sensitivity to pH

[maki]

Hi,

 

I hope to express the biomass variation considering the sensitivity to pH.

For example, a certain microbial community in the pyrite rock under the reductive condition decreases by acidification with progress of pyrite oxidation after boring. In contrast, acidophilic iron-oxidizing community increases under the low pH condition.

 

Can I set the rate constant depending on the variation of the calculated pH and so on?

Is there any other way to express it?

 

 

Best regards,

 

Maki

[Brian Farrell]

Hi Maki,

 

I think there are a few items to consider here. These include the form of the kinetic rate laws, the effects of approaching equilibrium on the rate of a reaction (the thermodynamic limits), and the microbial population dynamics (i.e. a microbe dying out when conditions become inhospitable).

 

Chapter 16 (Kinetics of dissolution and precipitation) in the Geochemical and Biogeochemical Reaction Modeling text describes three different rate laws for albite dissolution. Each of these is valid under a different pH range. You can set different rate laws (rate constants, promoting and inhibiting species, etc.) for different pH conditions using the Custom rate law capabilities of React, X1t, and X1t. As described in the GBRM text, you might consider adding H+ or OH- as promoting/ inhibiting species in some of your rate laws. A recent forum post discussed a similar topic, and more information can be found in section 5.1 of the GWB Reaction Modeling Guide.

 

Since you're considering microbial kinetics, I think the available/ usable energy for a particular metabolism will come into play in the thermodynamic term of the kinetic rate law. The Thermodynamic ladder paper you referenced in another post (Bethke et al. (2011) American Journal of Science Vol. 311 pp.183-210.) describes the effect of pH, among other variables, on the ability of a microbe to carry out its metabolic reaction.

 

If you decide on using multiple rate laws, you might consider different growth yields or decay constants under different conditions for a particular type of microbe. Just a few ideas.

 

Hope this helps,

 

Brian Farrell

Aqueous Solutions LLC

[maki]

Hi Brian,

 

Thank you for quick reply and very useful advice.

 

According to your advice, I will try to set the Custom rate law for expressing the sensitivity to pH in each of microbial communities.

 

On the other hand, I have another question regarding the rate law.

As you said, kinetics of dissolution and precipitation of albite are written in Chapter 16.

If the sensitivity to pH using the Custom rate law is explained, I think that the inputs of promoting species (eq. 16.4) are not needed, furthermore, the exponent P for higher pH (eq. 16.6), neither.

Are the promoting species and apower (H+) arbitrarily needed for calculating smoothly?

Or, is there any inevitability?

 

 

Best regards,

 

Maki

[Brian Farrell]

Hi Maki,

 

Rate laws are typically derived to fit experimental data, and when their forms change it is often interpreted that the mechanism of the reaction changes. This is the case with the three rate laws mentioned for albite.

 

pH < 1.5:

r_alb=A_Sk₊a_H+(1-Q/K)

rate = surface * rate_con * (activity("H+")^1) * (1 - Q/K)

 

1.5 < pH < 8:

r_alb=A_Sk₊(1-Q/K)

rate = surface * rate_con * (1 - Q/K)

 

pH > 8:

r_alb=A_Sk₊a_H+^-.5(1-Q/K)

rate = surface * rate_con * (activity("H+")^-1/2) * (1 - Q/K)

 

I don't think you can simply exclude promoting and inhibiting species from a rate law. In the first rate law, for example (pH < 1.5), the H+ activity will be different for pH 0.5, 1.0, and 1.5, so the rate is not constant - it will decrease from pH 0.5 to 1.5. Above pH 1.5 this rate won't change much until you get to pH 8. As you get to pH > 8, the rate will increase with higher pH.

 

In other words, the rate is variable below pH 1.5, constant between 1.5 and 8, and variable above pH 8. If you eliminated the promoting/ inhibiting species, then you would only have three distinct rates. Of course, this is slightly more complicated since surface area and the (1-Q/K) term can be affected by the system's chemistry as well.

 

In some cases, it might be possible to have a single reaction mechanism across a wide pH range. In this case, a rate law like r_alb=A_Sk₊a_H+(1-Q/K) could possibly be used by itself - the effect of pH upon the rate might be entirely accounted for by the activity of H+ in the rate law. There is no guarantee of this, however.

