A novel application of neural networks to identify potentially effective combinations of biologic factors for enhancement of bone fusion/repair.

INTRODUCTION: The use of biologic adjuvants (orthobiologics) is becoming commonplace in orthopaedic surgery. Among other applications, biologics are often added to enhance fusion rates in spinal surgery and to promote bone healing in complex fracture patterns. Generally, orthopaedic surgeons use only one biomolecular agent (ie allograft with embedded bone morphogenic protein-2) rather than several agents acting in concert. Bone fusion, however, is a highly multifactorial process and it likely could be more effectively enhanced using biologic factors in combination, acting synergistically. We used artificial neural networks, trained via machine learning on experimental data on orthobiologic interventions and their outcomes, to identify combinations of orthobiologic factors that potentially would be more effective than single agents. This use of machine learning applied to orthobiologic interventions is unprecedented. METHODS: Available data on the outcomes associated with various orthopaedic biologic agents, electrical stimulation, and pulsed ultrasound were curated from the literature and assembled into a form suitable for machine learning. The best among many different types of neural networks was chosen for its ability to generalize over this dataset, and that network was used to make predictions concerning the expected efficacy of 2400 medically feasible combinations of 9 different agents and treatments. RESULTS: The most effective combinations were high in the bone-morphogenic proteins (BMP) 2 and 7 (BMP2, 15mg; BMP7, 5mg), and in osteogenin (150ug). In some of the most effective combinations, electrical stimulation could substitute for osteogenin. Some other effective combinations also included bone marrow aspirate concentrate. BMP2 and BMP7 appear to have the strongest pairwise linkage of the factors analyzed in this study. CONCLUSIONS: Artificial neural networks are powerful forms of artificial intelligence that can be applied readily in the orthopaedic domain, but neural network predictions improve along with the amount of data available to train them. This study provides a starting point from which networks trained on future, expanded datasets can be developed. Yet even this initial model makes specific predictions concerning potentially effective combinatorial therapeutics that should be verified experimentally. Furthermore, our analysis provides an avenue for further research into the basic science of bone healing by demonstrating agents that appear to be linked in function.

Deriving testable hypotheses through an analogy between individual and collective memory.

The focus of this highly interdisciplinary essay is on an analogy between the formation of memory in individual brains and in collectives of individuals, and on the use of that analogy to derive two hypotheses. The first hypothesis involves the application of understanding of retrograde amnesia in individual brains, to the phenomenon of amnesia in collectives. The second hypothesis involves the application of observations of competition in the formation of collective memory, to memory formation in individuals. Evidence in support of both hypotheses is presented. This analogical reasoning leads to deeper understanding of memory on both individual and collective levels. It also raises many new questions-difficult questions that likely would not have arisen in the absence of the analogy.

Computational modeling of the monoaminergic neurotransmitter and male neuroendocrine systems in an analysis of therapeutic neuroadaptation to chronic antidepressant.

Second-line depression treatment involves augmentation with one (rarely two) additional drugs, of chronic administration of a selective serotonin reuptake inhibitor (SSRI), which is the first-line depression treatment. Unfortunately, many depressed patients still fail to respond even after months to years of searching to find an effective combination. To aid in the identification of potentially effective antidepressant combinations, we created a computational model of the monoaminergic neurotransmitter (serotonin, norepinephrine, and dopamine), stress-hormone (cortisol), and male sex hormone (testosterone) systems. The model was trained via machine learning to represent a broad range of empirical observations. Neuroadaptation to chronic drug administration was simulated through incremental adjustments in model parameters that corresponded to key regulatory components of the neurotransmitter and neurohormone systems. Analysis revealed that neuroadaptation in the model depended on all of the regulatory components in complicated ways, and did not reveal any one or a few specific components that could be targeted in the design of antidepressant treatments. We used large sets of neuroadapted states of the model to screen 74 different drug and hormone combinations and identified several combinations that could potentially be therapeutic for a higher proportion of male patients than SSRIs by themselves.

Computational Analysis of Therapeutic Neuroadaptation to Chronic Antidepressant in a Model of the Monoaminergic Neurotransmitter and Stress Hormone Systems.

