Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.The theory of medicine and its complement  As scientists we measure things; the position of stars in the sky, the amount of rainfall in a region over the year or the number of heart beats per minute of a patient in our care. These numbers tell us about the phenomena we want to understand. An astronomer deduces whether the faint dot over head is a fixed star, a moving planet or a rocketing comet using the physical theories of cosmology. The numbers tell the meteorologist if there is a pattern of increasing or decreasing rainfall and whether that pattern indicates an organized change in the weather. A physician determines whether the pattern in the heart beats reveals if the patient has a cardiovascular problem that requires intervention or s/he is having an anxiety attack. Each science organizes measurements in ways that communicate the most to the practitioner and taken as a group they constitute the scientific view of the world, which is to say that if it is a matter of science it can be measured.In keeping with the data-based perspective, the measurements in and theories of molecular biology and genetics in the latter half of the twentieth century produced a shift in medical outlook from the pathologies of the cardiovascular, respiratory and motor control networks to the influence of molecules on health and well being. However, in the past decade or so the pendulum has begun to swing back from the concentration on individual molecules to a focus on the properties of networks of molecules and a determination of the emergent properties of such complex interactive networks. This is particularly true in physiological networks, which, as Bashan et al.  point ouHerein we do not trace the various mechanisms  that produce scale-free microscopic  the errors are independent; the error in a given experiment does not depend on the error in any other experiment; (2) the errors are additive; the total error made is the sum of the separate errors; (3) the statistics of each error is the same; the statistical process producing the error does not change from experiment to experiment; and (4) the width of the distribution is finite; the standard deviation converges to a finite value as the number of measured errors increases. These criteria are recorded here because complex medical phenomena often violate one or more of these conditions necessary to satisfy the mathematical proof of the Central Limit Theorem and it is here that the real world deviates from the expected variability imposed by Normal statistics West, .There is a wide array of medical phenomena that manifest Normal statistics including height  given a random variable X, such as the height of a river or the magnitude of an earthquake, the successive measurements are statistically independent of one another; (2) the statistics are stationary in time, that is, the PDF is independent of an overall shift in time. The domain of attraction of this PDF encompasses most of the commonly used distributions, that is, PDF's for which there exists a mean and standard deviation such that as the number of data points becomes arbitrarily large, the limit of the extrema PDF approaches the Gumbel form.where μ is related to the mean and χ to the standard deviation of the extrema variable Figure It is evident from the figure where Equation (4) is plotted that the large excursion of the variate from the central values dominate the extrema PDF's.Of particular interest to us here are the extreme properties of fluctuations in medical observables. If the maximum fluctuation in body temperature doubles an individual may be in some distress but if the maximum interval between heart beats double the pathology may be life threatening. Part of the reason for this difference can be traced to the changes in the behavior of extrema properties for a Normal statistical process and non-Normal processes, say one described by Pareto, i.e., IPL statistics. Extrema in stock market fluctuations, Taleb's black swans Taleb , generatThe lack of interchangeability of black swans and dragon kings in the interpretation of medical pathologies has not yet been addressed explicitly, as we subsequently discuss. This distinction becomes important in a medical context given the recent progress by de Souza Cavalcante et al.  in real In Section 2 the idea is developed that the PDF's generated by complex phenomena, particularly those in medicine, require a new method of quantification; one based on fractal statistics, self-similarity, and the fractional calculus. Some renormalization group scaling ideas are taken from Zaslavsky  but otheFractal processes are dynamically rich in interconnected scales with no one scale or set of scales dominating. The solutions to the fractional equations of motion for a category of such processes are given in Section 3 using scaling arguments. The alpha-stable Lévy distribution is one such solution that has been suggested to describe the statistics of heart rate variability (HRV) of both healthy and diseased individuals  immediately disqualifies the traditional ordinary differential equations as a way of describing its dynamics since the ordinary derivative of a fractal function diverges. Consequently, it became necessary to show that a fractional derivative of a fractal function is another fractal function implying that the fractional calculus is the appropriate way to describe the dynamics of fractal phenomena  entails the notion of complex fractal dimensions. The real part of the complex dimension is the IPL index and the imaginary part yields a periodic modulation of the IPL distribution. The existence of such a complex dimension is sketched out using data from a number of physiologic phenomena.Pdx of a dynamic process X(t) along a fractal trajectory having a value in the interval  at time t. Zaslavsky  in time along chaotic trajectories whose local averages yield a FKE, which is to say an equation of motion for the PDF in phase space in terms of fractional derivatives. There are a number of alternative derivations of the FKE including the continuous time random walk (CTRW) of Montroll and Weiss  is sometimes called the fractional Fokker-Planck equation (FFPE) with zero potential because it can be generalized by introducing a potential function in complete analogy with the historical Fokker-Planck equation. When α = 1 Equation (5) reduces to the anomalous diffusion equation  or (6); the understanding required for our purposes can be achieved from their scaling properties.Zaslavsky  applied x, λT) are scaling parameters. He goes on to say that a basic feature of renormalization group kinetics is that the FKE is invariant under the operation of a renormalization group transformation R{·}:which apply after some averaging in a restricted space-time domain and  has an infinite number of solutionsn. Consequently, indexing the time parameter with the fixed point index the ratio of the time to space parameters becomeswhere the fixed point solutions have integer n is arbitrary and is only intended to distinguish among the various fixed point solutions to the FKE.Indexing the time parameter by In Section 3 we show that the solution to Equation (5) has the general scaling formusing the zero-order solution to Equation (12). Consequently the first moment