Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model—a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population. In the sensory periphery, stimuli are represented by patterns of spikes and silences across a population of sensory neurons. Because the neurons form an interconnected network, the code cannot be understood by looking at single cells alone. Recent recordings in the retina have enabled us to study populations of a hundred or more neurons that carry the visual information into the brain, and thus build probabilistic models of the neural code. Here we present a minimal (maximum entropy) yet powerful extension of well-known linear/nonlinear models for independent neurons, to an interacting population. This model reproduces the behavior of single cells as well as the structure of correlations in neural spiking. Our model predicts much better the complete set of patterns of spiking and silence across a population of cells, allowing us to explore the properties of the stimulus-response mapping, and estimate the information transmission, in bits per second, that the population carries about the stimulus. Our results show that to understand the code, we need to shift our focus from reproducing single-cell properties (such as firing rates) towards understanding the total “vocabulary” of patterns emitted by the population, and that network correlations play a central role in shaping the code of large neural populations. It is not immediately clear how these findings affect stimulus encoding, where one needs to distinguish the impact of correlated stimuli that the cells receive (“stimulus correlations”), from the impact of co-variance of the cells conditional on the stimulus (“noise correlations”). For small populations of neurons, it has been shown that taking into account correlations for decoding or reconstructing the stimulus can be beneficial compared to the case where correlations are neglected  model, which is a hybrid between linear-nonlinear models for single cells and the pairwise maximum entropy models. Applied to groups of We start by showing that linear-nonlinear (LN) models of retinal ganglion cells responding to spatially unstructured stimuli capture a significant part of the single neuron response, but still miss much of the detail; in particular, we show that they fail to capture the correlation structure of firing among the cells. We next present our new We recorded the simultaneous spiking activity of ency of  . This “fehaviors . We chosrity see . To consthe same for all the models considered, so the performance of the models cannot differ due to the differences in modeled stimulus sensitivities. With this setup, we are therefore able to fairly compare the performance and generalization of various models of joint population activity given the stimulus.All models of the population responses were fitted based on one half of our data (313 training repeats), and evaluated (tested) on the other half of repeats; overall, the train and test data were each almost 1 hr long. While fitting the stimulus-dependent maximum entropy model can be done using non-repeated stimuli, assessing the performance of the models requires many repeated presentations of the same stimulus to quantify both single cell and in particular population spiking patterns, as well as noise entropy and mutual information. Unlike for single neurons (which are fully characterized by their firing rate), in the case of large populations, capturing well the very high-dimensional distribution of codewords given the stimulus,  filters . FurtherUsing repeated presentations of the same movie, we estimated the average response of each of the cells across repeats, The performance gap of the canonical LN models in predicting single neuron responses suggests that either the single-neuron models need to be improved to account for the observed behavior, or that interactions between neurons play an important encoding role and need to be included. Clearly, the firing rate prediction performance can be improved for single neurons by models with higher-dimensional stimulus sensitivity e.g.  or dynamWe therefore sought a model of the neural code that would be able to reproduce the correlation structure of population codes. We asked whether a model that combined the LN (receptive-field based) aspect of single cells with the interactions between cells, could give a better account of the neural stimulus-response mapping. Importantly, the new model should capture not only the firing rate of single cells but also accurately predict the full distribution of the joint activity patterns across the whole population. Because the joint distributions of activity are high-dimensional  distribution of the population responses to stimuli, by treating each time point along the stimulus separately; since every moment of time maps uniquely into one stimulus, we start by building the model of the response given time. We thus find lls c.f. . Thus, wpairwise time-dependent maximum entropy (pairwise TDME or T2) model in first-order time-dependent maximum entropy model that reproduces exactly the firing rate of every neuron, T1.The Time-dependent maximum entropy models are powerful, since they make no assumption about how the stimulus drives the response; they often serve as useful benchmarks for other models . On the other hand, these models require repeated stimulus presentations to fit, involve a number of parameters that grows linearly with the duration of the stimulus, do not generalize to new stimuli, and do not provide an explicit map from the stimuli to the responses.(i), would give an explicit description of stimulus-dependent distribution of population patterns; (ii), would generalize to new stimuli; (iii), could be directly compared to the uncoupled LN models; and (iv), would not require repeats of the same stimulus to fit. Specifically, rather than having an arbitrary time-dependent parameter for every neuron for each time bin, We therefore present a more particular form of the model of pairwise stimulus-dependent maximum entropy (pairwise SDME or S2) model, which takes the following form:Concretely, we estimated the linear filter .e.  see ; as befoBy construction, the S2 model exactly reproduces the covariance of activities,   agrees w  and the pairwise SDME model (S2). At the level of single neurons, we found that the S2 model predicted the firing rates better than the S1 model see e.g. , with thThe differences between the S2 and the S1 models become more striking at the level of the activity patterns of the whole population. We found that S2 is orders of magnitude better in predicting the population neural responses to stimuli. This is quantified in We next examined how well various models of the neural codebook, 2.98 see .On average, S2 predicts the probabilities of the patterns of activity with minimal bias, and with a standard deviation of ersa see .The S2 model was constructed to capture exactly the total pairwise correlation in neuronal spiking, How should we interpret the inferred parameters of the S2 model? LN models have a clear mechanistic interpretation in terms of the cell's receptive field and the nonlinear spiking mechanism. Here, similarly, the stimulus dependent part of the model for each cell, The pairwise interaction terms in the S2 model, not due to the correlated stimulus inputs.Interestingly, we find that the pairwise interaction terms in the S2 model of At every instant in time, the probability of any activity pattern The S2 model is an approximation to the neural codebook, surprise about the output of the retina, and thus about the stimulus, which is given by The brain does not have direct access to the stimulus, but only receives codewords To estimate the information transmission, we have to subtract the noise entropy rate from the output entropy rate  is  see . While oLastly, we asked how important is the inclusion of pairwise interactions, We presented a modeling framework for stimulus encoding by large populations of neurons, which combines an individual neuronal receptive field model, with the ability to include pairwise interactions between neurons. The result is a stimulus-dependent pairwise maximum entropy (S2) model, which is the most parsimonious model of the population response to the stimulus that reproduces the linear-nonlinear (LN) aspect of single cells, as well as the pairwise correlation structure between neurons. In two limiting cases, the S2 model reduces to known models: if the single cell parameters We applied this modeling framework to the salamander retina presented with Gaussian white noise stimuli, and found that the interactions between neurons play an important role in determining the detailed patterns of population response. In particular, the S2 model gave better prediction of PSTH of single cells, yielded orders-of-magnitude improvement in describing the population patterns, and captured significant aspects of noise correlations. The deviations between the S2 and the S1 model became significant for The S2 model allowed us to improve over LN models for salamander retinal ganglion cells in terms of the PSTH prediction of single cells. But, more importantly, it gave a huge improvement in terms of describing and predicting the population activity patterns, or codewords. Interestingly, for parasol cells in the macaque retina under flickering checkerboard stimulation, the generalized linear model did not yield firing rate improvement relative to uncoupled LN models  within a single bin. This allows us to view activity patterns in successive time bins as codewords . Finally, from a modeling viewpoint, GLM lends itself to a clean and tractable maximum