The clinical practice of selective serotonin reuptake inhibitor (SSRI) augmentation relies heavily on trial-and-error. Unfortunately, the drug combinations prescribed today fail to provide relief for many depressed patients. In order to identify potentially more effective treatments, we developed a computational model of the monoaminergic neurotransmitter and stress-steroid systems that neuroadapts to chronic administration of combinations of antidepressant drugs and hormones by adjusting the strengths of its transmitter-system components (TSCs). We used the model to screen 60 chronically administered drug/hormone pairs and triples, and identified as potentially therapeutic those combinations that raised the monoamines (serotonin, norepinephrine, and dopamine) but lowered cortisol following neuroadaptation in the model. We also evaluated the contributions of individual and pairs of TSCs to therapeutic neuroadaptation with chronic SSRI using sensitivity, correlation, and linear temporal-logic analyses. All three approaches revealed that therapeutic neuroadaptation to chronic SSRI is an overdetermined process that depends on multiple TSCs, providing a potential explanation for the clinical finding that no single antidepressant regimen alleviates depressive symptoms in all patients.

Exploring the Correlation between the Cognitive Benefits of Drug Combinations in a Clinical Database and the Efficacies of the Same Drug Combinations Predicted from a Computational Model.

Identification of drug combinations that could be effective in Alzheimer's disease treatment is made difficult by the sheer number of possible combinations. This analysis identifies as potentially therapeutic those drug combinations that rank highest when their efficacy is determined jointly from two independent data sources. Estimates of the efficacy of the same drug combinations were derived from a clinical dataset on cognitively impaired elderly participants and from pre-clinical data, in the form of a computational model of neuroinflammation. Linear regression was used to show that the two sets of estimates were correlated, and to rule out confounds. The ten highest ranking, jointly determined drug combinations most frequently consisted of COX2 inhibitors and aspirin, along with various antihypertensive medications. Ten combinations of from five to nine drugs, and the three-drug combination of a COX2 inhibitor, aspirin, and a calcium-channel blocker, are discussed as candidates for consideration in future pre-clinical and clinical studies.

A geometric method for eigenvalue problems with low-rank perturbations.

We consider the problem of finding the spectrum of an operator taking the form of a low-rank (rank one or two) non-normal perturbation of a well-understood operator, motivated by a number of problems of applied interest which take this form. We use the fact that the system is a low-rank perturbation of a solved problem, together with a simple idea of classical differential geometry (the envelope of a family of curves) to completely analyse the spectrum. We use these techniques to analyse three problems of this form: a model of the oculomotor integrator due to Anastasio & Gad (2007 J. Comput. Neurosci.22, 239-254. (doi:10.1007/s10827-006-0010-x)), a continuum integrator model, and a non-local model of phase separation due to Rubinstein & Sternberg (1992 IMA J. Appl. Math.48, 249-264. (doi:10.1093/imamat/48.3.249)).

Knowledge-driven computational modeling in Alzheimer's disease research: Current state and future trends.

Neurodegenerative diseases such as Alzheimer's disease (AD) follow a slowly progressing dysfunctional trajectory, with a large presymptomatic component and many comorbidities. Using preclinical models and large-scale omics studies ranging from genetics to imaging, a large number of processes that might be involved in AD pathology at different stages and levels have been identified. The sheer number of putative hypotheses makes it almost impossible to estimate their contribution to the clinical outcome and to develop a comprehensive view on the pathological processes driving the clinical phenotype. Traditionally, bioinformatics approaches have provided correlations and associations between processes and phenotypes. Focusing on causality, a new breed of advanced and more quantitative modeling approaches that use formalized domain expertise offer new opportunities to integrate these different modalities and outline possible paths toward new therapeutic interventions. This article reviews three different computational approaches and their possible complementarities. Process algebras, implemented using declarative programming languages such as Maude, facilitate simulation and analysis of complicated biological processes on a comprehensive but coarse-grained level. A model-driven Integration of Data and Knowledge, based on the OpenBEL platform and using reverse causative reasoning and network jump analysis, can generate mechanistic knowledge and a new, mechanism-based taxonomy of disease. Finally, Quantitative Systems Pharmacology is based on formalized implementation of domain expertise in a more fine-grained, mechanism-driven, quantitative, and predictive humanized computer model. We propose a strategy to combine the strengths of these individual approaches for developing powerful modeling methodologies that can provide actionable knowledge for rational development of preventive and therapeutic interventions. Development of these computational approaches is likely to be required for further progress in understanding and treating AD.

