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Changes of enzyme activity in lipid signaling pathways related to substrate reordering
Authors:Salinas Dino G  De La Fuente Milton  Reyes Juan G
Affiliation:Facultad de Ciencias de la Salud, Universidad Diego Portales, Santiago, Chile.
Abstract:The static fluid mosaic model of biological membranes has been progressively complemented by a dynamic membrane model that includes phospholipid reordering in domains that are proposed to extend from nanometers to microns. Kinetic models for lipolytic enzymes have only been developed for homogeneous lipid phases. In this work, we develop a generalization of the well-known surface dilution kinetic theory to cases where, in a same lipid phase, both domain and nondomain phases coexist. Our model also allows understanding the changes in enzymatic activity due to a decrease of free substrate concentration when domains are induced by peptides. This lipid reordering and domain dynamics can affect the activity of lipolytic enzymes, and can provide a simple explanation for how basic peptides, with a strong direct interaction with acidic phospholipids (such as beta-amyloid peptide), may cause a complex modulation of the activities of many important enzymes in lipid signaling pathways.
Keywords:  mmlsi10"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si10.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=2a631700a3f590821cb49c39a602862b')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >a≡(Ad/Ah)?(0≤a≤1), the fraction of the total lipid area that is occupied by the domain phase     mmlsi11"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si11.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=a338aae97d2b0c7092a9335a173241af')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >Ah, area of total lipid phase with its lipid components distributed homogeneously   Ai, area of the i phase     mmlsi12"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si12.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=f93637b073e0458acdb16b9040ebfa78')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >AL, transverse area of a lipid molecule     mmlsi13"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si13.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=7cd91e262249c1aae257e664646be661')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >Ce, univalent electrolyte concentration     mmlsi14"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si14.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=72884b0c8e27e2ecbbb8b86bdee26c1a')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  21"   border="  0"   style="  vertical-align:bottom"   width="  19"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si14.gif"  >, peptide concentration in the water phase near the surface of the lipid phase     mmlsi15"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si15.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=10327304e98ccc8fb622edb79f3a520a')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >CP, peptide concentration in the bulk solution   e, elemental charge (positive)   [E], molar concentration of aqueous enzyme solution     mmlsi16"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si16.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=4d8a2b6b07d8e92b13824f18e1f1894d')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >[EB], molar concentration of total enzyme bound to the lipid phase     mmlsi17"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si17.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=9e96f62c328d0703d57804b0281ebb08')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >[ES], molar concentration of ES in the domain phase     mmlsi18"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si18.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=4427b4b20929f9f61bdd5ce36e1d8c71')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >[ESS], molar concentration of ESS in the domain phase     mmlsi19"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si19.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=a8771bb0783359582a6adeb79258ab5e')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ES, mole fraction of ES in the domain phase     mmlsi20"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si20.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=a88ad8aa5fb450b349e0f35ff0a789f8')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ESS, mole fraction of ESS in the domain phase     mmlsi21"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si21.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=ab9179daa27ce94fde6d15a4d0884a5a')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >[ES], molar concentration of E′S in the nondomain phase     mmlsi22"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si22.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=4a801a8932bdec8c366f4870083f25ad')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >[ESS], molar concentration of E′SS in the nondomain phase     mmlsi23"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si23.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=7f16fb6cc4b1457a24d3f784b770f039')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ES, mole fraction of E′S in the nondomain phase     mmlsi24"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si24.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=d34cbb94af86e7b202e70f03741a6483')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ESS, mole fraction of E′SS in the nondomain phase     mmlsi25"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si25.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=71999af0a979fb55745ba3aace22927b')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ET, total enzyme concentration   f, mole fraction of substrate S in a homogeneous interface of area Ah     mmlsi26"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si26.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=ed19d44499fb2cb9cec7dff3127e414c')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >fd, substrate (S) mole fraction in the domain phase     mmlsi27"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si27.