likelihood inference framework with regularization, whereas the SDME offers the tools and insights of statistical physics An alternative approach to describing the joint response of large populations of neurons to external stimuli has been presented in Ref Tkačik and colleagues The maximum entropy models presented here can be immediately applied to other brain areas where one can get stable recordings of many neurons over a few tens of minutes Ambystoma tigrinum. All experiments were in accordance with Ben-Gurion University of the Negev and government regulations. Extracted retinas were placed with the ganglion cell layer facing a multielectrode array with 252 electrodes , and superfused with oxygenated Ringer medium at room temperature. Extracellularly recorded signals were amplified  and digitized at 10 kHz, and spike-sorted using custom software written in MATLAB.Experiments were performed on the adult tiger salamander, Stimuli were projected onto the retina from a CRT video monitor (ViewSonic G90fB) at a frame rate of 60 Hz; each movie frame was presented twice, using standard optics. Full Field Flicker (FFF) stimuli were generated by independently sampling spatially uniform gray levels (with a resolution of 8 bits) from a Gaussian distribution, with mean luminance of 147 lux and the standard deviation of 33 lux. These data allow us to estimate the entropy rate of the source (as used in the main text), by multiplying the entropy of the luminance distribution with the refresh rate. To estimate the cells' receptive fields, checkerboard stimulus was generated by selecting each checker  for every timepoint, for a total of To evaluate the performance of the models on the testing data, we computed (i) the average per-codeword log-likelihood (reported in the


The Web provides widespread access to vast quantities of health-related information that can improve quality-of-life through better understanding of personal symptoms, medical conditions, and available treatments. Unfortunately, identifying a credible and personally relevant subset of information can be a time-consuming and challenging task for users without a medical background.The objective of the Personal Health Lens system is to aid users when reading health-related webpages by providing warnings about personally relevant drug interactions. More broadly, we wish to present a prototype for a novel, generalizable approach to facilitating interactions between a patient, their practitioner(s), and the Web.We utilized a distributed, Semantic Web-based architecture for recognizing personally dangerous drugs consisting of: (1) a private, local triple store of personal health information, (2) Semantic Web services, following the Semantic Automated Discovery and Integration (SADI) design pattern, for text mining and identifying substance interactions, (3) a bookmarklet to trigger analysis of a webpage and annotate it with personalized warnings, and (4) a semantic query that acts as an abstract template of the analytical workflow to be enacted by the system.A prototype implementation of the system is provided in the form of a Java standalone executable JAR file. The JAR file bundles all components of the system: the personal health database, locally-running versions of the SADI services, and a javascript bookmarklet that triggers analysis of a webpage. In addition, the demonstration includes a hypothetical personal health profile, allowing the system to be used immediately without configuration. Usage instructions are provided.The main strength of the Personal Health Lens system is its ability to organize medical information and to present it to the user in a personalized and contextually relevant manner. While this prototype was limited to a single knowledge domain (drug/drug interactions), the proposed architecture is generalizable, and could act as the foundation for much richer personalized-health-Web clients, while importantly providing a novel and personalizable mechanism for clinical experts to inject their expertise into the browsing experience of their patients in the form of customized semantic queries and ontologies. For the lay-person, free health information on the Web is a potentially valuable resource for better understanding personal symptoms, medical conditions, drugs, and nutrition. However, while sites such as WebMD  provide We recently published a novel framework for automatically synthesizing contextually-sensitive data retrieval and analysis workflows composed of dynamically-selected Semantic Web Services . The sysPersonalization of Web information necessitates the use of the individual’s personal medical profile, since this information can be used to identify both relevant and inappropriate advice within a webpage. There has been considerable work in the area of semantic representation of electronic patient records, both institutional  and persMuch of the prior work in “personalization” of a patient’s Web experience has been in the domain of facilitated search, particularly through the use of semantically-backed personal health portals eg, ,7) where where7])We now describe in detail our prototype system that attempts to identify drugs within the online literature that are potentially dangerous to the user based on their personal health record. We begin by giving an overview of the system and a description of the prototype implementation in the Methods section. In the Results section, we demonstrate use of the prototype in the context of a sample health profile. Finally, we discuss some high-level design issues and provide closing remarks in the Discussion section.All data within the Health Lens system were represented using the Resource Description Framework (RDF) model , which pThe Web Ontology Language (OWL)  also plaThe Health Lens system utilizes 2 Semantic Web projects that have been built on top of the RDF and OWL standards—Semantic Automated Discovery and Integration, and Semantic Health and Research Environment.SADI is a set of design patterns for producing stateless Web services that natively consume and produce RDF data. The structure of the input and output data for SADI services are formally described by an input OWL class and an output OWL class, respectively. Further details about SADI are described in .SHARE is a proof-of-concept Semantic Web query engine that resolves SPARQL Protocol and RDF Query Language  queriesrdfs:label predicate. This allows multiple labels to be assigned to the same entity, and also permits changes to the labels without adversely affecting other RDF data sets on the Web that refer to the entity in question. To aid the reader, comments are provided within the example data that provide translations from opaque URIs to human-readable labels.Many of the URIs in the example RDF data of this paper are opaque, making human interpretation of the data considerably more difficult than if human-readable identifiers had been used. For example, the URI of the “has attribute” predicate of the Semanticscience Integrated Ontology (SIO) ontology  is http:The Health Lens system operates in a cycle of 3 steps, as depicted in personal health profile, which is stored locally in the personal health database.The user creates or updates his/her The system executes a SHARE query to identify dangerous interactions between the user's personal health profile and any known drug. All discovered interactions are aggregated and stored in the personal health database for use in Step 3.From within a Web browser, the user clicks the Health Lens bookmarklet to identify mentions of drugs in the current webpage that may be personally dangerous. The bookmarklet accomplishes this by (a) identifying drug mentions within the text using one or more SADI entity recognition services, and (b) comparing the identified drugs against the list of drugs that have interactions with the personal health profile, as computed in Step 2.The circular arrows of Our prototype implementation of the Health Lens system includes a sample personal health profile . The proWhile the current focus of the profile is drug prescriptions, the use of RDF will allow future extension of the profile to include personal data such as allergies, medical conditions, diet, clinical test results, and genotyping.rdf:type of foaf:Person, and this node has a combination of FOAF and DBPedia )Finally, it is important to note that there is a potential privacy concern relating to the use of a public drug interaction service—the system must send the URIs of the user's prescribed drugs out over the Internet in order to retrieve the relevant interactions. In general, there is a trade-off between the degree of privacy the user wants to maintain and the ability to utilize all possible sources of data for identifying conflicts. In future work, this issue can be addressed by allowing the user to indicate which types of data are safe to send over the Web. In addition, the user might also choose to restrict the system to services that support HTTPS. With respect to privacy, the prototype implementation errs on the side of caution by using a locally hosted drug interaction service.We believe the SADI Personal Health Lens demonstrates that dynamically-generated, context-sensitive pipelines of data and analytical Semantic Web Services can be usefully applied to the personalization of health information on the Web. Moreover, this approach provides the unique ability to fine-tune these workflows through the utilization of expert knowledge within semantically-encoded guidelines. Thus, for the first time, the Personal Health Lens establishes a framework within which clinicians can provide on-demand guidance during their patient’s personal health explorations.


