Achieving Occam's razor: Deep learning for optimal model reduction.

All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam's razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model's degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

Diet modulates brain network stability, a biomarker for brain aging, in young adults.

Epidemiological studies suggest that insulin resistance accelerates progression of age-based cognitive impairment, which neuroimaging has linked to brain glucose hypometabolism. As cellular inputs, ketones increase Gibbs free energy change for ATP by 27% compared to glucose. Here we test whether dietary changes are capable of modulating sustained functional communication between brain regions (network stability) by changing their predominant dietary fuel from glucose to ketones. We first established network stability as a biomarker for brain aging using two large-scale (n = 292, ages 20 to 85 y; n = 636, ages 18 to 88 y) 3 T functional MRI (fMRI) datasets. To determine whether diet can influence brain network stability, we additionally scanned 42 adults, age < 50 y, using ultrahigh-field (7 T) ultrafast (802 ms) fMRI optimized for single-participant-level detection sensitivity. One cohort was scanned under standard diet, overnight fasting, and ketogenic diet conditions. To isolate the impact of fuel type, an independent overnight fasted cohort was scanned before and after administration of a calorie-matched glucose and exogenous ketone ester (d-ß-hydroxybutyrate) bolus. Across the life span, brain network destabilization correlated with decreased brain activity and cognitive acuity. Effects emerged at 47 y, with the most rapid degeneration occurring at 60 y. Networks were destabilized by glucose and stabilized by ketones, irrespective of whether ketosis was achieved with a ketogenic diet or exogenous ketone ester. Together, our results suggest that brain network destabilization may reflect early signs of hypometabolism, associated with dementia. Dietary interventions resulting in ketone utilization increase available energy and thus may show potential in protecting the aging brain.

Ground-truth "resting-state" signal provides data-driven estimation and correction for scanner distortion of fMRI time-series dynamics.

The fMRI community has made great strides in decoupling neuronal activity from other physiologically induced T2* changes, using sensors that provide a ground-truth with respect to cardiac, respiratory, and head movement dynamics. However, blood oxygenation level-dependent (BOLD) time-series dynamics are also confounded by scanner artifacts, in complex ways that can vary not only between scanners but even, for the same scanner, between sessions. Unfortunately, the lack of an equivalent ground truth for BOLD time-series has thus far stymied the development of reliable methods for identification and removal of scanner-induced noise, a problem that we have previously shown to severely impact detection sensitivity of resting-state brain networks. To address this problem, we first designed and built a phantom capable of providing dynamic signals equivalent to that of the resting-state brain. Using the dynamic phantom, we then compared the ground-truth time-series with its measured fMRI data. Using these, we introduce data-quality metrics: Standardized Signal-to-Noise Ratio (ST-SNR) and Dynamic Fidelity that, unlike currently used measures such as temporal SNR (tSNR), can be directly compared across scanners. Dynamic phantom data acquired from four "best-case" scenarios: high-performance scanners with MR-physicist-optimized acquisition protocols, still showed scanner instability/multiplicative noise contributions of about 6-18% of the total noise. We further measured strong non-linearity in the fMRI response for all scanners, ranging between 8-19% of total voxels. To correct scanner distortion of fMRI time-series dynamics at a single-subject level, we trained a convolutional neural network (CNN) on paired sets of measured vs. ground-truth data. The CNN learned the unique features of each session's noise, providing a customized temporal filter. Tests on dynamic phantom time-series showed a 4- to 7-fold increase in ST-SNR and about 40-70% increase in Dynamic Fidelity after denoising, with CNN denoising outperforming both the temporal bandpass filtering and denoising using Marchenko-Pastur principal component analysis. Critically, we observed that the CNN temporal denoising pushes ST-SNR to a regime where signal power is higher than that of noise (ST-SNR > 1). Denoising human-data with ground-truth-trained CNN, in turn, showed markedly increased detection sensitivity of resting-state networks. These were visible even at the level of the single-subject, as required for clinical applications of fMRI.

Making Sense of Computational Psychiatry.

