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Michaelis Menten Equation
~28.8 mins read
In biochemistry, Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. It is named after German biochemist Leonor Michaelis and Canadian physician Maud Menten. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate {displaystyle v} (rate of formation of product, {displaystyle [{ce {P}}]}) to {displaystyle [{ce {S}}]}, the concentration of a substrate S. Its formula is given by
![{displaystyle [{ce {P}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d4c666f77e34c220257d5840b2615c6882aabb89)
) to {displaystyle [{ce {S}}]}![{displaystyle [{ce {S}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ea89dfff9e9cad8e883f46fc400e35d23e6eb914)
, the 
Michaelis–Menten saturation curve for an enzyme reaction showing the relation between the substrate concentration and reaction rate.
![{displaystyle v={frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}={frac {V_{max }{[{ce {S}}]}}{K_{mathrm {M} }+[{ce {S}}]}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/94a7743232865ec7bb1e0de0d4e3b6bff3b8be4f)
This equation is called the Michaelis–Menten equation. Here, {displaystyle V_{max }} represents the maximum rate achieved by the system, happening at saturating substrate concentration. The value of the Michaelis constant {displaystyle K_{mathrm {M} }} is numerically equal to the substrate concentration at which the reaction rate is half of {displaystyle V_{max }}.[1] Biochemical reactions involving a single substrate are often assumed to follow Michaelis–Menten kinetics, without regard to the model's underlying assumptions.
ModelEdit
Change in concentrations over time for enzyme E, substrate S, complex ES and product P
In 1901, French physical chemist Victor Henri found that enzyme reactions were initiated by a bond (more generally, a binding interaction) between the enzyme and the substrate.[2] His work was taken up by German biochemist Leonor Michaelis and Canadian physician Maud Menten, who investigated the kinetics of an enzymatic reaction mechanism, invertase, that catalyzes the hydrolysis of sucrose into glucose and fructose.[3] In 1913, they proposed a mathematical model of the reaction.[4] It involves an enzyme, E, binding to a substrate, S, to form a complex, ES, which in turn releases a product, P, regenerating the original enzyme. This may be represented schematically as
{displaystyle {ce {E{}+S[{mathit {k_{f}}}][{mathit {k_{r}}}]ES->[k_{ce {cat}}]E{}+P}}}![{displaystyle {ce {E{}+S=[{mathit {k_{f}}}][{mathit {k_{r}}}]ES-[k_{ce {cat}}]E{}+P}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4bae00cd4d91917219daf235391295adeb36c84d)
where {displaystyle k_{f}}
(forward rate constant), {displaystyle k_{r}}
(reverse rate constant), and {displaystyle k_{mathrm {cat} }}
(catalytic rate constant) denote the rate constants,[5] the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).
(forward rate constant), {displaystyle k_{r}} (reverse rate constant), and {displaystyle k_{mathrm {cat} }} (catalytic rate constant) denote the rate constants,[5] the double arrows between S (substrate) and ES (enzyme-substrate complex) represent the fact that enzyme-substrate binding is a reversible process, and the single forward arrow represents the formation of P (product).Under certain assumptions – such as the enzyme concentration being much less than the substrate concentration – the rate of product formation is given by
{displaystyle v={frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}=V_{max }{frac {[{ce {S}}]}{K_{mathrm {M} }+[{ce {S}}]}}=k_{mathrm {cat} }[{ce {E}}]_{0}{frac {[{ce {S}}]}{K_{mathrm {M} }+[{ce {S}}]}}.}![{displaystyle v={frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}=V_{max }{frac {[{ce {S}}]}{K_{mathrm {M} }+[{ce {S}}]}}=k_{mathrm {cat} }[{ce {E}}]_{0}{frac {[{ce {S}}]}{K_{mathrm {M} }+[{ce {S}}]}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1833714311a25f57029345f68f11dc92649033b7)
The reaction order depends on the relative size of the two terms in the denominator. At low substrate concentration {displaystyle [{ce {S}}]ll K_{M}}![{displaystyle [{ce {S}}]ll K_{M}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/70e5ed70da3fe7f5f1ab381c37bf7adff9d995e5)