of the dynamic variable takes the formwhere the coefficient can be calculated to be Zaslavsky However, if we include the higher-order fixed point solutions from Equation (12) into the average we obtaint, the logarithm of time for time series data, having period ln λT.resulting in periodic variations in the average value, with variations in ln An in Equation (16) can be explicitly calculated when the kinetic equation of motion has a discrete renormalization invariance, see, for example, Hanson et al. (A0 = D(0)αβ. On the other hand, these coefficients can also be used heuristically as expansion coefficients much like what is done with empirical Fourier series fitting the expansion coefficients to time series data.The expansion coefficients n et al. , Montroln et al. , West etn et al. . The lowIt is important to note that the concept of fractal dimension implies that the underlying process is self-similar, but the fact that the dimension is complex implies even richer properties of the process. The real part of the complex dimension yields the inverse power-law index for the Pareto distribution. The time series data is seen to have bursts of activity followed by long quiescent intervals during which no event occurs. However, when one of these bursts is examined with higher resolution it is seen to be composed of bursts separated by relatively long quiescent intervals. The relative amount of bursting and resting is apportioned by the scaling index. The imaginary part of the dimension indicates that there is a memory superposed on the Pareto statistics producing log-periodic modulations of the moments. It is useful to understand that this apparently bizarre phenomenon is not new.Over 40 years ago Novikov  in his iThe log-periodic variability of an observable average was first discussed in a physiologic context by Shlesinger and West  to descrx; t〉 is the average diameter of the bronchial airway at generation t, A0 and A1 are empirical constants, and the generation t denotes the number of branchings of the bronchial tree starting from the trachea t = 0. Consequently, a result of TNE on the bronchial network is that it is characterized by having a complex fractal dimensionwhere 〈whose imaginary part produces the modulation of the dominant IPL behavior of the average diameter. This periodic modulation is clearly seen in Figure The log-periodic modulation of the IPL behavior of the average diameter in the bronchial airway network is only one of many such phenomenological regularities observed in physiology. Another is cerebral blood flow (CBF) velocity measured using transcranial Doppler ultrasonography, which is not strictly constant. West et al.  use the The CBF time series for 2 h of data from each of six subjects is processed to obtain the relative dispersions depicted in Figure These are only two examples of physiologic phenomena with complex fractal dimensions that are revealed through modulation of the processed time series data as a consequence of the TNE. Sornette  also empThis analysis suggest the possible use of extrema in the prediction of mortality as we subsequently discuss.αt[·] is the Caputo fractional derivative in time  is as shown in Appendix 6.2  is the Fourier transform of f(x). The Laplace transform of a Caputo fractional time derivative ∂αt[·] acting on the analytic function g(t) iswhere u) is the Laplace transform of g(t) and g(0) is its initial value. Consequently the phase space dynamics given by Equation (5) can be expressed as the joint Fourier-Laplace transformwhere k = 0, t) = 1. Therefore, after some rearrangement of terms in Equation (21) the solution in Fourier-Laplace space can be writtenand the asterisk denotes the double transform and we have used the normalization condition on the characteristic function in the form The PDF that solves the FKE is given by the inverse Fourier-Laplace transform of Equation (22).We note that the space-time representation of the solution to the FKE for various combinations of α and β and potential functions are reviewed by Metzler and Klafter , who shoThe inverse Laplace transform of the Fourier-Laplace solution to the FKE yields the characteristic function in terms of a function first obtained by the mathematician Mittag-Leffler at the turn of the twentieth century:in terms of the infinite series that now bears his nameThe time dependence of the Mittag-Leffler function (MLF) is extremely interesting. At early times the MLF has the analytic form of the stretched exponential  allows us to write the scaling relationk|nβ. A renormalization group scaling equation emerges when the parameters satisfy the equality λx = λα/βT, which is the lowest-order fixed-point solution to Equation (12), resulting in Equation (28) reducing towhere the second factor in the summation is the result of applying the Tauberian Theorem Zygmund,  to the iT = 1/t, so that in Equation (29) the scaled variable x/tα/β becomes the new dynamic variable we can writeIf we now select the time parameter to be λx/txμ satisfies the scaling equationFinally, the PDF that solves the FKE in terms of the similarity variable as introduced in Equation (13).Fx(·) in Equation (31) is left unspecified but it is analytic in the similarity variable x/txμ. In a standard diffusion process X(t) is the displacement of a diffusing particle from its initial position at time t, and for vanishing small dissipation the scaling parameter is μx = 1/2 since α = 1, β = 2 and the functional form of Fx(·) is a Gauss distribution. However, for general complex phenomenon there is a broad class of PDF's for which the functional form of Fx(·) is not Gaussian and the scaling index μx ≠ 1/2. For example, the stable Lévy process Montroll and West  yields the PDFLβ(·) with a Lévy index β and a “width” that increases linearly with time:When α = 1 we know that the MLF reduces to an exponential in which case the PDF is the alpha-stable Lévy distribution in space The series representation for the Lévy distribution is given in a number of places, see for example Montroll and West :whose lowest-order term is the IPLx as the “space” variable, but this choice of words was used to facilitate the presentation. In fact X(t) has been called the dynamic variable, variate or random variable of interest and x is the corresponding phase space variable. The variate could be the time interval between successive heart beats and t would then be the chronological time and the clock is started when the first of these beats occurred. Consequently both the random variable and the independent variable would be measures of time. For example, if the heart rate variability (HRV) were given by a Lévy distribution then x in Equation (34) would be the interbeat time interval and Lβ dx would be the probability that the interbeat interval falls in the interval  at time t.Note that in the discussion up to this point we have interpreted 4 heart beats). They also determined that the histogram for the heartbeat interval increments is well described by the above Lévy stable distribution as shown in Figure It has been over 20 years since Peng et al.  determinB(n) for the beat number n. Peng et al.  = B(n + 1) − B(n), the interbeat increments (x in our notation), which they heuristically determined to be stationary. The second moment of the interbeat increment time series data scale with time as a power-law and the spectrum scales as a power law in frequency S(f) ∝ fμ where μ = 1 − 2H and the mean-square level of the interbeat fluctuations increases as nH2, as depicted in Figure H = 0.5 corresponds to Brownian motion, so that μ = 0 indicates the absence of correlations in the time series x (“white noise”). They observed that for a diseased data set that μ is approximately zero in the low-frequency regime confirming that the x are not correlated over long times. On the other hand, they also observed that for the healthy data set μ is slightly less than 1 indicating a long-time correlation in the interbeat interval differences. The anti-correlated property of x are consistent with a non-linear feedback system that “kicks” the heart rate away from extremes. This tendency operates on a wide range of time scales not on a beat-to-beat basis.They Peng et al. , in ordeThe spectrum indicates the correlation of the heart beats. In normal healthy individuals shown in Figure More recent studies conclude that although the statistics of HRV have heavy tails they need not be strictly Lévy Hayano et al.  as we diIn the previous section we learned that what is of most interest in complex phenomena often resides in the tails of the PDF. Consequently, to understand complexity and its loss requires insight into the extremes of fluctuating time series. The discipline developed for the study of statistically unusual or rare events is extreme value theory, which is the branch of statistics that deals with extreme deviations from the median of the probability density. Half the data is greater than the median and half is less than the median and consequently the median is not the same as the mean or average except when the PDF is symmetric as in the case of the Normal PDF. The description of many complex phenomena has involved replacing the Normal with an IPL PDF, in fact, this replacement is often used to define complexity. The existence of the long tail implies that there are a great many more large magnitude events than in exponential processes.The importance of rare events in statistical processes cannot be over stated since extrema dominate such processes in general, for example, in determining mortality in heart beat irregularities. A data processing model for sudden cardiac death after atrial myocardial infarction (AMI) based on a measure of the degree of non-Gaussianity of HRV has been proposed  from the time series. In this study a number of individuals suffered a cardiac death, others died by non-cardiac causes and some survived. The statistical distributions determined by the time series for the three groups are indicated schematically.In Figure The first thing to notice about the results in Figure The variability statistics of the cardiac death patients are very different from those that survive even though there is a great deal of overlap in the central regions of the PDF's. The difference between the two curves suggests that those that survive might be modeled using a truncated Lévy distribution. This is consistent with the results of Kiyono et al.  who findWe hypothesize a feedback mechanism that produces a truncated Lévy distribution for those that survive, not unlike the “kicks” away from the extreme excursions postulated a quarter century ago by Peng et al.  to explaIn Section 3.3 we determined that the solution to the FKE with α = 1 is the alpha-stable Lévy distribution given by Equation (33). It was noted that such distributions have fat or IPL tails that decay more slowly than the typical exponential. Such fat tails can generate diverging variances, which are not plausible for healthy physiologic data. Consequently, it is necessary to find a PDF that behaves as an IPL for intermediate amplitudes but manifests physiologic control to mitigate the occurrence of extreme events such as dragon kings. For this reason we assume that the HRV statistics of healthy individuals are determined by a physiologic feedback mechanism in which the tails of a Lévy distribution are truncated.We hypothesize physiologic feedback to produce an exponential suppression of very large fluctuations. This exponential decay of large fluctuations can be formally incorporated into the anomalous diffusion equation Equation (6) in the following wayThe solution to the modified FKE is again given by means of Fourier transforms. The Fourier transform of the shifted operator is determined by the binomial expansion in Appendix 6.2 resulting in the equation for the characteristic functionk = 0, t) = 1, and introducing the phase ϕ for the inverse tangentIntegrating Equation (37) yields the characteristic function after including a term to insure proper normalization of the PDF, that is, The inverse Fourier transform of Equation (38) yields the truncated symmetric Lévy PDFx and γ with (Kβt)1/β. Consequently, in terms of the scaled variables xs = x/(Kβt)1/β and the scaled parameter γs = γ(Kβt)1/β the probability that an RR interval occurs in the interval  isThe truncated Lévy PDF was first studied numerically in the context of stock market fluctuations by Mantegan and Stanley  and soonLβ(sx) is the stable Lévy PDF with Lévy index β.where It has been hypothesized that disease is associated with the loss of complexity , are generated by underlying processes with normal, log-normal, Poisson or Weibull statistics; all of which have a finite variance. Thus, we would expect that extrema generated by the truncated Lévy PDF to be attracted to the type-I PDF, since the exponential asymptotically dominates in the truncated Lévy. On the other hand, type-II extrema, those represented by a Fréchet PDF Equation (67), are generated by process with diverging second moments such as in the case of IPL's and Lévy PDF's. Thus, we hypothesize that black swans are more like type-I extrema and dragon kings are more like type-II extrema. So how readily can we distinguish between the two?Leonard Tippet (1902–1985) was the founder of the field of extreme value statistics. He was employed by the British Cotton Industry Research Association, where he worked on understanding how to make cotton thread stronger. In his studies, he realized that the strength of a thread was controlled by the strength of its weakest fibers. He determined that perhaps the most intuitive comparison between the extrema PDF's is given by the return time, that is, after a given magnitude event occurs how long must we wait for another event of that magnitude to occur? In this way the statistics of the size of an event can be related to the variability of the size over time.Recall that the AMI cohort group introduced earlier was defined by having had an initial AMI event. So the question arises as to how long we expect a person to wait before the occurrence of a second event. This can be framed as a return time problem and depends on whether an individual's HRV is determined by a Lévy or by a truncated Lévy PDF. This is the kind of question encountered in the consideration of earthquakes and floods. The return time to an extreme value η is in general given byF(η) is the probability of achieving this extreme value. Figure where For a Gumbel PDF a magnitude “40” event (arbitrary units) occurs approximately every 50 units of time, say years for an earthquake, but for a Fréchet distribution this