In psychiatry we often speak of constructing "models." Here we try to make sense of what such a claim might mean, starting with the most fundamental question: "What is (and isn't) a model?" We then discuss, in a concrete measurable sense, what it means for a model to be useful. In so doing, we first identify the added value that a computational model can provide in the context of accuracy and power. We then present limitations of standard statistical methods and provide suggestions for how we can expand the explanatory power of our analyses by reconceptualizing statistical models as dynamical systems. Finally, we address the problem of model building-suggesting ways in which computational psychiatry can escape the potential for cognitive biases imposed by classical hypothesis-driven research, exploiting deep systems-level information contained within neuroimaging data to advance our understanding of psychiatric neuroscience.

Single-cell kinetics of siRNA-mediated mRNA degradation.

RNA interference (RNAi) enables the therapeutic use of small interfering RNAs (siRNAs) to silence disease-related genes. The efficiency of silencing is commonly assessed by measuring expression levels of the target protein at a given time point post-transfection. Here, we determine the siRNA-induced fold change in mRNA degradation kinetics from single-cell fluorescence time-courses obtained using live-cell imaging on single-cell arrays (LISCA). After simultaneous transfection of mRNAs encoding eGFP (target) and CayRFP (reference), the eGFP expression is silenced by siRNA. The single-cell time-courses are fitted using a mathematical model of gene expression. Analysis yields best estimates of related kinetic rate constants, including mRNA degradation constants. We determine the siRNA-induced changes in kinetic rates and their correlations between target and reference protein expression. Assessment of mRNA degradation constants using single-cell time-lapse imaging is fast (<30 h) and returns an accurate, time-independent measure of siRNA-induced silencing, thus allowing the exact evaluation of siRNA therapeutics.

Leveraging Julia's automated differentiation and symbolic computation to increase spectral DCM flexibility and speed.

Using neuroimaging and electrophysiological data to infer neural parameter estimations from theoretical circuits requires solving the inverse problem. Here, we provide a new Julia language package designed to i) compose complex dynamical models in a simple and modular way with ModelingToolkit.jl, ii) implement parameter fitting based on spectral dynamic causal modeling (sDCM) using the Laplace approximation, analogous to MATLAB implementation in SPM12, and iii) leverage Julia's unique strengths to increase accuracy and speed by employing Automatic Differentiation during the fitting procedure. To illustrate the utility of our flexible modular approach, we provide a method to improve correction for fMRI scanner field strengths (1.5T, 3T, 7T) when fitting models to real data.

Power spectrum scale invariance identifies prefrontal dysregulation in paranoid schizophrenia.

Theory and experimental evidence suggest that complex living systems function close to the boundary of chaos, with erroneous organization to an improper dynamical range (too stiff or chaotic) underlying system-wide dysregulation and disease. We hypothesized that erroneous organization might therefore also characterize paranoid schizophrenia, via optimization abnormalities in the prefrontal-limbic circuit regulating emotion. To test this, we acquired fMRI scans from 35 subjects (N = 9 patients with paranoid schizophrenia and N = 26 healthy controls), while they viewed affect-valent stimuli. To quantify dynamic regulation, we analyzed the power spectrum scale invariance (PSSI) of fMRI time-courses and computed the geometry of time-delay (Poincaré) maps, a measure of variability. Patients and controls showed distinct PSSI in two clusters (k(1) : Z = 4.3215, P = 0.00002 and k(2) : Z = 3.9441, P = 0.00008), localized to the orbitofrontal/medial prefrontal cortex (Brodmann Area 10), represented by ß close to white noise in patients (ß ≈ 0) and in the pink noise range in controls (ß ≈ -1). Interpreting the meaning of PSSI differences, the Poincaré maps indicated less variability in patients than controls (Z = -1.9437, P = 0.05 for k(1) ; Z = -2.5099, P = 0.01 for k(2) ). That the dynamics identified Brodmann Area 10 is consistent with previous schizophrenia research, which implicates this area in deficits of working memory, executive functioning, emotional regulation and underlying biological abnormalities in synaptic (glutamatergic) transmission. Our results additionally cohere with a large body of work finding pink noise to be the normal range of central function at the synaptic, cellular, and small network levels, and suggest that patients show less supple responsivity of this region.

