Proc. Pakistan Acad. Sci. 42(3): 187-193.2005

ON A FOURTH ORDER PSEUDOPARABOLIC EQUATION

Ye. A. Utkina and A. Maher

Department of Mathematics,Faculty of Science, Department of Differential Equations, Kazan State University,18 Kremlyovskaya St., Kazan, 420008, Russia, and Assiut University, 71516, Egypt

Received February 2005, accepted March 2005

Communicated by Prof. Dr. Q. K. Ghori

Abstract: The present paper is devoted to investigation of the Goursat problem of a fourth order psedudoparabolic equation, with the help of Riemann function.

Keywords: Partial differential equations, Goursat problem, Riemann function AMS Subject Classification: 35B, 35J, 35Q.

Introduction 2 uy x, y0 \1 x xq , \ ,\1 C q ,

In the domain D ^`x0 x x1, y0 y y1 y  p >@y0, y1 , xq >@x0, x1 . (2) we consider the equation Here we assume the following condition as L u u xxyy  a21u xxy  a12u xyy  satisfied:

a11u xy  a20u xx  a02u yy  a10u x  Mc y0 \1 x0 ,M y0 \ x0 ,\ c x0 M1 y0 . i j  a01u y  a00u f ,aij C D , f  22 Formulation of the problem C i 0,1,2, j 0,1,2 , We will be searching for the above- (1) mentioned function u(x‘ y) with the help of the where the classCk l means the existence and conti- Riemann function, which is defined as the solution of the integral equation nuity for all derivatives r 0,...k;s 0,...,l . y w i j v x, y  a x,W  y W a x,W We will call the solution of the class  ³ >@21 20 wx iwy j K C D i 0,1,2, j 0,1 as regular. The equation (1) is x v x,W dW  a t, y  the generalization of the Bussineska-Lyava equation ³ > 12 that describes longitudinal waves in a thin [ elastic shaft with allowance for the effects of x y the crosswise inertia. In this paper we study  x  t a t, y v t, y dt  02 @ ³ ³ the Goursat problem which consists of finding [ K of the function 2 2 1 0 0 1 a t,W  x  t a t,W  y W a t,W  uɋ  D ˆɋ  D‰ p ˆɋ  D‰q , which in D > 11 01 10

̓is a solution (1) and satisfies the following  x  t y W a t,W v t,W dWdt 1. (3) boundary conditions: 00 @

By virtue of [1], it exists and is unique. In u x0, y M y ,ux x0, y M1 y , y  p , cases where it is necessary to emphasize the 2 dependence of v ̓not only on (x‘ y), but also on M,M1 C p ;u x, y0 \ x , [,K , we will indicate it, as usually, R x, y;[,K . Fourth order pseudoparabolic equation 188

Here we should note that v ̓does not coincide Q Py  a20R ; with R as in ҏ[2-5]. Thus, here R x, y; x, y 1, T R a R a R a R ; while in the mentioned papers R x, y; x, y 0 . xy  21 x  12 y  11 However, v x, y remains the solution of the P Ry  a21R ; equation adjoint to (1), namely, K N a R ; * x  02 L v vxxyy  a21v xxy  a12v xyy  a11v xy F1 Ty  a20R x  a10R ;  a20v xx  a02v yy  a10v x  a01v y  a00v 0. F2 Tx  a02R y  a01R . Let us now solve the Goursat problem (G). First, we will prove the auxiliary result. This enables us to write (4) in the form:

Let u x, y belong to the class of the uR xxyy RL u  >@uP xxy  unknown functions of the Goursat problem. Then the following identity is true: >@uN xyy  >@uQ  >@uK yy  >@uT xy  xx uR { RL u  u R  a R  xxyy > y 21 @xxy >@>@uF1 x  uF2 y  >@u x R y  xy

>@>u Rx  a12 R xyy  u Ryy  a21R y  >@u yy R x  u y a 21 R x  u a 20 R x  x

 a20 R @xx  >@u Rxx  a12 R x  a02 R yy uR  u a R  u a R . (5) >@xxy x 12 y 02 y y  u R  a R  a R  a R  > xy 21 x 12 y 11 @xy Let us collect the auxiliary identities which will be needed during the integration of (5).

 >u Rxyy  a21R xy  a12 R yy  a11R y  N x, y, x, y { P x, y, x, y { T x, y, x, y { 0 ,

a20 R x  a10 R @   >u Rxxy  a21R xx  x Q x, y, x,K { K x, y,[, y {

a R  a R  a R  a R + 12 xy 11 x 002 y 01 @y F1 x, y, x,K { F2 x, y,[, y { 0 .

For example, let us verify that N x,y,x,y {0. u x Ry  ^u yy Rx ` ^uRxxy `  ^u y a21R ` + xy x y x x In reality, we put in (3) K y to obtain

x ^u x a12 R y `  ^`u a20 R x x  ^u a02 R y ` , (4) y y v x, y  >@a t, y  x  t a t, y v t, y dt 1 ³ 12 02 [ where arguments of a i 0,1,2; j 0,1,2 are ij Differentiating this relation with respect to x x, y , and at R ̓and its derivatives- x, y;[,K . we obtain The relation (4) is checked directly. Let us put x . vx x, y  a12 x, y v x, y  ³ a02 t, y v t, y dt 0 [ N Rx  a12 R ; Now let[ x . Hence 189 Ye. A. Utkina and A. Maher

y vx x, y  a12 x, y v x, y 0 .  u R  u a R  u a R x ,K dK  ³ > KK x K 21 x 20 x @ 0 Let us now start finding u x, y . We y0 change in (5) the roles of the variables x with[ u a12 R y x0 , y  and y with K and calculate the integral in the right x uR  u a R  u a R [, y d[. and left parts in the bounds x0 d [ d x , ³ > [[y [ 12 y 02 y @ 0 x0 y0 dK d y : In view of (2), the last equality can be written in the form u xy x, y u xy R x, y0  u x Ry x, y0 

u R x, y uR x, y y x 0  xy 0  c uxy x, y \1 x R x, y0 \ c x Ry x, y0  u xy R x0 , y  u x Ry x0 , y  u y Rx x0 , y  \1 x Rx x, y0 \ x Rxy x, y0 uRxy x0 , y  u xy R x0 , y0  c c  u x Ry x0 , y0  u y Rx x0 , y0  uRxy x0 , y0  M1 y R x0 , y M1 y Ry x0 , y M y Rx x0 , y  x y c M y R x , y M y R x , y ³³R [,K; x, y L u dKd[  xy 0 1 0 0 0 x00y M1 y0 Ry x0 , y0 \1 x0 Rx x0 , y0  x y  >@u x P x0 , y  >@uPx x0 , y  >@u x P x, y0  M y0 Rxy x0 , y0  R [,K; x, y L u dKd[ >@uPx x, y0  >@u x P x0 , y0  ³³ x00y M y P x , y M y P x , y \ c x P x, y   >@uPx x0 , y0  >u y N @ x0 , y  >uN y @ x0 , y  1 0 x 0 0

\ x Px x, y0  M1 y0 P x0 , y0 >@u y N x, y0  >@uN y x, y0   M y0 Px x0 , y0 Mc y N x0 , y   >u y N @ x 0 , y 0  >uN y @ x 0 , y 0  M y N y x0 , y \ 1 x N x, y0 \ x N y x, y0  y u Q  uQ x ,K dK x N x , y y N x , y ³ >@x x 0 \ 1 0 0 0 M 0 y 0 0  y 0 y x Q x , Q x , d  u K  uK [ , y d[  uT x , y  >@M1 K 0 K M K x 0 K K ³ >@y y 0 >@ 0 ³ y0 x0 y x uT x, y  uT x , y  uF x ,K dK  \ 1 [ K [, y0 \ [ K y [, y0 d[  >@ 0 >@ 0 0 ³ >@1 0 ³ >@ y0 x0 x M y T x0 , y \ x T x, y0  >@uF2 [ , y 0 d[  u x R y x0 , y  ³ >@ y x0 M y0 T x0 , y0  M K F1 x0 ,K dK  >@u x R y x, y 0  >@u x R y x0 , y 0 ³ y0  >@u y R x x, y 0  >@uR xy x, y 0  x \ [ F [, y d[ u a 21 R x x, y 0 ³ 2 0 x0

M1 y Ry x0 , y \ c x Ry x, y0 

M1 y0 Ry x0 , y0  Fourth order pseudoparabolic equation 190

\ 1 x Rx x, y0 \ x Rxy x, y0  y ª x º \ x a R x, y  M K R x ,K  u3 x, y exp« D1 t, y dt» 21 x 0 ³ > KK x 0 ³ y ¬« x0 ¼» 0 x t Mc K a21R x x0 ,K  M K a20 R x x0 ,K @dK  ª ª º º «C y  f t, y exp« D t , y dt»dt»; y a R x , y 3 ³ ³ 1 1 M 12 y 0  « x x » ¬ 0 ¬« 0 ¼» ¼ x ª y º  \ [ R [, y \ c [ a R u x, y exp« E x,W dW » ³ > [[y 0 12 y 2 ³ 1 (6) y x0 ¬« 0 ¼»

y [, y0 \ [ a02 R y [, y0 @d[. ª ª W º º «C x  u x,W exp E x,W dW dW »; 2 ³ 3 «³ 1 1 1 » « y y » Hence the solution of the Goursat problem is ¬ 0 ¬« 0 ¼» ¼ written in the form ª x º x y u1 x, y exp« D 2 t, y dt» u x, y M y \ x M y0  h [,K dKd[  ³ ³ ³ ¬« x0 ¼» x0 y0 x t x [ y K ª ª º º (6*) «C1 y  u2 t, y exp« D 2 t1 , y dt»dt»;  ³ ³ ³ ³ R t,K;[,K1 f [,K1 dK1dKd[dt, « ³ ³ » ¬ x0 ¬«x0 ¼» ¼ x0 x0 y0 y0 ª y º where h x, y - is the right part (6)without the u x, y exp  E x,W dW « ³ 2 » last addend. The above result can be formulated in ¬« y0 ¼» the form of: ª y ª W º º «C x  u x,W exp E x,W dW dW », ³ 1 «³ 2 1 1 » (9) « y y » Theorem 1: The problem (1) with the boundary ¬ 0 ¬« 0 ¼» ¼ condition (2) has the solution written as the formula (6*). where C1 y Mc y  E2 x0, y M y ,

c Special cases. Here we will be speaking about C2 x \ 1 x  E 2 x, y0 \ c x  the solution in quadratures by the direct D 2 x, y0 \ 1 x \ x E 2x x, y0  D 2 E 2 x, y0 integration of (1), when the operator in its left c part is split. For example, C3 y M1yy y  M1 y E1  E 2 x0 , y 

M yy y D 2 x0 , y  M1 y E 2 y  E1E 2 x0 , y  § w ·§ w ·§ w ·§ wu · . (7) ¨ D1 ¸¨  E1 ¸¨ D2 ¸¨  E2u¸ f  M y E  D E  D  D E x , y  © wx ¹© wy ¹© wx ¹© wy ¹ y 2x 2 2 2 y 2 1 0

M y E 2xy  D 2 E 2 y  E1E 2x  E 2D 2 y  Let us put  D E E x , y . 2 1 2 0

wu wu1  E2u u1 ; D2u1 u2 ; It is clear that now there is a problem of wy wx defining D1 x, y , D2 x, y , E1 x, y , E2 x, y wu2 wu3  E1u2 u3 ; D1u3 f (8) through the coefficients aij x,y of the equation wy wx (1). In order to do this, we will open the brackets of the operator (7). We collect the coefficients Direct calculations show that of corresponding derivatives of u : 191 Ye. A. Utkina and A. Maher

One of the ways of solving these two equations u xxyy  u xxy E1  E 2  u xyy D1  D 2  is to put D2 0, E2 0 . Since the arguments u xy D1E1  D 2 y  2E 2x  D 2 E 2  D 2 E1  x,y ̓occur in the equation (1) equally any  D1E 2  E1x  u xx E 2 y  E1E 2  exchange of the operators

u yy D 2x  D1D 2  u x 2E 2xy  D 2 E 2 y  E1E 2x  § w · § w · § w · § w · ¨  D1 ¸;¨  E1 ¸;¨  D 2 ¸;¨  E 2 ¸  E1E 2 x  D 2 E1E 2  D1E 2 y  D1E1E 2  © wx ¹ © wy ¹ © wx ¹ © wy ¹ u D D E  D  E  D E  y 1 2 1 2xy 2xx 2 2 x will lead to the result. In this way 24 variants  D 2 E1 x  D1D 2 y  D1E 2x  D1D 2 E 2  of the explicit construction of the solution ̓in the equation (1) during the splitting of the left u D1D 2 E1E 2  E 2xxy  D 2 E 2 xy  E1E 2x x  part of this equation is similar to (7), of which  D E E  D E  D D E  D E E f . 2 1 2 x 1 2xy 1 2 2 y 1 1 2x 18 are vitally different.