After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on:  Cellular functions and decisions are implemented through the coordinate interactions of a very large number of molecular species. Central unit of these processes is the DNA, a polymer that is in part segmented in subunits, called genes, which control the production of the key cellular molecules: the proteins, via the mechanism of the transcription. Some relevant proteins, called transcription factors, in turn interact with genes to modulate either the production of other proteins or their own production.Given the above rough outlook of the intracellular machineries it is not surprising that two modeling tools, actually born in other applicative domains, revealed to be of the utmost relevance in molecular biology. They are the inter-related concepts of feedback Mimicking general chemistry, bipartite graphs were initially introduced in cellular biochemistry simply to formalize the informal diagrams representing biomolecular reactions boolean networksNote that the concept of network is also historically important in early phases of Systems Biology. Indeed, the first dynamical models in molecular biology were particular finite automata  called The first key concept is that biomolecular networks are multistable The second key concept is that the dynamic behavior of a network is never totally deterministic Moreover, if noises were only pure nuisances, there would be an interesting consequence. Indeed, in such a case a monostable network in presence of noise should exhibit more or less large fluctuations around the unique deterministic equilibrium. In probabilistic languages this means that the probability distribution of the total signal  should be a sort of “bell” centered more or less at the deterministic equilibrium, i.e. the probability distribution should be unimodal. However, at the end of seventies it became clear in statistical physics that the real stochastic scenario is far more complex, and the above-outlined correspondence between deterministic monostability and stochastic monomodality in presence of external noise was seriously challenged Above we mainly focused on external random perturbations acting on genetic and other biomolecular networks. In the meantime, experimental studies revealed the other and equally important role of stochastic effects in biochemical networks by showing that many important transcription factors, as well as other proteins and mRNA, are present in cells with very low concentrations, i.e. with a small number of molecules Thus, after that for some time noise was mostly seen as a nuisance, more recently it has finally been appreciated that the above-mentioned and other noise-related phenomena may in many cases have a constructive, functional role  networks, in the important case of not only non-Gaussian, but also bounded, external perturbations. We stress that, at the best of knowledge, this was never analyzed before. Indeed, by imposing a bounded extrinsic noise we increase the degree of realism of a model, since the external perturbations must not only preserve the positiveness of reaction rates, but must also be bounded. Moreover, it has also been shown in other contexts such as mathematical oncology Here we assess the two most fundamental steps of this novel line of research.The first step is to identify a suitable mathematical framework to represent mass-action biochemical networks perturbed by bounded noises (or simply left-bounded), which in turn can depend on the state of the system. To this extent, in the first part of this work we derive a master equation for these kinds of systems in terms of the differential Chapman-Kolgomorov equation (DCKE) The second step relates to the possibility of extending, in this “doubly stochastic” context, the Michaelis-Menten Quasi Steady State approximation (QSSA) for enzymatic reactions Finally, we stress that the interplay between the extrinsic and intrinsic noises affecting a biomolecular network might impact on the dynamics of the involved molecules in many different and complex ways. As such, in our opinion this topic cannot be exhausted in a single work. For this reason, we provided three examples of interest in biology, and of quite different natures. One is the above-mentioned Michaelis-Menten reaction, the other two are illustrated in the third part of this work, and are the following: We start by recalling the Chemical Master Equation and the Stochastic Simulation Algorithm (SSA) by Doob and Gillespie Chemical Master Equation (CME) We recall the definition of the exact trajectory of the underlying process. Although equivalent formulations exist Direct Method formulation without loss of generality.The CME is a special case of the more general Kolmogorov Equations The SSA is a dynamic Monte-Carlo method describing a statistically correct trajectory of a discrete non-linear Markov process, whose probability density function is the solution of The correctness of the SSA comes from the relation between the jump process and the CME Stochastic Differential Equations and the SSA. Here we consider a system where each propensity function may be affected by a extrinsic noise term. In general, such a term can be either a time or state-dependent function, and the propensity function for reaction We now introduce a theory of stochastic chemically reacting systems with bounded noises in the jump rates by combining Note that in applications we shall mainly consider unitary mean perturbations, that isWe consider here that the extrinsic noisy disturbance Notice that the use of a vector in In Here, When We stress that the “complete” Langevin system in differential Chapman-Kolgomorov equation (DCKE) When a discrete-state jump process as one of those described in previous section is linked with a continuous noise the state of the stochastic process is the vectorHere We stress that, at the best of our knowledge, this is the first time where a master equation for stochastic chemically reacting systems combined with bounded noises is considered. LetThis equation is the natural generalization of the CME in Stochastic Simulation Algorithm with Bounded Noise (SSAn). The algorithm performs a realization of the stochastic process underlying the system where a (generic) realization of the noise is assumed. As for the CME and the SSA, this corresponds to computing a realization of a process satisfying exact. This, in future, will allow to use the SSAn as a base to define approximate simulation to sample from We now define the For a system with orithm 2 ; its skeAs for the SSA, jumps are determining by using two uniform numbers Once the jumpt time All these two equations, as well as the numerical method to solve Quasi Steady State Approximation (QSSA) Stochastic QSSA (SQSSA) may be applied as well, and that in such its limitations are identical to the deterministic QSSA. Thus, it is of interest to consider SQSSAs also in our “doubly stochastic” setting, even though possible pitfalls may arise due to the presence of the extrinsic noises. As an example, in Results section we will present numerical experiments similar to those of Large networks with large chemical concentrations, i.e. characterized by deterministic behaviors, are amenable to significant simplifications by means of the well known Of course, in a SQSSA not only the propensities may be nonlinear function of state variables, but they may depend nonlinearly also on the perturbations, so that instead of the elementary perturbed propensities we shall have generalized perturbed propensities of the formAs far as the simulation algorithm is concerned, it remains quite close to Algorithm 2  providedWe performed SSAn-based analysis of some simple biological networks, actually present in most complex realistic networks. We start by studying the legitimacy of the stochastic Michaelis-Menten approximation of when noise affects enzyme kinetics The bounded noise noise intensity and autocorrelation time. The average and the variance of this noise areProbably the best studied bounded stochastic process obtained by using this approach is the so-called Sine-Wiener noise Note that, since we mean to use noises of the form For this noise, the probability density is the following discretization step; it has to satisfy By these properties, this noise can be considered a realistic extension of the well-known symmetric dichotomous Markov noise Enzyme-catalyzed reactions are fundamental for life, and in deterministic chemical kinetics theories are often conveniently represented in an approximated non mass-action form, the well-known Michaelis-Menten kinetics In this section we investigate numerically whether the Michaelis-Menten approximations and the stochastic results obtained in The deterministic version of such reactions isHere we show that the same condition is sufficient to legitimate the Michaelis-Menten approximation with bounded noises arbitrarily applied to any of the involved reactions. We start by recalling the result in If noises are considered the models in Notice that the nonlinear approximated propensity Thus condition (31) becomes time-dependent and we rephrase it to beNote that if Each of the shown figures is the result of To strengthen this conclusion it becomes important to investigate whether it still holds when noises affects only a portion of the network and, also, whether it holds on the fast time-scale.As far as the number of noises is concerned, we investigated various single-noise configurations in Finally, as far as the legitimacy of the approximation in the fast time-scale is concerned, i.e. futile cycle, as the one computationally studied in In this section we consider a model of Experimental evidences related the presence of enzymatic cycles with bimodalities in stochastic chemical activities By using Our aim here is to investigate whether bounded noises affecting the kinetic constant, and thus not modifying the topology of the futile cycle network, may as well induce transition to bimodality in the system behavior. To this aim, here we analyze three model configurations: In We simulated the above three models according to the initial condition used in In Let us consider a model by Zhdanov Such a reaction scheme is a genetic toggle switch if the formation of Here In the top panels of In For the sake of confirming this hypothesis in We investigated the effect of a Sine-Wiener noise affecting protein synthesis rather than a perturbation, i.e. a new Here simulations are performed by using the SSAn where the reactions in For the sake of comparing the simulations with those in To investigate more in-depth this hypothesis we again performed Finally, for the sake of considering a wide range of biologically meaningful values for In this paper we investigated the effects of joint extrinsic and intrinsic randomness in nonlinear genetic and other biomolecular networks, under the assumption of non-Gaussian