, so that the reaction rate {displaystyle v=k_{mathrm {cat} }[{ce {E}}]_{0}{frac {[{ce {S}}]}{K_{mathrm {M} }}}}![{displaystyle v=k_{mathrm {cat} }[{ce {E}}]_{0}{frac {[{ce {S}}]}{K_{mathrm {M} }}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d92cea3402787a36d26e349eb76bdf2f699acf70)
varies linearly with substrate concentration {displaystyle {ce {[S]}}}![{displaystyle {ce {[S]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e5909e9989dfe9306325e8dab287928f3c984ee3)
(first-order kinetics).[6] However at higher {displaystyle {ce {[S]}}} with {displaystyle [{ce {S}}]gg K_{M}}![{displaystyle [{ce {S}}]gg K_{M}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/441b1072d0cd1724042f6a61792adf48b92dfde1)
, the reaction becomes independent of {displaystyle {ce {[S]}}} (zero-order kinetics)[6] and asymptotically approaches its maximum rate {displaystyle V_{max }=k_{ce {cat}}[{ce {E}}]_{0}}![{displaystyle V_{max }=k_{ce {cat}}[{ce {E}}]_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6f14353feb260ab781c8ec562dcb93247e57ee)
, where {displaystyle {ce {[E]_0}}}![{displaystyle {ce {[E]_0}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9a654ad516b5d2547fd9980bb7590464441d6c38)
is the initial enzyme concentration. This rate is attained when all enzyme is bound to substrate. {displaystyle k_{mathrm {cat} }}, the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second. Further addition of substrate does not increase the rate which is said to be saturated.
, so that the reaction rate {displaystyle v=k_{mathrm {cat} }[{ce {E}}]_{0}{frac {[{ce {S}}]}{K_{mathrm {M} }}}} varies linearly with substrate concentration {displaystyle {ce {[S]}}} (first-order kinetics).[6] However at higher {displaystyle {ce {[S]}}} with {displaystyle [{ce {S}}]gg K_{M}}, the reaction becomes independent of {displaystyle {ce {[S]}}} (zero-order kinetics)[6] and asymptotically approaches its maximum rate {displaystyle V_{max }=k_{ce {cat}}[{ce {E}}]_{0}}, where {displaystyle {ce {[E]_0}}} is the initial enzyme concentration. This rate is attained when all enzyme is bound to substrate. {displaystyle k_{mathrm {cat} }}, the turnover number, is the maximum number of substrate molecules converted to product per enzyme molecule per second. Further addition of substrate does not increase the rate which is said to be saturated.The value of the Michaelis constant {displaystyle K_{mathrm {M} }}
is numerically equal to the {displaystyle {ce {[S]}}} at which the reaction rate is at half-maximum,[1] and is a measure of the substrate's affinity for the enzyme—as with {displaystyle K_{mathrm {d} }}
, a small {displaystyle K_{mathrm {M} }} indicates high affinity, meaning that the rate will approach {displaystyle V_{max }}
with lower {displaystyle {ce {[S]}}} than those reactions with a larger {displaystyle K_{mathrm {M} }}.[7] The constant is not affected by the concentration or purity of an enzyme.[8] The value of {displaystyle K_{mathrm {M} }} is dependent on both the identity of enzyme and that of the substrate, as well as conditions such as temperature and pH.[9]
is numerically equal to the {displaystyle {ce {[S]}}} at which the reaction rate is at half-maximum,[1] and is a measure of the substrate's affinity for the enzyme—as with {displaystyle K_{mathrm {d} }}, a small {displaystyle K_{mathrm {M} }} indicates high affinity, meaning that the rate will approach {displaystyle V_{max }} with lower {displaystyle {ce {[S]}}} than those reactions with a larger {displaystyle K_{mathrm {M} }}.[7] The constant is not affected by the concentration or purity of an enzyme.[8] The value of {displaystyle K_{mathrm {M} }} is dependent on both the identity of enzyme and that of the substrate, as well as conditions such as temperature and pH.[9]The model is used in a variety of biochemical situations other than enzyme-substrate interaction, including antigen–antibody binding, DNA–DNA hybridization, and protein–protein interaction.[7][10] It can be used to characterise a generic biochemical reaction, in the same way that the Langmuir equation can be used to model generic adsorption of biomolecular species.[10] When an empirical equation of this form is applied to microbial growth, it is sometimes called a Monod equation.
