Figure - PMC

Skip to main content

An official website of the United States government

Here's how you know

Here's how you know

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

View full-text article in PMC

. 2014 Mar 11;26(3):876–893. doi: 10.1105/tpc.113.119685

Search in PMC
Search in PubMed
View in NLM Catalog
Add to search

© 2014 American Society of Plant Biologists. All rights reserved.

PMC Copyright notice

Figure 5. — Mechanistic Description of the Inhibition and Activation Effects on the Rates of Product Formation Using 4-Coumaric Acid as Substrate.

(A) Proposed interactions of 4CL3 and 4CL5 and the effects on product formation. The formation of the 4CL3/4CL5 complex with a 3:1 ratio leads to decreasing amounts of free enzymes and causes a rate reduction (Inhibition Path A and Inhibition Path B). The 4CL3/4CL5 complex is then involved in product formation and results in an increase in rate (Activation Path).

(B) The model described in (A) is extended for one substrate, 4-coumaric acid, using experimentally derived kinetic parameters, and deriving rate estimates at each step. Each enzymatic reaction for 4CL3, 4CL5, and the 4CL3/4CL5 complex is based on Michaelis-Menten kinetics. and are kinetic parameters of the 4CL3 enzymatic reaction. and are kinetic parameters of the 4CL5 enzymatic reaction. and are assumed as kinetic parameters of 4CL3/4CL5 complex, where represents activation effects of the complex on the rate. The interaction rate between 4CL3 and 4CL5 is assumed to be . The interactions occur for the formation of the 4CL3/4CL5 tetramer in succession, which leads to inhibition of the rate.

(C) A mathematical model is shown for multiple enzymes and 4-coumaric acid as a single substrate. The equation represents the rate of total product formation associated with 4CL3, 4CL5, and the 4CL3/4CL5 complex, where [E_1t] and [E_2t] are the total amounts of 4CL3 and 4CL5 respectively, [S] is the 4-coumaric acid concentration. k₁, k₂, and γ are unknown parameters defined for the enzyme–enzyme interaction. k₁ is and k₂ is , where is the association/disassociation rate between enzyme and enzyme complex in (A). α and β are the proportions of 4CL3 and 4CL5 involved with each interaction between enzymes (see Supplemental Methods for the derivation). γ represents the product rate of the enzyme complex. The optimized values of the unknown parameters are fitted by hybrid optimization using MATLAB. k₁, k₂, and γ values represent the mean ± sd of 100 optimized values.

Inline graphic — Mechanistic Description of the Inhibition and Activation Effects on the Rates of Product Formation Using 4-Coumaric Acid as Substrate.

(A) Proposed interactions of 4CL3 and 4CL5 and the effects on product formation. The formation of the 4CL3/4CL5 complex with a 3:1 ratio leads to decreasing amounts of free enzymes and causes a rate reduction (Inhibition Path A and Inhibition Path B). The 4CL3/4CL5 complex is then involved in product formation and results in an increase in rate (Activation Path).

(B) The model described in (A) is extended for one substrate, 4-coumaric acid, using experimentally derived kinetic parameters, and deriving rate estimates at each step. Each enzymatic reaction for 4CL3, 4CL5, and the 4CL3/4CL5 complex is based on Michaelis-Menten kinetics. and are kinetic parameters of the 4CL3 enzymatic reaction. and are kinetic parameters of the 4CL5 enzymatic reaction. and are assumed as kinetic parameters of 4CL3/4CL5 complex, where represents activation effects of the complex on the rate. The interaction rate between 4CL3 and 4CL5 is assumed to be . The interactions occur for the formation of the 4CL3/4CL5 tetramer in succession, which leads to inhibition of the rate.

(C) A mathematical model is shown for multiple enzymes and 4-coumaric acid as a single substrate. The equation represents the rate of total product formation associated with 4CL3, 4CL5, and the 4CL3/4CL5 complex, where [E_1t] and [E_2t] are the total amounts of 4CL3 and 4CL5 respectively, [S] is the 4-coumaric acid concentration. k₁, k₂, and γ are unknown parameters defined for the enzyme–enzyme interaction. k₁ is and k₂ is , where is the association/disassociation rate between enzyme and enzyme complex in (A). α and β are the proportions of 4CL3 and 4CL5 involved with each interaction between enzymes (see Supplemental Methods for the derivation). γ represents the product rate of the enzyme complex. The optimized values of the unknown parameters are fitted by hybrid optimization using MATLAB. k₁, k₂, and γ values represent the mean ± sd of 100 optimized values.