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To be honest I know very few about enzymes and absolutely nothing about Michaelis–Menten. However, when I "took the Michaelis-Menten equation, replaced v with 0.4Vmax, canceled the Vmaxes (one on each side), and solved for [S]", my result is positive: 0.4 * Vmax = S * Vmax / ( Km + S ) 0.4 = S / ( Km + S ) S = 0.4 * Km + 0.4 * S 0.6 * S = 0.4 * Km S = Km * ...


5

From the derivation of Michaelis-Menten kinetics you can see that: $$K_m=\frac{k_f + k_{cat}}{k_r}$$ Where $k_f$ and $k_r$ are binding and unbinding rate constants (for Enzyme-Substrate binding), respectively, and $k_{cat}$ is the turnover number. This is for the Quasi-Steady-State approximation (QSSA). For the equilibrium approximation: $$K_m=\frac{k_f}{...


5

Have you heard of something known as "Occam's Razor" ? It says when you have multiple possible explanations/hypotheses then select the one which is simplest (i.e least number of assumptions) Same with mathematical models. Chemical kinetics models usually assume first order unless there is some evidence against it. Similarly, for enzyme kinetics, as long ...


4

As Arthur Kornberg said: "Don't waste clean thinking on dirty enzymes." Discovering an assay for a biological event in a cell-free extract opens the way to its molecular resolution and reconstitution (Commandment I). Trying to devise a mechanism with a crude extract, even with ingenious experiments, is generally a waste of effort. An extract is too dirty; ...


4

That paper is describing the binding between the 5HT3 receptor and some high-affinity ligand, not serotonin. Numbers of serotonin probably vary according to the precise receptor (species, subunits, etc), but for a ballpark figure this source says 1.7/s, giving half time of ~400 ms. That estimate is based on solution changes, so I'd say it's an upper bound. ...


3

Set $ \dfrac{1}{V} = 0$ and solve for $\dfrac{1}{[S]}$: $ 0 = \dfrac{K_m}{V_{max}}\dfrac{1}{[S]}+ \dfrac{1}{V_{max}} $ $ -\dfrac{1}{V_{max}} = \dfrac{K_m}{V_{max}}\dfrac{1}{[S]}$ $ -1 = {K_m}\dfrac{1}{[S]}$ $ -\dfrac{1}{K_m} = \dfrac{1}{[S]} = $ x-intercept


3

The stochastic simulation algorithm by Gillespie makes the assumption that reaction propensity (probability) in an infinitesimally small interval of time is same as the macroscopic reaction rate. (For details, you can see my answer in Chemistry.SE). You can model and simulate every step of enzyme catalysis or you can also use the Michaelis-Menten model. In ...


3

Alan Boyd's answer covers the mechanistic aspects quite well, but there is another aspect he didn't quite touch on - what's going on at the molecular level. To understand this, you need to think about the actual conditions of the reaction: unless it's taking place inside a cell, which straight biochemical reactions of the kind you're talking about almost ...


3

In terms of Michaelis-Menten kinetics, the rate never reaches the maximum rate: $v = V_{max} \times \frac{S}{K_m + S}$ where $S$ is substrate concentration. Notice that however large $S$ is, the term on the bottom line ($K_m + S$) will be larger than $S$, so $v$ will be less than $V_{max}$. You can think about this in terms of the binding equilibrium ...


2

This expands my comment on the question to an answer. If an enzyme exhibits Michaelis-Menten kinetics, then it is valid to define a KM and this equates to the substrate concentration when reaction velocity is 0.5 * Vmax. However, many enzymes do not exhibit Michaelis-Menten kinetics. One example is when the enzyme shows a co-operative response to ...


2

Mammalian rod cells, the most numerous photoreceptor cells in the retina, reach a max depolarization after a single photon stimulus at 100-120 ms, implying a time constant (1/k) of about 25 ms (see Chen et al., Nature 404:557). This is on the same order of speed as the fly eye, maybe a tad faster. Non-photoreceptor GPCRs are probably slower, but few folks ...


2

Very interesting question. People use Gillespie's algorithm for several sort of kinetic functions such as Michaelis-Menten (MM), Hill etc., no matter what the original assumptions of Gillespie's algorithm are. Concerning MM, There was a 2011 paper by Gillespie himself that shows that the approximation is applicable in discrete stochastic models and that ...


1

When a variable is independent, it's not affected by any other variable. Relative fluorescence obviously depends on the time parameter in this case. If you stopped at 30 minutes and took readings ever 3 minutes, your data would look very different. Without more information about the experiment, however, it's hard to tell if there are additional variables.


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I think I figured it out myself. Since $a(S)$ is in $\frac{mol}{s}$ and $v$ is in $\frac{\frac{mol}{l}}{s}$, we have that $a(S)= v * \Omega$. Therefore $$ a(S) = \frac{V_{max}\cdot [S]}{K_M + [S]} \cdot \Omega = \frac{V_{max}\cdot S / \Omega \cdot \Omega}{K_M + S / \Omega} = \frac{V_{max}\cdot S}{K_M + S/\Omega}. $$


1

In a diploid organism there are two copies of DNA which means two copies or "molecules" of promoter in the entire cell. The volume of a typical eukaryotic cell (HeLa) would be 2.25×10-12 litres (Zhao et al. 2007, BioNumbers). $$\text{Concentration }(M)=\frac{\text{Molecules per cell}}{\text{Avogadro No.} \times \text{Volume of the cell }(l)}$$ This comes ...


1

Note: The term equilibrium is different from steady-state w.r.t chemical reactions. Steady state is the right term for the above example. Equilibrium is used in the sense of forward and reverse reactions in a single reversible reaction. The above example considers two irreversible reactions — production and degradation. ... ... the time required for the ...


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I'm going to try to lay out some basic definitions here in as plain language as I can find. Its difficult to study enzymes when they are outside the cell, where they may behave quite differently in different contexts. We categorize a given enzyme in its class by kcat, Km and by mechanism (the sort of reaction they catalyze. kcat is sort of a maximum ...


1

The answer is no really, but some variants might allow you to study inhibition. Michaelis Menten kinetics are experiments which try to characterize the catalysis characteristics of a reaction but to do so the numbers are obtained at concentrations of substrate that you dont find in a cell. Vmax is defined as the maximum rate at which the reaction is run ...


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