We will equate the coefficients of the w w § w ·§ wu · equation (1) to the coefficients of the obtained 1) ¨  D ¸¨  Eu¸ f , wx wy © wx ¹© wy ¹ equation § w ·§ w · w wu E  E a ,D D a , 2) ¨ D ¸¨  E ¸ f , 1 2 21 1 2 12 © wx ¹© wy ¹ wx wy D E D  2E  D E D E D E  E a , 1 1 2 y 2x 2 2 2 1 1 2 1x 11 § w ·§ w · w wu 3) ¨  E ¸¨ D ¸ f , E2 y  E1E2 a20 , D2x D1D2 a02 , © wy ¹© wx ¹ wx wy

2E 2xy  D 2 E 2  E1E 2x  E1E 2  § w · w w § wu · y x , 4) ¨ D ¸ ¨  Eu¸ f wx wx wy ¨ wy ¸ D 2 E1E 2  D1E 2 y  D1E1E 2 a10 © ¹ © ¹

D1D 2 E1  D 2xy  E 2xx  D 2 E 2  § w · w w § wu · x , 5) ¨  E ¸ ¨ Du¸ f , © wy ¹ wx wy © wx ¹ D 2 E1 x  D1D 2 y  D1E 2x  D1D 2 E 2 a01 D D E E  E  D E  E E  § w · w § w · wu 1 2 1 2 2xxy 2 2 xy 1 2x x 6) ¨ D ¸ ¨  E ¸ f , © wx ¹ wx © wy ¹ wy D 2 E1E 2 x  D1E 2xy  D1 D 2 E 2 y 

 D1E1E 2x a00 , § w · w § w · wu 7) ¨  E¸ ¨  D¸ f , © wyxx¹ w © w ¹ wy i.ɟ. E2 can be defined from the following equation § w · w § w · wu 8) ¨  D¸ ¨  E¸ f , © wxyy¹ w © w ¹ wx 2 E2 y  a21E2  E2 a20 . § w · w § w · wu 9) ¨  E ¸ ¨ D ¸ f , This equation is the Riccati equation, which is © wy ¹ wy © wx ¹ wx not solved, in the general case in quadratures. The analogous situation also takes place with w w § w ·§ wu · 10) ¨  E ¸¨ Du¸ f , D2 , only we find it from the relation wx wy © wy ¹© wx ¹ 2 D2x  a12D2 D2 a02 . Fourth order pseudoparabolic equation 192

w § w ·§ w · wu 5) a11  ^2a12y  a12a21`{ a20 { a02  11) ¨ D ¸¨  E ¸ f , wx © wx ¹© wy ¹ wy a12x { a10  ^`a12yy  a12y a21 {

{ a01  ^2a12xy  a12x a21`{ a00  w § w ·§ w · wu 12) ¨  E ¸¨ D ¸ f , a  a a { 0, wx © wy ¹© wx ¹ wy ^`12xyy 12xy 21 a 2a a a a a a w § w · w § wu · 6) 11  ^`21x  12 21 { 20 { 02 { 10 13) D ¨  Eu¸ f , , ¨ ¸ ¨ ¸ { a  a  a a { a { 0 wx © wx ¹ wy © wy ¹ 01 ^`21xx 12 21x 00 a  a  a a { a { a  a w § w · w § wu · 7) 11 ^ 12 y 12 21` 20 02 12x 14) ¨  E ¸ Du f , ¨ ¸ ¨ ¸ a a a a a a 0 wx © wy ¹ wy © wx ¹ { 10 { 01  ^`12xy  12x 21 { 00 {

w § w · w § wu · 8) a11  ^`a21x  a12 a21 { a20  a21y { a02 15) ¨ D ¸ ¨  Eu¸ f , wy © wx ¹ wx © wy ¹ { a10  ^`a21xy  a12 a21y { a01 { a00 { 0

w § w ·§ w · wu a11  ^2a12 y  a12 a21`{ a20 { a02 16 ) ¨  E ¸¨ D ¸ f , 9) y ¨ y ¸ x x w © w ¹© w ¹ w { a10  ^`a12 yy  a12 y a21 { a01 { a00 { 0,

w § w · w § wu · 10) a11 ^2a12y  a21x  a12a21`{ a20  a21y 17) ¨  E ¸ ¨ Du¸ f , y ¨ y ¸ x x w © w ¹ w © w ¹ { a02  a12x { a10 ^`a12yy  a21xy  a12a21 y { { a  2a  a a { a  w w § w · wu 01 ^ 12xy 12 21 x ` 00 18) § · f . ¨ D ¸¨  E ¸ a  a a { 0, wy © wx ¹© wy ¹ wx ^`12xxy 12 21 xy a  ^`2a  a a { a { a  a { They are provided by the following conditions 11) 11 21x 12 21 20 02 12x a a a a a a 0 respectively: 10 { 01  ^`21xx  12 21 x { 00 {

a11  ^a21x  a12y  a12a21`{ a20 { a02  a11 ^a12y  2a21x  a12a21`{ a20  a21y 1) 12) a12x { a10 { a01  ^`a12xy  a12a21 x { a00 { 0, { a02  a12x { a10 ^`2a21xy  a12a21 y {

{ a01  ^a12xy  a21xx  a12 a21 x `{ a11  ^`2a21x  a12a21 { a20  a21y { 13) a a a a 0, 00  ^`21xxy  12 21 xy { a02  a12x { a10  ^`2a21xy  a12a21 y {

2) a11  ^`a21x  a21a12 { a20 { { a01  ^a21xx  a12 a21 `{ a00 x a02 { a10 { a01 { a00 { 0, a a a 0,  ^`21xxy  12 21y x { a  2a  a  a a { a { a11  ^a12 y  a21a12 `{ a20 { 14) 11 ^ 12y 21x 12 21` 20 3) a  a { a  a  a a { a02 { a10 { a01 { a00 { 0, 02 12x 10 ^`12yy 12y 21

{ a01  ^2a12xy  a12 a21 x `{ a00  4) a11  ^`2a21x  a12a21 { a20  a21y { a a a 0, ^`12xyy  12 y 21 x { a02 { a10  ^`2a21xy  a12a21 y { { a  ^a  a a `{ a  01 21xx 12 21x 00 ^`a21xxy  a12 a21xy { 0, 193 Ye. A. Utkina and A. Maher

15) a11  ^a12y  2a21x  a12a21`{ a20  a21y { References

a { a  a  a a { 02 10 ^`21xy 12 21 y 1. Muenz, G. 1934. Integral equations. Moscow

{ a01  ^a21xx  a12 a21x `{ a00  State Technical and Theretical Press, Vol. 1., pp.330 [in Russian]. a  a a { 0, ^`21xxy 12 21x y 2. Rundell, W. and Stecher, M. 1977. Remarks concerning the supports of solutions of pseudo- 16) a11  ^2a12y  a12a21`{ a20  a21y { a02 parabolic equation. Proc. Amer. Math. Soc. 63:77- { a10  ^`a12yy  a12a21 y { a01 { a00 { 0 81. 3. Shkhanukov, M. Kh. 1982. On same boundary a11  ^2a12y  a12a21`{ a20  a21y { 17) problems for third order equations occurring during a02  a12x { a10  ^`a12yy  a12a21 y { the modeling of liquid filtration in the porous environment. Differential Equations 18:689- 699. { a01  ^2a12xy  a12 a21 `{ a00  x 4. Soldatov, A.P. and Shkhanukov, M.Kh. 1987. a  a a { 0, Boundary problems with the A. A. Samarskiy ^`21xxy 12x 21 y general nonlocal condition for peseudoparabolic 18) a11 ^a21x  a12y  a12a21`{ a20  a21y { a02 equation of higher order: Report of the Russian a a a a a a 0. Academy of Sciences (RRAS) 297: 547-552. { 10 ^ 21xy  12 21 y`{ 01 { 00 { 5. Zhegalov, V.I. and Kotukhov, M.P. 1998. On integral equations for the Riemann function. Izvestia Let us formulate the result in the form of: VUZov. Matematika, pp.26-30.

Theorem 2. Let the splitting (decomposition) in the left part for the equation (1) be written by formulas of type (7) (1-18). Then the explicit solution of the original problem is provided by the conditions (1-18) respectively.

Proc. Pakistan Acad. Sci. 42(3): 195-198. 2005

CONNECTION SYMBOLS IN DIFFERENTIAL AND RIEMANNIAN GEOMETRY

Ashfaque H. Bokhari and F. D. Zaman

Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received February 2005, accepted June 2005

Communicated by Dr. Iqbal Choudhary

Abstract: Whereas algebraic softwares have made many lengthy and tedious calculations possible through various packages, it is quite difficult to write one's own codes without having much of a programming skill. However, from ones experience with programming in Mathematica it can be realized that writing most of the codes in mathematica language does not demand lot of programming skill. With this point in mind, and the fact that algebraic computational techniques are vital for most of us to know, we have tried to write a Mathematica based code for beginners in algebraic computations who lack or have very little programming skill. This code, though written extremely naively, is an extremely powerful tool and can evaluate connection symbols that arise in Differential and Riemannian geometry in an arbitrary dimension greater than 2.

Keywords: Algebraic computations, Geometry

Introduction from the usual derivative (defined in terms of the

basis{ei }) by the term An n-dimensional Riemannian manifold is a set M together with a choice (for each k Dx X j Cij X k . (3) point p  M ) of an inner product ,! p in the i tangent space T (M ) such that for a given para- p In the above equation the C i is known as meterization X :U oM with pX (U) the jk D D D Christoffel symbols and the Einstein summa- functions tion convention is employed on the repeated w w index “k”. Requiring that the manifold is torsion i gij (u1 ,...,un ) , ! (1) free, the C jk becomes a symmetric tensor in its wui wu j lower indices. At this stage what is left is to are differentiable at x 1 ( p) . The (u ,...,u ) i D 1 n evaluate the C jk consistent with the covariant n are called the coordinates of the open set U D  R . derivatives. For this purpose we differentiate

In this notation of the inner product the gij equation (2) with respect to the coordinate uk represents a Riemannian metric [1] to get,

w g X , X ! (2) X ,X ! D X , X !  X , D X ! (4) ij i j i j Xk i j i Xk j wuk w where X . In this new basis the usual derivative i Cyclically permuting indices in equation (4), wui operator gets modified to define a new derivative, we get two more equations: w called covariant derivative. This derivative differs X , X ! D X , X !  X , D X ! (5) j k X i j k j X i k wui Differential Riemannian geometry 196

w In the next section we give our routine, X , X ! D X , X !  X , D X ! (6) k i X j k i k X j i wu j using commonly used commands of Mathematica that computes Christoffel symbols in any given Now adding equations (4) and (5) and subtrac- metric of dimension greater than 2. This is then ting equation (6) instantly gives followed by stepwise procedure to load and use this routine, and lastly by two illustrative examples 1 w w to show how this routine works for the metrics [ X i , X j !  X j , X k !  2 wu wu representing surface of a sphere of some constant k i (7) w radius and in 4-dimensional of the Schwarzschild X , X ! D X , X ! k i X k i j metric [4]. wu j

Routine for computing Christoffel Symbols Writing equation (7) in terms of the metric and its derivative, it becomes M[dim, coordinates, components]:= Block[{d},

m 1 wg ij wg jk wg ki dimension:=dim; C ki g mj [   ] (8) 2 wu k wui wu j metric coordinates:=coordinates; metric=components; Since the requirement on the metric is that it metricup=Inverse[metric]; must be non-degenerate (its determinant being metric derivative[a,b,c]:=D[metric[[a,b]], non-zero) over the entire manifold, its inverse metric coordinates[[c]]]; jk k exist such that g ij g G i . Thus, operating on Chris[a,b,c]:=Simplify[Sum[(1/2)*(metricup[[a ,d]])*(metric derivative[b,d,c]+ equation (8) by g pj and renaming the dummy Metric derivative[c,d,b]-metric index gives, derivative[b,c,d]),{d,1,dimension}]];]

p 1 pj wg ij wg jk wg ki Illustration of Computing Christoffel Cik g [   ] (9) 2 wuk wui wu j Symbols

p Example 1 The Cik is called Christoffel symbol. This symbol appears in many calculations in Geometry The metric for the surface of a unite sphere is where we use non-Cartesian coordinates. In n- given by [1] dimensions it has a total of n3 components. Thus, whereas it is easy to compute this symbol ds2 dr2  r2 sin2 T dT . (10) in 2 or 3 dimensions, it becomes highly tedious to k evaluate components of the Christoffel symbols To compute the Christoffel symbols “C ij ” in higher dimensions but it is quite an easy task for the above metric we perform the following to deal with such situations if one can use algebraic steps: computations for this purpose. However, it is Step 1 not always possible to have the ready made routines available that can be used in situations Open a note book in Mathematica and type like this. Thus, it is of great use if one can write the code as given in “Routine for computing small routines to algebraically compute such Christoffel symbols”. expressions. Nevertheless, these routines can be written only when one has a reasonable knowledge Step 2

of algebraic programming at the back of ones Load this routine in Mathematica note book mind [2,3]. by pressing shift and enter keys together.

