Stochastic theory of interfacial enzyme kinetics: A kinetic Monte Carlo study Biswajit Das, Gautam Gangopadhyay ⇑ S.N. Bose National Centre For Basic Sciences, Block-JD, Sector-III, Salt Lake, Kolkata 700098, India article info Article history: Received 3 June 2011 In final form 15 November 2011 Available online 3 December 2011 Keywords: Stochastic processes Interfacial enzyme kinetics Monte Carlo simulation abstract In the spirit of Gillespie’s stochastic approach we have formulated a theory to explore the advancement of the interfacial enzyme kinetics at the single enzyme level which is ultimately utilized to obtain the ensemble average macroscopic feature, lag-burst kinetics. We have provided a theory of the transition from the lag phase to the burst phase kinetics by considering the gradual development of electrostatic interaction among the positively charged enzyme and negatively charged product molecules deposited on the phospholipid surface. It is shown that the different diffusion time scales of the enzyme over the fluid and product regions are responsible for the memory effect in the correlation of successive turnover events of the hopping mode in the single trajectory analysis which again is reflected on the non-Gaussian distribution of turnover times on the macroscopic kinetics in the lag phase unlike the burst phase kinetics. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction The study of interfacial enzymatic reaction is gaining increasing importance in biological science as enzyme plays a crucial role as catalyst of lipid metabolism on the membrane and as mediator of cell signaling processes [1]. It is a heterogeneous enzymatic reaction where the rate of the reaction depends on both the mechanical and chemical steps involved. From the experimental observation it is well known that the activity of an interfacial en- zyme is maximum where both the fluid and gel state phospholipid molecules coexist [2,3]. Due to different packing pattern, gel state phospholipid molecules are tightly packed than the fluid state molecules whereby an enzyme adsorbs exclusively in the fluid region and gradually diffuses to the fluid–gel boundary [2,4]. With the progress of the reaction the product molecules i.e., lyso-phos- pholipids and fatty acids are accumulated in the surface and forms a product domain in between the gel and fluid domain [3,5–10]. Usually the product molecules i.e., fatty acids are negatively charged and with increase in size of the product domain the elec- trostatic interaction between the positively charged enzyme and the negatively charged surface also increases. It is observed that the formation of an appreciable size of product domain is respon- sible for the lag-burst kinetics which is characterized by initial slow hydrolysis in the lag phase followed by a sudden increase in activity of the enzyme by two or three orders of magnitude, the burst phase [11–16]. Lag-burst kinetics is the most important macroscopic features of interfacial enzyme kinetics and previously various kinetic analysis had been performed by considering the interactions among the enzyme-phospholipid molecules [12,13]. However, no microscopic theoretical study is found in terms of the dynamical processes by considering the single molecule activ- ity on the phospholipid monolayer. In this work we have studied the macroscopic feature of inter- facial enzyme kinetics starting from the single enzyme activity. At the single molecule level this reaction kinetics is a stochastic pro- cess and the analysis involves single molecule trajectory [17–19]. It is well known that due to thermal hopping an enzyme can come out from the gel domain or it can also keep on doing hydrolysis of successive substrate molecules in the scooting mode as well due to electrostatic binding of the enzyme molecule on the gel sur- face. We have simulated the stochastic processes for the hopping and scooting mode of motion as both the modes are operating at the same time probabilistically depending on the amount of prod- uct formed in the trajectory of a single enzyme to calculate the suc- cessive turnover events which on ensemble averaging gives the macroscopic rate of the reaction by which the lag-burst kinetics can be described. In the spirit of Gillespie’s method [20,21] we have studied the stochastic turnover events due to mechanical and chemical steps of the single enzyme activity. Finally, we have searched for any dynamic correlation which can develop due to the motion of enzyme over various time scales of motion in the differ- ent heterogeneous phases. In what follows we have introduced a model for the hopping mode and scooting mode of motion of the interfacial enzyme kinetics in Section 2. A stochastic formulation and simulation tech- nique is provided in Section 3. Numerical results are discussed in Section 4 by first providing single enzyme activity for some exper- imental parameters and then the ensemble average kinetics in the bulk. Finally the paper is concluded in Section 5. 0301-0104/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2011.11.024 ⇑ Corresponding author. E-mail address: gautam@bose.res.in (G. Gangopadhyay). Chemical Physics 393 (2012) 58–64 Contents lists available at SciVerse ScienceDirect Chemical Physics journal homepage: www.elsevier.com/locate/chemphys