bounded external perturbations. As we briefly mentioned in the introduction, the possible impact of bounded extrinsic noise on stochastic biomolecular networks might be manifold, so that this work has to be understood as a first step in this field of investigation. Our applications have shown that the combination of both intrinsic and extrinsic noise-related phenomena may have a constructive functional role also when the extrinsic noise is bounded. This is in line with other researches – only focusing on either intrinsic or extrinsic noise – recasting the classical interpretation of noise as a disturbance more or less obfuscating the real behavior of a network.This work required the combination of two well-known frameworks, often used to separately describe biological systems. We combined the theory of stochastic chemically reacting systems developed by Gillespie with Langevin systems describing the bounded variations of kinetic parameters. The former shall allow considering the inherent stochastic fluctuations of small numbers of interacting entities, often called intrinsic noise, and clearly opposed to classical deterministic models based on differential equations. The latter permits to consider the influence of bounded extrinsic noises. These noises are modeled as stochastic differential equations. For these kind of systems, although an analytical characterization is unlikely to be feasible, we were able to derive a differential Chapman-Kolgomorov equation (DCKE) describing the probability of the system to occupy each one of a set of states. Then, in order to analyze these models by sampling from this equation we defined an extension of the Gillespie's Stochastic Simulation Algorithm (SSA) with a state-dependent Langevin system affecting the model jump rates. This algorithm, despite being more costly than the classical Gillespie's SSA, allows for the exact simulation of these doubly stochastic systems.We outlined the role of bounded extrinsic noise for some biological networks of interest. In particular, we were able to extend classical results on the validity of the Michaelis-Menten approximation to the prototypical Enzyme-Substrate-Product enzymatic reaction by drawing a Stochastic Quasi Steady State Assumption (SQSSA) for noisy reactions. Along the line of the classical deterministic or stochastic uses of the Michaelis-Menten approximation, this should permit to reduce the size of more general enzymatic networks even in presence of extrinsic bounded noises.Moreover, we showed that in a recurrent pattern of genetic and enzymatic networks, i.e. the futile cycle, the presence of extrinsic noises induces the switching from a unimodal probability density  to a multimodal density.Similarly, in the case of the toggle switch, which is inherently multistable, the presence of extrinsic noise significantly modulates the probability density of the genes concentration. In this important network motif we also investigated the role of periodic perturbations against a realistic noise.Thus in general the co-presence of both intrinsic stochasticity and bounded extrinsic random perturbations might suggest the presence of possibly unknown functional roles for noise for these and other networks. The described noise-induced phenomena are shown to be strongly related to physical characteristics of the extrinsic noise such as the noise amplitude and its autocorrelation time.A relevant issue that we are going to investigate in the next future is the role of the specific extrinsic bounded perturbations. Indeed, in other biological and non-biological systems affected by bounded noises it has been shown that the effects of the perturbations depend not only on the above general characteristics of the noise, but also on its whole model Concerning these points, we stress that these peculiar properties of bounded extrinsic perturbations make it even more important the investigations, such as those of An explicit formalization of biomolecular networks by means of graph-theory and network topology-based analysis of response is outside of our scope and it is not strictly needed for the description and application of our algorithms. However, we want to outline here two important problems in this area, recently considered Finally, note that the methodologies introduced in this work can be applied, virtually without any formal modifications, to a wide range of problems in computational biology of human, animal and cellular populations. Indeed – since the Ross model of malaria spread in 1911


Networks of neurons produce diverse patterns of oscillations, arising from the network's global properties, the propensity of individual neurons to oscillate, or a mixture of the two. Here we describe noisy limit cycles and quasi-cycles, two related mechanisms underlying emergent oscillations in neuronal networks whose individual components, stochastic spiking neurons, do not themselves oscillate. Both mechanisms are shown to produce gamma band oscillations at the population level while individual neurons fire at a rate much lower than the population frequency. Spike trains in a network undergoing noisy limit cycles display a preferred period which is not found in the case of quasi-cycles, due to the even faster decay of phase information in quasi-cycles. These oscillations persist in sparsely connected networks, and variation of the network's connectivity results in variation of the oscillation frequency. A network of such neurons behaves as a stochastic perturbation of the deterministic Wilson-Cowan equations, and the network undergoes noisy limit cycles or quasi-cycles depending on whether these have limit cycles or a weakly stable focus. These mechanisms provide a new perspective on the emergence of rhythmic firing in neural networks, showing the coexistence of population-level oscillations with very irregular individual spike trains in a simple and general framework. Networks of the central nervous system display oscillations at many frequencies and scales of organization. Gamma oscillations (25–100 Hz) in cerebral cortex and hippocampus are implicated in a bewildering variety of neural phenomena, including many stages of sensory processing, and in a wide range of brain regions in many species Models for oscillations in nervous tissue fall into three types, depending on whether the oscillations arise within the individual neurons and then synchronize across the network, emerge purely at the population level, or occur due to a combination of the two. The first case includes coupled oscillator models such as those involving simplified model neurons In this paper we examine mechanisms by which oscillations emerge purely at the network level. We use a stochastic model of individual neurons which gives the elements no intrinsic oscillatory capacity but which makes the relationship of individual spike trains to the population oscillation transparent. The inspiration comes from complex systems beyond neural networks, where population-level oscillations without the individual components themselves oscillating are widespread. In ecology, oscillations occur in predator-prey systems in which the individual components are organisms, each of which may be born or die only once quasi-cyclesA stochastic network may oscillate when the mean-field equations follow a limit cycle, or also when the mean-field equations have a damped oscillation. In the latter case the noise causes a continual excitation which pushes the system away from its mean-field fixed point, causing a population-level resonant oscillation. This mechanism, called There are two principal differences between the results presented here and those by Brunel and co-workers We use the stochastic rate model This paper begins by summarizing the stochastic rate model. We show that, if the “mean-field” equations of the network, which are the Wilson-Cowan equations, have a stable limit cycle oscillation, then the full network activity will be a noisy limit cycle. The population oscillation coexists with irregular spike trains whose multimodal inter-spike-interval distribution has its peaks at multiples of the oscillation period. We show that noisy limit cycle oscillations persist in sparse networks, whose frequency varies with parameters for synaptic weights and sparseness of connectivity as well as the single-neuron parameters. Then, we show quasi-cycle oscillations and calculate their frequency, which also depends on the connectivity parameters. We discuss the two mechanisms, comparing the individual activity with population-level behaviour, and noting the transition from one oscillatory regime to the other as parameters vary. Both mechanisms are characterized by a single major peak in the power spectrum and a roughly power law decay at high frequencies; the stochastic model is informative about the tail of the power spectrum, unlike a deterministic Wilson-Cowan model. In the discussion we address the relation to previous models in detail, and the biological implications of the work.response function,We begin by summarizing the stochastic rate model The model specifies the rates of the transitions, but, to account for the presence of noise in actual biological networks, this is a stochastic process in which the time to the next event is a random variable; the network dynamics may be thought of as a random walk on a lattice, depicted in supplementary figure ??. We simulate the model according to Gillespie's stochastic simulation algorithm see .Our main analytical tool is the linear noise approximation, in which the number of neurons active in each population is approximated as the sum of a deterministic term, scaling with the population size, and a stochastic fluctuation term, scaling with the square root of this size:First we describe population-level oscillations in the stochastic rate model for a set of parameter values where the deterministic Wilson-Cowan equations produce limit cycles. As the raster plot in Noisy perturbations to the trajectory may be decomposed into a component transverse to the limit cycle and another parallel to it. Perturbations transverse to the limit cycle will cause fluctuations in the amplitude of the excitatory activity. Since the limit cycle is stable, these transverse fluctuations are damped over time. However, fluctuations away from the centre of the limit cycle are more persistent since they are amplified by the larger vector field in this region of the phase plane. Thus the stochastic system tends to take longer and slower loops surrounding the limit cycle; this accounts for the frequency of the noisy system being lower than that of the deterministic system. Unlike the transverse direction, there is no restorative force for perturbations in the parallel direction, so perturbations that change the phase of the oscillation accumulate over time until the relative phase of the deterministic and stochastic trajectories become independent, a phenomenon