197 Ashfaque H. Bokhari and F.D. Zaman

Step 3 Step 2

Insert the metric given in Eq. (10) at the Load this code in the same Mathematica note end of the code in the following format: book by pressing shift and enter keys together.

M[2, {r, th},{{1,0},{0,r^2}}] and load it again. Step 3 Step 4 Insert the metric given in Eq. (11) at the Write Chris [i, j, k] for i, j, k= 1, 2 to end of the code in the following format. k compute all of the C ij in fraction of a second (1 and 2 respectively represent - and M coordinates). M[4, {t, r, th, phi},{{(1-2*m/r), 0, 0, 0}, {0,- A copy of input and output command for computa- (1-2*m/r)^-1,0,0),{0,0,-^2,0},{0,0,0,- k (r*Sin[th])^2}}}] and load it again. tions of all the Christoffel symbols C ij for i, j, k=1,…,2 is listed below. Step 4

In[1]: Chris[1,1,1] Write Chris[i, j, k] for i, j, k= 1, …,4 to Out 0 k In[2]: Chris[1,1,2] compute all of the C ij (1, 2 , 3, 4, respectively, Out 0 represent t, r, - and M coordinates). A copy of In[3]: Chris[1,2,2] input and output command for computations of k Out r all of non-zero Christoffel symbols C ij for i, In[4]: Chris[2,1,1] j, k=1,…, 4 is listed below. Out 0 In[5]: Chris[2,2,1] In[1]: Chris[1,1,1] Out 1/r m Out In[6]: Chris[2,2,2] 2 Out 0 (r  2mr) In[2]: Chris[2,1,1] Example 2: m(r  2m) Out 0 We now consider a 4- dimensional r3 Schwarzschild metric of general relativity In[3]: Chris[2,2,2] given by [4], m Out 2 2 2 1 2 (2mr  r ) ds (1 2m / r)dt  (1 2m / r) dr  In[4]: Chris[2,3,3] r2d- 2  r2 sin2 T dI 2 (11) Out 2m  r In[5]: Chris[2,4,4] To compute the Christoffel symbols 2 k Out (2m  r)sin - “C ij ” for the above metric, we perform the In[6]: Chris[3,2,3] following steps once again. Out 1/ r In[7]: Chris[3,4,4] Step 1 Out [sin(2-)]/ 2 In[8]: Chris[4,2,4] Open the note book in Mathematica once Out 1/ r again and type the code as given in “Routine In[9]: Chris[4,3,4] for computing Christoffel symbols”. Out cot-

Differential Riemannian geometry 198

It is interesting to note that despite being References extremely simple, the routine is quite powerful in its own right as it can evaluate Christoffel 1. Docarmo, M.P. 1976. Differential geometry of curves and surfaces. Prentice Hall. symbols in any coordinated system in any 2. Wolfram, S. 1992. Mathematica. In: A system for arbitrary dimension greater than 2. doing Mathematics by Computer. Addison-Wesley Publishing Company. Acknowledgements 3. Aziz, A., Bokhari, A.H. and Qadir, A. 2001. Algebraic Computations for spinors in general The authors thank King Fahd University relativity. Nuovo Cimento B. 116: 483-491. of Petroleum and Minerals for providing facilities 4. Petrov, A.Z. 1969. Einstein Spaces. Pergamon Press. to complete this work.

199 Proc. Pakistan Acad. Sci.Muhammad 42(3):199-204.2005 Irfan et al.

Review GENE-CHIP TECHNOLOGY AND ITS APPLICATION

Muhammad Irfan1, Tayyab Husnain*1, Penny J. Tricker2, Gail Taylor2 and S. Riazuddin1

1National Centre of Excellence in Molecular Biology, 87-W Canal Bank Road, Lahore-53700, Pakistan, and 2School of Biological Sciences, University of Southampton, Bassett Crescent East, SO16 7PX, UK

Received April 2005, accepted June 2005

Summary: Gene Chips are finding extensive use in animal and plant science. Generally microarrays are of two kind, cDNA or oligonucleotide. cDNA microarrays were developed at Stanford University, whereas oligonucleotide were developed by Affymetrix. The construction of cDNA or oligonucleotide on a glass slide helps to compare the gene expression level of treated and control samples by labeling mRNA with green (Cy3) and red (Cy5) dyes. The hybridized gene chip emit fluorescence whose intensity and colour can be measured. RNA labeling can be done directly or indirectly. Indirect method involves amino allyle modified dUTP instead of pre-labelled nucleotide. Hybridization of gene chip generally occurs in a minimum volume possible and to ensure the hetroduplex formation, a ten fold more DNA is spotted on slide than in the solutions. A confocal or semi confocal laser technologies coupled with CCD camera are used for image acquisition. For standardization, house keeping genes are used or cDNA are spotted in gene chip that are not present in treated or control samples. Moreover, statistical analysis (image analysis) and cluster analysis softwares have been developed by Stanford University. The gene-chip technology has many applications like expression analysis, gene expression signatures (molecular phenotypes) and promoter regulatory element co-expression.

Gene-chip occasionally radioactive) tagged nucleotides and hybridized to the array. The fluorescence or The study of gene expression based on radioactive emission from each ‘spot’ is proportional hybridization of mRNA to high density arrays of to the relative specific transcript abundance in the immobilized target sequences that may correspond pool of cDNA hybridized to a cDNA spot. to specific genes is called gene-chip technology. Abundance of a specific transcript in a sample is There are two kinds of gene chips, cDNA and compared to the abundance of that transcript in a oligonucleotide. cDNA gene chips were developed control sample. This technique, although laborious, by groups led by Patrick Brown and Ronald Davis delivers a high-density, completely customized system at Stanford University [1,2]. The system is based with high detection specificity. on standard reverse transcription and PCR amplification followed by cloning of cDNA for each Oligonucleotide gene chips were developed by gene of interest. cDNA clones are then generally Fodor in 1991 [5] and Lipshutz et al. [6]. In this ‘printed’ on glass slides [3] using a robotic printer. system, oligonucleotide probes are directly Printing technologies have been developed that allow synthesized on a solid surface using chemical printing of 100,000 clones/spots on a single slide. synthesis supported by a lithophotographic technique This system allows for customized arrays [4]. mRNA (http://www.affymetrix.com). Originally, this strategy obtained from biological samples is reverse was developed to detect DNA single nucleotide transcribed and end-labelled using fluorescent (or polymorphisms (SNPs) [6]. Later, it was applied to ––––––––––––––––––––––– measure mRNA expression. In Affymetrix Address for Correspondence: Dr. Tayyab Husnain E-mail: [email protected] Arabidopsis arrays, each gene is represented by Gene-chip technology and its application 200

20 sense 25-base-long oligonucleotide probes and, nucleic acid from the sample in condition 1 is in as a control, by 20 mis-sense probes that have one abundance, the spot will be green, while if the nucleic base mismatch in the central part of the probe-- acid from the sample in condition 2 is in abundance, usually a base is substituted with a complementary it will be red. If both are equal, the spot will be yellow. one. Probe sequences are obtained from publicly If neither is present, it will not fluoresce and so appear accessed databases and, in most cases, cover the 3' black. Thus, from the fluorescence intensities and parts of the coding sequence to increase the sensitivity color for each spot, the relative expression levels of the assay and correct for SNPs. RNA obtained for the genes in both samples can be estimated. In from biological samples is processed prior to this way thousands of data points, individually hybridization. Double-stranded cDNA is obtained providing information about expression of a particular from total or mRNA (DNase treated) using reverse transcript, can be obtained from a single experiment. transcription. cRNA is then obtained using in vitro transcription with biotinylated nucleotides, and after fragmentation is hybridized to an oligonucleotide array. If biotinylated nucleotides are used to synthesize cRNA, the array is visualized by staining with streptavidin-phycoerythrin conjugate. The value representing expression of each gene is calculated based on fluorescence derived from each sense probe as compared to emission from each mis-sense probe. If the difference between fluorescence emitted from a set of sense probes and mis-sense probes is zero, the particular gene is not expressed in the sample. Figure 1. Microarray: General Functional Principle.

Construction of a Gene-chip The complexity of gene chip analysis means that tissue sample collection becomes a crucial factor Preparation of the sample in the data produced. As gene chips have been used with increasing frequency in recent years, the amount Gene chips may be used to measure gene of diversity in gene expression between samples, expression levels in different ways. One of the most even from the same tissue in the same individual, has popular gene chip applications is to compare the become clear. Precise sampling (including factors gene expression level in two different samples, e.g. such as the time of the day and month taken) and the same cells or cell type under two different the ability to sample homogeneous tissues, by using conditions. This is based on labeling mRNA techniques such as laser capture microdissection [7] extracted from one condition with one dye, e.g. are crucial steps in obtaining accurate analysis. At green, and from another condition with a different the same time, the amount of tissue required can be colored dye, e.g. red. The hybridized gene chip is a problem as a relatively large amount of RNA is excited by a laser and scanned at wavelengths required. However, more recent techniques to suitable for the detection of the red and green dyes amplify RNA have been developed that allow as shown in Figure 1. The amount of fluorescence extraction from minute tissue samples [8]. Brown’s emitted upon laser excitation corresponds to the group [9] at Stanford University has described a amount of nucleic acid bound to each spot. If the pool of RNAs derived from 11 diverse human tumor 201 Muhammad Irfan et al. cell lines that has become a kind of de facto universal protocols.html). human reference RNA. Recently a labelled oligonucleotide that is complementary to every Hybridization feature on an array has been shown to be an effective reference, without the complication associated with The incubation of the target with the gene chip references derived from mRNA [9]. Ultimately, the is typically performed at 65 0C for aqueous development of gene chip technology or other hybridization and 42 0C if 50 %( V/V) formamide is processes to allow high-throughput parallel measures present in the hybridization solution, in a manner of absolute RNA abundance are needed to provide similar to protocols used during other hybridization- a robust description of the transcriptome of specific based techniques. The hybridization of gene chips cellular lineage, development stages and disease generally occurs in the minimum volume possible. states. Many laboratories have adopted special chambers to enclose gene chips to enable their immersion in a RNA Labelling protocols waterbath to keep them at a constant temperature during the hybridization step. The hetroduplex Expression analysis labelling protocols are formation in the hybridization reaction is largely based on the reverse transcription of mRNA, either determined by the concentration of DNA on the glass from highly purified poly (A) mRNA or total RNA slide. To ensure the hetroduplex formation, 10-fold extract. Extensive purification of RNA is essential to more DNA is spotted on the slide than in the solution. remove all contaminating proteins, polysaccharides Other factors that can influence the rates of and other organic material, especially RNases. Many hybridization include the presence or absence of protocols have been developed for the extraction of monovalent cations and/or formamide, the high-quality RNA using various in-house and hybridization time, temperature and the length and commercial kits and reagents. Initial protocols for specific activity of the probes. Following target labelling, whereby reverse transcription of hybridization, the gene chip is washed repeatedly to mRNA is primed, used a poly (dT) primer in the remove the unbound and non-specific signal and is presence of fluorescently labelled nucleotides then ready for the acquisition of the image. The (typically cy3- or cy5- conjugated dCTP or dUTP). hybridization kinetics of the two labelled probes are Cy3- or cy5-conjugated nucleotides are bulky, different, Wang et al., [10] have developed a however, which makes their incorporation using method that makes this validation easy to implement standard enzymes very inefficient. In addition the rate to ensure reliability in two-color gene chips. of incorporation can differ between dyes, potentially resulting in dye biases. Image acquisition