ApplicationsEdit
Parameter values vary widely between enzymes:[11]
| Enzyme | {displaystyle K_{mathrm {M} }} (M) | {displaystyle k_{text{cat}}} (s−1) | {displaystyle k_{text{cat}}/K_{mathrm {M} }} (M−1s−1) |
|---|---|---|---|
| Chymotrypsin | 1.5 × 10−2 | 0.14 | 9.3 |
| Pepsin | 3.0 × 10−4 | 0.50 | 1.7 × 103 |
| T-RNA synthetase | 9.0 × 10−4 | 7.6 | 8.4 × 103 |
| Ribonuclease | 7.9 × 10−3 | 7.9 × 102 | 1.0 × 105 |
| Carbonic anhydrase | 2.6 × 10−2 | 4.0 × 105 | 1.5 × 107 |
| Fumarase | 5.0 × 10−6 | 8.0 × 102 | 1.6 × 108 |
The constant {displaystyle k_{text{cat}}/K_{mathrm {M} }} (catalytic efficiency) is a measure of how efficiently an enzyme converts a substrate into product. Diffusion limited enzymes, such as fumarase, work at the theoretical upper limit of 108 – 1010 M−1s−1, limited by diffusion of substrate into the active site.[12]
(catalytic efficiency) is a measure of how efficiently an enzyme converts a substrate into product. Diffusion limited enzymes, such as fumarase, work at the theoretical upper limit of 108 – 1010 M−1s−1, limited by diffusion of substrate into the active site.[12]Michaelis–Menten kinetics have also been applied to a variety of spheres outside of biochemical reactions,[5] including alveolar clearance of dusts,[13] the richness of species pools,[14] clearance of blood alcohol,[15] the photosynthesis-irradiance relationship, and bacterial phage infection.[16]
The equation can also be used to describe the relationship between ion channel conductivity and ligand concentration.[17]
DerivationEdit
Applying the law of mass action, which states that the rate of a reaction is proportional to the product of the concentrations of the reactants (i.e. {displaystyle [E][S]}![{displaystyle [E][S]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dead094fd544541ee2dde5755a488d1d113b186c)
), gives a system of four non-linear ordinary differential equations that define the rate of change of reactants with time {displaystyle t}
[18]
{displaystyle {begin{aligned}{frac {mathrm {d} [{ce {E}}]}{mathrm {d} t}}&=-k_{f}[{ce {E}}][{ce {S}}]+k_{r}[{ce {ES}}]+k_{mathrm {cat} }[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {S}}]}{mathrm {d} t}}&=-k_{f}[{ce {E}}][{ce {S}}]+k_{r}[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {ES}}]}{mathrm {d} t}}&=k_{f}[{ce {E}}][{ce {S}}]-k_{r}[{ce {ES}}]-k_{mathrm {cat} }[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}&=k_{mathrm {cat} }[{ce {ES}}].end{aligned}}}), gives a system of four non-linear ordinary differential equations that define the rate of change of reactants with time {displaystyle t}[18]![{displaystyle {begin{aligned}{frac {mathrm {d} [{ce {E}}]}{mathrm {d} t}}&=-k_{f}[{ce {E}}][{ce {S}}]+k_{r}[{ce {ES}}]+k_{mathrm {cat} }[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {S}}]}{mathrm {d} t}}&=-k_{f}[{ce {E}}][{ce {S}}]+k_{r}[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {ES}}]}{mathrm {d} t}}&=k_{f}[{ce {E}}][{ce {S}}]-k_{r}[{ce {ES}}]-k_{mathrm {cat} }[{ce {ES}}][4pt]{frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}&=k_{mathrm {cat} }[{ce {ES}}].end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/fef60952725615b295c3f3460a431e2b084e42b8)