known as phase slipping Every individual neuron fires irregularly, sometimes skipping an oscillation cycle, sometimes firing once or even twice within one oscillation period. This may be seen from the two inhibitory and two excitatory spike trains highlighted in the raster plot of The presence of some very short ISIs is possible in our model because there is no absolute refractory period, so that a neuron may fire a spike, then transition back to the quiescent state, and then fire another spike, in an arbitrarily short amount of time. Although this is possible, it is highly improbable and we feel that the small proportion of unphysiologically short ISIs is a harmless artefact.0F) of population activity in 0F is at 14.9 ms (black dotted line), and in the excitatory AC0F at 14.3 ms, corresponding to frequencies of 69.9 Hz and 67.1 Hz respectively, consistent with the power spectrum peak at 68 Hz in The normalized autocovariances . Since the Wilson-Cowan system here has a single attractive fixed point, after an initial transient the Jacobian matrix Taking the Fourier transform of (27) allows us to approximate the power spectrum of the fluctuations, giving the squared amplitude of the oscillations in each frequency band. A standard calculation, summarized in the appendix, shows that the power spectrum for the excitatory activity consists of a delta peak at zero and a fluctuating componentWe can now ask, for what size network the deterministic Wilson-Cowan equation is a good approximation to the full stochastic system? For the simulation shown in In the simulation presented here, there is a 10 Hz difference between the peak frequency in the simulation and that predicted by the linear noise approximation. The curves match better in networks with less noise or further from the Hopf bifurcation (data not shown).Every individual neuron fires irregularly, sometimes skipping several oscillation cycles, sometimes firing more than once within an oscillation period, as can be seen in the two inhibitory and two excitatory spike trains highlighted in the raster plot of 0F) in 0Fs, at 12.2 ms (black dotted line), corresponds to a frequency of 82 Hz, close to the power spectrum peak at 76 Hz in The autocorrelation functions . 0F; comparison of the results reveals much lower amplitude AC0F oscillations for quasi-cycles which nearly vanish within a few periods, while the AC0F oscillations for noisy limit cycles are larger in amplitude and are maintained for many periods, indicating a longer phase memory in the limit cycle case. Pineda-Krch et al. 0F generally exhibits much slower decay in its oscillations for noisy limit cycles than for quasi-cycles.The autocovariance of activity was used to distinguish limit cycles and quasi-cycles in ecological models by Pineda-Krch et al Another finding in the limit cycle case is another peak in the inhibitory ISI distribution at 2 msec , relatedThe two forms of population oscillations also respond differently to changes in the noise amplitude. We have conceptualized the stochastic network's dynamics as a small stochastic perturbation of a deterministic system, expressed in equations (25) and (27). Noisy limit cycles were viewed as a perturbation of a deterministic limit cycle, and quasi-cycles as a perturbation of a deterministic stable focus. So for noisy limit cycles, the deterministic term oscillates and the stochastic term perturbs these oscillations, whereas for quasi-cycles the deterministic term goes to a stable fixed point while oscillatory fluctuations persist in the stochastic term. This means that, as the noise amplitude decreases, we expect a noisy limit cycle to continue oscillating with increasing regularity in amplitude and phase, whereas quasi-cycle oscillations, which are noise-driven, would decrease in amplitude and remain irregular. This is experimentally testable in nervous tissue by injecting white noise current, in the first case weakening population oscillations and in the second case enhancing them.in vivo is not well understood.In our model, due to the scaling of synaptic strength with population size Despite our conceptualization of the system's dynamics as a small stochastic perturbation of a deterministic system, both the deterministic and stochastic population variables arise from exactly the same microscopic stochastic dynamics. In the stochastic rate model there is no clean separation between trend and noise; nor is there a clean separation between one deterministic regime and another. This is seen here most clearly in In the light of this we return to the question of what causes the discrepancies between frequency trends with parameters in the different plots in In noisy networks trajectories may explore the exterior of the limit cycle, so that the frequency of the noisy system is lower than that of the deterministic system. A stochastic trajectory may also explore the interior, including the vicinity of fixed point, causing phase slips and resembling more a quasi-cycle system. In other words, in a noisy nonlinear system there are many competing effects as parameters vary and it is hard to predict which will dominate. The larger the noise amplitude, the less the stochastic system will resemble the deterministic system; and in the sparse case the fixed randomness in the weights acts as a second source of noise. This extra noisiness in sparse networks means that noisy limit cycle trajectories explore a larger region of the phase plane, including the interior of the limit cycle, meaning that the period of the oscillations will be derived from averaging the dynamical behaviour over this entire region, including the fixed point. We are not aware of perturbative approaches which are usefully predictive in these very noisy situations, but thankfully it is possible to explore the full stochastic system directly with simulations.Noisy limit cycles and quasi-cycles are mechanisms of emergent oscillations in neural networks, both of which allow the maximal firing rates of individual neurons to be lower than the network oscillation frequency. This phenomenon, referred to as cycle skipping, has been observed during physiological oscillations in visual cortex and during pathological oscillations in the form of fast ripples Power law tails in the power spectrum of neuronal networks are widely observed in vivo from electrocorticogram Differences in spike-time reliability between quasicycles and limit cycles should also be detectable experimentally. This may be the mechanism behind the observation that low frequency oscillations , we use the expressionsIf the deterministic system is at a fixed point, thenWe simulate the entire network as a single continuous-time Markov process, using Gillespie's exact stochastic simulation algorithm Find neuronal transition rates Pick time increment Pick In the case of homogenous all-to-all networks, if one only wants to simulate the number of neurons active in each population, one may simplify this algorithm along the lines of Gillespie's original presentation for a well-mixed chemical system, since the upwards transition rates All simulations were performed in Matlab 7.1 ; code is available on the corresponding author's website.To produce plots of the mean firing rate, we counted the number of spikes The activity signal pochs in  and 5 orHere we review how to calculate the power spectrum from a stable linear stochastic differential equation such as (30). This calculation is standard, and presented in, for example, We have a two-dimensional linear system (30) governing the fluctuations, Then, the power spectrum in (40) has diagonal componentsSince To make the ISI histograms, we extracted spike trains of individual neurons from the simulations, and stored all the ISIs. Since all neurons in the excitatory population are statistically identical, we then took the histogram of ISIs from all excitatory neurons together, and likewise for the inhibitory neurons.0F). For the cross-correlation of excitatory and inhibitory activity, we analogously divided the output of xcov by the product of the standard deviations of each activity.We used Matlab's xcov function to calculate the autocovariance (ACF) of the excitatory and inhibitory population activity respectively, and then divided this by the variance to obtain the normalized autocovariance  are shown with black arrows and discussed in the population dynamics section of the results. Grey arrows represent transitions into the state  from adjacent states.Two-population network dynamics visualized. If there are (EPS)Click here for additional data file.


However, a recently discovered copper awl from a Middle Chalcolithic burial at Tel Tsaf, Jordan Valley, Israel, suggests that cast metal technology was introduced to the region as early as the late 6th millennium CalBC. This paper examines the chemical composition of this item and reviews its context. The results indicate that it was exported from a distant source, probably in the Caucasus, and that the location where it was found is indicative of the social status of the buried individual. This rare finding indicates that metallurgy was first defused to the southern Levant through exchange networks and only centuries later involved local production. This copper awl, the earliest metal artifact found in the southern Levant, indicates that the elaborate Late Chalcolithic metallurgy developed from a more ancient tradition.The beginning of metallurgy in the ancient Near East attracts much attention. The southern Levant, with the rich assemblage of copper artifacts from the Nahal Mishmar cave and the unique gold rings of the Nahal Qanah cave, is regarded as a main center of early metallurgy during the second half of the 5 According to the current state of research the initial appearance of copper in the southern Levant is dated to the Late Chalcolithic period . The elaborate assemblage of prestige items from the Cave of the Treasure in Nahal Mishmar, displaying lost wax casting technology, and the electrum and gold items from Nahal Qanah cave place the southern Levant as a major center of metallurgy in the Near East 2 were opened, and a poorly preserved layer of Late Byzantine–Early Islamic occupation was noted just below the topsoil. The main occupation of the site is composed of a densely built Middle Chalcolithic settlement, with a few stratigraphic phases, radiometrically dated between 5100–4600 CalBC. For the archaeology of the southern Levant, the term “Middle Chalcolithic” refers to the time-span between the Wadi Rabah Culture  and the Ghassulian Culture , and has been explained in detail elsewhere Tel Tsaf was surveyed and tested in the past The complex mud-brick architectural settings include courtyard buildings combining rectilinear rooms, rounded rooms and silos, as well as many cooking facilities. Four burials were uncovered. Two of these were found inside two distinct silos, while the other two graves were