Mathematical Models of Biological Processes

2015 ◽  
pp. 1672-1672
Keyword(s):  
Mathematical Models ◽  
Biological Processes

Methodology of Research in Micropollutants – Heavy Metals

1982 ◽  
Vol 14 (12) ◽  
pp. 107-125 ◽  
Author(s):  
Roland Wollast
Keyword(s):  
Heavy Metals ◽  
Mathematical Models ◽  
Aqueous Phase ◽  
Suspended Matter ◽  
Solid Phase ◽  
Aquatic Organisms ◽  
Biological Processes ◽  
Particulate Phase ◽  
Sources Of Pollution ◽  
Adsorption Desorption

A comparison of the concentration of dissolved and of particulate heavy metals in the aquatic system indicates that these elements are strongly enriched in the suspended matter. The transfer between the aqueous phase and the solid phase may be due to dissolution-precipitation reactions, adsorption-desorption processes or biological processes. When these processes are identified, it is further possible to develop mathematical models which describe the behaviour of these elements. The enrichment of heavy metals in the particulate phase suspended or deposited and in aquatic organisms constitutes a powerful tool in order to evaluate sources of pollution.

Survival characteristics of the free-living cercarial population of the ectoparasitic digenean Transversotrema patialensis (Soparker, 1924)

Parasitology ◽  
1975 ◽  
Vol 70 (3) ◽  
pp. 295-310 ◽  
Author(s):  
R. M. Anderson ◽  
P. J. Whitfield
Keyword(s):  
Mathematical Models ◽  
Life Span ◽  
Conceptual Understanding ◽  
Biological Processes ◽  
Energy Reserves ◽  
Age Dependence ◽  
Maximum Life Span ◽  
Free Living ◽  
Age Dependent ◽  
Low Levels

The survival characteristics of free-living cercarial populations of Transversotrema patialensis were described and shown to be age-dependent. The maximum life-span was found to be 44 h with a 50% survival at 26 h. Activity and infectivity of the larvae were also characterized by age-dependence, and were demonstrated to be closely correlated with one another. For individual cercariae, both activity and infectivity had dropped to extremely low levels many hours before death occurred. An attempt was made to interrelate activity and infectivity, in a theoretical manner, with the availability of energy reserves.Conceptual understanding of the biological processes involved was aided by the formulation of simple mathematical models.

Integrated mathematical models for describing complex biological processes

BIOPHYSICS ◽  
2017 ◽  
Vol 62 (5) ◽  
pp. 778-795
Author(s):  
E. L. Mishchenko ◽  
O. V. Petrovskaya ◽  
A. M. Mishchenko ◽  
E. D. Petrovskiy ◽  
N. V. Ivanisenko ◽  
...  
Keyword(s):  
Mathematical Models ◽  
Biological Processes

Application of a dynamic nitrogen model to reduce nutrient pollution by dairy cows

2002 ◽  
Vol 2002 ◽  
pp. 106-106
Author(s):  
E. Kebreab ◽  
J.A.N. Mills ◽  
L.A. Crompton ◽  
J. France
Keyword(s):  
Mathematical Models ◽  
Environmental Pollution ◽  
Dairy Cows ◽  
Dairy Herds ◽  
Nutrient Pollution ◽  
Dairy Production ◽  
Biological Processes ◽  
Annual Output ◽  
N Utilization ◽  
N Pollution

Agriculture is one of the major sources of nitrogen (N) pollution. Dairy production causes losses of N in faeces and urine that contribute to environmental pollution with an estimated annual output of 320 kt N and 80 kt ammonia in the U.K. alone. Therefore, improving N utilization in dairy cows and especially reducing N output in excreta is desirable to reduce environmental N pollution, particularly as ammonia. Mathematical models have been used to predict potential N excretion from dairy cows. However, these models generally are empirical in nature, hence not process based and therefore there is a need to develop a model that can describe biological processes in the animal. The objective of the present study was to develop a dynamic N model to predict the amount and form of N excreted by dairy herds and seek to make appropriate recommendations that will reduce N excretion from dairy cows.

scholarly journals Effective Time-Stepping For The Tau-Leaping Method for Stochastic Simulation Of Well-Stirred Biochemical Networks