event occurs approximately every 10 units of time or so; a factor of five more frequently. The return time increase for type-I extrema is approximately exponential with extrema size (amplitude). On the other hand, the return time increase for type-II extrema parallels the type-I for small values of the amplitude but seems to approach a saturation level at large extrema. Consequently the return time for type-I extrema diverges from that of type-II extrema with increasing size. It is not clear that it is easier to identify what needs to be done to develop protection against the rare events of a truncated Lévy process (type-I extrema) than for the significantly more frequent Lévy process (type-II extrema). However, the relative frequency of the two classes of extrema would suggest very different strategies for suppressing them, particularly in identifying and fixing a disrupted control process that results in the loss of truncation resulting in Lévy distributed HRV.A second example of a physiologic phenomenon that is asymptotically described by IPL variability is epileptic seizure. Recently Osorio et al.  presenteWhat is perhaps most significant in the discussion of brainquakes for our purposes is the observation first made by Davies et al.  regardinIs it true that, “The longer it has been since the last event, the longer the expected time till the next?.”t denoted by 〈τ |t〉 increases with t. Sornette and Johansen  is denoted as ψ(t) dt given that the last quake occurred at time t = 0. The waiting-time PDF is given by ψ(t) so that the probability that no event has occurred in the time interval , the survival probability, is given byThe probability that an event occurs in the time interval (P(τ |t)dτ the probability that the next event will occur in the time interval  conditional on the fact that the last quake had not occurred up to the time t. The formal expression for this probability density is given by Bayes' theorem to be where which when inserted into Equation (44) allows us to determine the conditional expected time to the next quake for μ > 1It is evident that for an inverse power-law waiting-time PDF the conditional expected waiting time to the next quake increases linearly with the elapsed time since the last quake. Consequently, the longer it has been since the last quake the larger is the conditional expected waiting time.Figure Sornette and Johansen  determinIs it true that: “The longer it has been since the last earthquake, the longer the median time till the next.”Note that “expected time” in the original question is replaced with “median time” in the new question since in the analysis the median time is always finite whereas the expected time may in fact diverge.Medicine concentrates on keeping us healthy, and extending our life expectancy through the maintenance of the complexity of the human body. However, we all die in the end. Therefore, we have a vested interest in determining if science can find ways to facilitate life extension. Cluett and Melzer  mention Budovsky et al.  were theContinuing in this departure from the trend of focusing on individual genes and/or their products Wolfson et al.  emphasizIn this context TNE would support the hypothesis that ARD's and longevity networks are interconnected through the signaling of the proteins on the network and that such signaling can be associated with the control of lifespan Warner, . In addiIt is often the case in presenting mathematical arguments in support of a clinical interpretation that the latter is lost in the torturous details of the former. So let us recap the most important aspects of the formal discussion. First of all the statistics most often observed with time series generated by physiological phenomena, both healthy and diseased, are fractal and therefore they scale. This scaling suggests the hypothesis that the behavior of the PDF is described by a FKE. In general the fractal dimensions associated with the scaling of the FKE are complex, they have a real and imaginary part, with the real part denoting the index for the IPL and the imaginary part determining the period of a log-periodic modulation of the statistics.One solution to the FKE was the Mittag-Leffler PDF and another was the Lévy stable PDF, both of which have a Pareto IPL form asymptotically. A generalization of the FKE that incorporated a physiological control mechanism to suppress large-scale fluctuations yields a truncated Lévy PDF. The truncated distribution was associated with a healthy HRV time series, whereas the Lévy PDF was associated with the statistics for a diseased HRV time series. Since the variability for a Lévy process is greater than for its truncated counterpart this seemed to contradict the hypothesis that a healthy physiologic process is more complex than a diseased one. This is not the case.Scientific American article  that has finite central moments. A process was generated in which mechanisms were introduced that scaled in time with increasing values b, b2,.. with probabilities a, a2,.., respectively, resulting in the renormalization group relation for the new PDFThis partitioning into the simple and the complex was made evident in an argument put forward by Montroll and Shlesinger  in whichg(z) as long as it has finite central moments. As stated in the text this argument was applied to the scaling of the bronchial airway network in the mammalian lung  for small values of the argument but having an IPL (Pareto) form asymptotically with index μ = log a/log b.They used this argument to derive the Pareto IPL form for the PDF of income for the highest few percent of income earners in Western countries independently of the form of Consequently, the level of complexity is a balance between regularity and variability, not just the result of variability alone. Thus, the truncated Lévy PDF has this balance built in with the possibility of extreme variability at short time intervals, but suppressed extreme variability at very long time intervals. In keeping with this new perspective, homeostasis, which focuses on the long time control of a physiologic process, and inverse power laws that focus on unfettered variability each have only part of the answer. TNE is intended to capture the full range of complexity characteristic of physiological phenomena that have evolved through the development of complex dynamic networks.Herein we have stressed that the TNE hypothesis encompasses the fact that the statistics of physiologic processes are not the Normal statistics of simple physical systems. Instead complex physiological phenomena are dominated by IPL's of various forms. The scaling of physiologic time series data manifest in the IPL's strongly suggest that the equations of motion for the PDF describing this behavior have fractional derivatives in the variate, in time or both. The solutions to the FKE's have this IPL structure as evidenced by the asymptotic behavior of both the Lévy and Mittag-Leffler PDF's. A generalization of the FKE, under the additional hypothesis that there exists a physiological mechanism to inhibit large excursions of physiological fluctuations, was shown to produce a truncated Lévy PDF. Although it was not shown here a similar generalization can be made to generate a truncated Mittag-Leffler function.We have argued that a dragon king extreme (generated