In this mechanism, the enzyme E is a catalyst, which only facilitates the reaction, so that its total concentration, free plus combined, {displaystyle [E]+[ES]=[E]_{0}}![[E] + [ES] = [E]_0](https://wikimedia.org/api/rest_v1/media/math/render/svg/ad13d24a63d5ee09ed542b5a281471be77a68b09)
is a constant (i.e. {displaystyle [E]_{0}=[E]_{total}}![{displaystyle [E]_{0}=[E]_{total}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd9c6e4effb29d5eaa78ae40407c2774f8877464)
). This conservation law can also be observed by adding the first and third equations above.[18][19]
is a constant (i.e. {displaystyle [E]_{0}=[E]_{total}}). This conservation law can also be observed by adding the first and third equations above.[18][19]Equilibrium approximationEdit
In their original analysis, Michaelis and Menten assumed that the substrate is in instantaneous chemical equilibrium with the complex, which implies[4][19]
{displaystyle k_{f}[{ce {E}}][{ce {S}}]=k_{r}[{ce {ES}}].}![{displaystyle k_{f}[{ce {E}}][{ce {S}}]=k_{r}[{ce {ES}}].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a027a53d0cef2086d7b096e9ed7a1952d708346b)
From the enzyme conservation law, we obtain[19]
{displaystyle [{ce {E}}]=[{ce {E}}]_{0}-[{ce {ES}}].}![{displaystyle [{ce {E}}]=[{ce {E}}]_{0}-[{ce {ES}}].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82aa61ab7633797beff11f364f755a233e74b1df)
Combining the two expressions above, gives us
{displaystyle {begin{aligned}k_{f}([{ce {E}}]_{0}-[{ce {ES}}])[{ce {S}}]&=k_{r}[{ce {ES}}][4pt]k_{f}[{ce {E}}]_{0}[{ce {S}}]-k_{f}[{ce {ES}}][{ce {S}}]&=k_{r}[{ce {ES}}][4pt]k_{r}[{ce {ES}}]+k_{f}[{ce {ES}}][{ce {S}}]&=k_{f}[{ce {E}}]_{0}[{ce {S}}][4pt][{ce {ES}}](k_{r}+k_{f}[{ce {S}}])&=k_{f}[{ce {E}}]_{0}[{ce {S}}][4pt][{ce {ES}}]&={frac {k_{f}[{ce {E}}]_{0}[{ce {S}}]}{k_{r}+k_{f}[{ce {S}}]}}[4pt][{ce {ES}}]&={frac {k_{f}[{ce {E}}]_{0}[{ce {S}}]}{k_{f}({frac {k_{r}}{k_{f}}}+[{ce {S}}])}}[4pt]end{aligned}}}![{displaystyle {begin{aligned}k_{f}([{ce {E}}]_{0}-[{ce {ES}}])[{ce {S}}]&=k_{r}[{ce {ES}}][4pt]k_{f}[{ce {E}}]_{0}[{ce {S}}]-k_{f}[{ce {ES}}][{ce {S}}]&=k_{r}[{ce {ES}}][4pt]k_{r}[{ce {ES}}]+k_{f}[{ce {ES}}][{ce {S}}]&=k_{f}[{ce {E}}]_{0}[{ce {S}}][4pt][{ce {ES}}](k_{r}+k_{f}[{ce {S}}])&=k_{f}[{ce {E}}]_{0}[{ce {S}}][4pt][{ce {ES}}]&={frac {k_{f}[{ce {E}}]_{0}[{ce {S}}]}{k_{r}+k_{f}[{ce {S}}]}}[4pt][{ce {ES}}]&={frac {k_{f}[{ce {E}}]_{0}[{ce {S}}]}{k_{f}({frac {k_{r}}{k_{f}}}+[{ce {S}}])}}[4pt]end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ff8e088fe1b70c019604d85715c47b8cb6570b21)
