Some mathematical aspects of chemotherapy—II: The distribution of a drug in the body

In a previous paper (Bellman, Jacquez, and Kalaba,Bull. Math. Biophysics,22: 181–198, 1960) a model of the processes occurring in the exchange of a drug between capillary plasma, extracellular space and intracellular space was developed. This included the possibility of a reaction between the drug and a component of the intracellular space. The equations developed thus describe the events within a capillary bed. In the present paper, a simplified model of the body is set up. Each organ is treated as a single capillary bed and is linked to other organs via the circulation, in the parallel and/or series arrangements found in the body. Mixing in the circulation is included at the simplest possible level. The concentration of drug entering any one capillary bed is determined by the concentrations leaving all other capillary beds, the time lags, and mixing involved in the circulation. The equations describing these processes in conjunction with the equations of the processes occurring within each capillary bed lead to a large set of differential-difference equations.     

Agar-Gel Precipitin Technique in Anthrax Antibody Determinations

A modification of the agar-gel precipitation inhibition technique of Thorne and Belton for detecting anthrax antibodies reduces inconsistency of visually determined end points on the same sera observed by different technicians. Determination of the minimal reacting concentrations of the anthrax antigen and antibody reagents, modifications of the visualization apparatus, methods for combining reagents, and length of incubation periods contribute to the ease of the end-point determinations and the uniformity of results. When compared with the previous technique, the modified procedure is less time-consuming while retaining satisfactory reproducibility, simplicity, specificity, and sensitivity.     

Isolation of Salmonellae from Foods Samples: IV. Comparison of Methods of Enrichment

A comparison of various methods of enhancing frequency of Salmonella isolations revealed that inoculation of a second enrichment broth, with culture from the first, was no improvement over the single direct enrichment method. It was inferior to centrifugation.

Selenite was observed to produce more positive isolations at 48 hr than at 24. No change occurred in tetrathionate. Reconstitution of dried albumen with water produced a significant increase in isolations over direct inoculation of enrichment broth in the case of tetrathionate but not selenite broth.

Pre-enrichment in lactose broth before inoculation of enrichment media was vastly superior to reconstitution in water for both enrichment broths. A comparison of results obtained using dulcitol, mannitol, lactose and carbohydrate-free purple broths in pre-enrichment indicated that the carbohydrate added was immaterial.

     

Factors Controlling the Production of Lysogenic Cultures of B. megatherium

(1) The proportion of infected B. megatherium cells which develop lysogenic colonies depends on the number and kind of infecting virus particles and on the culture medium in which the cells are growing. (2) Cells infected with 100 or more T virus particles (from megatherium 899) in yeast extract peptone disintegrate, produce very few virus particles, and less than one lysogenic colony per 10⁷ infected cells. Cells infected with one or a few particles produce 500 to 1000 virus particles each and about 30 lysogenic colonies per 10⁷ infected colonies. (3) T phage obtained from lysogenic magatherium KM cultures produces many more lysogenic cells than does the original megatherium 899 virus. (4) Cells infected with megatherium 899 T virus in peptone medium and then transferred to asparagine medium give rise to 10⁶ lysogenic colonies per 10⁷ infected cells and this transformation will occur even after the infected cells have been in peptone for 60 to 90 minutes and are beginning to produce virus particles. (5) Continued growth of KM strain with either C or T virus from megatherium 899 for several hundred generations in the steady state apparatus results in a lysogenic strain which produces several different types of virus.     

Action of External Divalent Ion Reduction on Sodium Movement in the Squid Giant Axon

Voltage clamp measurements of the sodium potential have been made on the resting squid giant axon to study the effect of variations in external divalent ion concentration upon net sodium flux. From these measurements the intracellular sodium concentration and the net sodium inflow were calculated using the Nernst relation and constant activity coefficients. While an axon bathed in artificial sea water shows a slow increase in internal sodium concentration, the rate of sodium accumulation is increased about two times by reducing external calcium and magnesium concentrations to 0.1 times their normal values. The mean inward net sodium flux increases from a mean control value of 97 pmole/cm² sec. to 186 pmole/cm² sec. in low divalent solution. Associated with these effects of external divalent ion reduction are a marked decrease in action potential amplitude, little or no change in resting potential, and a shift along the voltage axis of the curve relating peak sodium conductance to membrane potential similar to that obtained by Frankenhaeuser and Hodgkin (1957). These results implicate divalent ions in long term (minutes to hours) sodium permeability.