Once the enzyme is immobilized, issues of diffusion and transport arise. If there is an unstirred boundary layer near the surface, the substrate concentration at the surface may differ from the substrate concentration in the bulk fluid. Also, product will accumulate at the surface, potentially inhibiting the reaction. This can be a problem in a microfluidic situation, or with beads if they are not kept in motion. The higher the molecular weight of the substrate and product, the bigger the problem, since diffusion rates through the unstirred layer slow down as the molecules get larger.

Aside from the above, steady-state enzyme kinetics should be applicable as long as the usual conditions are met, such as that the substrate concentration is not significantly reduced due to binding to the enzyme. In a flow-through system with immobilized enzyme, this requirement may  be easily met because the substrate is continually replenished. With beads, you would have to be careful not to put in too much enzyme.

Calculating kcat may be tricky because of the difficulty of measuring the immobilized enzyme concentration, but the measurement of Km should not be a problem as long as initial rate can be measured.

Once the enzyme is immobilized, issues of diffusion and transport arise. If there is an unstirred boundary layer near the surface, the substrate concentration at the surface may differ from the substrate concentration in the bulk fluid. Also, product will accumulate at the surface, potentially inhibiting the reaction. This can be a problem in a microfluidic situation, or with beads if they are not kept in motion. The higher the molecular weight of the substrate and product, the bigger the problem, since diffusion rates through the unstirred layer slow down as the molecules get larger.

Aside from the above, steady-state enzyme kinetics should be applicable as long as the usual conditions are met, such as that the substrate concentration is not significantly reduced due to binding to the enzyme. In a flow-through system with immobilized enzyme, this requirement may  be easily met because the substrate is continually replenished. With beads, you would have to be careful not to put in too much enzyme.

Calculating kcat may be tricky because of the difficulty of measuring the immobilized enzyme concentration, but the measurement of Km should not be a problem as long as initial rate can be measured.

I agreed with Adam B shapiro. Its totally depend upon the reaction mixture as well as surface to which enzyme is immobilized.If there is any changes in structure of enzyme its might be to decrease in Km and Vmax of that enzymes towards the particular substrate. Mean times primary object of immobilization is to make them stable.

Mass transfer from liquid bulk to enzymes changes from free to immobilized enzymes. Mass transfer phenomena must be considered in the same way of chemical surface reactions both fro substrates and products. The most depends on the geometrical size and shape of support and reactor and the liquid mixing.

If immobilization is on a porous scaffold an additional mass transfer resistance is introduced. Again the methods of chemical reaction engineering for reaction in porous media can be used.

On the other hand the enzymes activity can change because the immobilization technique. Immobilization modify the shape of enzyme, it could reducie the availability of the reaction part of the protein for substrate. The modification of activity cannot be predicted by simple calculations.

If the question is about a measure, a gradientless fixed bed can be used to identify the role of transport phenomena and measuring an apparent immobilized enzyme activity. The most depends on the scaffold (shape and dimension) used for immobilization.

If no modification of protein shape and a simple transport description is used a simplified model can be used to predict the depletion of apparent v Km etc.

A gradient from liquid bulk to surface can be consedered resultion in a concentration difference for both substrates DS=(Sbulk - Ssurface) and products DP=(Psurface-Pbulk) the diffenerces dipends on the mixing conditions or mass transport resistance.

Immobilized enzymes work at the surface concentration while free enzimes work at bulk concentration.

vfree = f(Sbulk)

vImm = f(Ssurface)=f(Sbulk-DS)

For simple Michaelis Menten kinetics you can rerrange the equation to have Kmimm=Kmfree-DS v0free=v0imm  and a term that shift  down the reaction rate.

The limit of approach is how to predict the values of DS and DP.

 Hi Jitendra, I totally agree with Adam. Classical enzyme kinetics are based on the assumption that the interactions of enzyme and substrate occur in solution phase and that their interactions are not hindered in any way.

 If the enzyme-substrate interactions are affected by immobilizing the enzyme, then the regular way of measuring enzyme kinetics is not valid.   