In an alternative method, an amino allyl The readout from the gene chip is captured as modified dUTP is used instead of pre-labelled an image that is acquired using a scanner for nucleotide. After reverse transcription, the free amine fluorescent signal detection or a phosphorimager for group on the amino allyl modified dUTP can be the detection of radioactive signals. The scanners coupled to a reactive N-hydroxysuccinimydl ester currently available use either scanning confocal laser fluorescent dye. Although this technique is longer than technologies or a charge-coupled device (CCD) direct labelling, its benefits, including better sensitivity, camera. Most current scanners are designed to fewer dye biases and decreased costs, seem to be detect four wavelengths of light emission, but a worth the extra effort (http://www.microarrays.org/ scanner with the capacity to read up to five different Gene-chip technology and its application 202 wavelengths on any one slide has recently been efficiency, pin geometry, and the degree of DNA released. fixation to the array surface. In addition, the quality of starting RNA, reverse transcription, and labelling Standardization efficiency can vary, as can the hybridization efficiency, amount of non-specific hybridization, amount of Gene chips are affected by the differential overlap from neighboring spots and image analysis labelling and hybridization efficiencies of the targets. [11]. Using at least three replicates in an experiment Traditional housekeeping genes or maintenance genes reduces the number of false positives and false can be included on all arrays to assist in normalizing negatives providing more reliable results overall [14]. individual hybridization differences. Another In addition, normalization methods, usually using a approach is to spike each sample with a cDNA that set of housekeeping genes or other control genes, is present on the array but not present with the control can be applied in an attempt to account for this or test sample to act as an internal control for the inherent variability [15,16]. labelling and hybridization processes [11]. Analysis

Given the multitude of platforms and Although gene chip technology is still being methodologies, a growing concern for researchers refined, the basic methods of analysis are well using gene chip information is a reporting standard established. An image analysis program, in most for all gene chip experiments. This allows researchers cases, is used to calculate the quantitative ratio of to assess all aspects of experimental design and the level of gene expression between the two samples execution of array experiments. This led to the being compared. Before the software is able to creation of a Minimum Standard About Gene Chip interpret the intensity value for each probe a grid Experiment (MIAME) compliance. Major publishing must be overlaid on the image of the gene chip to houses now advocate MIAME compliance with any map the location of pixels representing each spot. A published DNA gene chip experiments [12]. software package for initial image analysis was Information regarding the requirements for MIAME developed at Stanford University (http:// compliance, design of experiments and data storage www.rana.stanford.edu/software/) and is freely can be found at the Gene chip Gene Expression Data available for academic users. Most scanners are sold Society website (http://www.mged.org/ with an option of an image analysis software package Workgroups/MIAME/miame.html). The European such as Imagene (Biodiscovery, Los Angeles, CA, Bioinformatics Institute (EBI) has also created a USA) Quantarray (GSI Lumonics) or GenePix 2.0 public database where MIAME compliant data can (Axon instruments, Foster City, CA, USA). Some be stored and uploaded in XML data exchange of these packages use cluster analysis algorithms to format Gene Expression Markup Language group the genes on an array according to their (MAGE-ML., http://www.ebi.ac.uk/arrayexpress/ expression profiles over a number of experiments. [12] and Boussioutas and Haviv [13]). Once A version of this type of program, called Cluster, is obtained, raw DNA array data must be processed also available from Stanford University. before biologically relevant information can be extracted. This is one of the most challenging aspects Bilban et al. [17] introduced a method to filter of transcriptome analysis. There are many sources false-positives and false-negatives from DNA gene of variation in gene chip experiments. These include chip experiments. This was achieved by evaluating the amount of DNA delivered to each individual spot a set of positive and negative controls by receiver on the array, which in turn can be affected by PCR operating characteristic (ROC) analysis. An 203 Muhammad Irfan et al. advantage of this approach is that users may define Acknowledgements thresholds on the basis of sensitivity and specificity considerations. The area under the ROC curve Financial support of Commonwealth allows quality control of gene chip hybridizations. Scholarship Commission, United Kingdom, to This method has been applied to custom-made gene Tayyab Husnain (Reference No. PKCF-2003-218) chips developed for the analysis of invasive and from Higher Education Commission, Pakistan, melanoma derived tumour cells and yielded fewer to Muhammad Irfan (PIN 041201588 B-027) is mis-classified genes. Provided that a set of gratefully acknowledged. appropriate positive and negative controls is included on the gene chip, ROC analysis obviates the inherent References problem of arbitrarily selecting threshold levels in gene chip experiments. The proposed method is 1. Schena, M., Shalon, D., Heller, R., Chai, A., Brown, applicable to both custom-made and commercially P.O. and Davis, R.W. 1996. Parallel human genome analysis: microarray-based expression monitoring available cDNA gene chips and can help to improve of 1000 genes. PNAS, USA. 93:10614-10619. the reliability of predictions from gene chip 2. Schena, M., Shalon, D., Davis, R.W. and Brown, experiments. P.O. 1995. Quantitative monitoring of gene- expression patterns with a complementary- DNA microarray. Science 270:467-470. Applications 3. Holloway, A.J., Van, L.R.K., Tothill, R.W. and Bowtell, D.D.L. 2000. Options available-from start Clustering the expression data can identify to finish for obtaining data from DNA microarray II. groups of genes with similar expression patterns that Nature Genetics Supplement 32: 481-489. 4. Rose, D. 2000. Micro fluidic technologies and may be controlled by shared regulators. In carefully instrumentation for printing DNA microarrays. In: designed time course studies, gene chips also allow Microarray Biochip Technology. Ed. Schena, M., the temporal sequence of transcription induction or pp.19-38, Eaton Publishing. repression to be followed. Such information is useful 5. Fodor, S.P.A., Read, J.L., Pirrung, M.C., Stryer, L., Lu, A.T. and Solas, D. 1991. Light-directed, spatially for determining the order of events during the addressable parallel chemical synthesis. Science activation of plant defense responses and separation 251:767-773. of primary and secondary effects triggered by an 6. Lipshutz, R.J., Morris, D., Chee, M., Hubbell, E., infectious agent or signaling molecules. The large- Kozal, M.J., Shah, N., Shen, N., Yang, R. and Fodor, S.P.A. 1995. Using oligonucleotide probe arrays to scale nature of the survey using gene chips also access genetic diversity. Biotechniques 19:442-447. produces a ‘gene expression signature’ that is a new 7. Simone, N.L., Bonner, R.F., Gillespie, J.W., Emmert- form of molecular phenotype. Gene chips can also Buck, M.R. and Liotta, L.A. 1998. Laser-capture be used to find the similarities or differences between microdissection: opening the microscopic frontier to molecular analysis. Trends Genet. 14:272-276. different treatments (e.g. the effect of pathogen 8. Hertzberg, M., Sievertzon, M., Aspeborg, H., Nilsson, infection or chemical signals or hormones on gene P., Sandberg, G. and Lundeberg, J. 2001. cDNA expression) and to determine the level of potential microarray analysis of small plant tissue samples cross-talk between different the signaling pathways. using a cDNA tag-target amplification protocol. Plant J. 25:585-591. Another novel use of gene chips is the direct 9. Dudley, A.M., John, A., Martin, A.S. and George, identification of DNA binding proteins [18]. Thijs et M.C. 2002. Measuring absolute expression with al. [19] modified an original Gibbs sampling microarrays with a calibrated reference sample and algorithm for motif finding [20] and looked for an extended signal intensity range. PNAS, USA 99:7554-7559. potential promoter regulatory elements in the 10. Wang, R., Okamoto, M., Xing, X., Crawford, N.M., upstream region of co-expressed genes. 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N.M. 2003. Microarray analysis of the nitrate 15. Hedge, P., Qi, R., Abernathy, K., Gay, C., Dharap, S., response in Arabidopsis roots and shoots reveals Gaspard, R., Earle-Hughes, J., Snesrud, E., Lee, N. over 1,000 rapidly responding genes and new and Quackenbush, J. 2000. IA concise guide to linkages to glucose, trehalose- 6-phosphate, iron, cDNA microarray analysis. Biotechniques 29:548-562. and sulfate metabolism. Plant Physiol. 132:556-567. 16. Colebatch, G., Trevaskis, B. and Udvardi, M. 2002. 11. Schuchhardt, J., Beule, D., Malik, A., Wolski, E., Functional genomics: tools of the trade. New Phytol. Eickhoff, H., Lehrach, H. and Herzel, H. 2000. 153:27-36. Normalization strategies for cDNA microarrays. 17. Bilban, M., Buehler, L.K., Head, S., Desoye, G. and Nucleic Acids Research 28: 47. Quaranta, V. 2002. Defining signal thresholds in 12. Brazma, A., Parkinson, H., Sarkans, U., Shojatalab, DNA microarrays: exemplary application for invasive M., Vilo, J., Abeygunawardena, N., Holloway, E., cancer. BMC Genomics 3:19. Kapushesky, M., Kemmeren, P., Lara, G.G., 18. Kazan, K., Schenk, P.M., Wilson, L. and Manners, Oezcimen, A., Rocca-Serra, P. and Sansone, S.A. J.M. 2001. DNA microarrays: new tools in the analysis 2003. ArrayExpress--a public repository for of plant defence responses. Mol. Plant Pathol. 2:177- microarray gene expression data at the EBI. Nucleic 185. Acids Research 31:68-71. 19. Thijs, G., Marchal, K., Lescot, M., Rombauts, S., 13. Boussioutas, A. and Haviv, I. 2003. Current and De-Moor, B., Rouze, P. and Moreau, Y. 2002. A Gibbs potential uses for DNA microarrays in transplantation sampling method to detect overrepresented motifs medicine: lessons from other disciplines. Tissue in the upstream regions of coexpressed genes. J. Antigens 62:93-103. Comput. Biol. 9:447-464. 14. Lee, M.L.T., Kuo, F.C., Whitmore, G.A. and Sklar, 20. Lawrence, C., Altschul, S., Boguski, M., Liu, J., J. 2000. Importance of replication in microarray gene Neuwald, A., and Wootton, J. 1993. Detecting subtle expression studies: statistical methods and evidence sequence signals: a Gibbs sampling strategy for from repetitive cDNA hybridizations. Proc. Nat. multiple alignment. Science 262 : 208-214. Acad. Sci. USA 97:9834-9839. 205 Proc. Pakistan Acad. Sci. 42(3):205-214.2005Mohammad Anees

Review

CELL SURFACE PROTEASE, GUANIDINOBENZOATASE, AND CANCER

Mohammad Anees

Department of Biology, G.T. Road College, The University of Gujrat, Gujrat, Pakistan

Received March 2005, accepted August 2005

Communicated by Prof. Dr. Iftikhar A. Malik

Abstract. Tumour cells and cells capable of migration possess a protease, referred to as guanidino- benzoatase (GB), which is similar in function to tissue plasminogen activator, but not identical with it. GB may exist in different iso-enzymic forms and can be located by different fluorescent inhibitors in cryostat and wax embedded sections. It is suggested that these inhibitors could be of value in diagnostic pathology and possibly in therapeutic medicine by coupling these inhibitors with cytotoxic drugs or radioactive metals in the hope that these would be selectively cytotoxic to the tumour cells. In the present review, evidence from the current literature has been discussed on the possible role of proteases, their inhibitors, and specially GB iso-enzyme interactions, with low and high molecular weight inhibitors with reference to cancer.

Keywords: Proteases, inhibitors, tumors, guanidinobenzoatase, fluorescence microscopy.