Development of an MRI-Compatible Nasal Drug Delivery Method for Probing Nicotine Addiction Dynamics.

Substance abuse is a fundamentally dynamic disease, characterized by repeated oscillation between craving, drug self-administration, reward, and satiety. To model nicotine addiction as a control system, a magnetic resonance imaging (MRI)-compatible nicotine delivery system is needed to elicit cyclical cravings. Using a concentric nebulizer, inserted into one nostril, we delivered each dose equivalent to a single cigarette puff by a syringe pump. A control mechanism permits dual modes: one delivers puffs on a fixed interval programmed by researchers; with the other, subjects press a button to self-administer each nicotine dose. We tested the viability of this delivery method for studying the brain's response to nicotine addiction in three steps. First, we established the pharmacokinetics of nicotine delivery, using a dosing scheme designed to gradually achieve saturation. Second, we lengthened the time between microdoses to elicit craving cycles, using both fixed-interval and subject-driven behavior. Finally, we demonstrate a potential application of our device by showing that a fixed-interval protocol can reliably identify neuromodulatory targets for pharmacotherapy or brain stimulation. Our MRI-compatible nasal delivery method enables the measurement of neural circuit responses to drug doses on a single-subject level, allowing the development of data-driven predictive models to quantify individual dysregulations of the reward control circuit causing addiction.

Multi-layering of SU-8 exhibits distinct geometrical transitions from circular to planarized profiles.

The negative tone photoresist SU-8 permits the creation of micrometer-scale structures by optical lithography. It is also the most used photoresist in soft lithography for the fast-prototyping of microfluidic devices. Despite its importance, the effect of capillary forces on SU-8 multi-layering onto topographical features has not been thoroughly studied. In particular, the profile of the added layer has not been examined in detail. The overlaying process exhibits a set of distinct behaviors, or regimes, depending on the relative thickness of the overlay and the underlying rectangular pattern. We demonstrate how capillary effects control the profile of multi-layer microchannels in a predictable manner. We derive a simple static model to describe the evolution of the overlay as a function of dimensionless geometric parameters. Our study provides a critical understanding of the parameters that govern multi-layer spin coating.

Enzymatic-based cytometry, a sensitive single-cell cytometric method to assess BCR-ABL1 activity in CML.

We developed a simple, rapid and cost-effective enzymatic-based cytometry platform to measure intracellular signaling pathway activity. Our single-cell microwell array platform quantifies protein phosphorylation using enzymatic signal amplification and exploiting Michaelis-Menten kinetics. Our method provides a two-fold increase in resolution compared to conventional flow cytometry.

Diffusion of circular DNA in two-dimensional cavity arrays.

Through a two-dimensional cavity array with connecting pores of submolecular size, diffusion of relaxed circular and linear DNA molecules is visualized by fluorescence microscopy. Across the entropic barriers transport regime, associated with spatially heterogeneous confinement of flexible polymers, circular DNA diffuses slower than linear DNA of the same length, a trend indicating that linear DNA preferably moves through connecting pores by the threading of an end rather than the looping of a midsection.

Estimation of parameters from time traces originating from an Ornstein-Uhlenbeck process.