by a Lévy stable PDF) is much more likely to occur in a given interval of time for a physiologic process than a black swan extreme (generated by a truncated Lévy stable PDF). Consequently, if the extreme event is medically critical a person is more likely to die as the result of a dragon king than of a black swan. However, if we can identify the physiological mechanism that produces the truncation in the Lévy statistics, the one whose suppression transforms an unpredictable black swan into a more tractable dragon king, then a judicious intervention could make a person less vulnerable to the more frequent dragon kings.The existence of an explicit physiological mechanism that suppresses large scale excursions of heart beat intervals has been hypothesized. Such a mechanism would seem to explain the clinical data and to be consistent with the fractional calculus developed in this paper as a way of systematically describing the dynamics of HRV for both the healthy and those with a variety of heart diseases. Moreover it is not unlikely that such a mechanism is not process specific but is a natural consequence of biological evolution. It has been shown elsewhere that fractal statistics confer a survival advantage West,  and therWe close with a speculation having to do with the relatively flat region of the conditional waiting time for an event observed in Figure The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Virtual screening is used in biomedical research to predict the binding affinity of a large set of small organic molecules to protein receptor targets. This report shows the development and evaluation of a novel yet straightforward attempt to improve this ranking in receptor-based molecular docking using a receptor-decoy strategy. This strategy includes defining a decoy binding site on the receptor and adjusting the ranking of the true binding-site virtual screen based on the decoy-site screen. The results show that by docking against a receptor-decoy site with Autodock Vina, improved Receiver Operator Characteristic Enrichment (ROCE) was achieved for 5 out of fifteen receptor targets investigated, when up to 15 % of a decoy site rank list was considered. No improved enrichment was seen for 7 targets, while for 3 targets the ROCE was reduced. The extent to which this strategy can effectively improve ligand prediction is dependent on the target receptor investigated. Virtual screening is a widely used technique in the field of medicinal chemistry to identify lead compounds from a diverse library that can bind to a receptor. The receptor based virtual screening approach involves a process called molecular docking which employs an algorithm that docks each molecule from a library into the binding site in order to predict a binding energy or a binding score . In receSeveral software for molecular docking are available  and haveLigand and decoy sets for fifteen target proteins were downloaded from the Database of Useful Decoys . The comx% was calculated as the fraction of true positives divided by the fraction of false positives at x% of the ligand/decoy database according to the equation:The fraction of decoy-site docking results was varied in order to find a cut-off where maximum enrichment is achieved. The numbers of active ligands in the database were then used to calculate the ROC Enrichment (ROCE) factors at 1 % and 2 % of the number of molecules. The ROCEfactives = (number of actives at x%) / ,Where Ndecoys = the total number of inactive decoys,Ninactives = the number of decoys chosen at x% of the ligand/decoy database.Binding site and decoy sites were analysed post-docking with the KVFinder Cavity Detection PyMol Plugin  to proviHigh predicted binding affinities between a ligand and a receptor may not always correspond with the best binding molecules for the target site investigated , 16. In The results show a considerable variation between the fifteen targets investigated confirming the general consensus that virtual screening accuracy is highly dependent on the target Tables  and 2. OThe rationale behind the receptor decoy strategy was that the number of false positive binders could be reduced by determining molecules, which have a tendency to bind non-specifically to molecular surfaces that are different to the binding site. As a result a higher number of active ligands would remain after adjusting the rank list for the true binding site with the rank list for the decoy site. However, the results show that this approach is unlikely to help in the identification and selection of molecules for experimental testing as a higher number of true positives were recalled for only 5 out of 15 targets. The extent of enrichment achieved for the top 1 % and 2 % differed for all targets due to properties that determine the binding interactions between amino acid residues of the target and the ligand-decoy dataset used for docking. The optimum cut-off for maximum enrichment at the top 1 % of a binding site list was obtained when considering 15 % of the decoy list (Table The largest improvement in enrichment was achieved with the targets CDK2 and Pparg. For the targets PR, Hsp90 and ampC the ROCE at 1 % and 2 % remained at zero until considering at least 30 % of molecules in the decoy list, indicating that true and false ligands cannot be distinguished by the Autodock Vina docking algorithm. Cavity analyses of the binding site and decoy site (Table 2 which appears not to be easily surface accessible, so it is expected that this receptor only binds ligands which are complementary in shape. Although, this was not seen as a higher number of active ligands were found in the top 1 % of the decoy site list compared to the binding site list. Thus, when the re-ranking formula to generate the adjusted list is applied, the binding site list is re-ordered such that the active ligands do not appear in the top positions. This highlights the shortcoming, if applying this strategy to a virtual screening experiment where active molecules are not known, it cannot be guaranteed that any improved prediction accuracy will result.The targets Inha, MR and VEGFr2 show a significant decrease in ROCE indicating this strategy makes the retrieval of active ligands in the top ranks worse for these targets. The actual binding site for VEGFr2 appears to be non-specific, open and flat, therefore binds molecules which also bind easily to the decoy site, resulting in a high proportion of active molecules at the top of the decoy list. However, the Inha binding site is a small, deep pocket with a total cavity area of 838.4 ÅThe novel development and evaluation of docking with a decoy binding site shows that improved prediction of active ligands could not be achieved in general. It should be noted that the ligand/decoy dataset used for this evaluation is especially challenging as decoys physico-chemical similar to ligands were chosen . The cho


