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Researchers used mathematical models to calculate estimated dosages of a peptide to increase bone density.
seem rigid and set in their ways, but your bones are actually under
constant construction and deconstruction. They give up their nutrient
treasures (calcium) to the body and then rebuild in a constant
give-and-take sort of rhythm.
When that rhythm shifts with advancing age or the onset of
osteoporosis, the rebuilding process decreases. Bones lose density and
strength and become more prone to fracture.
More than 10 million people in the United States live with
osteoporosis and the resulting fractures demand more than $17 billion in
related health care each year.
Now two University of Delaware researchers and their students have
joined forces - applying the mathematical modeling expertise of one to
the biological inquiry of the other - to point the way to a promising
The biologist - Anja Nohe - has shown that treating a mouse with a peptide known as CK2.3 increases bone mineral density. The mathematician/engineer - Prasad Dhurjati - has calculated estimated dosages for human beings.
According to their model, injections of CK2.3 can raise bone mineral
density of bones badly degraded by osteoporosis back to healthy levels.
Their work has just been published in Pharmacometrics and Systems Pharmacology.
Bone mineral density is affected by two processes: bone formation and
bone degradation. Current drug treatments, especially bisphosphonates,
address the cells involved in bone degradation (osteoclasts). Only the
approved drug PTH addresses the cells involved in bone formation
(osteoblasts) but doctors must prescribe bisphosphonates with it to
target bone degradation simultaneously. The peptide used in this
research -- CK2.3 -- is the only one that decreases bone degradation
while simultaneously increasing bone formation.
Dhurjati has published mathematical models for many different
systems. The professor of chemical and biomolecular engineering (with a
joint appointment in mathematical sciences and biological sciences) has
40 years of research experience and is an often-cited author.
His recent modeling work in biological sciences has included: autism
spectrum disorders, leukemia, spinal muscular atrophy, dosages of
lithium for pregnant women who have bipolar disorder, the gut microbiome
and plant disease.
Models can be of many different kinds -- conceptual models, simple
pictorial connection maps, a set of rules or a complex set of
mathematical equations. Dhurjati looks at various types to make sense of
the time-varying interactions between variables in the entire system.
This allows for meaningful analysis of the enormous amount of data
researchers are generating in almost every field.
"My focus is on converting data to knowledge using models," he said. "I want more students to work in this domain."
High-speed computers are sophisticated tools that are made more
valuable with good models, he said. Reliable models based on good data
can save time, money and many laboratory animals.
"A math model cannot capture the full complexity of a mouse or a
human," he said. "I'm not claiming that; however, as you interface math
with experiments and as you interface math with reality, the models
become better and more reliable."
In this case, the work included students from four departments - Chemical and Biomolecular Engineering, Biological Sciences, Mathematical Sciences and Biomedical Engineering -- some at graduate-level study, some undergraduate.
Nohe's team designed the mimetic peptide CK2.3 and showed that
it increased bone mineral density in a mouse model by blocking the CK2
protein's interaction with the BMPR1a protein -- an interruption that
allows the cells that form new bone (osteoblasts) to increase.
Subcutaneous (below the skin) injection increased bone formation in the
crown of the skull (known as calvaria), while systemic injection
decreased bone degradation and increased bone mineral density.
Dhurjati's team used that information to calculate ideal dosages for healthy humans and those with osteoporosis.
A mouse and a human are different in many ways, Dhurjati said, so
calculating a dosage is more complex than just adjusting for differences
in weight, for example.
Dhurjati developed part of the model using the concepts in
physiology-based pharmacokinetic (PBPK) models pioneered by the late
Kenneth Bischoff, UD professor of chemical engineering for many years.
Such models can be used to calculate how a pharmaceutical molecule
distributes in different parts of the body.
In this case, Dhurjati needed to know what the local concentration of
CK2.3 would be at the site where bone is formed. Once this was
determined, another math model was used to calculate bone mineral
These considerations prevent a proposed remedy from becoming a toxin,
and the model can address such questions as how much to take, how
often, whether it should be taken by mouth or injection and how to
adjust for age, gender, ethnicity, height, weight, overall health.
The collaboration between Nohe and Dhurjati has been underway for
some time and has produced other insights into biological questions.
"She's a believer in models," he said. "These are two different
cultures. Biology emphasizes qualitative details, and engineering relies
more on mathematical models. But if the two cultures can communicate,
that brings new ways of looking at the same problem."
In addition to Dhurjati and Nohe, the project and publication
included the following students: Rebecca Ellis (chemical engineering),
Kristen Thomas Nicholson (mathematics), Allison Lisberg (biomedical
engineering), Prashanth Moku (biological sciences), Aparna Swarup
The study was supported by a grant from the National Institutes of Health.
Prasad Dhurjati is a professor of chemical and biomolecular
engineering with a joint appointment in mathematical sciences and
biological sciences. His research interests are in systems medicine,
systems biology, chemical process diagnostics and artificial
intelligence. He earned his bachelor’s degree in chemical engineering at
the Indian Institute of Technology in Kanpur, India, and his doctorate
at Purdue University. He is an elected fellow of the American Institute
of Medical and Biological Engineering. He also is president of the UD
Anja Nohe is associate professor of biological sciences, with
interest in differentiation of stem cells, development of new imaging
techniques and new delivery techniques into the cell nucleus. She earned
her undergraduate degree at the University of Würzburg, Germany, and
her doctorate at Theodor Boveri Institute at the same university. She
did postdoctoral work at the University of Western Ontario in Canada. More about her earlier work with bone mineral density and peptides can be found in this 2014 article.
Article by Beth Miller; illustration by Jeffrey Chase
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