Upon simplification, we get
{displaystyle [{ce {ES}}]={frac {[{ce {E}}]_{0}[S]}{K_{d}+[{ce {S}}]}}}![{displaystyle [{ce {ES}}]={frac {[{ce {E}}]_{0}[S]}{K_{d}+[{ce {S}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/097cd93112fd2bce222f6065b551bda9ce86ea80)
where {displaystyle K_{d}=k_{r}/k_{f}}
is the dissociation constant for the enzyme-substrate complex. Hence the velocity {displaystyle v}
of the reaction – the rate at which P is formed – is[19]
{displaystyle v={frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}={frac {V_{max }{[{ce {S}}]}}{K_{d}+[{ce {S}}]}}} is the dissociation constant for the enzyme-substrate complex. Hence the velocity {displaystyle v} of the reaction – the rate at which P is formed – is[19]![{displaystyle v={frac {mathrm {d} [{ce {P}}]}{mathrm {d} t}}={frac {V_{max }{[{ce {S}}]}}{K_{d}+[{ce {S}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d8b24862cf866c3ae645194a5284c1c5f98baa5d)
where {displaystyle V_{max }=k_{mathrm {cat} }[{ce {E}}]_{0}}![{displaystyle V_{max }=k_{mathrm {cat} }[{ce {E}}]_{0}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7d9476dfc33c4c323b9becb9fa1e6bbe4fb86845)
is the maximum reaction velocity.
is the maximum reaction velocity.Quasi-steady-state approximationEdit
An alternative analysis of the system was undertaken by British botanist G. E. Briggs and British geneticist J. B. S. Haldane in 1925.[20][21] They assumed that the concentration of the intermediate complex does not change on the time-scale of product formation – known as the quasi-steady-state assumption or pseudo-steady-state-hypothesis. Mathematically, this assumption means {displaystyle k_{f}[{ce {E}}][{ce {S}}]=k_{r}[{ce {ES}}]+k_{mathrm {cat} }[{ce {ES}}]=(k_{r}+k_{mathrm {cat} })[{ce {ES}}]}![{displaystyle k_{f}[{ce {E}}][{ce {S}}]=k_{r}[{ce {ES}}]+k_{mathrm {cat} }[{ce {ES}}]=(k_{r}+k_{mathrm {cat} })[{ce {ES}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f44026ab5de910033fa61c3b882f915c34c6743f)
. This is mathematically the same as the previous equation, with {displaystyle k_{r}} replaced by {displaystyle k_{r}+k_{mathrm {cat} }}
. Hence, following the same steps as above, the velocity {displaystyle v} of the reaction is[19][21]
{displaystyle v={frac {V_{max }{[{ce {S}}]}}{K_{mathrm {M} }+[{ce {S}}]}}}. This is mathematically the same as the previous equation, with {displaystyle k_{r}} replaced by {displaystyle k_{r}+k_{mathrm {cat} }}. Hence, following the same steps as above, the velocity {displaystyle v} of the reaction is[19][21]![{displaystyle v={frac {V_{max }{[{ce {S}}]}}{K_{mathrm {M} }+[{ce {S}}]}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2bde0878e92a154c2c8dbcfbe93221614f545f53)
where
{displaystyle K_{mathrm {M} }={frac {k_{r}+k_{mathrm {cat} }}{k_{f}}}}
is known as the Michaelis constant.