Intermediate care is a health care model developed to optimize the coordination of health care services and functional independence. In Central Norway, an intermediate care hospital (ICH) was established in a municipality to improve hospital discharge and follow-up among elderly patients with chronic conditions and comprehensive care needs. The aim of this study was to investigate the effectiveness of hospital discharges to a municipality with an ICH compared to discharges to a municipality without an ICH.n = 328) admitted to a general hospital from February 2010 through September 2011 were included in the study and followed for 12 months. The data were analyzed using descriptive statistics, analysis of covariance (ANCOVA) and Cox proportional hazard regression.This was a non-randomized controlled observational study of hospitalized patients aged 60 years and older from two municipalities. Patients (p = 0.046) fewer hospital days during 1 year compared to patients from the municipality without an ICH. Otherwise, no statistical significant differences were found between the municipalities in terms of hospital readmissions, admissions, mortality, activities of daily living, primary health care utilization or total care days. A post hoc analysis of patients discharged to the ICH compared to the municipality without an ICH, showed that the ICH patients were older and frailer, but the outcome was similar to the main analysis.Each patient discharged from the general hospital to the municipality with an ICH had a shorter length of stay and used on average 4.2 (Having an ICH in the municipality facilitated shorter length of hospital stay and kept the risk of readmissions, mortality and post-hospitalization care needs at the same level as without an ICH. Many health care systems worldwide are facing challenges due to an increasing ageing population , 2. CurrHospitalizations  and discIn response to these health care challenges, interventions and models to improve the coordination of services and safety during hospital discharge have been introduced –15. InteIntermediate care services range from nurse-led units to services delivered in the patients’ own home . Due to We previously studied the impact of hospital discharges to an intermediate care hospital (ICH) that was a part of the primary health care system and found that the ICH reduced the length of hospital stays for the municipality inhabitants’, but had only minor influence on the primary health care consumption . HoweverThis was a non-randomized controlled observational study including patients from two municipalities admitted to the same local general hospital in Central Norway Fig. . The intwww.clinicaltrials.gov .The Regional Committee for Medical Research Ethics approved the study (2009/1697a) as well as the patient information and consent schemes. The participating municipalities, the ICH and the local general hospital also approved the study. Each participating patient signed a written informed consent at the general hospital prior to inclusion in the study. The study was registered in The Norwegian health and social care system is primarily a public system. It is organized within two main sectors; the secondary care with hospitals and specialist services on the one hand and primary health care on the other. The hospitals are state owned and organized within health enterprises managed by four regional health authorities. The municipalities are responsible for primary health care services including home care, nursing homes and general practitioners (GPs) .The patients in this study resided in one of two municipalities; the Intermediate care hospital municipality (ICHM) and the Comparative municipality (CM). In 2011 the population size was 21,659 in the ICHM and 14,334 in the CM. Both municipalities are located in the catchment area of a 200-bed general hospital named “Sykehuset Levanger” within the health enterprise “Helse Nord-Trøndelag”.The hospital admission rates from the ICHM and the CM were stable in the years before the study (2005–2009) and until the end of the follow-up 2010–2012) . In 20100–2012 . In 2007, the ICHM established the ICH in collaboration with the general hospital and the regional health authorities to offload the hospital with patients ready for discharge and to improve the coordination of services . The ICHPatients from the ICHM who are not discharged to the ICH and patients from the comparative municipality (CM) were discharged as usual. They were hospitalized until discharge to their homes or until necessary primary health care services were available.Health professionals’ experiences of patient discharge to municipalities with and without the ICH have been described in a previous qualitative study .The inclusion and exclusion criteria were selected to establish a group of patients who were eligible for an ICH stay regardless of whether an ICH was available. The inclusion criteria were patients living in the ICHM or the CM, aged 60 years and older, admitted from their own homes to the medical or surgical department at the general hospital, assessed to be in need of in-patient care for at least 3 days after completion of the hospital diagnostics and the initial treatment and expected to return home after in-patient care. The exclusion criteria were patients without the ability to consent  and short life expectancy.The main comparison groups were patients from the ICHM and CM. However, the ICHM patients comprised two groups; those discharged directly from the hospital to the ICH and those who were discharged directly to home with or without the need for primary health care services.Nurses included patients during the first days of hospitalization at the general hospital (index stay). Inclusion was performed before the hospital physicians had decided where the patients should be discharged. The data were collected at the index stay and during 1 year of follow-up after hospital discharge or until death.Information on hospital stays were collected from the general hospital’s register, the university hospital’s register and from the national register . Stays at specialized rehabilitation centers were collected directly from the rehabilitation institutions in Central Norway and supplemented by national data from the NPR.Data on the use of primary health care services were collected from the municipalities’ own registers. The ICH stay data were collected from the ICH and subsequently added to the institutional primary health care stays in the ICHM.Nurses in the general hospital and in the primary health care services were selected to measure and record 17 ADL variables at index hospital stay and at 3 and 6 months follow-up. These ADLs have been compulsorily and routinely recorded for individuals who request or are in need of primary health care services in all Norwegian municipalities since 2006 (IPLOS) , 36. IPLPublicly available population data was collected from Statistics Norway .The outcomes were measured 3 months and 1 year from index hospital admission except for the proportion of patients with readmissions within 30 days. The functional status was measured at 3 and 6 months from the index hospital admission. Hospitalization and rehabilitation stays were taken from a national data register. Hospital admissions, hospital days and length of hospital stay included the patients’ index stay. Hospital admissions were calculated as any in-patient stay (acute and elective) as well as the number of acute admissions after index hospital discharge was counted. A readmission was defined as any acute hospital admission within 30 days from a previous discharge  regardlet-test was used for continuous variables. Between-group differences for readmissions, health care use