In this article, we develop a Bayesian approach to estimate parameters from time traces that originate from an overdamped Brownian particle in a harmonic potential, or Ornstein-Uhlenbeck process (OU). We show that least-square fitting the autocorrelation function, which is often the standard way of analyzing such data, is significantly underestimating the confidence intervals of the fitted parameters. Here, we develop a rigorous maximum likelihood theory that properly captures the underlying statistics. From the analytic solution, we found that there exists an optimal measurement spacing (Δt=0.7968τ) that maximizes the statistical accuracy of the estimate for the decay-time τ of the process for a fixed number of samples N, which plays a similar role than the Nyquist-Shannon theorem for the OU process. To support our claims, we simulated time series with subsequent application of least-square and our maximum likelihood method. Our results suggest that it is quite dangerous to apply least-squares to autocorrelation functions both in terms of systematic deviations from the true parameter values and an order-of-magnitude underestimation of confidence intervals. To see whether our findings apply to other methods where autocorrelation functions are typically fitted by least-squares, we explored the analysis of membrane fluctuations and fluorescence correlation spectroscopy. In both cases, least-square fits exhibit systematic deviations from the true parameter values and significantly underestimate their confidence intervals. This fact emphasizes the need for the development of proper maximum likelihood approaches for such methods. In summary, our results have strong implications for parameter estimation for processes that result in a single exponential decay in the autocorrelation function. Our analysis can directly be applied to single-component dynamic light scattering experiments or optical trap calibration experiments.

Osmotically induced helix-coil transition in poly(glutamic acid).

Protein folding and conformational changes are influenced by protein-water interactions and, as such, the energetics of protein function are necessarily linked to water activity. Here, we have chosen the helix-coil transition in poly(glutamic acid) as a model system to investigate the importance of hydration to protein structure by using the osmotic stress method combined with circular dichroism spectroscopy. Osmotic stress is applied using poly(ethylene glycol), molecular weight of 400, as the osmolyte. The energetics of the helix-coil transition under applied osmotic stress allows us to calculate the change in the number of preferentially included water molecules per residue accompanying the thermally induced conformational change. We find that osmotic stress raises the helix-coil transition temperature by favoring the more compact alpha-helical state over the more hydrated coil state. The contribution of other forces to alpha-helix stability also are explored by varying pH and studying a random copolymer, poly(glutamic acid-r-alanine). In this article, we clearly show the influence of osmotic pressure on the peptide folding equilibrium. Our results suggest that to study protein folding in vitro, the osmotic pressure, in addition to pH and salt concentration, should be controlled to better approximate the crowded environment inside cells.

Electrostatically driven self-assembly of hybrid elastin-DNA liquid crystals.

Self-assembled, hybrid liquid crystals of elastin-like peptides complexed with DNA exhibit inverse temperature-transition behavior and demonstrate functional materials design strategies.

Signal Fluctuation Sensitivity: An Improved Metric for Optimizing Detection of Resting-State fMRI Networks.

Task-free connectivity analyses have emerged as a powerful tool in functional neuroimaging. Because the cross-correlations that underlie connectivity measures are sensitive to distortion of time-series, here we used a novel dynamic phantom to provide a ground truth for dynamic fidelity between blood oxygen level dependent (BOLD)-like inputs and fMRI outputs. We found that the de facto quality-metric for task-free fMRI, temporal signal to noise ratio (tSNR), correlated inversely with dynamic fidelity; thus, studies optimized for tSNR actually produced time-series that showed the greatest distortion of signal dynamics. Instead, the phantom showed that dynamic fidelity is reasonably approximated by a measure that, unlike tSNR, dissociates signal dynamics from scanner artifact. We then tested this measure, signal fluctuation sensitivity (SFS), against human resting-state data. As predicted by the phantom, SFS-and not tSNR-is associated with enhanced sensitivity to both local and long-range connectivity within the brain's default mode network.

Rapid and continuous magnetic separation in droplet microfluidic devices.

We present a droplet microfluidic method to extract molecules of interest from a droplet in a rapid and continuous fashion. We accomplish this by first marginalizing functionalized super-paramagnetic beads within the droplet using a magnetic field, and then splitting the droplet into one droplet containing the majority of magnetic beads and one droplet containing the minority fraction. We quantitatively analysed the factors which affect the efficiency of marginalization and droplet splitting to optimize the enrichment of magnetic beads. We first characterized the interplay between the droplet velocity and the strength of the magnetic field and its effect on marginalization. We found that marginalization is optimal at the midline of the magnet and that marginalization is a good predictor of bead enrichment through splitting at low to moderate droplet velocities. Finally, we focused our efforts on manipulating the splitting profile to improve the enrichment provided by asymmetric splitting. We designed asymmetric splitting forks that employ capillary effects to preferentially extract the bead-rich regions of the droplets. Our strategy represents a framework to optimize magnetic bead enrichment methods tailored to the requirements of specific droplet-based applications. We anticipate that our separation technology is well suited for applications in single-cell genomics and proteomics. In particular, our method could be used to separate mRNA bound to poly-dT functionalized magnetic microparticles from single cell lysates to prepare single-cell cDNA libraries.