Assumptions and limitationsEdit
The first step in the derivation applies the law of mass action, which is reliant on free diffusion. However, in the environment of a living cell where there is a high concentration of proteins, the cytoplasm often behaves more like a gel than a liquid, limiting molecular movements and altering reaction rates.[22] Although the law of mass action can be valid in heterogeneous environments,[23] it is more appropriate to model the cytoplasm as a fractal, in order to capture its limited-mobility kinetics.[24]
The resulting reaction rates predicted by the two approaches are similar, with the only difference being that the equilibrium approximation defines the constant as {displaystyle K_{d}}
, whilst the quasi-steady-state approximation uses {displaystyle K_{mathrm {M} }}. However, each approach is founded upon a different assumption. The Michaelis–Menten equilibrium analysis is valid if the substrate reaches equilibrium on a much faster time-scale than the product is formed or, more precisely, that [
{displaystyle varepsilon _{d}={frac {k_{mathrm {cat} }}{k_{r}}}ll 1.}, whilst the quasi-steady-state approximation uses {displaystyle K_{mathrm {M} }}. However, each approach is founded upon a different assumption. The Michaelis–Menten equilibrium analysis is valid if the substrate reaches equilibrium on a much faster time-scale than the product is formed or, more precisely, that [
By contrast, the Briggs–Haldane quasi-steady-state analysis is valid i
{displaystyle varepsilon _{m}={frac {ce {[E]_{0}}}{[{ce {S}}]_{0}+K_{ce {M}}}}ll 1.}![{displaystyle varepsilon _{m}={frac {ce {[E]_{0}}}{[{ce {S}}]_{0}+K_{ce {M}}}}ll 1.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/438c880796d0bff343d10a74392b3dba9e7c1fd8)
Thus it holds if the enzyme concentration is much less than the substrate concentration or {displaystyle K_{mathrm {M} }} or both.
or both.In both the Michaelis–Menten and Briggs–Haldane analyses, the quality of the approximation improves as {displaystyle varepsilon ,!}
decreases. However, in model building, Michaelis–Menten kinetics are often invoked without regard to the underlying assumptions.
decreases. However, in model building, Michaelis–Menten kinetics are often invoked without regard to the underlying assumptions.It is also important to remember that, while irreversibility is a necessary simplification in order to yield a tractable analytic solution, in the general case product formation is not in fact irreversible. The enzyme reaction is more correctly described as
{displaystyle {ce {E{}+S[{mathit {k_{f_{1}}}}][{mathit {k_{r_{1}}}}]ES[{mathit {k_{f_{2}}}}][{mathit {k_{r_{2}}}}]E{}+P.}}}![{displaystyle {ce {E{}+S=[{mathit {k_{f_{1}}}}][{mathit {k_{r_{1}}}}]ES=[{mathit {k_{f_{2}}}}][{mathit {k_{r_{2}}}}]E{}+P.}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b661b61bc9cfd6e6dd3eb133e7cfd63d6deafb6b)
In general, the assumption of irreversibility is a good one in situations where one of the below is true:
1. The concentration of substrate(s) is very much larger than the concentration of products:{displaystyle {ce {[S]gg [P].}}}![{displaystyle {ce {[S]gg [P].}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6505b0b596821fdbe306e0357a8a25fcb0246f1a)
This is true under standard in vitro assay conditions, and is true for many in vivo biological reactions, particularly where the product is continually removed by a subsequent reaction.
2. The energy released in the reaction is very large, that is{displaystyle Delta {G}ll 0.}
In situations where neither of these two conditions hold (that is, the reaction is low energy and a substantial pool of product(s) exists), the Michaelis–Menten equation breaks down, and more complex modelling approaches explicitly taking the forward and reverse reactions into account must be taken to understand the enzyme biology.
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Joyfrank
PHILOSOPHY
~7.7 mins read
ToPhilosophy (from Greek: φιλοσοφία, philosophia, 'love of wisdom') is the study of general and fundamental questions about existence, knowledge, values, reason, mind, and language.Such questions are often posed as problemsto be studied or resolved. The term was probably coined by Pythagoras (c. 570 – 495 BCE). Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation.
The School of Athens (1509–1511) by Raphael, depicting famous classical Greek philosophers in an idealized setting inspired by ancient Greek architecture
Classic philosophical questions include, "Is it possible to know anything?", and if so, "Can we prove it?"However, more practical and concrete questions may be posed, such as: "Is there a best way to live?", "Is it better to be just, even if one could get away with being unjust?",and "Do humans have free will?"
Historically, philosophy encompassed all bodies of knowledge and a practitioner was known as a philosopher.From the time of Ancient Greek philosopher Aristotle to the 19th century, "natural philosophy" encompassed astronomy, medicine, and physics.For example, Newton's 1687 Mathematical Principles of Natural Philosophy later became classified as a book of physics.