Introduction lung and colonic tumours tissues, and its interactions have been studied, both with membranes bound- Proteolytic processes are necessary for normal GB in thin sections, and free GB in solution [9,10]. physiological functions in the body and are regulated This protease had the ability to continuously by specific protein inhibitors produced by the cells hydrolyze the two active site titrants for trypsin-like [1]. Many of the natural and synthetic inhibitors of enzymes, with the production of guanidinobezoate the proteases prevent the dissemination of cancer [9,11,12]. Steven and his coworkers have provided cells, and have also inhibitory effect on tumor growth considerable information on this enzyme, its location [2]. Failure in the biological control mechanisms of on cells and its interactions on the basis of studies proteolytic activities may enable tumor invasion and on colon and lung carcinoma using frozen sections metastasis [3]. In the metastatic process, proteolytic and fluorescence microscopy [11,13-18]. The enzymes play an important role in mediating passage enzyme exists in different iso-enzymic forms on the of the malignant cell through the cell membrane [4]. normal and colonic carcinoma cells [13]. All forms Tumor cell migration and invasion into the of GB iso-enzymic can be located by the active site surrounding extracellular matrix is facilitated by a directed low molecular weight, yellow fluorescent variety of cell surface-associated proteolytic probe 9-aminoacridine (9-AA), a competitive enzymes [5,6]. inhibitor of GB, when observed under fluorescent microscope [14]. The iso-enzymic form of GB can Proteases have also been used as marker be differentiated by high molecular weight serum protein for cancers [7,8]. A marker protease, inhibitor, cytoplasmic inhibitors, plasminogen guanidinobenzoatase (GB), has been isolated from activator inhibitor (Steven et al. [15-17]) and –––––––––––––––––––––––––––––––– pentosan polysulphated compounds (Anees [18]). Address for Correspondence: E-mail Address: [email protected] In order to understand the mechanism of invasion Guanidianobenzoatase and cancer 206 and metastasis, it is important to understand the role mass is a potential site for discharge of tumor cells of the proteases. After their synthesis proteases are into the circulation [25]. exported from the cell, attach to the receptor proteins, start to hydrolyze the barrier of extracellular matrix, Lymphatic vessels are also ports of entry for and finally spread throughout the body, resulting in the malignant cells, but tumours do not induce their cancer [19,20]. own lymphatic network [26]. Lymphatic vessels normally drain away excess fluid from the interstitial What is Cancer? spaces; the lack of lymphatic in tumours may contribute to the build up of hydrostatic pressure The word cancer is likely to strike most people within the tumour mass. This internal pressure may with fear and dread. The word “cancer” comes from actually disrupt the tumour and initiate the first step Latin for “crab” due to the morphology and of metastasis by pushing the tumour cells into the adherence of cancer cells in an obstinate manner to circulation, where they dissociate and disseminate any part they seize upon like the crab [21]. Another to start secondary tumours [27]. Current work corresponding term “carcinoma” comes from Greek reveals that most cancers originate from epithelial for “eating”. These two words paint a gruesome tissues in which oncogenes are activated or tumour- picture of the disease as a “crab eating” into the suppressor genes are lost [25-28]. For instance, Yao victim’s flesh and spreading, until its victim dies [22]. et al. [28] identified a protein, on the basis of gene expression analysis, as a potential diagnostic in the Cancer is not one disease, but many diseases clear cell renal carcinoma. A potential metastasis gene that occur in different areas of the body. Each type nm 23 has been shown by Steeg et al. [29] to be of cancer is characterized by the uncontrolled growth missing or inactive in metastatic primary breast cancer of cells. Under normal conditions, cell reproduction patients but is present in high levels in normal and is carefully controlled by the body [21]. However, non-metastatic tumour cells. Such genetically these controls can malfunction, resulting in abnormal abnormal epithelium is supported by normal stromal cell growth, and the development of a lump, mass, cells that become activated during tumour or tumor. A tumor may be benign (non-cancerous) progression to produce proteases, inhibitors and or malignant (cancerous). Cells from cancerous other regulatory factors. These proteases then tumors can spread throughout the body. This activate the tumour cells to pass through the barrier process, occurring when cancer cells break away of extracellular matrix that surrounds the cells [30]. from the original tumor and travel in the circulatory or lymphatic systems, until they are lodged in a small Cancer and Proteases capillary network in another area of the body, is termed as metastasis [21]. Tumour cells also possess proteases, which are The growth of solid tumours is dependent on present as soluble proteins in the cytoplasm. Electron new blood vessel formation, known as angiogenesis microscopic studies have elucidated that the soluble [23]. During angiogenesis, endothelial cells respond proteases are released from the irregular to tumour-derived stimuli by dissolving the underlying pseudopodia or invadopodia, projected in the basement membrane followed by sprouting of blood direction of migration [5,31]. These pseudopodia vessels into the underlying tissue towards the tumour penetrate the barrier of extracellular matrix (stroma) [24]. The newly formed blood vessels in tumours at the adhesion contact between pseudopodia and are leaky; malignant cells can cross their walls fairly the matrix molecules. The host tissue cells near the easily. Any branch of the vascular tree within a tumour invading neoplasia cells, may obtain a substantial 207 Mohammad Anees

Figure 1. Mechanism of proteolysis of extracellular matrix in tumor invasion and metastasis [5]. Different types of proteases have been released from the pseudopodia of tumour cell, which are responsible for the destruction of extracellular matrix. Activators have also been released from the tumour cell, which trigger the normal cells to secrete more proteases for enhancing the process of proteolysis. The process of proteolysis is further supported by the proteases contributed from the surrounding blood vessels. Guanidianobenzoatase and cancer 208 proteolytic potential that contributes to the active center of GB have enabled location of cells destruction of extracellular matrix at the site of that possess membrane-bound active GB. Anees invasion [5,32], as shown in Fig 1. It can also be [18] has shown that the iso-enzymic forms of GB, seen here that the destruction of the host tissue matrix which were recognized by specific iso-inhibitors, is counteracted, however, by the presence of various appear to be bound with cell surface receptors. The inhibitors that are produced by the host cells isolation of both GB and inhibitors from the extract themselves and also probably by inhibitors that of tumour tissues, led to further study of the kinetics diffuse from the blood [33]. In neoplasia, this of these reactions in free solution [15,38]. delicate control gets out of balance favouring increased proteolysis due to an increase in the ratio Active form of GB of proteases to inhibitors. The final outcome is the removal of the matrix substances, after which the The epithelial cell surfaces of carcinoma cells tumour cells can migrate [5,34]. Interactions of lung and colon tissues possess active form of GB, between tumour and stromal cells control the two which binds to fluorescent probes, and fluoresces protease systems that are responsible for most of yellow or red under appropriate microscopic the proteolysis outside the cell [35]. These are the conditions [39,40]. The fluorescent probe, 9- urokinase plasminogen activator, and the matrix aminoacridine (9-AA), is an active site-directed metallo-proteinase, which are produced as inactive competitive inhibitor for GB, and has been used to precursors, and then activated on the surface of locate GB on cell surface in thin sections of tumour tumour cells, thus allowing malignant cells to breach tissues. 9-AA binds to the active center of GB, and basement membranes [36]. makes the cell surfaces to fluoresce yellow [38] under the fluorescence microscope (Fig. 2a,b). The role of serine proteases in tumor biology has changed with the discovery of a family of Latent form of GB protease-activated receptors in human colon cancer cells [19]. Reverse transcriptase-polymerase chain When GB is present in latent form (enzyme- reaction analysis showed that these receptors are inhibitor complex), it fails to bind 9-AA and the cell present in human colon cancer cell lines tested, but surfaces do not fluoresce yellow. However, Anees not in normal human colonic epithelial cells [30]. [39] has shown that the enzyme-inhibitor complexes Several studies described below have shown that can be dissociated, and GB regains its ability to bind the protease GB has characteristics similar to those 9-AA and the cell surfaces fluoresce yellow. In Fig. of other proteases. 2a, GB enzyme is not completely active, due to the formation of enzyme-inhibitor complexes. When Cancer and GB these sections are treated with formaldehyde, the inhibitor is displaced from the active center of GB, GB was first found by Steven and A-Ahmad 9-AA then binds strongly to make these sections [9] in the extracellular fluid surrounding Ehrlich ascites fluoresce bright yellow [39] (Fig. 2b). 9-AA can tumour cells, cultivated in the peritoneal cavity of thus be used to determine the status of the GB mice. This enzyme is similar in function to tissue complex or dissociated form, and demonstrate plasminogen activator [10], but now has been shown whether the extracted cytoplasm inhibitors can to be a distinct protease, and a possible marker for recognize and inhibit tumour cell surface iso-enzymic carcinoma cells [7,8]. Fluorescent probes designed forms of GB. Lung carcinoma tissues after co- in the laboratory of Steven et al. [37] to block the stacking with 9AA/propidium iodide fluoresce 209 Mohammad Anees

Figure 2 a-f. Carcinoma and normal tissues of lung and colon after exposing to different stains. a. Frozen section of lung squamous cell carcinoma, directly after staining with 9AA shows little yellow fluorescence, indicating the presence of partially active GB [39]. X250. b. Formalin treated section of lung squamous cell carcinoma stained with 9AA, cells fluoresce brightly yellow, indicating the complete active GB, after the displacement of inhibitor [15]. X500. c. Frozen section of lung carcinoma tissue treated with haematoxylin, followed by 9AA and PI staining. These cells, after binding with both stains, show orange red fluorescence with darkly stained nuclei [15]. X500. d. Frozen section of normal epithelial lung cells stained with 9AA; appear as green, due to the lack of active GB [40]. X250. e. Frozen section of colonic carcinoma stained with Rh-PAI-1, the cell surfaces after binding with Rh-PAI-1, fluoresce red due to active GB [36]. X500. f. Frozen section of colonic carcinoma epithelial cells stained with TR-PPS, cells fluoresce red, and indicate that these cells have active GB [18]. X500. Guanidianobenzoatase and cancer 210 orange red (Fig. 2c), whilst the normal epithelial cells exposure to fibrin fibrils. The advantage of using do not possess active GB and fluoresce green (Fig. sections is obvious when it is a reversible reaction, 2d) instead of orange red [40]. each of which can be monitored by fluorescence microscopy and also by direct kinetic analysis of the Cell surface location of GB purified proteins in solution [41].

The cells surface location of GB was Iso-enzymic form of GB demonstrated by spreading intact cells rather than sectioned cells [9]. In this study, leukemia cells were Studies with frozen sections of colonic obtained from the spleen of leukemia rats. These carcinoma and normal colon have shown presence cells when spread directly on a glass slide, showed of different iso-enzymic forms of GB on these two lack of active GB and failed to bind 9AA. This classes of epithelial cells. Normal colonic epithelial observation was reversed, if the cells were exposed cells possess an iso-enzymic form of GB which is to formaldehyde; the process resulted in activation rapidly recognized by human serum and also of latent form of GB on the leukemia cells. It was cytoplasmic protein inhibitor, extracted from normal shown that the cytoplasm of fresh leukemia cells colonic epithelial cells [18]. Colonic carcinoma cells possessed a protein inhibitor (70K) of GB which possess a distinct iso-enzymic form of GB which was capable of recognizing GB on formaldehyde- was not recognized by an inhibitor prepared from treated leukemia cells and reforming an enzyme the cytoplasm of normal donor colonic cells or by inhibitor complex which could again be reactivated human serum. These subtle differences in the cell with formaldehyde [9]. Clearly, the original cell bound GB iso-enzymic forms were also recognized surface possessed the latent GB enzyme, the by the appropriate inhibitors, when the purified activation and reinhibition with the cytoplasmic proteins were subjected to kinetic analyses with protein inhibitor must have been confined to the MUGB as substrate [17]. These distinct iso-enzymic events taking place on the surface of the cell forms of GB were also observed in other tissues membrane of these leukemia cells. These such as breast carcinoma [42], squamous cell observations with leukemia cells led to studies of carcinoma of the lung [43], sputum cells [44] and interactions of cytoplasmic inhibitors with GB in pre-neoplastic epithelial cells in cervical smears [45]. frozen sections [38,39], instead of intact cell spreads It could be tentatively concluded that each type of on slides. tumour cell so far examined possesses a unique iso- enzymic form of cell surface GB, which is recognized Early experiments [40] demonstrated similar by iso-inhibitor unique to the cytoplasm of each inhibition systems in colonic epithelial cells, which respective cell type. later led to the displacement of both GB and the inhibitor from the cell surface receptors following Interaction of GB with cytoplasmic inhibitors application of a fibrin overlay technique. This enabled both GB and the inhibitor proteins to be isolated Hela cells derived from a line of tumour cells and studied by kinetic analysis in free solution [39], provide a good source of cytoplasmic inhibitor using the fluorogenic substrate 4-methylumbellifery1- capable of recognizing the iso-enzyme of GB present p-guanidinobenzoate (MUGB) [9]. Three techniques on the surface of Hela cells [46].When labeled with have been used to dissociate the cell surface GB- rhodamine, the cytoplasmic inhibitor endows the cell inhibitor complexes: (a) formaldehyde treatment, (b) surface of pre-neoplastic cells with an orange exposure to sodium dodecyl sulphate, and (c) fluorescence, whilst the normal mature epithelial cells 211 Mohammad Anees in the smear lack this form of GB, and do not bind type of competitive inhibition to exfoliated cells, for the probe. On the other hand, the rhodamine labeled example abnormal epithelial cells in cervical smears inhibitor derived from Hela cells does not recognize [45]. The use of competitive inhibitors which cultured colonic carcinoma cells or such cells in differentiate between iso-enzymic forms of GB on frozen sections [46]. Again, these observations cell surfaces is not confined to exfoliated cells such indicate the selectivity of isoinhibitor-isoenzyme as the cervical smears [46]. The concept is equally recognition in a manner similar to antigen-antibody applicable to the study of GB iso-enzymes in thin recognition. It suggests the possibility of iso-inhibitors sections, if the same test conditions are used to locate as carriers of cytotoxic agents to the surface of cells cells carrying a specific iso-enzymic form of GB on with appropriate iso-enzymes of GB. their surfaces [17].

