units help

[B_Miller]

Hi,
I am reading about nutrient uptake in aquatic plants. Nutrient uptake often increases over time, saturating once their capacity to increase uptake is limited. Two descriptors of this relationship are often reported, Vmax, the rate of maximum uptake, and Ks, the half-saturation constant (the concentration at which half the maximum uptake is reached independent of slope). The units of Vmax are (in this case) μmol N g dw-1 h-1 where N is Nitrogen and dw is dry weight of the plant tissue. The units of Ks are μM (micromolar) which is μmol L-1. A lot of people use the ratio of Vmax to Ks as an indication of how well the plant species competes for nutrients, as it represents the slope of the uptake when nutrient concentrations are low.

My question is about the units of that ratio. I have tried to figure them out but I'm not sure i got them right, and they don't make intuitive sense to me. Can someone help? Thank you!

 

[Dr.Peterson]

Because you didn't use the tools to format your units, or attach an image, I'm not sure what they re meant to look like, especially where N and dw fit in -- are they supposed to be subscripts? They aren't units, so I don't think they belong here, only in variable names. And I don't know what h means.

I'll take it as this, ignoring subscripts:

V_max: μmol g^-1 h^-1​

K_s: μmol L^-1​

Is that right?

Then I think the units of V_max/K_s would be

μmol g^-1 h^-1 * μmol^-1 L = L g^-1 h^-1​

Since I have no background in this, I have no idea whether it makes sense.

 

[B_Miller]

Yes, thank you! h is hour. And yes, the N and dw should not have been there. Sorry I didn't use the tools.

I really appreciate your answer, that's what I figured the units were.

I think the units say that this ratio represents the volume of water that a given mass of algae can clear of nutrients in an hour at the half-saturation concentration. I suppose that makes sense. Most papers about this don't even report units for the ratio, they just say that higher values indicate a steeper slope and higher nutrient uptake capability.