Affine space

The definition of a mathematical space begins with the set of objects X, Y, Z,. .. that occupy the space (an intrinsically empty space being a physically problematic concept). Among the simplest algebraic structures that can characterize such objects is that of a linear manifold, also called a linear vector space, affine space, etc. By definition, such a manifold has only two operations— addition (X + Y) and multiplication by a scalar (AX)— resulting in each case in another element of the manifold. These operations have the usual distributive,... 

Absorption. Some inks (eg, oil-based newspaper inks) dry by penetration or absorption into the pores of the printed stock, which has a blotter or sponge effect. This is accompHshed by the gross penetration of the ink vehicle into the pores of the substrate, the partial separation of the vehicle from the pigment, and the diffusion of the vehicle throughout the paper. The abiHty of an ink to penetrate into paper depends on the number and size of the air spaces present in the paper, the affinity or receptivity of the stock for the ink, and the mobiHty of the ink. 

The catalytic cycle of the Na+/K+-ATPase can be described by juxtaposition of distinct reaction sequences that are associated with two different conformational states termed Ei and E2 [1]. In the first step, the Ei conformation is that the enzyme binds Na+ and ATP with very high affinity (KD values of 0.19-0.26 mM and 0.1-0.2 pM, respectively) (Fig. 1A, Step 1). After autophosphorylation by ATP at the aspartic acid within the sequence DKTGS/T the enzyme occludes the 3 Na+ ions (Ei-P(3Na+) Fig. la, Step 2) and releases them into the extracellular space after attaining the E2-P 3Na+ conformation characterized by low affinity for Na+ (Kq5 = 14 mM) (Fig. la, Step 3). The following E2-P conformation binds 2 K+ ions with high affinity (KD approx. 0.1 mM Fig. la, Step 4). The binding of K+ to the enzyme induces a spontaneous dephosphorylation of the E2-P conformation and leads to the occlusion of 2 K+ ions (E2(2K+) Fig. la, Step 5). Intracellular ATP increases the extent of the release of K+ from the E2(2K+) conformation (Fig. la, Step 6) and thereby also the return of the E2(2K+) conformation to the EiATPNa conformation. The affinity ofthe E2(2K+) conformation for ATP, with a K0.5 value of 0.45 mM, is very low. 

Substrate specificity is determined by high affinity for the cognate neurotransmitter substrate. However, low affinity uptake does also have a part in the clearance of transmitters from the interstitial space (e.g., in uptake mediated by the extraneuronal monoamine transporter, EMT) and in the intestinal absoiption of glycine and glutamate. It is obvious that there is an evolutionary relation of neurotransmitter transporters and amino acid and cation transporters in epithelia. 

Neurotransmitter transporters determine the neurotransmitter concentration in the interstitium. High-affinity transporters can efficiently remove neurotransmitter from the extracellular space because cellular uptake is typically coupled to the translocation of sodium ions. 

The cationization of the monomer proceeds, according to Eq. (20), as an exothermic process (proton affinity of ethene) and without any activation. The great exothermic effect and the small space need of a free proton are responsible for the latter fact. 

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