found in proximity to two other silos. The silos uncovered in courtyard structures reached a storage capacity estimated at 15–30 tons of grain, far beyond the yearly need of a nuclear family, a clear indication of the accumulation of surpluses on a scale unprecedented in the ancient Near East. The material culture of the site presents rich assemblages of elaborately painted pottery, over 2,500 beads made of ostrich egg-shell which were found mainly in two distinct concentrations, about 100 stone beads, many obsidian items originating in Anatolia or Armenia, four Ubaid pottery shards imported from either north Syria or Mesopotamia and a Nilotic shell from Egypt. No other known site of this period exhibits long-distance connections in a similar dimension. An exceptionally rich faunal assemblage was also noted, dominated by large numbers of cattle and pigs We present here the copper awl found in one of the silo-graves at Tel Tsaf and discuss the characteristics of this unique artifact, its chemical composition and its significance for early metallurgy in the Near East. Tel Tsaf exhibits an exceptionally rich community, with storage capacity previously unknown in the prehistoric Near East, accumulation of wealth, and long distance exchange networks with different parts of the ancient Near East. The available dating from Tel Tsaf and the item context suggest that this awl is the earliest known copper artifact in the southern Levant, suggesting that cast metal technology was introduced to the southern Levant centuries before the onset of the full-blown Ghassulian Chalcolithic.The metal awl was discovered in the fills of Grave C555, set within Silo C339 in the northeast corner of the courtyard of Building I, during the 2007 excavations (Israel Antiquities Authority License number: 2007/G38) –3. The bThe process of excavating the silo and identifying its components involved several stages. First the rounded peripheral wall was noted. Later, large stones were recognized in the center of the silo. Further excavations uncovered the silo floor, which was paved with bricks. At the center of the silo, below the stones, the pavement was missing. Further excavations in the area where the paving was missing uncovered a human burial. The copper awl was uncovered while sieving the sediment collected during the exposure of the burial . It was probably hidden by sediment that enveloped it and that sediment was removed during the sieving process. As the awl was found in the sediment collected in association with the skeleton, it was apparently a burial offering.The location of the awl was nearly 1.5 m. below the original topsoil. It was found in association with a rich burial, in the middle of a built silo, and the burial pit was covered with stones. No other occupational phases were found above or below the burial. Thus, the awl was found in a secure context. As the burial was rich in body ornaments (a belt of 1668 beads) the awl was probably directly associated with the burial.The metal object is an elongated pin made of cast copper, with a rounded cross-section . It is 4The awl is totally corroded with no original metal left. The chemical composition of the corroded metal was analyzed on the cleaned, relatively flat, corroded sections of the pin on both broken inner surfaces. Due to the corroded state of this object we could not observe the original microstructure; no rare remains of the original production process visible, nor the original relative quantities of the various elements preserved. The corroded inner sections of both fractures were analyzed by a portable Niton ED-XRF using a beam size of 3 mm. in diameter. The results  show copnd millennium CalBC, and later periods. Thus, not only does the Tel Tsaf awl predate all known metals in the southern Levant by several centuries, it also predates all known tin bronze items in this region by ca. 3,000 years.The ratios between elements are not as they were in the original metal and may have been altered during the corrosion process. Still, the appearance of tin, even if highly enriched in the corrosion process, raises important questions. Until now, copper items of such chemical composition have not been found in the Late Chalcolithic or the Early Bronze Age of the southern Levant, nor does the metal composition of this object, which includes tin, fit the known compositions of local native copper. In fact, items with similar chemistry have been documented in the southern Levant up to now only from the Middle Bronze Age, the 2According to the current understanding of the archaeological record, the usage of copper minerals was developed in three main stages in the Near East. During the first stage, natural Malachite chunks were used for the production of pigments and ornaments, as early as the Epipalaeolithic of Anatolia th millennium CalBC when beads and other decorative objects were made from hammered native copper. Such items have, for example, been reported at Aşıklı Höyük At the second stage, a major development is reported in Anatolia during the Pre-Pottery Neolithic B of the 7th millennium CalBC The third phase, dated to the late 6th millennium CalBC, includes smelting and melting of ores to extract copper, a much more complicated process than simply using native copper: A single error in the complex and lengthy production chain will ruin the finished product. This was discovered at various sites in the Balkans 14C dates show that the prestige items were manufactured as early as 4350–4250 CalBC The earliest extractive metallurgy in the southern Levant is typically connected with the Late Chalcolithic period  and reliable The elaboration of south Levantine Late Chalcolithic metallurgy means that with our current archaeological record, the peak of the technical evolution of copper metallurgy is set at its beginning. In our opinion, this suggests that large parts of the technological evolution of metallurgy have not yet been discovered. Indeed, the Tel Tsaf awl dated to ca. 5100–4600, centuries earlier, would thus fill an important gap in the picture. However, the high percentage of tin in the awl could be used to argue that the item was an intrusive object from a much later period—although during the excavation no disturbances were documented and the context was sealed by mudbricks and stone slabs and cobbles.Recently, new data on very early copper artifacts in the northeastern Near East and the Balkans indicate that tin was found in some of the early metal items known in this area inter alia in Mušiston, Tajikistan th millennium CalBC Even though it could be argued that the items from Aruchlo I and Tel Tsaf are later intrusions which were brought into earlier archaeological layers by post-depositional processes, this seems to be less plausible because there are no known later settlement traces at either site. Since artificial alloying would also be very improbable at such an early time, a natural copper-tin alloy is, at the moment, an interpretation worth considering. Copper sources with a natural tin-copper alloy are known th millennium CalBC. This, in turn, also opens the possibility that the item from Tel Tsaf was made from a natural tin-copper source and transported to the Jordan Valley via long-distance exchange networks, which also brought obsidian, groundstone items and other goods from Armenia, Anatolia and Syria through the Levantine Corridor If one accepts the Aruchlo I bead as non-intrusive, it demonstrates the possibility of the extraction and use of natural tin-copper alloys as early as the 6The Middle Chalcolithic site of Tel Tsaf exhibits an extremely wealthy community, with large-scale silos, unprecedented in the ancient Near East. In addition, no evidence was found for human activity at Tel Tsaf between the Middle Chalcolithic period and the Late Byzantine–Early Islamic periods.The copper awl was a grave good, associated with a primary undisturbed burial. The skeleton was found in articulation, adorned with a bead necklace placed on the corpse or worn by the deceased. The ostrich-egg-shell beads found on the deceased are morphologically similar to hundreds of beads found on the floor of the same courtyard, stressing that the grave (and thus the copper awl) and the courtyard, are contemporaneous. In addition, the grave was dug in the center of a built silo base, protected from all sides by the mud bricks, and was covered by stone cobbles. No rodent dens were documented during the excavation of the grave. Very richly furnished graves are not unknown from the Chalcolithic; gold and copper items were included as grave goods, for instance, in prestige burials of the Late Chalcolithic such as Nahal Qanah and Peqi’in caves th millennium CalBC Ubaid sites in the Near East: Tepe Gawra Layer XIII and Ugarit Layer IIIb The copper awl from Tel Tsaf is typologically comparable to others from 5In addition, it should be noted that the Middle Chalcolithic period was recognized as a cultural phase only rather late in the history of research th–early 5th millennia CalBC. The available contextual evidence clearly indicates that the awl, the grave and the building all belong to a single phase in the Middle Chalcolithic period. A number of implications emerge from this conclusion. First, it suggests that the inhabitants of the southern Levant were exposed to copper metallurgy as early as the late 6th–early 5th millennia CalBC and clearly much before the emergence of the Late Chalcolithic Ghassulian culture in the southern Levant. It seems possible that the Tel Tsaf awl was the result of smelting and melting, but the poor preservation and heavy corrosion of the object make the chemical analysis difficult to interpret and therefore leave this important question yet unanswered. Second, metallurgical technology was spread by diffusion from the north The copper awl from Tel Tsaf is a hitherto exclusive example of metallurgy in the southern Levant during the late 6This suggests that the elaborate Late Chalcolithic metallurgy was the product of a longer tradition. Thus, the fact that only a single item has thus far been found in such an early context may indicate primarily the current state of research and that greater emphasis should be placed upon the study of the Middle Chalcolithic period. Third, the fact that the copper awl was found in the most elaborate burial of its period in the entire Levant suggests that metal items were perceived as rare prestige goods. Finally, it appears that the occupants of Courtyard Building I belonged to a family or selected group within the community that controlled local cultivation and storage of grain as well as long-distance trade. This aggregation of wealth in the form of surplus accumulation by specific segments of the community may also have led to or stemmed from trade in exotic items obtained from remote sources over 1,000 kilometers from Tel Tsaf.The Tel Tsaf Copper awl (Item #1-Basket number C1029) was found during the 2007 Hebrew University of Jerusalem excavations at the Tel (Israel Antiquities Authority License number: 2007/G38), directed by Prof. Y. Garfinkel


