A dynamic model of nutrient uptake by root hairs.

Root hairs are known to be important in the uptake of sparingly soluble nutrients by plants, but quantitative understanding of their role in this is weak. This limits, for example, the breeding of more nutrient-efficient crop genotypes. We developed a mathematical model of nutrient transport and uptake in the root hair zone of single roots growing in soil or solution culture. Accounting for root hair geometry explicitly, we derived effective equations for the cumulative effect of root hair surfaces on uptake using the method of homogenization. Analysis of the model shows that, depending on the morphological and physiological properties of the root hairs, one of three different effective models applies. They describe situations where: (1) a concentration gradient dynamically develops within the root hair zone; (2) the effect of root hair uptake is negligibly small; or (3) phosphate in the root hair zone is taken up instantaneously. Furthermore, we show that the influence of root hairs on rates of phosphate uptake is one order of magnitude greater in soil than solution culture. The model provides a basis for quantifying the importance of root hair morphological and physiological properties in overall uptake, in order to design and interpret experiments in different circumstances.

Botulinum toxin in writer's cramp: objective response evaluation in 31 patients.

OBJECTIVES: To quantify the treatment effect of local botulinum toxin injections in writer's cramp a newly developed rating scale of writing performance and a computer assisted analysis of writing speed were used in 31 patients undergoing botulinum toxin therapy. METHODS: Baseline data of the writer's cramp rating scale (WCRS, see appendix) and computer based writing speed analysis were compared with those obtained at the time of subjective best response as recorded during follow up visits. RESULTS: The mean dose injected per session was 133.2 units Dysport divided between two forearm muscles. Of all 124 injection sessions during mean follow up of one year 76% produced a good improvement. The most common side effect was weakness (72% of the follow up visits). The WCRS scores as assessed by a blinded videotape review by four independent raters showed good reliability between raters and a significant improvement after treatment (P < 0.001). The speed of pen movements showed a significant (P < 0.05) increase after treatment at subjective best effect recordings and a significant correlation with WCRS subscores, documenting the validity of the scale. CONCLUSION: The present study is the first to show significant effects of botulinum toxin treatment in patients with writer's cramp on the basis of a quantifiable scale for writing performance which correlates significantly with writing speed measurements. The WCRS as employed in this study might therefore prove a useful rating instrument in other studies assessing severity and treatment response in patients with writer's cramp.