2021 ◽  
Author(s):  
Mahmuda Binte Mostofa Ruma
Keyword(s):  
Mathematical Models ◽  
Stochastic Simulation ◽  
Practical Interest ◽  
Cellular Level ◽  
Biochemical Networks ◽  
Biological Processes ◽  
Time Stepping ◽  
Effective Time ◽  
Numerical Tests ◽  
Biochemical Systems

Biological processes at the cellular level are noisy. The noise arises due to random molecular collisions, and may be substantial in systems with low molecular counts in some species. This thesis introduces a variable tau-leaping method for the simulation of stochastic discrete mathematical models of well-stirred biochemical systems which is theoretically justified. Numerical tests on several models of biochemical systems of practical interest illustrate the advantages of the adaptive tau-leap method over the existing schemes.

The Analysis of Complex Population Processes

1964 ◽  
Vol 96 (1-2) ◽  
pp. 335-347 ◽  
Author(s):  
C. S. Holling
Keyword(s):  
Mathematical Models ◽  
Population Ecology ◽  
Population Models ◽  
Biological Processes ◽  
Complex Population ◽  
Distinctive Type ◽  
Population Processes ◽  
Whole Systems ◽  
Considerable Complexity ◽  
Digital Computers

AbstractPopulation ecology requires realistic and precise analyses of whole systems, or processes, and not just fragments of them. This poses some difficult problems because of the distinctive complexity of these processes. Recent studies of predation have shown, however, that it is possible to achieve great analytical depth and to simulate whole systems in the form of realistic and precise mathematical models. This is accomplished by ignoring the degree of simplicity traditionally required of population models and by emphasizing the need for reality. Extensive experimentation is required to suggest and test possible explanations for the action of each component of the process so that the explanation evolves in gradual steps to include one component after another. The form of the explanation and the resulting equations is hence dictated by the process itself and not by the need for mathematical neatness. The considerable complexity of the predation model arose from features common to many biological processes i.e. the prevalence of limits and thresholds, the presence of important discontinuities and the historical character of biological events. These features can be analyzed effectively only by establishing an intimate feed-back between experiment and theory. Mathematical models incorporating these features are admirably solved using digital computers. Computers, and the languages used to program them, seem to be ideally suited to handle the distinctive type of complexity shown by population processes.

scholarly journals The Modulation of Pain by Circadian and Sleep-Dependent Processes: A Review of the Experimental Evidence

2017 ◽  
Author(s):  
Megan Hastings Hagenauer ◽  
Jennifer A. Crodelle ◽  
Sofia H. Piltz ◽  
Natalia Toporikova ◽  
Paige Ferguson ◽  
...  
Keyword(s):  
Sleep Deprivation ◽  
Mathematical Models ◽  
Pain Sensitivity ◽  
Experimental Pain ◽  
Biological Processes ◽  
Experimental Conditions ◽  
Sleep Behavior ◽  
Laboratory Rodents ◽  
Sleep Drive ◽  
The Impact

AbstractThis proceedings paper is the first in a series of three papers developing mathematical models for the complex relationship between pain and the sleep-wake cycle. Here, we briefly review what is known about the relationship between pain and the sleep-wake cycle in humans and laboratory rodents in an effort to identify constraints for the models. While it is well accepted that sleep behavior is regulated by a daily (circadian) timekeeping system and homeostatic sleep drive, the joint modulation of these two primary biological processes on pain sensitivity has not been considered. Under experimental conditions, pain sensitivity varies across the 24 h day, with highest sensitivity occurring during the evening in humans. Pain sensitivity is also modulated by sleep behavior, with pain sensitivity increasing in response to the build up of homeostatic sleep pressure following sleep deprivation or sleep disruption. To explore the interaction between these two biological processes using modeling, we first compare the magnitude of their effects across a variety of experimental pain studies in humans. To do this comparison, we normalize the results from experimental pain studies relative to the range of physiologicallymeaningful stimulation levels. Following this normalization, we find that the estimated impact of the daily rhythm and of sleep deprivation on experimental pain measurements is surprisingly consistent across different pain modalities. We also review evidence documenting the impact of circadian rhythms and sleep deprivation on the neural circuitry in the spinal cord underlying pain sensation. The characterization of sleep-dependent and circadian influences on pain sensitivity in this review paper is used to develop and constrain the mathematical models introduced in the two companion articles.

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