Interaction of GB with plasminogen activator Dansyl fluoride is well known to selectively Iso-enzymic forms of cell surface GB can also interact with the hydroxyl group of the reactive seryl be recognized by the protein inhibitor of plasminogen residue in the active centre of trypsin-like proteins. activator referred to as PAI-1 [40]. Rohdamine Treatment of frozen sections of colon with dansyl labeled PAI-1 (Rh-PAI-1) recognizes the iso- fluoride results in blue fluorescence, associated with enzymic form of GB associated with the colonic both normal and colonic carcinoma tissue [47]. It is carcinoma tissue. After binding these cells appear possible to isolate the dansyl-GB from carcinoma red [40], whilst the surrounding normal epithelial cells tissue using the fibrin overlay technique [18], and fail to recognize these cells, and they appear black transfer this complex to the receptors for GB on (Fig. 2e). This is a further example of a protein- sections of normal colon, where it bind with the latter. protein interaction distinguishing between two forms Under the fluorescence microscope, this binding of of cell surface GB, both of which have an active dansyl-GB receptors for GB is evidenced by blue centre which appears to be functionally similar to fluorescence. Thus, dansyl-GB from colonic tissue plasminogen activator. Both iso-enzymic forms carcinoma cells can be artificially exchanged with of GB also have the ability to bind to fibrin fibrils the original iso-enzymic forms of GB on both normal [18], with consequent detachment of GB from the and carcinoma cells [41]. The method clearly cell surface receptor protein. Pentosan polysulphate demonstrates the mechanism of attachment of GB (PPS) is a highly negatively charged sulphated to the common cell surface receptor which shows polysaccharide and behaves similar to Rh-PAI-1 in no preference towards either of these two iso- recognizing the iso-enzymic form of GB associated enzymic forms of GB. Now, if the blue fluorescent with normal and colonic carcinoma tissues (Fig. 2f). dansyl carcinoma iso-enzymic form of GB artificially placed on the receptors of normal colonic epithelial Interaction of GB with dansyl fluoride cells is challenged with Rh-PAI-1, these normal colonic epithelial cells can now bind this red probe It is possible to use inexpensive low molecular and fluoresce red [18]. Clearly, the colonic carcinoma weight probes in the presence of a competitive iso-enzymic form of dansyl-GB has been recognized inhibitor of GB such as dansyl fluoride [47] to achieve by the red Rh-PAI-1. Yet, the original GB iso- inhibition. This approach has been used to distinguish enzyme on these normal colonic epithelial cells was between two iso-enzymic forms of GB associated not recognized by Rh-PAI-1. This type of protein- with normal donor colonic epithelial cells and colonic protein recognition does not involve the active centre carcinoma cells in frozen sections of tissues [18]. but the conformation of GB protein is recognized by The morphology of the cells within the colonic tissue the inhibitor protein. confirms this selectivity. It is possible to extend this Guanidianobenzoatase and cancer 212

Conclusion Carboxypeptidases, cathepsins x and b display distinct protein profile in human cells and tissues. The regulation of protease GB activity on the Exp. Cell Res. 306:103-113. surface of cells by iso-inhibitors may play a role in 3. Nippon, S., Fujinka, G., Zasshi. N. 1996. Mechanism of tumor cell-induced Extracellular Matrix normal cell migration, and also in the movement of degradation -- inhibition of cell-surface proteolytic invasive carcinoma cells. It is particularly interesting activity might have a therapeutic effect on tumor that serum rapidly recognizes the iso-enzymic form Cell. Invasion and Metastasis 514:1-15. of GB on normal colonic epithelial cells, but fails to 4. Yamamoto, M., Sawaya, R., Mohanam, S., Rao, V.H., Bruner, J.M., Nicolson, G.l., Ohshima, K. and Rao, recognize and inhibit the iso-enzymic form of GB on J.S. 1994. Activities, localizations, and roles of serine colonic carcinoma cells. This suggests that this proteases and their inhibitors in human brain tumor protein-protein recognition similar in nature to Progression. J. Neuro. Oncol. 22:139-151. antigen-antibody recognition. If this is the case, a 5. Tryggvason, K., Hoyhtya, M. and Salo,T. 1987. Proteolytic degradation of extracellular matrix in method for the selective delivery of cytotoxic tumour invasion. Biochem. Biophys. Acta 907:191- molecules to specific cell types, possessing specific 217. iso-enzymes, may be possible in future. The 6. Noel, A., Maillard, C., Rocks, N., Jost, M., appropriate iso-inhibitor could be obtained from cell Chabottaux, V., Sounni, Ne., Maquoi, E., Cataldo, D. and Foidart, J.M. 2004. Membrane associated culture as has been demonstrated with crude inhibitor proteases and their inhibitors in tumour prepared from Hela cells for selective recognition of angiogenesis. J. Clin. Pathol. 57:577-584. pre-neoplastic epithelial cells of the cervix [48]. 7. Poustis, D.C., Descompes, R., Auberger, P., Delque- Perhaps of even greater significance is the Bayer, P., Sudak, A.P. and Rossi, B. 1992. Purification and characterization of guanidinobenzoatase--a observation that fibrin fibrils bind cell surface GB possible marker for human renal carcinoma. Cancer (both active and latent forms) with the dissociation Res. 52:3622-3628. of the cytoplasmic inhibitor, which might enable 8. Murza, A., Sanchez, C.S., Garcia, J.V., Guisan, J.M., invading cancer cells to initiate the process of Alfonso, C. and Rivas, G. 2000. Interaction of the antitumor drug 9-aminoacridine, with fibrinolysis via the activation of plasminogen also on guanidinobenzoatase studied by spectroscopic the surface of the fibrin fibrils. It is hoped that further methods: a possible tumor marker probe based on studies of this cell surface enzyme, its iso forms and the fluorescence exciplex emission. Biochemistry inhibitors will be rewarding in our understanding of 39:10557-10565. 9. Steven, F.S. and Al-Ahmad, R.K. 1983. Evidence for the potential reactions taking place on the surface of an enzyme which cleaves the Guanidinobenzoate tumour cells. moiety from active-site titrants specifically designed to inhibit and quantify trypsin. Eur. J. Biochem. Acknowledgements 130:335-339. 10. Murza, A., Fernandez, L.R. and Guisan, J.M. 2000. I wish to express my gratitude to Dr F.S. Essential role of the concentration of immobilized Steven, Department of Biochemistry, The University ligands in affinity chromatography: purification of guanidinobenzoatase on an ionized ligand. J. of Manchester, England, for his help in the Chromatogr. B. Biomed. Sci. Appl. 740:211-218. preparation of this manuscript. 11. Steven, F.S., Griffin, M.M., Cederholm-Williams, S.A., Mangel, W.F. and Maier, H. 1991. Evidence for References the functional similarity between tumour cell surface protease and tissue plasminogen activator. 1. Jedinak, A. and Maliar, T. 2005. Inhibitors of Anticancer Res. 11:641-647. proteases as anticancer drugs. Neoplasma 52:185- 12. Maurizi, M.R. 2004. Endopeptidase Clp. In: 192. Handbook of Proteolytic Enzymes, 2nd ed. Elsevier, 2. Kos, J., Sekirnik, A., Premzl, A., Zavasnik, B.V., London, pp. 2017-2023. Langerholc, T., Repnik, U., Turk, B., Werle, B., 13. Steven, F.S. and Talbot, I.C. 1994. Differential Golouh, R., Jeras, M. and Turk, V. 2005. competitive inhibition of a cell surface protease on 213 Mohammad Anees

normal epithelial cells and carcinoma cells of the 28. Yao, M., Tabuchi, H. and Naagashima, Y. 2005. Gene colon. Anticancer Res. 14:2013-2016. expression analysis of renal carcinoma- a protein as 14. Steven, F.S., Griffin, M.M. and Bullied, N.J. 1991. a potential diagnostics biomarker of clear cell Studies on the interaction and exchange of inhibitors carcinoma. J. Pathol. 205:377-387. and proteases on the surface of tumour cells in frozen 29. Steeg, P.S., Bevilacua, G., Sobel, M.E. and Liotta, sections. Anticancer Res. 11:17-22. L.A. Cancer proteases and metastasis. Basic Life 15. Steven, F.S., Griffin, M.M., Anees, M. and Benbow, Sci. 57:355-360. E.W. 1992. Observation on the conformational 30. Dylan, R.E. and Gillian, M. 1998. Cancer-proteases- changes in the structure of cell surface proteases. J. invasion and more. Nature 394:527-528. Enz. Inhibition 6:251-258. 31. Moscatelli, D. and Rifkin, D.B. 1988. Proteases and 16. Steven, F.S., Anees, M., Myers, J. and Hasleton, P.S. metastasis. Biochem. Biophys. Acta 948:67-85. 1993. Association and dissociation of a protease 32. Yves, A. D., Arthur, M. M., Sharon, S.M., Harold, and its inhibitor on the surface of lung squamous A.C., Mary, M.Z. and Ruth, J. M. 2004. Proteases, cell carcinoma cells. Anticancer Res. 13:1063-1068. extracellular matrix, and cancer. Am. J. Pathol. 17. Steven, F.S., Anees, M. and Booth, N. 1995. Selectivity 164:1131-1139. of the plasminogen activator inhibitor (PAI-1) for 33. Rooprai, H.K. and Mccormick, D. 1997. Proteases the iso-enzyme of guanidinobenzoatase on the and their inhibitors in human brain tumours: A surface of colonic carcinoma cells. Anticancer Res. Review. Anticancer Res. 17:4151-4162. 15:205-210. 34 Rubin, H. 2003. Complementary approaches to 18. Anees, M. 1996. Location of tumour cells in colon understanding the role of proteases and their natural tissue by Texas red labelled pentosan polysulphate, inhibitors in neoplastic development: Retrospect and an inhibitor of a cell surface protease. J. Enz. prospect. Carcinogenesis 24:803-816. Inhibition 10:203-214. 35. Keld, D., Niels, B., Gunilla, H., Morten, J., Leif, 19. Cavallo-Medved, D.J., Mai, J., Dosescu, M., Sameni, R.L., Michael, P. and John, R. 2005. Plasminogen N. and Sloane, B. F. 2005. Caveolin-1 mediates the activation and cancer. Thrombosis and Haemostasis expression and localization of cathepsin B, pro- 93:676-681. urokinase plasminogen activator and their cell- 36. Thomas, K. 2004. It’s the Matrix! ECM, Proteases, surface receptors in human colorectal carcinoma and Cancer. American J. Pathol. 164:1141-1142. cells. J. Cell Sci. 118:1493-1503. 37. Steven, F.S., Griffin, M.M., and Al-Ahmad, R.K. 1985. 20. Boonacker, E. and Noorden, C. J. 2001. Enzyme The design of fluorescent probes which bind to the cytochemical techniques for metabolic mapping in active centre of guanidinobenzoatase. Eur. J. living cells, with special reference to proteolysis. J. Biochem. 149:35-40. Histochem. Cytochem. 49:1473-1486. 38. Anees, M. and Steven, F.S. 1994. Retinoic acid 21. Kumar, V., Cotran, R.S. and Robin, S.L. 1992. Basic inhibition of a tumour protease immobilized on cell pathology, 5th Edition W.B. Saunders Co. surfaces and in free solution. J. Enz. Inhibition 8:51- Philadelphia, pp. 172-214. 59. 22. Brown, B.S. and Steven, F.S. 1993. Review on 39. Anees, M. 1996. Inhibition of a tumour protease with proteases and cancer. Biol. Sciences Review 10: 36- 3,4-dichloroisocoumarin, pentamidine-isethionate 37. and guanidino derivatives. J. Enz. Inhibition 8:213- 23. Paris, D., Quadros, A., Patel, N., Delledonne, A., 221. Humphrey, J. and Mullan, M. 2005. Inhibition of 40. Anees, M. 1996. Interaction of tissue plasminogen angiogenesis and tumor growth by Beta and Gamma- activator inhibitor with cell surface secretase inhibitors. Eur. J. Pharmacol. 14:1-15. guanidinobenzoatase and urokinase plasminogen 24. Swiercz, R., Keck, R.W., Skrzypczak, J.E., Selman, activator. J. Enz. Inhibition 281-288. S.H. and Jankun, J. 2001. Recombinant Pai-1 Inhibits 41. Steven, F.S., Anees, M., Talbot, I.C., Blakey, D.C. angiogenesis and reduces size of in cap prostate and Hasleton, P.S. 1993. The interactions of protein cancer xenografts in Scid mice. Oncol. Rep. 8:463- inhibitors with tumour proteases studied in solution 470. and immobilized on cell surfaces in frozen sections. 25. Liotta, L.A. and Stetler, S.W. 1991. Cancer cell Anticancer Res. 13:2003-2010. invasion and metastasis. Cancer Res. 51:5054-5059. 42. Steven, F.S., Griffin, M.M., Ellis, I.O., Bell, J. and 26. Liotta, L.A. 1992. Cancer cell invasion and Palcic, B. 1992. Demonstration of a cell surface metastasis. Scientific American 6: 34-41. protease iso-enzyme specific for breast carcinoma 27. Kim, Y.S. Liotta, L.A. and Khon, E.C. 1993. Cancer cells which is not present on normal breast cells. and metastasis. Hosp. Pract. 28:92-96. Clin. Chem. Enzym. Comm. 4:367-371. Guanidianobenzoatase and cancer 214

