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Computational systems biology is largely driven by mathematical modeling and simulation of biochemical networks, via continuous deterministic methods or discrete event stochastic methods. Although, the deterministic methods are efficient in predicting the macroscopic behavior of a system, they are severely limited by their inability to represent the stochastic effects of random molecular fluctuations at lower concentration. In this work, we have presented a novel method for simulating biochemical networks based on a deterministic solution with a modification that permits the incorporation of stochastic effects. To demonstrate the feasibility of our approach, we have tested our method on two previously reported biochemical networks. The results, while staying true to their deterministic form, also reflect the stochastic effects of random fluctuations that are dominant as the system transitions into a lower concentration. This ability to adapt to a concentration gradient makes this method particularly attractive for systems biology based applications.