In the 19th century, the growth of modern research universities led academic philosophy and other disciplines to professionalize and specialize.In the modern era, some investigations that were traditionally part of philosophy became separate academic disciplines, including psychology, sociology, linguistics, and economics. Other investigations closely related to art, science, politics, or other pursuits remained part of philosophy. For example, is beauty objective or subjective?Does the scientific method reflect how science is actually practiced?What criteria separate science from pseudoscience? Is political utopia a hopeful dream or hopeless fantasy?
Major subfields of academic philosophy include metaphysics, which is concerned with the fundamental nature of existence and reality; epistemology, which studies the nature of knowledge and belief; ethics, which is concerned with moral value; and logic, which studies the rules of inference that allow one to deduce conclusions from true premises. Other notable subfields include philosophy of science, political philosophy, aesthetics, philosophy of language, and philosophy of mind.
The Main Branches of Philosophy are divided as to the nature of the questions asked in each area. The integrity of these divisions cannot be rigidly maintained, for one area overlaps into the others.
The Main Branches of Philosophy are divided as to the nature of the questions asked in each area. The integrity of these divisions cannot be rigidly maintained, for one area overlaps into the others.
Axiology: the study of value; the investigation of its nature, criteria, and metaphysical status. More often than not, the term "value theory" is used instead of "axiology" in contemporary discussions even though the term “theory of value” is used with respect to the value or price of goods and services in economics.
Some significant questions in axiology include the following:
Nature of value: is value a fulfillment of desire, a pleasure, a preference, a behavioral disposition, or simply a human interest of some kind?
Criteria of value: de gustibus non (est) disputandum (i.e., (“there's no accounting for tastes”) or do objective standards apply?
Status of value: how are values related to (scientific) facts? What ultimate worth, if any, do human values have?
Axiology is usually divided into two main parts.
Ethics: the study of values in human behavior or the study of moral problems: e.g., (1) the rightness and wrongness of actions, (2) the kinds of things which are good or desirable, and (3) whether actions are blameworthy or praiseworthy.
Consider this example analyzed by J. O. Urmson in his well-known essay, "Saints and Heroes":
"We may imagine a squad of soldiers to be practicing the throwing of live hand grenades; a grenade slips from the hand of one of them and rolls on the ground near the squad; one of them sacrifices his life by throwing himself on the grenade and protecting his comrades with his own body. It is quite unreasonable to suppose that such a man must be impelled by the sort of emotion that he might be impelled by if his best friend were in the squad."
Did the soldier who threw himself on the grenade do the right thing? If he did not cover the grenade, several soldiers might be injured or be killed. His action probably saved lives; certainly an action which saves lives is a morally correct action. One might even be inclined to conclude that saving lives is a duty. But if this were so, wouldn't each of the soldiers have the moral obligation or duty to save his comrades? Would we thereby expect each of the soldiers to vie for the opportunity to cover the grenade?
Æsthetics: the study of value in the arts or the inquiry into feelings, judgments, or standards of beauty and related concepts. Philosophy of art is concerned with judgments of sense, taste, and emotion.
E.g., Is art an intellectual or representational activity? What would the realistic representations in pop art represent? Does art represent sensible objects or ideal objects?
Is artistic value objective? Is it merely coincidental that many forms in architecture and painting seem to illustrate mathematical principles? Are there standards of taste?
Is there a clear distinction between art and reality?
Epistemology: the study of knowledge. In particular, epistemology is the study of the nature, scope, and limits of human knowledge.
Epistemology investigates the origin, structure, methods, and integrity of knowledge.
Consider the degree of truth of the statement, "The earth is round." Does its truth depend upon the context in which the statement is uttered? For example, this statement can be successively more accurately translated as …
"The earth is spherical"
"The earth is an oblate spheroid" (i.e., flattened at the poles).
But what about the Himalayas and the Marianas Trench? Even if we surveyed exactly the shape of the earth, our process of surveying would alter the surface by the footprints left and the impressions of the survey stakes and instruments. Hence, the exact shape of the earth cannot be known. Every rain shower changes the shape.
(Note here as well the implications for skepticism and relativism: simply because we cannot exactly describe the exact shape of the earth, the conclusion does not logically follow that the earth does not have a shape.)
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