Computational Model of Antidepressant Response Heterogeneity as Multi-pathway Neuroadaptation.

Current hypotheses cannot fully explain the clinically observed heterogeneity in antidepressant response. The therapeutic latency of antidepressants suggests that therapeutic outcomes are achieved not by the acute effects of the drugs, but rather by the homeostatic changes that occur as the brain adapts to their chronic administration. We present a computational model that represents the known interactions between the monoaminergic neurotransmitter-producing brain regions and associated non-monoaminergic neurotransmitter systems, and use the model to explore the possible ways in which the brain can homeostatically adjust to chronic antidepressant administration. The model also represents the neuron-specific neurotransmitter receptors that are known to adjust their strengths (expressions or sensitivities) in response to chronic antidepressant administration, and neuroadaptation in the model occurs through sequential adjustments in these receptor strengths. The main result is that the model can reach similar levels of adaptation to chronic administration of the same antidepressant drug or combination along many different pathways, arriving correspondingly at many different receptor strength configurations, but not all of those adapted configurations are also associated with therapeutic elevations in monoamine levels. When expressed as the percentage of adapted configurations that are also associated with elevations in one or more of the monoamines, our modeling results largely agree with the percentage efficacy rates of antidepressants and antidepressant combinations observed in clinical trials. Our neuroadaptation model provides an explanation for the clinical reports of heterogeneous outcomes among patients chronically administered the same antidepressant drug regimen.

Computational Analysis of the Hypothalamic Control of Food Intake.

Food-intake control is mediated by a heterogeneous network of different neural subtypes, distributed over various hypothalamic nuclei and other brain structures, in which each subtype can release more than one neurotransmitter or neurohormone. The complexity of the interactions of these subtypes poses a challenge to understanding their specific contributions to food-intake control, and apparent consistencies in the dataset can be contradicted by new findings. For example, the growing consensus that arcuate nucleus neurons expressing Agouti-related peptide (AgRP neurons) promote feeding, while those expressing pro-opiomelanocortin (POMC neurons) suppress feeding, is contradicted by findings that low AgRP neuron activity and high POMC neuron activity can be associated with high levels of food intake. Similarly, the growing consensus that GABAergic neurons in the lateral hypothalamus suppress feeding is contradicted by findings suggesting the opposite. Yet the complexity of the food-intake control network admits many different network behaviors. It is possible that anomalous associations between the responses of certain neural subtypes and feeding are actually consistent with known interactions, but their effect on feeding depends on the responses of the other neural subtypes in the network. We explored this possibility through computational analysis. We made a computer model of the interactions between the hypothalamic and other neural subtypes known to be involved in food-intake control, and optimized its parameters so that model behavior matched observed behavior over an extensive test battery. We then used specialized computational techniques to search the entire model state space, where each state represents a different configuration of the responses of the units (model neural subtypes) in the network. We found that the anomalous associations between the responses of certain hypothalamic neural subtypes and feeding are actually consistent with the known structure of the food-intake control network, and we could specify the ways in which the anomalous configurations differed from the expected ones. By analyzing the temporal relationships between different states we identified the conditions under which the anomalous associations can occur, and these stand as model predictions.

Computational identification of potential multi-drug combinations for reduction of microglial inflammation in Alzheimer disease.