Precise pooling and dispensing of microfluidic droplets towards micro- to macro-world interfacing.

Droplet microfluidics possesses unique properties such as the ability to carry out multiple independent reactions without dispersion of samples in microchannels. We seek to extend the use of droplet microfluidics to a new range of applications by enabling its integration into workflows based on traditional technologies, such as microtiter plates. Our strategy consists in developing a novel method to manipulate, pool and deliver a precise number of microfluidic droplets. To this aim, we present a basic module that combines droplet trapping with an on-chip valve. We quantitatively analyzed the trapping efficiency of the basic module in order to optimize its design. We also demonstrate the integration of the basic module into a multiplex device that can deliver 8 droplets at every cycle. This device will have a great impact in low throughput droplet applications that necessitate interfacing with macroscale technologies. The micro- to macro- interface is particularly critical in microfluidic applications that aim at sample preparation and has not been rigorously addressed in this context.

Chemosensory cues to conspecific emotional stress activate amygdala in humans.

Alarm substances are airborne chemical signals, released by an individual into the environment, which communicate emotional stress between conspecifics. Here we tested whether humans, like other mammals, are able to detect emotional stress in others by chemosensory cues. Sweat samples collected from individuals undergoing an acute emotional stressor, with exercise as a control, were pooled and presented to a separate group of participants (blind to condition) during four experiments. In an fMRI experiment and its replication, we showed that scanned participants showed amygdala activation in response to samples obtained from donors undergoing an emotional, but not physical, stressor. An odor-discrimination experiment suggested the effect was primarily due to emotional, and not odor, differences between the two stimuli. A fourth experiment investigated behavioral effects, demonstrating that stress samples sharpened emotion-perception of ambiguous facial stimuli. Together, our findings suggest human chemosensory signaling of emotional stress, with neurobiological and behavioral effects.

DNA cholesteric pitch as a function of density and ionic strength.

The nature of chiral interactions among chiral biopolymers, such as DNA, protein alpha-helices, and rodlike virus particles, remains elusive. In particular, a satisfactory model connecting molecular chiral interactions and the pitch of the resulting chiral mesophases is lacking. We report the measurement of short-fragment (146-bp) DNA cholesteric spherulite pitch as a function of osmotic pressure, average DNA interaxial spacing, and salt concentration. We determined cholesteric pitch and interaxial spacing by polarizing optical microscopy and x-ray scattering, respectively, from which the twist-angle between DNA molecules can be calculated. Surprisingly, we found that decreasing ionic strength resulted in weaker chiral interactions between DNA chains, as evidenced by the decrease in the twist-angle, and consequent increase in the cholesteric pitch, for a fixed interaxial spacing. We propose that this behavior can be explained by increased smearing-out of the helical charge pattern along DNA as the Debye screening length is increased.

Brownian motion of DNA confined within a two-dimensional array.

Linear DNA molecules are visualized while undergoing Brownian motion inside media patterned with molecular-sized spatial constraints. The media, prepared by colloidal templating, trap the macromolecules within a two-dimensional array of spherical cavities interconnected by circular holes. Across a broad DNA size range, diffusion does not proceed by the familiar mechanisms of reptation or sieving. Rather, because of their inherent flexibility, DNA molecules strongly localize in cavities and only sporadically "jump" through holes. Jumping closely follows Poisson statistics. By reducing DNA's configurational freedom, the holes act as molecular weight-dependent entropic barriers. Sterically constrained macromolecular diffusion underlies many separation methods and assumes an important role in intracellular and extracellular transport.