With exome sequencing becoming a tool for mutation detection in routine diagnostics there is an increasing need for platform-independent methods of quality control. We present a genotype-weighted metric that allows comparison of all the variant calls of an exome to a high-quality reference dataset of an ethnically matched population. The exome-wide genotyping accuracy is estimated from the distance to this reference set, and does not require any further knowledge about data generation or the bioinformatics involved. The distances of our metric are visualized by non-metric multidimensional scaling and serve as an intuitive, standardizable score for the quality assessment of exome data. In recent years, next-generation sequencing (NGS)-based exome screens have become an invaluable tool in Mendelian disease gene discovery and are now being introduced as clinical diagnostic tools for genetic disorders of high phenotypic and genetic heterogeneity ,2. VarioAlthough these parameters may serve as valuable indicators for quality they do not directly indicate the accuracy of a sequenced exome and to our knowledge there is no criteria for assessing whether the variants identified by whole exome sequencing represent a comprehensive list. Specifically, it is not possible to estimate an exome-wide false positive or negative rate for variant detection that is purely based on the quality scores of genotype calls. Sequencing technology-specific error signatures  can yielt priors , and metIn order to enable interoperability and platform independence, we have developed a method to measure the accuracy of a set of variants by assessing its composition. In our metric, the distance between sets of variants from two exome samples is computed without considering genotyping quality scores. The basic idea is that the distance between variant sets of comparable quality is closer than the distance between variant sets of very different quality. In our comparison, the variant data of individuals of the 1000 genomes project  serve asGenomic DNA of European individuals was enriched for the target region of all human CCDS exons with SureSelect Human All Exon Kit  according to the manufacturer's protocol and sequenced on a HiSeq 2000 , yielding more than 5 gigabases raw sequence data per exome. The Charité University Medicine ethics board approved this study, which conforms to the Helsinki Declaration, and we obtained informed consent of all participants.et al. were used for testing the accuracy predictions [Publicly available NGS raw data and variant calls of 1,063 individuals of different populations were downloaded from the ftp server of the 1000 genomes project . Exome vdictions ,21.Exomes of test samples were enriched with Human All Exon SureSelect baits from Agilent and sequenced on Illumina Genome Analyzer IIx and Illumina HiSeq 2000 as 100 bp single-end reads or paired-end reads according to the manufacturers' protocols. Short sequence reads were mapped by Novoalign  or BWA to the rThe distance and I is weighted by the reciprocal of the genotype frequency This means that for the same genotypes the indicator For genotypes that were present only in the test sample but not observed at all in the reference set, we set their frequency toBased on that the distance where Therefore, a disagreement at a position of low variability in the reference set contributes more to the total distance than one at a highly variable position.In the resulting distance matrix, isoMDS function of the MASS R-package was used to minimize the goodness of fit, called stress S, of Kruskal and Shepard , that is, a visualization method such as principal component analysis or metric MDS. However, in contrast to principal component analysis (PCA) and metric MDS, non-metric MDS does not make any assumptions about the distribution of the underlying high-dimensional data. With a pre-specified number of dimensions for the embedding φ and an appropriate initial configuration, the ard (see ). To prowhere p equaling the specified genotyping error and the number of trials For coverage-adjusted comparisons, we randomly removed sequence reads from the original alignments. Variants were recalled on these down-sampled exomes as described above. As genotyping accuracy we define the percentage of the entire exome that was correctly genotyped, that is the sum of true positive genotype calls  divided by the entire size of the exomic target region. For our simulations, we assumed that the reference set had a genotyping accuracy of 100% and introduced genotyping errors at random positions. As most of the exomic positions had low variability in the reference set, the contribution of genotyping errors to the distance function could be approximated by adding twice a binomial distributed random variable, Distances between all individuals of the reference set were measured and the averaged values of the median and interquartile range of all columns of the distance matrix were computed to standardize the median of a test sample. The median of the distances from a test sample to all individuals of the reference set was computed and normalized by subtracting the pre-calculated median of the reference set and dividing the interquartile range (IQR) of the reference set. The reference curve and both 5% and 95% quartiles for the standardized dissimilarity score (SDS) were computed for the reference set and simulated data sets of decreasing error groups.Like any metric, the distance measure that we used to compare different sequences of a set of test samples induces a topology. Variant calls, which describe the measurable differences between samples, represent true genetic variation, as well as genotyping errors. The subject of our work is the quality assessment of a set of exome genotypes, thus our metric needs to induce a topology that is sensitive to sequencing errors while being robust to true genetic differences. By using a weighting method for genotypes that uses their frequency of occurrence, we achieved higher precision in accuracy prediction compared to an unweighted hamming distance  individuals from the 1000 genomes project, which is shown in Figure We measured the mean distance to the reference set for 85 exomes of European descent that were all analyzed in the context of NGS research projects. The two samples displayed in Figure We looked for similarities of these outliers and computed the GC content of 100 bases flanking the variant alleles that were present in more than half of the individuals analyzed in the 1000 genomes project but in only one or less of our analyzed samples. The distribution of the GC content of these variants clearly deviates from the distribution that one would expect for randomly located variants in the exome Figure .et al. studied the bias caused by GC content depending on read coverage in detail for Illumina sequencing data and showed that it also varies between technical replicates [To investigate the reasons for the higher false negative error rate for variants in a GC-rich sequence context, we computed the mean read coverage of the target region depending on the GC-content. Figure plicates . This alWe hypothesized that the distance to the high quality reference set should grow when the amount of raw sequence data decreases. We therefore successively reduced the sequence coverage in the raw exome data of NA06986, called variants anew, and observed an increasing distance to the reference set . Although the visualization in metric MDS clearly shows that the test samples are closest to the Illumina samples from the reference set  Exome Variant Server, https://gene-talk.de/qcGeneTalk, ftp://ftp.1000genomes.ebi.ac.uk./vol1/ftp/ftp server of the 1000 genomes project, bp: base pair; CCDS: consensus coding sequence; CEU: central European; dbSNP: National Center for Biotechnology Information Single Nucleotide Polymorphism Database; Kb: kilobase; Mb: megabase; MDS: multidimensional scaling; NGS: next-generation sequencing; SDS: standardized dissimilarity score; ti/tv: ratio of transitions versus transversions.The authors declare that they have no competing interests.VH, PNR and PMK conceived and designed the study. VH developed the original code, TK and DP implemented modifications for GeneTalk. JH contributed exome data. JS and TD supervised and contributed to the statistical analysis. VH, PNR, TD and PMK wrote the paper. All authors read and approved the final manuscript.Supplementary material. Figure S1: Distribution of dissimilarities of simulated error groups for different distance metrics. The distance of simulated test samples of different error groups were to the reference set was measured with an unweighted hamming metric and a genotype frequency weighted metric. The variance of the dissimilarities of the test samples is smaller in the genotype frequency weighted metric and thus allows a more precise prediction of the error group. Figure S2: Visualization of distances and estimation of error rates for different target regions. The distances of two test samples  to the reference data were computed for five different target regions that differ in size. The CCDS exome comprises 29 Mb, the human phenotype ontology (HPO) [gy (HPO)  panel cogy (HPO) , all codClick here for file