Like other neurodegenerative diseases, Alzheimer Disease (AD) has a prominent inflammatory component mediated by brain microglia. Reducing microglial inflammation could potentially halt or at least slow the neurodegenerative process. A major challenge in the development of treatments targeting brain inflammation is the sheer complexity of the molecular mechanisms that determine whether microglia become inflammatory or take on a more neuroprotective phenotype. The process is highly multifactorial, raising the possibility that a multi-target/multi-drug strategy could be more effective than conventional monotherapy. This study takes a computational approach in finding combinations of approved drugs that are potentially more effective than single drugs in reducing microglial inflammation in AD. This novel approach exploits the distinct advantages of two different computer programming languages, one imperative and the other declarative. Existing programs written in both languages implement the same model of microglial behavior, and the input/output relationships of both programs agree with each other and with data on microglia over an extensive test battery. Here the imperative program is used efficiently to screen the model for the most efficacious combinations of 10 drugs, while the declarative program is used to analyze in detail the mechanisms of action of the most efficacious combinations. Of the 1024 possible drug combinations, the simulated screen identifies only 7 that are able to move simulated microglia at least 50% of the way from a neurotoxic to a neuroprotective phenotype. Subsequent analysis shows that of the 7 most efficacious combinations, 2 stand out as superior both in strength and reliability. The model offers many experimentally testable and therapeutically relevant predictions concerning effective drug combinations and their mechanisms of action.

Temporal-logic analysis of microglial phenotypic conversion with exposure to amyloid-ß.

Alzheimer Disease (AD) remains a leading killer with no adequate treatment. Ongoing research increasingly implicates the brain's immune system as a critical contributor to AD pathogenesis, but the complexity of the immune contribution poses a barrier to understanding. Here I use temporal logic to analyze a computational specification of the immune component of AD. Temporal logic is an extension of logic to propositions expressed in terms of time. It has traditionally been used to analyze computational specifications of complex engineered systems but applications to complex biological systems are now appearing. The inflammatory component of AD involves the responses of microglia to the peptide amyloid-ß (Aß), which is an inflammatory stimulus and a likely causative AD agent. Temporal-logic analysis of the model provides explanations for the puzzling findings that Aß induces an anti-inflammatory and well as a pro-inflammatory response, and that Aß is phagocytized by microglia in young but not in old animals. To potentially explain the first puzzle, the model suggests that interferon-γ acts as an "autocrine bridge" over which an Aß-induced increase in pro-inflammatory cytokines leads to an increase in anti-inflammatory mediators also. To potentially explain the second puzzle, the model identifies a potential instability in signaling via insulin-like growth factor 1 that could explain the failure of old microglia to phagocytize Aß. The model predicts that augmentation of insulin-like growth factor 1 signaling, and activation of protein kinase C in particular, could move old microglia from a neurotoxic back toward a more neuroprotective and phagocytic phenotype.

Computational identification of potential multitarget treatments for ameliorating the adverse effects of amyloid-ß on synaptic plasticity.

The leading hypothesis on Alzheimer Disease (AD) is that it is caused by buildup of the peptide amyloid-ß (Aß), which initially causes dysregulation of synaptic plasticity and eventually causes destruction of synapses and neurons. Pharmacological efforts to limit Aß buildup have proven ineffective, and this raises the twin challenges of understanding the adverse effects of Aß on synapses and of suggesting pharmacological means to prevent them. The purpose of this paper is to initiate a computational approach to understanding the dysregulation by Aß of synaptic plasticity and to offer suggestions whereby combinations of various chemical compounds could be arrayed against it. This data-driven approach confronts the complexity of synaptic plasticity by representing findings from the literature in a course-grained manner, and focuses on understanding the aggregate behavior of many molecular interactions. The same set of interactions is modeled by two different computer programs, each written using a different programming modality: one imperative, the other declarative. Both programs compute the same results over an extensive test battery, providing an essential crosscheck. Then the imperative program is used for the computationally intensive purpose of determining the effects on the model of every combination of ten different compounds, while the declarative program is used to analyze model behavior using temporal logic. Together these two model implementations offer new insights into the mechanisms by which Aß dysregulates synaptic plasticity and suggest many drug combinations that potentially may reduce or prevent it.

Computational search for hypotheses concerning the endocannabinoid contribution to the extinction of fear conditioning.

