Prediction uncertainty and optimal experimental design for learning dynamical systems.

Dynamical systems are frequently used to model biological systems. When these models are fit to data, it is necessary to ascertain the uncertainty in the model fit. Here, we present prediction deviation, a metric of uncertainty that determines the extent to which observed data have constrained the model's predictions. This is accomplished by solving an optimization problem that searches for a pair of models that each provides a good fit for the observed data, yet has maximally different predictions. We develop a method for estimating a priori the impact that additional experiments would have on the prediction deviation, allowing the experimenter to design a set of experiments that would most reduce uncertainty. We use prediction deviation to assess uncertainty in a model of interferon-alpha inhibition of viral infection, and to select a sequence of experiments that reduces this uncertainty. Finally, we prove a theoretical result which shows that prediction deviation provides bounds on the trajectories of the underlying true model. These results show that prediction deviation is a meaningful metric of uncertainty that can be used for optimal experimental design.

Onset timing of cross-sensory activations and multisensory interactions in auditory and visual sensory cortices.

Here we report early cross-sensory activations and audiovisual interactions at the visual and auditory cortices using magnetoencephalography (MEG) to obtain accurate timing information. Data from an identical fMRI experiment were employed to support MEG source localization results. Simple auditory and visual stimuli (300-ms noise bursts and checkerboards) were presented to seven healthy humans. MEG source analysis suggested generators in the auditory and visual sensory cortices for both within-modality and cross-sensory activations. fMRI cross-sensory activations were strong in the visual but almost absent in the auditory cortex; this discrepancy with MEG possibly reflects the influence of acoustical scanner noise in fMRI. In the primary auditory cortices (Heschl's gyrus) the onset of activity to auditory stimuli was observed at 23 ms in both hemispheres, and to visual stimuli at 82 ms in the left and at 75 ms in the right hemisphere. In the primary visual cortex (Calcarine fissure) the activations to visual stimuli started at 43 ms and to auditory stimuli at 53 ms. Cross-sensory activations thus started later than sensory-specific activations, by 55 ms in the auditory cortex and by 10 ms in the visual cortex, suggesting that the origins of the cross-sensory activations may be in the primary sensory cortices of the opposite modality, with conduction delays (from one sensory cortex to another) of 30-35 ms. Audiovisual interactions started at 85 ms in the left auditory, 80 ms in the right auditory and 74 ms in the visual cortex, i.e., 3-21 ms after inputs from the two modalities converged.

A Computational Model of Inhibition of HIV-1 by Interferon-Alpha.

Type 1 interferons such as interferon-alpha (IFNα) inhibit replication of Human immunodeficiency virus (HIV-1) by upregulating the expression of genes that interfere with specific steps in the viral life cycle. This pathway thus represents a potential target for immune-based therapies that can alter the dynamics of host-virus interactions to benefit the host. To obtain a deeper mechanistic understanding of how IFNα impacts spreading HIV-1 infection, we modeled the interaction of HIV-1 with CD4 T cells and IFNα as a dynamical system. This model was then tested using experimental data from a cell culture model of spreading HIV-1 infection. We found that a model in which IFNα induces reversible cellular states that block both early and late stages of HIV-1 infection, combined with a saturating rate of conversion to these states, was able to successfully fit the experimental dataset. Sensitivity analysis showed that the potency of inhibition by IFNα was particularly dependent on specific network parameters and rate constants. This model will be useful for designing new therapies targeting the IFNα network in HIV-1-infected individuals, as well as potentially serving as a template for understanding the interaction of IFNα with other viruses.

Statistically robust measurement of evoked response onset latencies.

Onset latencies of evoked responses are useful for determining delays in sensory pathways and for indicating spread of activity between brain areas, therefore inferring causality. Previous studies have applied several different methods and parameters for detecting onsets, mainly utilizing thresholds based on the mean and standard deviation (SD) of the pre-stimulus "baseline" time window, or using t-tests of group data to determine when the response first differs significantly from the baseline. However, these methods are not statistically robust, have low power when the baseline data are not normally distributed, and are heavily influenced by outliers in the baseline. Here, we examine using a modified boxplot method known as the "median rule" for determining onset latencies. This rule makes no assumptions about the baseline distribution, is resistant to outliers, and can be applied to individual level data therefore allowing intersubject and interregional comparisons. We first show with simulations that the median rule is significantly less sensitive to outliers in the baseline than the SD method. We then use simulations to demonstrate the effect of skewness on onset latencies. Finally, we use magnetoencephalography (MEG) to show that the median rule can be easily applied to real data and gives reasonable results. In most situations the different methods give similar results, which enhances comparability across studies, but in data sets with a high noise level there is a clear advantage to using a statistically robust method. In conclusion, the median rule is an excellent method for estimating onset latencies in evoked responses.