S im p lifie d L ine 2S ha pe M a c rom o le cula r D ynam ics M ode ling a nd S im ula tion

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1 JOU RNAL O F SHAN GHA I J IAO TON G UN IV ER S IT Y V o l. 39 N o. 12 D ec : (2005) ,,, (, ) :, 2,,.,,. : ; ; ; ; ; : T P 15 : A S im p lifie d L ie 2S ha pe M a c rom o le cula r D yam ics M ode lig a d S im ula tio FU Z huag, L IU Y ag, ZH A O Y a2z heg, CA O Q i2x i ( R esearch I sṫ of Robo tics, Shaghai J iao tog U iv., Shaghai , Ch ia ) A bs tra c t: To model the state of low 2eergy cofigu ratio of liear b iom acromo lecu lar by simp lificatio, th is paper p rese ted a ball2virtual sp rig model to bu ild the tra sverse vib ratio model ad ax ial to rsioal vib ratio model, respectively, ad com e to the ex t step to p robe i to the m echa ics affectig the flex ib ili2 ty of liear mo lecu lar. T he sim u latio resu lt show s that the tra sverse flex ig vib ratio of the sigu lar equ ivale t atom i the liear mo lecu lar is a sig ifica t reaso of the tra sitio of the mo lecu lar cofigu ra2 tio. A d the ifluece of the ax ial to rsioal vib ratio of liear mo lecu lar ca be om itted. Ke y w o rds: simp lified liear mo lecu lar; cofigu ratio; virtual sp rig; tra sverse vib ratio; to rsioal vib ratio; equ ivale t atom, [1, 2 ]. [3 ],, [1, 4, 5 ].,,. [6 ],.,. 2. 2, [3, 4 ]. [3 ]. : : ( ) : (19722),,,,. (T el. ) : ; E2m ail: zhfu@ sjtu. edu. c.

2 12, : 2041,,, ;,,.,, [7 ].,,.,.,,,. 1,,., (N C O ) H ().,, [1 ]. 1. 1, [4, 5 ]., 1. 1, F x 1 F ig. 1T rasverse vibratio model. Q i (t) Q i (t) = - i (E vdw + E elec + E H) (1) E vdw = A ij r 12 - ij E elec = 1 Ε E H = M r 12 - qiqj rij N r 10 B ij r 6 ij : Q i (t) F x (t) F y ( t) F z ( t), 3 [1 ] ; E vdw ; A ij ; B ij ; rij [1 ] ; E elec; Ε ; qi qj [1 ] ; E H ; r D A ;M N [1 ].,., : m 1 x gg 1 + (k 1 + k 2) x 1 - k 2x 2 = F 1 (t) m i x gg i + (k i + k i+ 1) x i - k ix i- 1 - k i+ 1x i+ 1 = F i (t) m x gg + k x - : k x - 1 = F (t) [M ]{X gg (t) } + [K ]{X (t) } = {F (t) } (2) [M ] = diag [m 1, m 2,, m i,, m ] {X (t) } = {F (t) } = [x 1x 2x ] T [F 1F 2F ] T, m i= m c+ m H i [8, 9 ], m c C N O, m H H.,, : [K ]{u} = Ξ 2 [M ]{u} Ξi {u (i) },, 2,,, [u ] = [ {u (1) }, {u (2) },, {u () } ] : [u ] T [M ] [u ] = I [u ] T [K ] [u ] = diag [Ξ 2 1, Ξ 2 2,, Ξ 2 i,, Ξ 2 ] : {x (t) } = [u ]{Γ(t) } [u ], {x gg (t) } = [u ]{Γ gg (t) } (2), [u ] T, {Γ gg (t) } + diag [Ξ 2 1, Ξ 2 2,, Ξ 2 i,, Ξ 2 ]{Γ(t) } = {N (t) } (3), {N (t) }= [ u ] T {F ( t) }{Γ(t) }

3 (3) gg Γi (t) + Ξ 2 i Γi (t) = N i (t) (4), Γi (t) i. (4),., m = 1, F (Σ) = N i (Σ), Ξi = Ξ Γi (t) = Ξi 1 t N (Σ) 0 i si Ξi (t - Σ) dσ {x (t) } = [u ]{Γ(t) } = 1 {u (i) } t Ξi 0 N i (t) si Ξi (t - Σ) dσ (5) (2),,, {x (t) } = {u (i) } Ξi 1 t {u (i) } T [M ]{x 0}co s Ξit + 1 {u (i) } T [M ]{x 0}si Ξit Ξi N i (Σ) si Ξi (t - Σ) dσ F ig. 2A xisal to rsioal vibratio model,,, 2, : [J ] = {Η(t) } = {T (t) } = [J ]{Η gg (t) } + [K ]{Η(t) } = {T (t) } (6) [J 1J 2J ] T [Η1Η2Η ] T [T 1 (t) T 2 (t) T (t) ] T : J i, m i, H ; T i (t) H,,. 2,, M at2 lab : {F (t) } (N ), [M ] (kg), [K ] (kggs 2 ). {F (t) }(1),, F i ( t) = N ico s (Ξ0t) PH z,,. Ξ0= radgs, [N ] = [N 1N 2N 7 ] T = [ ] T 10-2 ΛN [M ]. (O N C S ) (H ), 1434., [M ] = [ ] T [K ],,,., [K ] = , {x (t) } = [u ]{Γ(t) } = {u (i) } C 1co s Ξit + C 2si Ξit + N ico s Ξ0t Ξ 2 i - Ξ 2 0 : C 1= 1 pm ; C 2= 3 pm., 3., ball.