Fear conditioning, in which a cue is conditioned to elicit a fear response, and extinction, in which a previously conditioned cue no longer elicits a fear response, depend on neural plasticity occurring within the amygdala. Projection neurons in the basolateral amygdala (BLA) learn to respond to the cue during fear conditioning, and they mediate fear responding by transferring cue signals to the output stage of the amygdala. Some BLA projection neurons retain their cue responses after extinction. Recent work shows that activation of the endocannabinoid system is necessary for extinction, and it leads to long-term depression (LTD) of the GABAergic synapses that inhibitory interneurons make onto BLA projection neurons. Such GABAergic LTD would enhance the responses of the BLA projection neurons that mediate fear responding, so it would seem to oppose, rather than promote, extinction. To address this paradox, a computational analysis of two well-known conceptual models of amygdaloid plasticity was undertaken. The analysis employed exhaustive state-space search conducted within a declarative programming environment. The analysis reveals that GABAergic LTD actually increases the number of synaptic strength configurations that achieve extinction while preserving the cue responses of some BLA projection neurons in both models. The results suggest that GABAergic LTD helps the amygdala retain cue memory during extinction even as the amygdala learns to suppress the previously conditioned response. The analysis also reveals which features of both models are essential for their ability to achieve extinction with some cue memory preservation, and suggests experimental tests of those features.

Exploring the contribution of estrogen to amyloid-Beta regulation: a novel multifactorial computational modeling approach.

According to the amyloid hypothesis, Alzheimer Disease results from the accumulation beyond normative levels of the peptide amyloid-ß (Aß). Perhaps because of its pathological potential, Aß and the enzymes that produce it are heavily regulated by the molecular interactions occurring within cells, including neurons. This regulation involves a highly complex system of intertwined normative and pathological processes, and the sex hormone estrogen contributes to it by influencing the Aß-regulation system at many different points. Owing to its high complexity, Aß regulation and the contribution of estrogen are very difficult to reason about. This report describes a computational model of the contribution of estrogen to Aß regulation that provides new insights and generates experimentally testable and therapeutically relevant predictions. The computational model is written in the declarative programming language known as Maude, which allows not only simulation but also analysis of the system using temporal-logic. The model illustrates how the various effects of estrogen could work together to reduce Aß levels, or prevent them from rising, in the presence of pathological triggers. The model predicts that estrogen itself should be more effective in reducing Aß than agonists of estrogen receptor α (ERα), and that agonists of ERß should be ineffective. The model shows how estrogen itself could dramatically reduce Aß, and predicts that non-steroidal anti-inflammatory drugs should provide a small additional benefit. It also predicts that certain compounds, but not others, could augment the reduction in Aß due to estrogen. The model is intended as a starting point for a computational/experimental interaction in which model predictions are tested experimentally, the results are used to confirm, correct, and expand the model, new predictions are generated, and the process continues, producing a model of ever increasing explanatory power and predictive value.

Predictive encoding of moving target trajectory by neurons in the parabigeminal nucleus.

Intercepting momentarily invisible moving objects requires internally generated estimations of target trajectory. We demonstrate here that the parabigeminal nucleus (PBN) encodes such estimations, combining sensory representations of target location, extrapolated positions of briefly obscured targets, and eye position information. Cui and Malpeli (Cui H, Malpeli JG. J Neurophysiol 89: 3128-3142, 2003) reported that PBN activity for continuously visible tracked targets is determined by retinotopic target position. Here we show that when cats tracked moving, blinking targets the relationship between activity and target position was similar for ON and OFF phases (400 ms for each phase). The dynamic range of activity evoked by virtual targets was 94% of that of real targets for the first 200 ms after target offset and 64% for the next 200 ms. Activity peaked at about the same best target position for both real and virtual targets. PBN encoding of target position takes into account changes in eye position resulting from saccades, even without visual feedback. Since PBN response fields are retinotopically organized, our results suggest that activity foci associated with real and virtual targets at a given target position lie in the same physical location in the PBN, i.e., a retinotopic as well as a rate encoding of virtual-target position. We also confirm that PBN activity is specific to the intended target of a saccade and is predictive of which target will be chosen if two are offered. A Bayesian predictor-corrector model is presented that conceptually explains the differences in the dynamic ranges of PBN neuronal activity evoked during tracking of real and virtual targets.

Data-driven modeling of Alzheimer disease pathogenesis.

