LA TRANSPARENCIA ACTUAL DE LA OBRA DE MARX EL CAPITAL

The most common treatment of transporter kinetics is the Michaelis-Menten (MM) model. Michaelis-Menten kinetics are measured under conditions where depletion of substrates is minimal and a single substrate concentration is varied while all others are at saturation concentrations. This experimental scenario allows for rate determination based on single substrate variation and are known as initial rate conditions [182]. Following on logically, if substrate concentrations are effectively constant, the concentrations of all transporter- substrate intermediates during the transport cycle will also be at steady state after the first turnover of the transport. This first assumption of Michaelis-Menten kinetics is known as the steady-state assumption [183-185].

The steady-state assumption applies to physiological conditions for sodium and chloride in the intestinal and proximal tubule lumens, where a large excess concentration is maintained. However, it does not apply to the significant changes in neutral amino acid concentrations experienced by B0AT1 and B0AT3 before and after meals (see Tables 1.1 and 1.2). Other important assumptions are at time zero, i.e. the beginning of experimental measurement, trans-substrate concentration is zero and no reverse transport occurs.

Michaelis-Menten kinetics are a useful model because its assumptions allow a transporter (T) catalysing substrate (S) translocation to be described by a simplified chemical equation:

25 and the resulting steady-state transport rate or velocity (𝑣) described by:

𝑣 = 𝑉𝑚𝑎𝑥[𝑆] 𝐾𝑚+ [𝑆]

(eq. 1.11)

the Michaelis-Menten equation, which is derived from the differential rate laws of equation 1.9 (p. 228) incorporating the steady-state assumption (see e.g. [183]). It is the saturation curve for the variation of one substrate’s concentration ([𝑆]) under initial rate conditions. The parameter 𝑉𝑚𝑎𝑥 refers to the maximal (saturation) transport rate. The parameter 𝐾𝑚 (the Michaelis constant) has the experimental meaning:

𝐾_𝑚 = [𝑆] → 𝑣 ≡1 2𝑉𝑚𝑎𝑥

(eq. 1.12)

in units of concentration, which is invariant given initial rate conditions and steady-state assumptions. However, it is also a macroscopic rate constant, whose meaning varies depending on whether the second Michaelis and Menten assumption is accepted or not. They assumed substrate binding and dissociation to be much faster than any subsequent step (i.e.

𝑘−1≫ 𝑘2) and to form a rapid equilibrium. Under this simplified condition, 𝐾𝑚 approximates the dissociation constant (𝐾𝑚 ≈ 𝑘−1⁄ )𝑘1 for the reaction and 𝑘2 is rate- limiting, i.e. 𝑉_𝑚𝑎𝑥 ≈ 𝑘₂. Chemically, the lower the Michaelis constant the ‘tighter’ substrate binding to the transporter, i.e. the greater the non-covalent bond formation energy. This assumption is not necessarily correct [186], in which case 𝐾_𝑚 has the canonical definition :

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𝐾_𝑚= 𝑘2+ 𝑘−1 𝑘₁

(eq. 1.13)

Where 𝑘₂ is not the sole rate-limiting step in the transporter cycle and instead, binding and subsequent turnover have reached steady-state. The meaning of the Michaelis constant can change based on the relative rates of discrete chemical steps occurring after initial substrate binding. If we assume the Michaelis constant equals the dissociation constant, then 𝐾_𝑚 is equal to the ‘affinity’ of the substrate. However, unless this can be demonstrated, 𝐾𝑚is best described as representing ‘apparent’ affinity. The assumption the 𝐾_𝑚 equals 𝐾_𝑑 is justified for most transporters as turnover (𝑘_𝑐𝑎𝑡) is typically of the range of 10−2 to 10−3seconds, whereas binding is measured in sub-millisecond ranges.

The possible meanings of the Michaelis constant is not just an empty academic exercise as it gives important information what steps in the transport cycle are rate-limiting. For example, the substrate specificity of B0AT1 and B0AT3 is determined largely by changes in apparent

𝐾𝑚 rather than 𝑉𝑚𝑎𝑥, suggesting changes are due to substrate binding. Mouse B0AT1 has the highest apparent affinity for L-leucine (0.63-1.16 mM), followed by glutamine (0.52-3.2 mM), alanine (4.1 mM), phenylalanine (0.59-4.7 mM) and glycine (11.7 mM) [39, 40, 168]. B0AT3’s apparent 𝐾_𝑚 for its two main substrates alanine and glycine is 0.9 mM and 2.3 mM, respectively [106, 132]. What is notable about B0AT1 and B0AT3 is their high 𝐾𝑚 values compared with most other SLC6 transporters (see [100]). If the rapid equilibrium assumption is made ( 𝐾_𝑚 ≈ 𝑘₋₁⁄𝑘₁ ), this suggests much weaker substrate binding than the neurotransmitter SLC6 transporters (e.g. DAT 𝐾_𝑚 = 2.5 μM [100, 187, 188]). The low affinity of B0AT1 for many substrates for which it is the only brush border transporter, e.g.

27 tryptophan, is probably compensated for by absorption time along the intestinal tract and the high number of kidney nephrons [189] (section 1.1.2). Furthermore, the relatively high 𝐾_𝑚 of B0AT1 is reflective of its physiological role in the brush border membrane, where combined neutral amino concentration after a meal is several mM (Tables 1.1. and 1.2).

For B0AT1 a four-step kinetic model has been proposed [39]. The isolated chemical steps proposed in this model are consistent with subsequent x-ray crystal structures from isolated B0AT1 and B0AT3 homologues (section 6.2.3) and several steady-state kinetic features of B0AT1. For example, the apparent 𝐾_𝑚 of sodium and AA0 are highly dependent on each other’s steady-state concentration [39, 131]. Given the rapid equilibrium assumption (i.e.

𝑘₋₁≫ 𝑘₂) this indicates binding of both substrates is co-dependent and simultaneous [190], and is explained by coordination of sodium by the substrate carboxylate group (see section 1.3.4).

The ancillary partners of B0AT1 and B0AT3, collectrin and ACE2, are involved in trafficking the transporters to the plasma membrane (section 1.5.2). As a function of increased plasma membrane expression, the kinetic property affected by ancillary protein co-expression is 𝑉_𝑚𝑎𝑥. However, steady-state kinetics measurements of isolated B0AT1 and B0AT3 were initially measured in the absence of either ancillary (e.g. [39, 40, 131, 168, 171]).

Little is known about B0AT1 or B0AT3 microscopic rate constants, making it difficult to derive any comprehensive rate equations other than simplified Michaelis-Menten models. However, based on crystal structures of B0AT1 and B0AT3 ancestors, a general SLC6 structure, transport cycle and binding mechanism has been proposed [95, 191].

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