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=326aa9d6dfd36b1c278ae611b83304d0')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >fn, substrate mole fraction in the nondomain phase     mmlsi28"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si28.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=07fe66612a76119b4fa8de1a3c869ca6')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >fi, total initial substrate mole fraction in the i phase     mmlsi29"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si29.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=6efc335a08bb9c6e902679ba373c7523')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  20"   border="  0"   style="  vertical-align:bottom"   width="  18"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si29.gif"  >, free substrate mole fraction in i phase     mmlsi30"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si30.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=6c9f8c9cab24da1f98ed3608f59e97ed')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  20"   border="  0"   style="  vertical-align:bottom"   width="  25"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si30.gif"  >, peptide (P) bound substrate mole fraction in i phase     mmlsi31"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si31.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=038da0f2b5ba9638a2843caf55d57617')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  20"   border="  0"   style="  vertical-align:bottom"   width="  28"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si31.gif"  >, average of the square of the substrate mole fraction weighted by the phase area     mmlsi32"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si32.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=80ab59a9d39f422e8016b72e6332f9bf')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  20"   border="  0"   style="  vertical-align:bottom"   width="  29"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si32.gif"  >, average of the substrate mole fraction not bound to the peptide, weighted by the phase area, in the i phase     mmlsi33"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si33.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=99d98382d5f908fbc6a9b4042f2d51d8')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  20"   border="  0"   style="  vertical-align:bottom"   width="  35"   alt="  View the MathML source"   title="  View the MathML source"   src="  http://ars.els-cdn.com/content/image/1-s2.0-S0006349505727405-si33.gif"  >, average of the substrate square mole fraction not bound to the peptide, weighted by the phase area, in the i phase   F, Faraday constant   i, corresponding to the phase i (i = d for the domain phase and i = n for the nondomain phase)     mmlsi34"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si34.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=7b597d451c2b97df31ff0b2a043db600')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >k,?k,?k1,?k1,?k−1,?k−1,?k2,?k2,?k−2,?k−2, (each of these individual kinetic constants defined as shown in Schemes 1 and 2)     mmlsi35"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si35.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=36d3e470b6c90714a7d9754353d2950c')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >km≡((k−2+k)/k2), interfacial Michaelis constant in the domain phase (dimensionless)     mmlsi36"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si36.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=fd3ee7fda1764b29bafa7c101ff77eaf')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >km≡((k−2+k)/k2), interfacial Michaelis constant in the nondomain phase (dimensionless)     mmlsi37"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si37.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=5b7381a14ef7cfc566851025c744cc97')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ks≡(k−1/k1), dissociation constant in the domain phase (mol/vol)     mmlsi38"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si38.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=47f870a964792e07e9d950cf69fa8f52')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ks≡(k−1/k1), dissociation constant in the nondomain phase (mol/vol)     mmlsi39"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si39.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=edc861e35f0a466796f03349cf26d65e')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >KP, intrinsic binding constant of substrate binding to a peptide (vol/mol)   L, total lipid concentration     mmlsi40"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si40.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=f70a0a8eb6725397c7e04d0e13c3bdc5')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >NA, Avogadro's number     mmlsi41"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si41.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=973d90ab18185eff9f6ae93be138c29e')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >Ni, mol of lipids in the i phase   [P], total product molar concentration from the enzymatic reaction (mol/vol)   R, gas constant   T, temperature (°K)   V, total rate of product formation (mol/(vol time))   z, valence of the ionic multivalent peptide   Greek symbols: ?0, permittivity of free space   ?r, dielectric constant of the solution     mmlsi42"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si42.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=c65af5a62e77127261b675d119328fe8')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >θi, substrate fraction that is bound to the peptide in the i phase     mmlsi43"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si43.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=5c3f7364900229eb088cc44bb73d2bb2')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >σi, surface charge density in i phase     mmlsi44"   onclick="  submitCitation('/science?_ob=MathURL&  _method=retrieve&  _eid=1-s2.0-S0006349505727405&  _mathId=si44.gif&  _pii=S0006349505727405&  _issn=00063495&  _acct=C000069490&  _version=1&  _userid=6211566&  md5=a0f40d4c52a52522847800384418a893')"   style="  cursor:pointer  "   alt="  Click to view the MathML source"   title="  Click to view the MathML source"  >  formulatext"   title="  click to view the MathML source"  >ψi, membrane potential in the i phase
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