43. Steven, F.S., Lam, S., Macaulay, C. and Palcic, B. 46. Steven, F.S., Johnson, J. and Eason, P. 1993. A 1992. Fluorescent location of abnormal cells in cell protein inhibitor, extracted from Hela cells, which smears obtained from the lungs of patients with lung recognizes a cell surface protease on pre-neoplastic cancer. Anticancer Res. 12:625-630. cells obtained from cervical smears. Anticancer Res. 44. Steven, F.S., Payne, P.W. and Palcic, B. 1993. The 13:1059-1061. status of the surface enzyme guanidinobenzoatase 47. Anees, M. and Benbow, E.W. 1996. Dansyl fluoride on mature epithelial cells in sputum cell monolayers. for the fluorescent location of tumour cells in the Anticancer Res. 13:311-315. human tissues. J. Enz. Inhibition 10:195-201. 45. Steven, F.S., Palcic, B., Sin, J. and Desai, M. 1997. A 48. Steven, F.S., Johnson, J., Eason, P. and Palcic, B. simple clinical method for the preparation of 1992. Immunofluorescent probes designed to locate improved cervical smears-approximating to pre-neoplastic and carcinoma cells with possible monolayers. Anticancer Res. 17:629-632. application to automated analysis. Cancer J. 5:149- 153. 215 Proc. Pakistan Acad. Sci. 42(3):215-217.2005Book Review

Book Review 50 YEARS OF RESEARCH AND DEVELOPMENT IN PAKISTAN by Dr. Mazhar M. Qurashi and Abdul Qayyum Kazi, 1997

Published by Pakistan Council for Science and Technology, Shahrah-e-Jamhuriat, G-5/2, Islamabad (Pakistan). pp. 134.

Price, local Rs. 150/paper back. Overseas U.S. $ 10.00 Post Free.

Urdu translation of this book printed in 2004 under the title:

Urdu Language Authority, H-8, Islamabad, priced at Rs. 140/-.

This condensed 134-page volume contains an of socio-economic importance. A number of new abridgement and extension of a comprehensive specialized monodiscipline R&D institutions were earlier book, by the same authors, titled “Research established in the eighties e.g. National Institute of and Development in Pakistan: Review (194789) and Electronics, National Physical and Standards Future Perspective”, which covered in detail the Laboratory; National Institute of Silicon Technology, period of first 40 years since the creation of Pakistan. etc. The National Science and Technology Policy Apart from the abridgement of the significant material was approved in 1984, and subsequently a separate in the earlier publication, this condensed volume National Technology Policy, along with Action Plan attempts to describe the important initiatives taken for Technology Development, was approved in in the last 10-15 years and also to identify some 1993. basic imperatives that would need to be addressed in the future. Chapter 2 describes the organization and structure of Science and Technology at the federal, A unique feature of this publication is that it provincial and local levels and their inter-relationship, provides a complete picture of the past, present and as existing in the nineteen eighties. It also includes some future requirements for the growth of science structure of Research Councils and Institutes under and technology in the indigenous Pakistani milieu, other Ministries and Provincial Governments. The as well as in the globalized international world of overall organizational chart displays the structure for new opportunities and constraints. Science and Technology in Pakistan, as in 1997.

Chapter 1 gives a brief history of the growth Chapter 3 gives a critical analysis of the growth of science and technology in Pakistan from 1947 to of S&T manpower from 1950 to 1980 and its 1997, divided into six periods. It describes in detail projections. The authors have pointed out the the process of the formulation of national science increasingly dismal situation with regard to the high- policy and the creation of organizations for promotion level manpower engaged in R&D; the situation has and coordination of research activities in the country been practically stagnating from 1975 onwards. during this period. Following the National Science Measures for development of high-level S&T/R&D Commission’s Report of 1961, a separate Ministry manpower, in terms of quantity and quality, have been of Science and Technology was created in 1972; proposed, based on the 1990 P.A.S. Report on Pakistan Science Foundation was established in High-Level S&T Manpower – Its Training and 1973 for the promotion of Science in society and to Utilization. Incentives for attractive career-structure provide financial support for research on problems for scientists in research and teaching have been Book Review 216 proposed. Anticipating the requirements of highly the government, the industry and the scientists. trained manpower in emerging technologies, the Human Resource Development Programme had Chapter 6 concerns Promotion of Science and been launched by the Government of Pakistan, which Technology in the context of Pakistan. The authors envisaged training of scientists and engineers at post- have presented an over-view of the present status graduate level in advanced science and engineering of promotional activities for Science awareness in fields. Furthermore it was recommended that a major the society. At the Federal Government level, the portion of trained S&T manpower should be Pakistan Science Foundation is the lead agency for inducted into industry, and that a large bulk of applied promotion of science. It has established a scientific research should be conducted for industry and within & technological information centre (P AS TIC) and industry, having provision for greater mobility of the Pakistan Museum of Natural History. It renders professional persons to industry. financial and technical assistance for organizing science exhibitions and fairs. There are four Chapter 4 describes the R&D programmes and categories of societies for: promotion and priorities in the important economic sectors, based popularization of science; specialized societies on the recommendations in the 1984 National dealing with a particular discipline of science; Science and Technology Policy and the reports of professional societies; and prestigious societies & expert panels and working group. These are then learned bodies. The authors have emphasized the integrated with the overall planning process through need to strengthen the role of NGOs through financial the Planning Commission, Ministry of Science and and administrative help, so that they may play an Technology and the executing Ministry. The S&T effective role in promotion of science for all strata of component and its financial requirements are worked society, including the student community, housewives, out, which is then translated into detailed R&D labourers in the factory and small formers in the projects for execution by the relevant research remote villages. organization/institutes. It has been proposed that no major development project should be approved Chapter 7 deals with Science and Technology unless its R&D component is worked out and fully Cooperation at the bilateral, regional and international integrated with the planning machinery of the country. level. Mention has been made of bilateral agreements with· China, West Germany, U.S.A., regional Chapter 5 deals with several complex problems cooperation with ECO and SAARC countries; and of Technology Development in the modern age. It international level cooperation with U.N. specialized provides an in-depth study of the vast canvas of agencies as well as O.I.C. countries. Special mention Technology-Development Process, including the has been made of the O.I.C. Standing Committee international implications of Technological gap and on Scientific and Technological Cooperation controlled Technology-Transfer: The authors have (COMSTECH); its secretariat is located in analyzed the history of industrial technology in Islamabad. ISESCO is located in Rabat; Islamic Pakistan during the past 40 years and pointed out Institute of Technology in Dhaka; and Islamic that new technologies have been imported almost Development Bank in Jeddah. Mention has also been entirely on a turn-key basis, with minimal made of the Commission on Science and Technology unpackaging of technology. They have indicated the for Sustainable Development in the South strategy of the National Technology Policy, which (COMSATS), which has developed a network of could include: commercialization of local R&D 13 international science & technology “centers-of- system; development of information network; excellence” in the South; it is now one of the major strengthening the Metrology, Standards, Testing internet-service providers in Pakistan. Quality (MSTQ) system; and cooperation between 217 Book Review

Chapter 8 on “Science, Scientists and Society” management of R&D Institutes. Recommendations is a good mix of the pre-conditions, individual of World Bank Report on Higher Education and qualities and desirable Societal Characteristics for Research, Cabinet Committee to Review Activities the growth of Science and Technology. It has an of R&D Organizations, and High-Level Review interesting section on the “common attitudes” of Committee on Science and Technology have been Pakistani society and of individuals which are in analyzed and pooled by the authors in a systematic direct opposition to the qualities required for good manner. S&T. The authors have pin-pointed the crux of the matter in these words: ‘’To be really effective, this Section 10.6 in this chapter discusses a novel change has to be based on the roots of national feature, which provides food for thought for scholars culture, i.e., on the Islamic values of true learning, and researchers in the S&T field. This is the problem practical observation, collaboration, mutual respect, of “integration of science with Islamic knowledge”. etc. Proper dissemination of these teachings is It has been mentioned that the Makkah Conference therefore on essential requirement”. (1977) defined the goals of Islamic education as: “Education should aim at the balanced growth of Chapter 9 deals with the “Industrial the total personality of man, through the training of Development and Research”. It mentions the causes man’s spirit, intellect, the rational self, feeling and of backwardness in the industrial sector and bodily senses ...”. Several attempts at “Islamization” elaborates proposals of the Industrial Commission in the fields of Social Sciences, Technology and for eradication of these deficiencies. They have Natural Science have accordingly been made during pointed out that the lesson for developing countries the last two decades with varying degrees of success. like Pakistan is “if Pakistan hopes for faster economic There are two streams at the back of present-day growth, it needs increased government funding for resurgence of Islam, “the Reformist” and “the science, but should simultaneously adopt measures Modernist”. There is a dire necessity for a synthesis to promote general industrial activities”. The secret of the two currents. lies in the competitiveness and quality consciousness of industry. As an example of R&D effort within At the end of the book, the authors have given Productive Enterprise, they have mentioned the a chapter-wise Bibliography and References for example of rapidly developing Asian countries, like those interested in further reading. There is hardly Korean Republic and Singapore, with 40% to 50% any topic on S&T development which has not been of their R&D manpower working in the productive dealt with effectively in this thin volume of 134 pages. sector. For Pakistan they have proposed that R&D This speaks volumes for the breadth of vision, depth within the industry and industrial units should be of knowledge and life-long experience of the eminent encouraged and R&D scientists need to be employed authors in planning, execution and management of to work on down-to-earth problems. The authors research and development. This comprehensive and have quoted the examples of successful economies stimulating publication is highly recommended for of Japan, Korea and Malaysia. They have study by the planners, policy-makers, administrators recommended that in Pakistan R&D units, can be and research workers in the field of science and catalyzed by placing some of the more directly technology. related governmental R&D units within the appropriate industry. Dr. S.M. Jafar, Chapter 10 is entitled “Scientific Research and (Retd.) Senior Scientific Adviser Management”. It includes a broad-spectrum of issues Ministry of Science & Technology concerning, directly or indirectly, the problems of Islamabad 219 Proc. Pakistan Acad. Sci. 42(3):219-220.2005Obituary

Obituary

PROF. DR. NASIMA TIRMIZI (1933-2005)

It is with a very heavy heart that I am writing identification of Pakistan’s crabs and anomurans. She this obituary note for Professor Dr. (Mrs) Nasima would not only be remembered as an eminent Tirmizi, Founder Director, Marine Reference Carcinologist but also as an all-round Zoologist. She Collection & Resource Centre, University of served as Chairperson, Department of Zoology Karachi, and a well known Marine Zoologist. A (1972-74, 1978-80), Director, Marine Reference career spanning over thirty-five years devoted to Collection & Resource Centre, University of Karachi marine biology, especially crustacean research and (1968-95), Director, Centre of Excellence in Marine exploration, came to a close when she passed away Biology, University of Karachi (1980-1990), in Karachi on 11th March 2005. Dr. Nasima Tirmizi Director, Institute of Marine Sciences, University of was born in Delhi, India on 12th July, 1933. She Karachi (1982-1993) and Dean, Faculty of Science, was the granddaughter of a great scholar of the University of Karachi (1991-1993). Indian subcontinent, Deputy Nazir Ahmed. Dr. Nasima was a humanist who was always From Delhi, Dr. Tirmizi’s family migrated to willing to guide and groom her students. Throughout Karachi in 1946 where she passed her matriculation her career at the Karachi University, where she taught in 1948 and left the S. M. Science College in 1950 for 35 years, her students sought guidance, help and passing her pre-medical Intermediate Examination. advice from her at all times. She was a stickler for She passed her B.Sc Hons. in 1953 and obtained professional excellence in guiding her students and Masters in Zoology (Entomology) in 1955 from in preparing her lectures, based on the most current Karachi University, securing first division and first developments on the subject. She was highly position in the entire Faculty of Science. She respected by all students of the Zoology Department continued higher studies at Oxford and obtained D. and the Centre of Excellence in Marine Biology. Phil degree in 1958. She was the first Pakistani woman to get a doctorate from England. At Oxford, Dr. Tirmizi was my mentor, my leading light, she worked with Isabella Gordon and R.W. Ingle. my supervisor for M.Sc., M.Phil. and Ph.D theses, She specialized in the field of Carcinology, an area and this led to an association that lasted almost thirty in which most of her publications have been devoted. years. When I joined her lab as a Research Assistant, As a Systematist she carved a niche for herself as a she was always patient with me while transferring Systematist and pioneered research in the field of knowledge of crustacean systematics and the Marine Zoology. She received D.Sc in 1972 from methodology of illustrations with the microscope. Karachi University; again being the first woman in Through these years both of us worked on various Pakistan to get a D.Sc. After her superannuation research projects, mostly on carcinological fauna of from Karachi University, she held the status of Pakistan and cruise samples from abroad. Professor Emeritus at Hamdard University, Karachi. Her monographs on Brachyura and Anomura of Dr. Nasima Tirmizi not only established the Pakistan will always be valuable sources for the Marine Reference Collection & Resource Centre at Obituary 220