Alzheimer Disease (AD) is the most prevalent form of dementia and the sixth leading cause of death in developed world. A substantial amount of data concerning the pathogenesis of this neurological disorder is available, but the complexity of the interactions they reveal makes it difficult to reason about them. This paper describes a computational model that represents known facts concerning AD pathophysiology and demonstrates the implications of those facts in the aggregate. The computational model is written in a mathematical language known as Maude. Because a Maude specification is an executable mathematical theory, it can be used not only to simulate but also to logically analyze the system it models. This model is based on the amyloid hypothesis, which posits that AD results from the build-up of the peptide beta-amyloid. The AD model represents beta-amyloid regulation, and shows through model analysis how that regulation can be disrupted through the interaction of pathological processes such as cerebrovascular insufficiency, inflammation, and oxidative stress. The model demonstrates many other effects that depend in complex ways on interactions between elements. It also shows how treatments directed at multiple targets could be more effective at reducing beta-amyloid than single-target therapies, and it makes several experimentally testable predictions. The work demonstrates that modeling AD as an executable mathematical theory using a specification language such as Maude is a viable adjunct to experiment, which allows insights and predictions to be derived that take more of the relevant biology into account than would be possible without the aid of the computational model.

Simulating the shaping of the fastigial deep nuclear saccade command by cerebellar Purkinje cells.

Early lesion and physiological studies established the key contributions of the cerebellar cortex and fastigial deep nuclei in maintaining the accuracy of saccades. Recent evidence has demonstrated that fastigial oculomotor region cells (FORCs) provide commands that are critical both for driving and braking saccades. Modeling studies have largely ignored the mechanisms by which the FORC activity patterns, and those of the Purkinje cells (PCs) that inhibit them, are produced by the mossy fiber (MF) inputs common to both. We have created a hybrid network of integrate-and-fire and summation units to model the circuitry between PCs, FORCs, and MFs that can account for all observed PC and FORC activity patterns. The model demonstrates that a crucial component of FORC activity may be due to the rebound depolarization intrinsic to FORC neurons that, like the MF-driven activity of FORCs, is also shaped by PC inhibition and disinhibition. The model further demonstrates that the shaping of the FORC saccade command by PCs can be adaptively modified through plausible learning rules based on cerebellar long-term depression (LTD) and long-term potentiation (LTP), which are guided by climbing fiber (CF) input to PCs that realistically indicates only the direction (but not the magnitude) of saccade error. These modeling results provide new insights into the adaptive control by the cerebellum of the deep nuclear saccade command.

Using input minimization to train a cerebellar model to simulate regulation of smooth pursuit.

Cerebellar learning appears to be driven by motor error, but whether or not error signals are provided by climbing fibers (CFs) remains a matter of controversy. Here we show that a model of the cerebellum can be trained to simulate the regulation of smooth pursuit eye movements by minimizing its inputs from parallel fibers (PFs), which carry various signals including error and efference copy. The CF spikes act as "learn now" signals. The model can be trained to simulate the regulation of smooth pursuit of visual objects following circular or complex trajectories and provides insight into how Purkinje cells might encode pursuit parameters. In minimizing both error and efference copy, the model demonstrates how cerebellar learning through PF input minimization (InMin) can make movements more accurate and more efficient. An experimental test is derived that would distinguish InMin from other models of cerebellar learning which assume that CFs carry error signals.

Bifurcation theory explains waveform variability in a congenital eye movement disorder.

In dynamical systems, configurations that permit flexible control are also prone to undesirable behavior. We study a bilateral model of the oculomotor pre-motor network that conforms with the neuroanatomical constraint that brainstem neurons project to cerebellar Purkinje cells on both sides, but Purkinje cells project back to brainstem neurons on the same side only. Bifurcation analysis reveals that this network asymmetry enables flexible control by the cerebellum of brainstem network dynamics, but small changes in connection pattern or strength lead to behavior that is unstable, oscillatory, or both. The model produces the full range of waveform types associated with the hereditary eye movement disorder know as congenital nystagmus, and is consistent with findings linking the disorder with abnormal connectivity or limited plasticity in the cerebellum.