in the cellular milieu. Cellular environment is
polydisperse containing large and small crowding agents. AO arguments suggest
that proteins would be localized between large (sizes exceeding that of the
proteins) crowders, which are predicted to have negligible effect on stability.
{\it In vitro} experiments containing mixtures of crowding particles could
validate or invalidate the predictions.