and functional status were analyzed with analysis of covariance (ANCOVA). The Cox proportional hazard regression was used to estimate adjusted hazard ratios (HRs) for death. Departure from the proportional hazard assumption was evaluated by graphical procedures (log-log plots).A comparison of the outcomes for the two municipalities (ICHM and CM) was the primary analysis. Descriptive analyses were used to describe the samples. For categorical variables, Pearson’s chi-square tests were used to identify any differences in proportions between the municipalities; Student’s p < 0.05) was chosen. The analysis was performed using SPSS 21.0 for Windows .Patient characteristics are predictors of the use of health care services. Therefore, age, gender, number of diagnoses, functional status and having primary health care (yes/no) at the index stay were included as adjustment variables. A post hoc analysis was conducted to examine the group of patients in the ICHM discharged directly to the ICH (ICHM-ICH) to those discharged to the CM. A significance level of 5 % . The average diagnosis related group (DRG) weight was higher  than in the ICHM-group. The index hospital stay was longer in the CM than in the ICHM .At baseline, the ICHM and CM patients were comparable with respect to gender, number of diagnoses, functional status, proportion having acute admissions and proportion receiving primary health care Table . The CM-p = 0.001; during 12 months it was 4.19 days, p = 0.046) (Table p < 0.001).Each patient from the CM spent statistically significantly more days in the hospital during 1 year compared to patients from the ICHM . Of the days spent in primary health care institutions in the ICHM, 8.7 days per patient was spent in the ICH  and the patients from the ICHM (12.0 %) Table . There wAt baseline, the patients discharged from hospital directly to the ICH (ICHM-ICH) were 5.3 years older than the CM-group Table . Gender,p = 0.004), better functional status  and shorter length of index hospital stay  compared to the CM-group.The patients in the ICHM who were discharged directly to home  had a lower DRG weight at baseline  in the hospital within 3 months than the ICHM-ICH group. During 1 year of follow-up, the average length of hospital stay was 2.33 more days per patient in the CM-group (p = 0.002).The post hoc analysis of the outcomes comparing the CM and the ICHM-ICH group did not substantially deviate from the results of the comparison on the municipality level presented above Table . The maiThere were no statistical significant differences in the number of hospital admissions, readmissions, total days with institutional care, received primary health care, functional status or mortality between the groups Tables  and 4.The main result from this study was that patients discharged from the hospital to the municipality with an ICH (the ICHM) had 4.2 fewer hospitalization days and shorter length of stays during 12 months of follow-up than the municipality without an ICH (the CM). No statistical significant differences in the other outcomes were observed. A post hoc analysis of those that were discharged directly to the ICH compared to the CM, gave similar findings as the main analysis.The main finding here is comparable to a previous cohort study of all hospitalized patients aged 60 years and older residing in the ICHM and the CM from 2008 through 2012 . In bothPreventing prolonged hospital stays, strengthening primary health care and improving coordination of services are prominent goals of the Norwegian health policy . The firIn accordance with the target group of the ICH (elderly patients in need of follow-up care), this study confirms that the patients discharged directly to the ICH were the oldest with the poorest functionality, highest number of diagnoses and most in need of primary health care. One could assume that this group of patients, that was more frail than the average of the ICHM-group would need longer hospital stays. Still, the number of days in hospital for the patients discharged directly to the ICH was similar to patients in the ICHM-group. This suggested that the ICH helped reduce the hospital utilization for frail patients.During the 1 year follow-up, the number of days in hospital was 31 % higher in the CM (4.2 days) than in the ICHM. The average length of hospital stays per patient in the CM was 45 % (2.4 days) longer. The number of days spent in institutional primary health care was similar in the municipalities even when this included the stays in the ICH, which comprised 61 % of all primary health care days in the ICHM. Also, utilization of hour-based care was similar in the municipalities. Hence, early discharges did not influence the utilization of primary health care services in the ICHM compared to the CM. This confirms previous qualitative findings in which ICH was used as a discharge unit in the chain of care . The ICHDecreases in the length of hospital stay over the last decade  have raiThe strengths of this study were the inclusion of participants from two municipalities that were comparable on most baseline characteristics, the adjustment of the analyses for the differences in the groups, the collection of data from reliable electronic registers and the linkage of data on an individual level. The patients included in this study seem to be representative of all patients discharged to the ICH: For all patients from the ICHM aged 60 years and older who were discharged from the general hospital to the ICH from 2008 to 2011 , the aveThe major limitation was the study design, which was chosen because the ICH was already in operation. Hence, randomizing patients to the ICH or not was omitted due to both practical and ethical reasons. Additionally, we were interested in how the ICH operated within the primary health care service, i.e. the municipality level.It should also be noted that the patients who lived alone were not registered and thus not adjusted for. Some patients could not consent due to their condition . Moreover, the ICH model may be different in other settings which limits the generalizability. Cost analysis of alternative care models should be considered in future research.The results show that patients from the municipality with access to an ICH used fewer hospital days and had a similar primary health care utilization among patients aged 60 years and older as patients from the municipality without an ICH. Having an ICH facilitated early hospital discharge for the patients and kept the risk of readmissions, mortality and the abilities to perform activities of daily living at the same level as without an ICH.


