Theoretical Biology and Medical Modelling

The method of mathematically controlled comparison provides a structured approach for the comparison of alternative biochemical pathways with respect to selected functional effectiveness measures. Under this approach, alternative implementations of a biochemical pathway are modeled mathematically, forced to be equivalent through the application of selected constraints, and compared with respect to selected functional effectiveness measures. While the method has been applied successfully in a variety of studies, we offer recommendations for improvements to the method that (1) relax requirements for definition of constraints sufficient to remove all degrees of freedom in forming the equivalent alternative, (2) facilitate generalization of the results thus avoiding the need to condition those findings on the selected constraints, and (3) provide additional insights into the effect of selected constraints on the functional effectiveness measures. We present improvements to the method and related statistical models, apply the method to a previously conducted comparison of network regulation in the immune system, and compare our results to those previously reported.

Murray's Law states that, when a parent blood vessel branches into daughter vessels, the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of daughter blood vessels. Murray derived this law by defining a cost function that is the sum of the energy cost of the blood in a vessel and the energy cost of pumping blood through the vessel. The cost is minimized when vessel radii are consistent with Murray's Law. This law has also been derived from the hypothesis that the shear force of moving blood on the inner walls of vessels is constant throughout the vascular system. However, this derivation, like Murray's earlier derivation, is based on the assumption of constant blood flow. To determine the implications of the constant shear force hypothesis and to extend Murray's energy cost minimization to the pulsatile arterial system, a model of pulsatile flow in an elastic tube is analyzed. A new and exact solution for flow velocity, blood flow rate and shear force is derived. For medium and small arteries with pulsatile flow, Murray's energy minimization leads to Murray's Law. Furthermore, the hypothesis that the maximum shear force during the cycle of pulsatile flow is constant throughout the arterial system implies that Murray's Law is approximately true. The approximation is good for all but the largest vessels (aorta and its major branches) of the arterial system. A cellular mechanism that senses shear force at the inner wall of a blood vessel and triggers remodeling that increases the circumference of the wall when a shear force threshold is exceeded would result in the observed scaling of vessel radii described by Murray's Law.

Severe Acute Respiratory Syndrome (SARS) and Middle East Respiratory Syndrome (MERS) are two coronaviruses with demonstrated potential to generate significant nosocomial outbreaks. In particular, MERS continues to pose a significant threat in the Middle East since 2012. Currently, no licensed vaccine or drug treatment is available to treat patients infected with either coronavirus. However, there are some MERS vaccines in the preclinical stage of development. We sought to evaluate the potential impact of targeted vaccination strategies for mitigating SARS and MERS outbreaks in healthcare settings using simple mathematical models and detailed historic transmission trees describing the progression of past nosocomial outbreaks of SARS and MERS. Our findings suggest that vaccination strategies targeting patients and healthcare workers, which have been disproportionately affected during past outbreaks, and assuming two vaccination coverage levels at 50 and 75% have the potential to avert nearly 50% or more of MERS or SARS cases. Our modeling results informed by historic outbreak data for SARS and MERS suggest that vaccination strategies targeting patients could be an effective measure to mitigate and prevent outbreaks in the healthcare setting.

Graves’ is disease an autoimmune disorder of the thyroid gland caused by circulating anti-thyroid receptor antibodies (TRAb) in the serum. TRAb mimics the action of thyroid stimulating hormone (TSH) and stimulates the thyroid hormone receptor (TSHR), which results in hyperthyroidism (overactive thyroid gland) and goiter. Methimazole (MMI) is used for hyperthyroidism treatment for patients with Graves’ disease. We have developed a model using a system of ordinary differential equations for hyperthyroidism treatment with MMI. The model has four state variables, namely concentration of MMI (in mg/L), concentration of free thyroxine - FT4 (in pg/mL), and concentration of TRAb (in U/mL) and the functional size of the thyroid gland (in mL) with thirteen parameters. With a treatment parameter, we simulate the time-course of patients’ progression from hyperthyroidism to euthyroidism (normal condition). We validated the model predictions with data from four patients. When there is no MMI treatment, there is a unique asymptotically stable hyperthyroid state. After the initiation of MMI treatment, the hyperthyroid state moves towards subclinical hyperthyroidism and then euthyroidism. We can use the model to describe or test and predict patient treatment schedules. More specifically, we can fit the model to individual patients’ data including loading and maintenance doses and describe the mechanism, hyperthyroidism→euthyroidism. The model can be used to predict when to discontinue the treatment based on FT4 levels within the physiological range, which in turn help maintain the remittance of euthyroidism and avoid relapses of hyperthyroidism. Basically, the model can guide with decision-making on oral intake of MMI based on FT4 levels.