 

Hope this helps,

Brian

Edited February 20, 2013 by Brian Farrell
Left H+ activity out of the rate law

[maki]

Hi Brian,

 

Thank you for your detailed explanation.

 

I understand as follows: Setting promoting and inhibiting species by inputting “apower” or “mpower” in the React means to vary the reaction rate (by catalyzing and impeding formation of the activated complex (Chapter 16)) according to the species concentration. If the promoting/inhibiting species is set to H+ by Custom rate law, it means that the reaction rate depends on pH.

Do I understand what you mean?

 

I have a further question.

At the beginning of your previous reply, you said that rate laws are typically derived to fit experimental data.

The examples in Chapter 16 use two kinds of exponent (1 for pH<1.5, and -1/2 for pH>8) in the term of activity (“H+”).

Should I arbitrarily set the promoting/inhibiting species and their exponent (positive or negative) for fitting the experimental data to the simulation value and for reproducing in-situ data on the simulation?

 

Regarding arbitrary setting of the exponents, is the same concept (to fit experiment data to the simulation) applied to ω and Ω in the case of Q/K?

 

Best regards,

 

Maki

[Brian Farrell]

Hi Maki,

 

Promoting and inhibiting species in general have the same effect whether you use the Built-in rate law or you write a Custom rate law. Since you're a microbiologist, I'll try to explain this in terms of the Michaelis-Menten equation:

 

dC/dt = r = k(m_D/K_D+m_D)

 

where C is the concentration (molality) of a product species, k is the rate constant, m_D is the molality of the substrate, and K_D is the half-saturation constant.

 

for m_D << K_D, the rate looks like it's first order (r = k(m_D/K_D), or r = k m_D)

for m_D >> K_D, the rate looks like it's zero order (r = k(m_D/m_D), or r = k)

 

With a first-order rate law, the rate is proportional to m_D, the molality of substrate. This is what it means to have a promoting species with a power of 1. As the substrate is used up, the rate of reaction will decrease, since the rate is proportional to concentration.

 

With a zero-order rate law, the rate does not depend on m_D. Thus, there are no promoting or inhibiting species. If you'd like, you could think of m_D as having a power of 0. Remember, anything raised to the power of 0 is equal to 1 - thus not affecting the rate. Try adding a promoting/ inhibiting species using the GUI (where it says power, click "add"), then setting the power to 0. It will be removed automatically.

 

To set a rate law of the form r = k (m_D)(m_D), or r = k(m_D)^2, you would add the promoting species m_D and set the power to 2. If the rate took the form r = k (1/m_D), you would set the power of the substrate to -1. That is an inhibiting species.

 

The difference between mpower and apower is whether the molality or activity of a promoting or inhibiting species is carried in the rate law, raised to whatever power you specify. I think concentration is used more than activity in rate laws (especially by non-geochemists), but activity is sometimes used instead of molality for H+ and OH-. For your question about pH, yes, adding H+ as a promoting or inhibiting species will make the reaction pH dependent, since pH = -log[activity_H+].

 

I think the powers are commonly integers in practice but they don't need to be. The promoting and inhibiting species (and their powers) aren't really chosen arbitrarily; they make the most sense when you think about elementary reactions and collisions of individual molecules. For an overall reaction, the relationships can be less clear.

 

In most cases ω and Ω are set to 1. If you want to read more about nonlinear rate laws, you can see Section 4.2.2 in the GWB Reaction Modeling Guide, or Appendix 4 in the Geochemical and Biogeochemical Reaction Modeling text.

 

Hope this helps,

Brian

[maki]

Hi Brian,

 

Thank you for your reply.

 

I think I understand the concept of promoting/inhibiting species in the case of a first-order rate law and a zero-order rate law, thanks to the explanation using the Michaelis-Menten equation.

 

On the other hand, I don’t understand how to set the powers concretely, yet.

After I do several trials of the REACT simulation, I want to ask you the concerning questions as a new topic in Forum.

 

Thank you for your courteous response to my basic questions.

 

Best regards,

 

Maki