The function of antibodies (Abs) involves specific binding to antigens (Ags) and activation of other components of the immune system to fight pathogens. The six hypervariable loops within the variable domains of Abs, commonly termed complementarity determining regions (CDRs), are widely assumed to be responsible for Ag recognition, while the constant domains are believed to mediate effector activation. Recent studies and analyses of the growing number of available Ab structures, indicate that this clear functional separation between the two regions may be an oversimplification. Some positions within the CDRs have been shown to never participate in Ag binding and some off-CDRs residues often contribute critically to the interaction with the Ag. Moreover, there is now growing evidence for non-local and even allosteric effects in Ab-Ag interaction in which Ag binding affects the constant region and vice versa. This review summarizes and discusses the structural basis of Ag recognition, elaborating on the contribution of different structural determinants of the Ab to Ag binding and recognition. We discuss the CDRs, the different approaches for their identification and their relationship to the Ag interface. We also review what is currently known about the contribution of non-CDRs regions to Ag recognition, namely the framework regions (FRs) and the constant domains. The suggested mechanisms by which these regions contribute to Ag binding are discussed. On the Ag side of the interaction, we discuss attempts to predict B-cell epitopes and the suggested idea to incorporate Ab information into B-cell epitope prediction schemes. Beyond improving the understanding of immunity, characterization of the functional role of different parts of the Ab molecule may help in Ab engineering, design of CDR-derived peptides, and epitope prediction. Antibodies (Abs) have two distinct functions: one is to bind specifically to their target antigens (Ags); the other is to elicit an immune response against the bound Ag by recruiting other cells and molecules. The association between an Ab and an Ag involves myriad of non-covalent interactions between the epitope – the binding site on the Ag, and the paratopes – the binding site on the Ab. The ability of Abs to bind virtually any non-self surface with exquisite specificity and high affinity is not only the key to immunity but has also made Abs an enormously valuable tool in experimental biology, biomedical research, diagnostics and therapy. The diversity of their binding capabilities is particularly striking given the high structural similarity between all Abs. The availability of increasing amounts of structural data in recent years now allows for a much better understanding of the structural basis of Ab function in general, and of Ag recognition in particular. This review surveys the recent developments and the current gaps and challenges in this field. We focus specifically on the current understanding of the determinants within the Ab structure that contribute to Ag binding. We first discuss the motivations for, and applications of, the study of the structural basis of Ag recognition. Then we describe and discuss the Ab-Ag interface, with specific focus on the paratopes and the complementarity determining regions (CDRs), and their role in Ag binding. The last part focuses on the contribution of the non-CDRs parts of the Ab  to Ag binding and on the recent suggestions regarding non-local and allosteric effects in Ab function. Over the last few years numerous reviews have addressed issues that are related or tangential to the topics we review here. This includes reviews of the engineering of Abs , their sThe adaptive immune response involves two types of lymphocytes: T cells, which recognizes Ags that have been processed and their fragments are presented by MHC molecules, and B cells which produce soluble Abs that can identify also the intact Ag in its native form. While the way in which T cells recognize their epitopes has been extensively studied to a level that enables the successful prediction of T-cell epitopes , 6, the The immune system enables Abs to distinguish between foreign and self molecules . AutoimmA fundamental characteristic of the immune system is its ability to continuously generate novel protein recognition sites. Ab-Ag interfaces, therefore, are often considered a model system for elucidating the principles governing biomolecular recognition –13. For The specificity of the Ab molecule to its cognate Ag has been exploited for the development of a variety of immunoassays, vaccinations, and therapeutics. Ab engineering may offer to expand the application of Abs by permitting improvements of affinity , 21 and Antibody epitopes (sometimes referred to as B-cell epitopes) are the molecular structures within an Ag that make specific contacts with the Ab paratope. B-cell epitopes are used in the development of vaccines and in immunodiagnostics. Correct identification of B-cell epitopes within an antigenic protein, may open the door for the design of molecules (biologic or synthetic) that mimic potentially protective epitopes and could be used to raise specific Abs or be used as a prophylactic or therapeutic vaccines. Identification of B-cell epitopes could promote protective immunity in the context of emerging and re-emerging infectious diseases and potential bioterrorist threats. This may be achieved by choosing from among the putative epitopes those that may provide immunity . The choice of such epitopes is believed to be relevant for understanding and controlling protective immunity. In the case of the vaccinia virus, for example, which was used as smallpox vaccine and is the only vaccine that has led to the complete eradication of an infectious disease from the human population, individuals possessing a high frequency of memory B-cells specific for major neutralizing Ags of the vaccinia virus are better protected from smallpox than individuals with a memory B-cell pool dominated by specificities for non-protective Ags . Thus, uIn general, current methods are trying to identify epitopic residues based on the presence of features associated with residues that bind the Ab –50. One This lack of intrinsic properties that clearly differentiate between epitopic and non-epitopic residues and the fact , the IMGT scheme avoids the use of insertion codes for all but the least common very long loops, and the Aho numbering scheme places insertions and deletions symmetrically around a key position. However, Abs with unusually long insertions may be hard to annotate using these methods and, as a result, their CDRs may not be identified correctly. For instance, the recently determined 3-D crystal structure of two bovine Abs  reveal eWhile identification of paratopes is often done through identification of CDRs, not all the residues within the CDRs bind the Ag. In fact, an early analysis of the 3-D structures of Abs suggested that only 20–33% of the residues within the CDRs participate in Ag binding . In 1996The number of publicly available structures of Ab-Ag complexes increased in recent years to a level that enabled large-scale analyses. In a recent analysis  we utiliDesigned systems are often characterized as either modular or integral. In a modular system different components, or modules, function independent of the function of other modules. The generation of Abs in the immune system is based on combining different elements, in a way that may be considered modular where each component is capable of binding the Ag regardless of the others. However, some analyses suggest that Ag binding warrants a more integrative view of the relationships between the different components of the Ab.The binding-sites of interacting proteins are usually composed of surface patches that have good shape and electrostatic complementary , 75, 76.Several studies have shown that each CDR has its own unique amino-acid composition, different from the composition of the other CDRs , 58, 78.Despite this integrated effect of the CDRs, Abs can be also considered as a modular system, composed of different elements , which may bind the Ag on their own. Such smaller Ab fragments that retain Ag binding affinity and specificity, hold a great potential for drug design –81 as thThe CDRs may provide additional level of modularity. According to the commonly accepted hotspot hypothesis, the binding energy of two proteins is largely determined by a very small number of critical interface residues , 88–90. Within the variable domain, the CDRs are believed to be responsible for Ag recognition, while the FR residues are considered a scaffold for the CDRs. However, it is now well established that some of the FR residues may play an important role in Ag binding , 108. AsFramework region residues that affect Ag binding can be divided into two categories. The first are FR residues that contact the Ag, thus are part of the binding-site , 116–123In the second category of FR residues that affect Ag binding, are residues that are not in contact with the Ag, but affect Ag binding indirectly , 121. ThFramework region residues that are more distant from the paratope are suggested to play a role in maintaining the overall structure of the Fv domains . HoweverUnderstanding the role of FR residues in Ag binding is crucial for efficient Ab design in general and for humanization in particular. Specifically, knowing in advance which FR residues may affect Ag binding, one may consider back-mutating these residues into their murine sequence, to improve affinity during CDR grafting. To this end, attempts were made to identify positions that contribute to Ag binding in multiple cases , 119. FoUntil recently, Ab constant domains were considered responsible for the isotype and for effector function, such as complement activation, Fc receptor binding, avidity, and serum half-life . Howeverin vivo and survival  or in its conformation  may lead to a rearrangement of the constant domains relative to each other and relative to the variable domains, which may result in a change to the VH-VL relative orientation , thus re+ cell infection more efficiently, IgG1 and IgA2 act synergistically to block HIV-1 transfer from Langerhans cells to T cells. Thus, it has been suggested that a mucosal IgA-based vaccine response should complement an IgG-based vaccine response in blocking HIV-1 transmission.The potential influence of the constant region on Ag affinity or specificity suggests that the process of class-switch may be considered, in combination with somatic hypermutations, as a mechanism for Ab diversity , 132. EnAs Abs are one of the most versatile naturally occurring biosensors, it is of high importance to decipher the structural and molecular mechanisms by which they recognize and bind their Ags. Such knowledge is crucial for understanding immunity, may enable better prediction of Ab epitopes, and assist in Ab engineering.While the commonly accepted view has been that CDRs hold the key for Ab-Ag recognition, recent findings indicate that not all the positions in the traditionally defined CDRs are important for binding. Furthermore, it has been shown that many positions that contribute critically to the binding energy reside outside of the transitional CDRs. Moreover, different CDR identification methods may often identify radically different stretches as “CDRs,” indicating that CDRs are not well defined and thus are not necessarily a good proxy for the binding site. The hypervariable loops that accommodate the CDRs differ significantly from each other on various aspects. Understanding the way in which their binding preferences are integrated to yield the overall specificity of the Ab is an intriguing structural and biophysical challenge.Accumulation of recent data suggests that elements that may be spatially distant from the Ag binding site also play a crucial role in Ag recognition. The unorthodox suggestion that non-local and even allosteric effects influence epitope recognition warrants additional analysis and research.Addressing the open questions regarding the structural basis of Ag recognition requires additional structural data in the form of crystal structures of Abs bound to Ags of different types . Large-scale analysis of such structures will allow for the generation and testing of new hypotheses regarding the way in which Abs find and bind their epitopes.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.