Karachi University, but also played an important part Nasima Manning & Holthuis and several species in the establishment of National Institute of are named after her. In recognition of her long and Oceanography of Pakistan and established the devoted service to science, she was conferred many Institute of Marine Sciences with its chair at the gold medals, honours and awards. She was on the University of Karachi. While working as Director of editorial board of several magazines of zoology. In the Center of Excellence in Marine Biology, she did order to solidify our close association, which began not neglect her own research work on crustaceans. when I joined her as her assistant and to counteract She worked on some very important collections (e.g. the feeling of retirement, I proposed that she should John Murray, Rumphius, IIOE, Fridtjof Nansen and continue working at the Centre with full access to NASEER ) entrusted to her. She was in personal working facilities. Unfortunately her health contact with other giants in the field of Zoology, Prof. deteriorated and she stopped coming to the Centre. Holthuis, Dr. Farfante, Dr. Guinot, Dr. Haig, Dr. Barnse, Dr. Vannucci, Dr. Zakir Hussain, Dr. Qasim, She will live in the hearts of all her family Dr. Moosa, Dr. Manning and Dr. Banner and members and all her students scattered all over the vigorously persuide her work in the field. She was world. Apart from her research work on crustaceans, an amazing woman in many respects. She used to Dr. Nasima will be remembered for her service in take great care in combining minute details, accuracy developing the field of marine sciences in Pakistan. and technical perfection in presentation of drawings She will also remain in the hearts of all those readers in her articles. who may have read her articles in the daily column of the Urdu newspaper “Jang”. The loss of Dr. Her association with the Marine Reference Nasima Tirmizi has left a void in the hearts of all -- Collection & Resource Centre, a project that was her colleagues, friends and students. Words do not her brainchild, is legendary. She was the first Pakistani suffice to express adequately my feelings and my scientist to bring home the ever largest amount under gratitude for Dr. Tirmizi, whom I called Nasima Apa, this ONR (USA) projects on marine living resources for all that she did for me. She was a beautiful woman in the Karachi University. She was a member of scientist, a human being full of modesty and one who scores of academic and professional bodies since always brought charm to the laboratory. May her 1955. She paid visit to research laboratories and soul rest in eternal peace (Ameen). participated in seminars in U.K., U.S.A., China, India, Japan, Holland, France, Egypt, Kuwait, Dr. Quddusi B. Kazmi Bahrain, Thailand, Singapore, Malaysia, Iran, Italy, Marine Reference Collection & Resource Centre Bangladesh, Australia and Seychelles. One genus University of Karachi, Karachi-75270, Pakistan 221

INSTRUCTIONS TO AUTHORS

Proceedings of the Pakistan Academy of Sciences publishes original research papers on a broad range of topics of basic and applied sciences. State-of-the-art reviews (~ 20 pages, well supported by recent references) which adequately summarise work in a particular area of science, especially in the context of Pakistan and indicate lines of further research are also considered for publication. All original research articles are classified under 4 sections: Life Sciences, Physical Sciences, Medical Sciences and Engineering Sciences & Technology. All papers are refereed externally. Authors are not required to be members or fellows of the Academy. Manuscripts may be submitted from any country; however, all manuscripts must be submitted in English. The authors are requested to read the following instructions carefully before submitting a manuscript. Failure to comply with these guidelines is liable to delay the review process and possible publication of the manuscript. Manuscript preparation: Manuscripts should be typewritten, double-spaced on 8.5" x 11" paper with 1" margin on all sides. Two copies should be submitted, including Figures and Tables. Papers are subject to editorial revision for purpose of conformity to the style adopted. Manuscripts should in general not exceed 20 typewritten pages including Tables, Figures and illustrations. The authors must submit a 3.5" high density (HD) diskette containing a copy in Microsoft (MS) Word of the final version of the manuscript, or as e-mail attachment preferably to Sectional Editors (or Editor-in-Chief) through a fellow of the Academy (see Website). Each of the following sections of the manuscript should be typed on a separate page and in the sequence shown below: TITLE PAGE: Should carry: (A) title (in capital letters) of the article to have no more than 160 characters, in a concise but informative style. Do not use abbreviations or acronyms, (B) first name, middle initial, last name of each author, (C): name of the department(s) and institution(s) to which the work should be attributed, (D) name and address of author to whom correspondence should be addressed, include Email address if available, (E) short running title of no more than 50 characters. ABSTRACT AND KEYWORDS: The second page should carry an abstract of 250 words or less. The abstract should be self-explanatory, without reference to the text. The abstract should state the objective of the study, the methods used, main findings and principal conclusions. Abbreviations may be used provided they are defined on first mention in the abstract and in the main text. Review articles may be submitted without an abstract. Please suggest five to eight keywords excluding any that are already used in the title. TEXT: For original research articles the text should be divided into sections with the headings: Introduction: provide a clear and concise statement of the problem and the aims of the investigation, and cite the relevant literature on the subject. Materials and Methods: Provide an adequate account of the procedures including statistical tests (if any). Describe briefly but in such a way that sufficient information is provided to replicate the work. Results: to be clearly and concisely described with the help of appropriate tables, figures and other illustrative material. Results should have no repetition of data in figures, tables and text. Discussion. Provide a brief interpretation of your results in the light of relevant previous studies. Comments and interpretations should be supported by evidence or references. Do not use more than 3 levels of heads in the text. For review articles the text can be appropriately sectioned. ACKNOWLEDGEMENTS: Acknowledge financial support and other types of assistance in a brief statement. REFERENCES: References must be limited to directly related published papers. Authors bear total responsibility for the accuracy of the references. All references in the text are to be included in the list of References and vice versa. Only published articles or articles accepted for publication qualify for references. References to manuscripts submitted to other journals but not yet accepted are not permitted. In the text, references should be cited as consecutive numerals in square brackets, for example. “Brown et al. [2] reported ...” or “.. as previously described [3,6-8]”. They should be listed in the same numerical order in the References list at the end of the manuscript on a separate sheet or sheets. List all authors. Examples of references: a. Articles in Journals- 1 . Speh, B. and Vogan, D.A. 1980. Reducibility of generalized principal series representations. Acta Math. 145: 227-299. 2. Williams, R.L., Hilton, D.J., Pease, S., Wilson, T.A., Stewart, C.L., Grearing, D.P., Wagner, .F., Metcalf, D., Nicola, N.A. and Gough, N.M. 1988. Myeloid leukaemia inhibitory factor (LIF) maintains the developmental potential of embryonic stem cells. Nature 336: 684-687 b. Chapters in books 3. Cox, A.W. 1988. Solar and geothermal energy. In: Information Sources in Energy Technology. Ed. Anthony, L.J. pp. 263-289. Butterworths, London. 222

4. Smolen, J.E. and Boxer, L.A. 1991. Functions of neutrophils. In: Hematology. Eds. Williams, W.J., Butler, E. and Litchman, M.A. 4th ed. pp. 3-101. McGraw Hill, New York. c. Books: 5. Leeper, G.W. 1978. Managing Heavy Metals on the Land. Marcel Dekker, New York. 6. Adams, D.O., Edelson, P.J. and Koren, H.S. 1981. Methods for studying Mononuclear Phagocytes. Academic Press, San Diego. TABLES: Tables must be typewritten on separate sheets and submitted in duplicate. They should be numbered consecutively according to order of citation, using arabic numbers. Each table must have a concise heading and should be comprehensible without reference to the text. The approximate position of each table in text should be indicated. Tables should be as simple as possible. Round off numbers within the table to the nearest whole number or significant digit. Place essential explanatory material below the table. Identify footnotes with superscript letters or symbols keyed to data in the table. Do not use vertical lines. Use horizontal lines only to separate the column heads from the data. Refer to published tables in a recent issue of the journal to verify the appropriate style. ILLUSTRATIONS: Figures should be carefully and professionally prepared. Two sets of high quality camera-ready illustrative material are required. Number figures consecutively with Arabic numerals (1,2,3) in the order in which they are cited in the text. Glossy prints must be submitted for photomicrographs, gels and other halftones. Photocopies of line drawings are acceptable at submission as long as two sets of high quality camera copies are provided. Figures should be identified by a black lead pencil, on the top or back of each figure with figure number and the last name of the first author. Type legends, double-spaced, in numerical order, on a separate sheet or sheets. Use numbers and letters consistent in style with those used in the illustration. Please note that the Figures may be printed (with or without reduction) in two styles. Figures layouts may either match the columns size of 8.2 x 24.0 cm or the entire page of 16.0 x 24.0 cm maximum size. Line drawings: Computer generated figures produced on a laser printer are acceptable. Alternatively, original line drawings should be made with black ink on white drawing or tracing paper. Do not use lettering smaller than 9 points or unnecessarily large. Lettering should be proportional on all figures within an article. In graphs, the abscissa and ordinate should be clearly labelled, and the units of measurement given. Photographs: Photographs must be of the highest quality and provided as glossy prints. They should be mounted if they are to form multiple panels on the journal page. All prints should be trimmed to exclude areas not relevant to the paper and be separated from adjacent photographs by uniform spaces. A scale bar should be included on all photomicrographs or magnification (e.g. x 400, x 8000 etc.) be given at the end of the legend. . Declaration: Submission of the manuscript must be accompanied by the declaration that the results are original; approval of all authors concerned has been obtained to submit manuscript for consideration; the same material is neither ‘in press’ nor under consideration elsewhere and that the copyright of the paper will be assigned to the Pakistan Academy of Sciences in case the article is accepted for publication. Manuscripts should be submitted to the following Sectional Editors (or to Editor-in-Chief). Life Sciences Physical Sciences Prof. Dr. S. Irtifaq Ali Prof. Dr. M. Iqbal Choudhary B-356, Block 6, Gulshan-e-Iqbal HEJ Research Institute of Chemistry Karachi, Pakistan Karachi University E-mail: [email protected] Karachi, Pakistan E-mail: [email protected] Medical Sciences Engineering Sciences & Technology Prof. Dr. Iftikhar A. Malik Prof. Dr. A. Raouf Principal 36-P, Model Town Extension Foundation University, Rawalpindi Lahore, Pakistan E-mail: [email protected] E-mail: [email protected] For enquiries contact: Prof. Dr. M.A. Hafeez Editor-in-Chief Telephone: 92-51-9207140 and 9207789 Pakistan Academy of Sciences Fax: 92-51-9206770 3-Constitution Avenue, G-5/2 Email: [email protected] and [email protected] Islamabad, Pakistan Website: www.paspk.org

OF THE PAKISTAN ACADEMY OF SCIENCES

Volume 42 No. 3, September 2005

Research Articles

Life Sciences

Level and trends of fertility in Bangladesh 159 — Sabina Islam, K. N. S. Yadava and M. A. Alam

Butyrylcholinesterase inhibitory lignans from Sarcostemma viminale 167 — Viqar Uddin Ahmad, Muhammad Zubair, Muhammad Athar Abbasi, Farzana Kousar, Sarfraz A. Nawaz, M. Iqbal Choudhary and Syed Raziullah Hussaini

Physical Sciences

— Matrix elements for the Morse potential 173 M. Enciso-Aguilar, J. López-Bonilla and S. Vidal-Beltrán

Semi-compactness in fuzzfiying topology 177 — O.R. Sayed

On a fourth order pseudoparabolic equation 187 — Ye. A. Utkina and A. Maher

Connection symbols in differential and Riemannian geometry 195 — Ashfaque H. Bokhari and F. D. Zaman

Reviews

Gene-chip technology and its application 199 — Muhammad Irfan, Tayyab Husnain, Penny J. Tricker, Gail Taylor and S. Riazuddin

Cell surface protease, guanidinobenzoatase, and cancer 205 — Mohammad Anees

Book Review

50 years of research and development in Pakistan 215 by Dr. Mazhar M. Qurashi and Abdul Qayyum Kazi, 1997

Obituary

Prof. Dr. Nasima Tirmizi 219

Instructions to Authors 221

THE PAKISTAN ACADEMY OF SCIENCES – ISLAMABAD, PAKISTAN