4 12, : F ig. 3T rasverse vibratio curve 2. 2 : [J ] (kgm 2 ) ; [K ] (Jgrad) ; [T ] (N m ). : [J ]= [ ] T [K ]= [T ]= [ ] T 10-11, {Η(t) } = [u ]{Γ(t) } = {u (i) } C 3co s Ξit + C 4si Ξit + N isi Ξ 0t Ξ 2 i - Ξ 0 2 : C 3 = rad; C 4 = rad; Ξ 0 = radgṡ,, , 10 pm, r 0. 1 m,,,, ; rad ( ),,,,. 3 4 F ig. 4To rsioal vibratio curve 2,.,,,,.,, [5, 7 ].. : [1 ],. [M ]. :, [2 ],,,. [J ]., 2003 (4): LUO X iao2m i, J IAN G H ua2liag, SH EN J ia2hua, et al. T he study p rogress of drug mo lechular desig [J ]. Subject D evelopme t, 2003 (4): [3 ]. [M ]. :, ; [4 ]R apapo rt D C. M o lecular dyam ics sim ulatio [J ]. Com putig i Sc iece & Eg ieer ig, 1999 ( 1): [5 ]E rco lessi F. U se of classical fo rces [ EBgOL ]. h ttp: gwww. fisica. uiud. itgerco lessigm dgm d. [6 ],,. [J ]., 1994, 18 (4): TAN G Yu, CH EN Kai2xia, J I R u2yu. R easoable drug desig study [ J ]. Pharm ic Progress, 1994, 18 (4): (2047 )

5 12, : cp= 10, Σp= 2, C r= 200 Tab. 3The simulatio result whe cp= 10, Σp= 2, C r= 200 Cm R N T 1 T 2 T 3 T 4 T 5 c Cm = 80, cp= 10, Σp= 2 Tab. 4The simulatio result whe Cm = 80, cp= 10, Σp= 2 C r R N T 1 T 2 T 3 T 4 T 5 T 6 T 7 c ,,.,,.,,,,,.,,,,,.,. : [ 1 ]Barlow R E, H uter L C. Op tim um p revetive m ai2 teace po licies [ J ]. Operatio s Research, 1960, 8 (1): [ 2 ]Sheu S H, Griffith W S, N akagaw a T. Exteded op2 tim al rep lacem et model w ith radom m iim al repair co sts [ J ]. Europea Joural of Operatioal Research, 1995, 85 (3): [ 3 ]L ai K K, L eug F K N, T ao B, et al. P ractices of p revetive m aiteace ad rep lacem et fo r egies: A case study [J ]. Research, 2001, 124 (2): Europea Joural of Operatioal [ 4 ]Sheu S H, Griffith W S. Exteded block rep lacem et po licy w ith shock models ad used item s [J ]. Europea Joural of Operatioal Research, 2002, 140 (1): [ 5 ]Pham H, W ag H Z. Imperfect m aiteace [J ]. Europea Joural of Operatioal Research, 1996, 94 (3): [ 6 ]M alik M A K. R eliable p revetive m aiteace po li2 cy [J ]. A IIE Tra sactio s, 1979, 11 (3): [ 7 ]N akagaw a T. Sequetial imperfect p revetive m ai2 teace po licies [J ]. ty, 1988, 37 (3): IEEE Tra sactio s o Rel iabil i2 [ 8 ]L eviti G, L isiask i A. Op tim izatio of imperfect p revetive m aiteace fo r m ulti2state system s [J ]. Rel iabil ity Eg ieer ig ad System Safety, 2000, 67 (2): [ 9 ]Zhao Y X. O p revetive m aiteace po licy of a critical reliability level fo r system subject to degrada2 tio [J ]. Reliability Eg ieer ig ad System Safety, 2003, 79 (3): [10 ],,,. [J ]., 2003, 9 (3): HAN Bag2ju, FAN X iu2m i, M A D eg2zhe, et al. Op tim izatio of equipm et p revetive m aite2 ace cycle i p roductio system based o geetic algo rithm [J ]. System, 2003, 9 (3): Com puter I tegrated M aufactur ig (2043 ) [7 ],,. [J ]., 1998, 18 (1): ZHAO Yu2ju, J IAN G M ig, CAO Pei2li. Calcula2 tio from begiig i m o lecular dyam ics [ J ]. Progress i Physics, 1998, 18 (1): [8 ]ZHAN G M ig, Kavrak i L E.. A ew m ethod fo r fast ad accurate derivatio of m o lecular cofo rm atios [ J ]. Chem ical Iformatio ad Com putig Sc iece, 2002, 42: [9 ]N akao A, Kalla R, V ash ish ta P. Scalable mo lecular2 dyam ics, visualizatio, ad data2m aagem et algo2 rithm s fo r m aterials sim ulatio [ J ]. Com putig i Sc iece & Eg ieer ig, 1999, 1 (5):

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