Thanks Dr. Stefansson, Dr Sassi , Dr Faizal, and Dr Adam for the answers. It would be great if I can get a paper regarding the same.

regards

jitendra

This web page and article look useful:

http://www1.lsbu.ac.uk/water/enztech/diffusion.html

http://www.ncbi.nlm.nih.gov/pubmed/20865399

Thanks a lot Dr. Shapiro

I do agree with the above comments or answer given. Depending on the molecular wieght of the substrate, strategy for  immobilization must be chosen.

If you need a general and specific enzyme immobilization method, on a material with excellent fluid properties (i.e. minimal diffusion limitations) which is stable in aqueous and organic media, have a look at this:

http://pubs.rsc.org/en/content/articlelanding/2014/cc/c4cc02605e#!divAbstract

The material, EziG, can be purchased from EnginZyme (www.enginzyme.com).

As expected, after an immobilization process, the apparent Km and Vmax values are significantly affected. In literature, for example, the Vmax value for immobilized laccase compared to that of the free enzyme is reduced of about 2–5 times compared to the free enzyme, due to substrate diffusion to the catalytic site, with an increase of Km value. The increase of Km can be explained as a result of diffusional limitation of the substrate or to conformational changes of the enzyme resulting in a lower affinity of the substrate for the enzyme. 

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The previous answers give qualitative answers, theory but little experimental data that support the theory. There are unfortunately few studies available were the changes in intrinsic enzyme properties are given for the same enzyme immobilized in different supports, and different substrates.

The intrinsic properties Vmax or kcat and Km of immobilized enzymes can only be determined in systems that are not mass transfer-limited – that is, where the stationary effectiveness factor η equals 1. This applies always when [S] ≫K´m – that is, for the determination of V´max (see Fig. 10.7). The turnover number k´cat can only be determined for enzymes of which the active sites can be titrated. A simple method is available to determine η. The particles can be disintegrated by homogenization or sonication to reduce R and the Thiele modulus to a value where η ≈ 1. By comparing the initial rate of the enzyme-catalyzed reaction with the same initial substrate content for the same amount of whole and disintegrated particles, η for the whole particles can be determined or estimated (Figs. 10.3 and 10.12). Even when η ≈ 1, the turnover number determined may not be an intrinsic property (Fig. 10.12 b). This applies for reactions where acids or bases are either produced or consumed. A pH gradient may then be formed in the particles which perturbs the pH-dependent intrinsic properties (see Section 2.7). To avoid this, a buffer with high buffering capacity at the pH where measurements are performed should be used. This implies that the pK-value of the buffer should be near this pH-value (Tischer and Kasche, 1999). For such measurements a buffer with an ionic strength of 0.05 M is sufficient (Fig. 10.12). The buffer must be inert; therefore TRIS should not be used as it can act as a nucleophile and react with acyl- and glycosyl-enzyme intermediates.

Another property of the particles used for the immobilization must also be considered, its stationary charge. Even in non ion-exchange particle they influence the intrinsic enzyme properties.

One important property of immobilized biocatalysts that frequently is not measured is the stationary charge density, which can be determined by titration. When this has been carried out, net charge densities of more than 10 mM have been observed. This is much larger than net charge densities due to immobilized enzymes, where nE is

Great Thanks Dr. Kasche

regards

To answer your question I need more information. What enzyme, substrate, support used to immobilize the enzyme, the buffer used to determine the enzyme kinetics and its ionic strength. How were the unused reactive sites used for the immobilization inactivated? 

Generally it has been shown for all enzymes that their enzyme kinetic properties can be changed when they bind activators or non-competitive inhibitors, or are chemically modified. Thus similar changes can be expected when an enzyme is immobilized, with covalent bonds or only adsorbed. 

For hydrolases we and other groups have studied this in detail. In reactions where H+ is formed or consumed a pH-gradient is formed in the particles with immobilized enzyme.  This can influence kcat and Km - either up or down- especially when the ionic strength of the buffer is to small to reduce the pH-gradient. Here also the stationary charge on the support can influence the enzyme kinetics, especially for charged substrates.  See my previous answer and our paper : Immobilized enzymes: crystals or carriers that you can download or our book: Biocatalysts and enzyme technology Chapter 10 from 2012 where you find more articles that deal with your problem.

 I can send you the chapter of the book privately where this is dealt with in detail. In that case I need your e-mail.