Cachexia affects most patients with incurable cancer. We hypothesize that in metastatic cancer the mass of the tumor as well as its level of anaerobic energy metabolism play a critical role in describing its energetic cost, which results in elevated resting energy expenditure and glucose utilization, leading to cachexia. Prior models of cancer cachexia may have underestimated the specific energetic cost of cancer as they have not taken the range of tumor mass and anaerobic energy metabolism fully into account. We therefore modelled the energetic cost of cancer as a function of the percentage of energy the cancer produces anaerobically, based on resting energy expenditure, glucose turnover, glucose recycling, and oxygen consumption in cancer patients found in previous studies. Data from two clinical studies where tumor burden was estimated and resting energy expenditure or oxygen consumption were measured lead to a broad range of estimates of tumor cost from 190 to 470 kcal/kg tumor/day. These values will vary based of the percentage of energy the cancer produces anaerobically (from 0 to 100 %), which in and of itself can alter the cost over a 2 to 3-fold range. In addition to the tumor cost/kg and the degree of anaerobic metabolism, the impact on a given individual patient will depend on tumor burden, which can exceed 1 kg in advanced metastatic disease. Considering these dimensions of tumor cost we are able to produce a 2-dimensional map of potential values, with an overall range of 100–1400 kcal/day. Quantifying the energetic cost of cancer may benefit an understanding of the tumor’s causation of cachexia. Our estimates of the range of tumor cost include values that are higher than prior estimates and suggest that in metastatic disease the tumor cost could be expected to eclipse attempts to stabilize energy balance through nutrition support or by drug therapies. Tumor mass and the percentage of anaerobic metabolism in the tumor contribute to the cost of the tumor on the body and potentially lead directly to negative energy balance and increased muscle wasting.

Superficial bladder cancer has been the subject of numerous studies for many years, but the evolution of the disease still remains not well understood. After the tumor has been surgically removed, it may reappear at a similar level of malignancy or progress to a higher level. The process may be reasonably modeled by means of a Markov process. However, in order to more completely model the evolution of the disease, this approach is insufficient. The semi-Markov framework allows a more realistic approach, but calculations become frequently intractable. In this context, flowgraph models provide an efficient approach to successfully manage the evolution of superficial bladder carcinoma. Our aim is to test this methodology in this particular case. We have built a successful model for a simple but representative case. The flowgraph approach is suitable for modeling of superficial bladder cancer.

Attention Deficit Hyperactivity Disorder, commonly referred to as ADHD, is a common, complex, predominately genetic but highly treatable disorder, which in its more severe form has such a profound effect on brain function that every aspect of the life of an affected individual may be permanently compromised. Despite the broad base of scientific investigation over the past 50 years supporting this statement, there are still many misconceptions about ADHD. These include believing the disorder does not exist, that all children have symptoms of ADHD, that if it does exist it is grossly over-diagnosed and over-treated, and that the treatment is dangerous and leads to a propensity to drug addiction. Since most misconceptions contain elements of truth, where does the reality lie? We have reviewed the literature to evaluate some of the claims and counter-claims. The evidence suggests that ADHD is primarily a polygenic disorder involving at least 50 genes, including those encoding enzymes of neurotransmitter metabolism, neurotransmitter transporters and receptors. Because of its polygenic nature, ADHD is often accompanied by other behavioral abnormalities. It is present in adults as well as children, but in itself it does not necessarily impair function in adult life; associated disorders, however, may do so. A range of treatment options is reviewed and the mechanisms responsible for the efficacy of standard drug treatments are considered. The genes so far implicated in ADHD account for only part of the total picture. Identification of the remaining genes and characterization of their interactions is likely to establish ADHD firmly as a biological disorder and to lead to better methods of diagnosis and treatment.

Previously it has been shown that insulin-mediated tyrosine phosphorylation of myosin heavy chain is concomitant with enhanced association of C-terminal SRC kinase during skeletal muscle differentiation. We sought to identify putative site(s) for this phosphorylation event.

A combined bioinformatics approach of motif prediction and evolutionary and structural analyses identified tyrosines163 and 1856 of the skeletal muscle heavy chain as the leading candidate for the sites of insulin-mediated tyrosine phosphorylation.

Our work is suggestive that tyrosine phosphorylation of myosin heavy chain, whether in skeletal muscle or in platelets, is a significant event that may initiate cytoskeletal reorganization of muscle cells and platelets. Our studies provide a good starting point for further functional analysis of MHC phosphor-signalling events within different cells.

The different phases of the eukaryotic cell cycle are exceptionally well-preserved phenomena. DNA decompaction, RNA and protein synthesis (in late G1 phase) followed by DNA replication (in S phase) and lipid synthesis (in G2 phase) occur after resting cells (in G0) are committed to proliferate. The G1 phase of the cell cycle is characterized by an increase in the glycolytic metabolism, sustained by high NAD+/NADH ratio. A transient cytosolic acidification occurs, probably due to lactic acid synthesis or ATP hydrolysis, followed by cytosolic alkalinization. A hyperpolarized transmembrane potential is also observed, as result of sodium/potassium pump (NaK-ATPase) activity. During progression of the cell cycle, the Pentose Phosphate Pathway (PPP) is activated by increased NADP+/NADPH ratio, converting glucose 6-phosphate to nucleotide precursors. Then, nucleic acid synthesis and DNA replication occur in S phase. Along with S phase, unpublished results show a cytosolic acidification, probably the result of glutaminolysis occurring during this phase. In G2 phase there is a decrease in NADPH concentration (used for membrane lipid synthesis) and a cytoplasmic alkalinization occurs. Mitochondria hyperfusion matches the cytosolic acidification at late G1/S transition and then triggers ATP synthesis by oxidative phosphorylation. We hypothesize here that the cytosolic pH may coordinate mitochondrial activity and thus the different redox cycles, which in turn control the cell metabolism.