Neural inhibition can explain negative BOLD responses: A mechanistic modelling and fMRI study.

Functional magnetic resonance imaging (fMRI) of hemodynamic changes captured in the blood oxygen level-dependent (BOLD) response contains information of brain activity. The BOLD response is the result of a complex neurovascular coupling and comes in at least two fundamentally different forms: a positive and a negative deflection. Because of the complexity of the signaling, mathematical modelling can provide vital help in the data analysis. For the positive BOLD response, there are plenty of mathematical models, both physiological and phenomenological. However, for the negative BOLD response, no physiologically based model exists. Here, we expand our previously developed physiological model with the most prominent mechanistic hypothesis for the negative BOLD response: the neural inhibition hypothesis. The model was trained and tested on experimental data containing both negative and positive BOLD responses from two studies: 1) a visual-motor task and 2) a working-memory task in conjunction with administration of the tranquilizer diazepam. Our model was able to predict independent validation data not used for training and provides a mechanistic underpinning for previously observed effects of diazepam. The new model moves our understanding of the negative BOLD response from qualitative reasoning to a quantitative systems-biology level, which can be useful both in basic research and in clinical use.

Effects of IL-1ß-Blocking Therapies in Type 2 Diabetes Mellitus: A Quantitative Systems Pharmacology Modeling Approach to Explore Underlying Mechanisms.

Recent clinical studies suggest sustained treatment effects of interleukin-1ß (IL-1ß)-blocking therapies in type 2 diabetes mellitus. The underlying mechanisms of these effects, however, remain underexplored. Using a quantitative systems pharmacology modeling approach, we combined ex vivo data of IL-1ß effects on ß-cell function and turnover with a disease progression model of the long-term interactions between insulin, glucose, and ß-cell mass in type 2 diabetes mellitus. We then simulated treatment effects of the IL-1 receptor antagonist anakinra. The result was a substantial and partly sustained symptomatic improvement in ß-cell function, and hence also in HbA1C, fasting plasma glucose, and proinsulin-insulin ratio, and a small increase in ß-cell mass. We propose that improved ß-cell function, rather than mass, is likely to explain the main IL-1ß-blocking effects seen in current clinical data, but that improved ß-cell mass might result in disease-modifying effects not clearly distinguishable until >1 year after treatment.

Structural robustness of biochemical network models-with application to the oscillatory metabolism of activated neutrophils.

Sensitivity of biochemical network models to uncertainties in the model structure, with a focus on autonomously oscillating systems, is addressed. Structural robustness, as defined here, concerns the sensitivity of the model predictions with respect to changes in the specific interactions between the network components and encompass, for instance, uncertain kinetic models, neglected intermediate reaction steps and unmodelled transport phenomena. Traditional parametric sensitivity analysis does not address such structural uncertainties and should therefore be combined with analysis of structural robustness. Here a method for quantifying the structural robustness of models for systems displaying sustained oscillations is proposed. The method adopts concepts from robust control theory and is based on adding dynamic perturbations to the network of interacting biochemical components. In addition to providing a measure of the overall robustness, the method is able to identify specific network fragilities. The importance of considering structural robustness is demonstrated through an analysis of a recently proposed model of the oscillatory metabolism in activated neutrophils. The model displays small parametric sensitivities, but is shown to be highly unrobust to small perturbations in some of the network interactions. Identification of specific fragilities reveals that adding a small delay or diffusion term in one of the involved reactions, likely to exist in vivo, completely removes all oscillatory behaviour in the model.

Conservation laws and unidentifiability of rate expressions in biochemical models.

New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis.

Elimination of the initial value parameters when identifying a system close to a Hopf bifurcation.

One of the biggest problems when performing system identification of biological systems is that it is seldom possible to measure more than a small fraction of the total number of variables. If that is the case, the initial state, from where the simulation should start, has to be estimated along with the kinetic parameters appearing in the rate expressions. This is often done by introducing extra parameters, describing the initial state, and one way to eliminate them is by starting in a steady state. We report a generalisation of this approach to all systems starting on the centre manifold, close to a Hopf bifurcation. There exist biochemical systems where such data have already been collected, for example, of glycolysis in yeast. The initial value parameters are solved for in an optimisation sub-problem, for each step in the estimation of the other parameters. For systems starting in stationary oscillations, the sub-problem is solved in a straight-forward manner, without integration of the differential equations, and without the problem of local minima. This is possible because of a combination of a centre manifold and normal form reduction, which reveals the special structure of the Hopf bifurcation. The advantage of the method is demonstrated on the Brusselator.

Improved parameter estimation for systems with an experimentally located Hopf bifurcation.

When performing system identification, we have two sources of information: experimental data and prior knowledge. Many cell-biological systems are oscillating, and sometimes we know an input where the system reaches a Hopf bifurcation. This is the case, for example, for glycolysis in yeast cells and for the Belousov-Zhabotinsky reaction, and for both of these systems there exist significant numbers of quenching data, ideal for system identification. We present a method that includes prior knowledge of the location of a Hopf bifurcation in estimation based on time-series. The main contribution is a reformulation of the prior knowledge into the standard formulation of a constrained optimisation problem. This formulation allows for any of the standard methods to be applied, including all the theories regarding the method's properties. The reformulation is carried out through an over-parametrisation of the original problem. The over-parametrisation allows for extra constraints to be formed, and the net effect is a reduction of the search space. A method that can solve the new formulation of the problem is presented, and the advantage of adding the prior knowledge is demonstrated on the Brusselator.