A mathematical model of cell movement and clustering due to chemotaxis.

This paper presents a numerical method for modelling cell migration and aggregation due to chemotaxis where the cell is attracted towards the direction in which the concentration of a chemical signal is increasing. In the model presented here, each cell is represented by a system of springs connected together at node points on the cell's membrane and on the boundary of the cell's nucleus. The nodes located on a cell's membrane are subject to a force which is proportional to the gradient of the concentration of the chemical signal which mimics the behaviour of the chemical receptors in the cell's membrane. In particular, the model developed here will consider what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells. The methods described in this paper will be illustrated with a number of typical examples simulating cells moving in response to a chemical signal and how they combine to form clusters.

Modelling the motion of clusters of cells in a viscous fluid using the boundary integral method.

In experiments clusters of cells are often observed to move in response to a chemical signal which is present in the fluid surrounding the cells. This process is known as chemotaxis. This paper presents a method for modelling the motion of clusters of cells moving through a viscous fluid in response to a known chemical signal using a boundary integral formulation of the governing equations rather than the more usual differential equation formulation. The numerical results presented in this paper show that the boundary integral method can be used to simulate the motion of cell clusters through the fluid. The results of the simulations are compared to some experimental observations of cell and cluster motion.

A simple mathematical model of cell clustering by chemotaxis.

Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modeled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge-Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.

Experiments towards the synthesis of the ergot alkaloids and related structures. Part 8. The total synthesis of 4-methyl-2,3,4,4a,5,6-hexahydrobenzo[f]quinoline-2-carbonitrile hydrochloride hemihydrate, an immediate precursor of the despyrrole analogues of lysergic acid and its amides.

Exposure of the N-methoxycarbonyl-bicyclic-keto-acid 5 (improved preparation) to the Barnick beta-keto-acid synthesis yielded an aqueous solution of the sodium salts of the beta-keto-acids 26 and 27 which on heating at 60-65 degrees C furnished the N-methoxycarbonyl-tricyclic-ketone 9 (55%) plus the hydroxy-ketone 28 which on acid treatment raised the yield of 9 to 68%. Reduction (NaBH4) of 9 yielded the alcohol 32 (94%) which was treated with thionyl chloride followed by copper (I) cyanide and sodium iodide in acetonitrile to give the tricyclic-N-methoxycarbonyl nitrile 35 whose relative configuration was obtained by X-ray analysis. Attempts to remove the N-methoxycarbonyl group from 35 were unsuccessful. Conversion of the alcohol 32 to its methoxypropyl ether 41 followed by reaction with ethereal MeLi-LiBr yielded the amino-alcohol 39 (75%) converted to the N-formyl-tricyclic alcohol 42 with formic-acetic anhydride (70%). The alcohol 42 was then converted into the N-formyl nitrile 44 via the chloride 43 as employed in the earlier synthesis of the nitrile 35. Removal of the N-formyl group from the nitrile 44 was achieved by refluxing methanolic hydrochloric acid to give the required amino-nitrile hydrochloride 46 (91%) whose structure was confirmed by X-ray analysis. Reaction of the free base with methyl iodide in ethyl acetate in the presence of calcium carbonate furnished the N-methyl base 48 isolated as its hydrochloride, hemihydrate 49 (59%). The overall yield of 49 via this eleven-step synthesis was 3.4%.