Cellular maintenance of the extracellular matrix requires an effective regulation that balances enzymatic degradation with the repair of collagen fibrils and fibers. Here, we investigate the long-term maintenance of elastic fibers under tension combined with diffusion of general degradative and regenerative particles associated with digestion and repair processes. Computational results show that homeostatic fiber stiffness can be achieved by assuming that cells periodically probe fiber stiffness to adjust the production and release of degradative and regenerative particles. However, this mechanism is unable to maintain a homogeneous fiber. To account for axial homogeneity, we introduce a robust control mechanism that is locally governed by how the binding affinity of particles is modulated by mechanical forces applied to the ends of the fiber. This model predicts diameter variations along the fiber that are in agreement with the axial distribution of collagen fibril diameters obtained from scanning electron microscopic images of normal rat thoracic aorta. The model predictions match the experiments only when the applied force on the fiber is in the range where the variance of local stiffness along the fiber takes a minimum value. Our model thus predicts that the biophysical properties of the fibers play an important role in the long-term regulatory maintenance of these fibers. The extracellular matrix (ECM) plays a role in tissue development, damage repair, diseases and aging by influencing cellular responses. For example, the stiffness of the substratum on which stem cells are cultured has been found to direct cellular differentiationCellular maintenance of the ECM requires an effective regulation that balances enzymatic degradation with replacement of the digested fragments with newly synthesized molecules forming and shaping the fibrils and fibers of the ECM including collagen and elastin. In several organs and tissues such as the vasculature, skin, heart and periodontium, a quick turnover of collagen with half-lives between 20 and 250 days have been observed4Despite the strong and constant cellular maintenance, the micro-structure of collagen appears to remain in a stable homeostatic state throughout most of adult life even when demanding mechanical stresses lead to incessant remodeling. For example, while the diameter distribution of collagen in mouse tail tendon undergoes major changes until the age of 3 months due to development, the distribution remains nearly independent of age between 4 and 23 months12An important feature of the ECM is that its fibers are maintained under tension. Because tension is known to influence stiffnessR) and degradative (D) particles. The R and D particles representing collagen monomers and collagen-cleaving enzymes such as matrix metalloproteinases, respectively, carry out the local fiber repair and digestion. The fiber consists of a one-dimensional chain of Ns linearly elastic springs in series  ≡ k0.To study how cells can balance enzymatic digestion and repair of a collagen fiber, we use a random walk model to mimic the diffusion along the fiber of two different types of molecular complex, which we refer to as regenerative  and the particle type. For D particles, the diffusion and binding processes are similar in the sense of probability resulting in an isotropic diffusion for all models considered. For R particles, the binding process depends on the specific model used and the process can be isotropic or anisotropic;The probability for a particle to move up from the bottom layer or move down from the top layer is poff. This parameter controls the unbinding process and is associated with repair or degradation;The probability for a bound particle of either type to leave the fiber and move up to the top layer or move down to the bottom layer is To carry out fiber maintenance, we apply the following rules to the diffusion and reaction processes depending on the type of particle:D or an R particle unbinds, the local spring constant k is reduced (k → γk) or increased (k → k/γ), respectively, by a constant factor γ. The reason for this is as follows. The fiber is composed of molecules in parallel and series. If the fiber was a regular array of molecules, cleavage would decrease the number of molecules in parallel. This would result in a linear decrease in the spring constant during subsequent cleavages and over a long time scale, it becomes possible that the local spring constant reaches zero effectively rupturing the chain. In reality, the molecules overlap and are connected via multiple inter-molecular as well as inter-fibril cross-links in a complex manner , we incorporate the notion that cells are capable of actively measuring the stiffness of their surrounding matrix18tu. If the stiffness is impaired (K < K0), a fraction f of the particles are randomly selected to be relabeled as R particles. Alternatively, if the stiffness is too high (K > K0), the same fraction f of the particles are randomly chosen to be relabeled as D particles. It is important to note that during this relabeling process the system does not recognize the particle type to be relabeled. However, statistically, this replacement process mimicking cellular response to alterations in fiber stiffness is able to change the overall concentration of particles around the fiber so as to regulate the overall maintenance process to be degradative or regenerative if the fiber is too stiff or too soft, respectively.We consider two models with self-regulatory dynamics. In the first model, called the K surpasses a predefined threshold below or above the target K0. We find, however, that such details about how the control is performed do not influence the general behavior of the system. Nevertheless, the presence of some periodic control is fundamental. If it was absent, it would be impossible for the fiber stiffness K to reach a steady state value, even if the number of particles of both types is always the same. The reason is that K is the harmonic mean of individual spring stiffnesses which introduces strong nonlinearity in the model with a tendency to decrease the overall fiber stiffness. Note, for example, that if one spring binds a D particle whereas another spring of the same stiffness binds an R particle, the two events do not compensate each other and the overall effect is to reduce K. To see this, consider the change in stiffness:It is possible to define the periodic control in many ways. For example, the stiffness of the fiber can be checked at every time step and relabeling particles can be based on whether TCM produces a stationary K. However, the TCM is unable to produce a homogeneous fiber since the standard deviation of fiber stiffness, σk, diverges as shown in tν with ν = 0.5, in our simulations the standard deviation for the distribution of α ~ log k varies according to σ ~ tν with ν ≈ 0.7. Here α is simply the difference between the number of visits of D and R particles a given spring has received. α at five different time points.In order to maintain proper functionality, the cellular maintenance of a fiber needs to preserve the fiber’s elastic properties within a narrow target range. While a simple random walk model without control cannot achieve this, the R particles. We call this model spatio-temporal control model (STCM). While the behavior of the D particles remains the same as in the TCM, the probability pon,R for an R particle to bind to the fiber now depends on the local stiffness with spring constant k as follows:To control both the mean and homogeneity of fiber stiffness, we introduce an additional feature in the model, the local control of the binding event based on the observation that the absence of tension on the ECM leads to disorganized fibersF is the force, per unit of length, applied to the ends of the chain. The force can be generated internally by contractile cells in the ECMF is the same at any location along the chain, a lower local value of k generates a higher local stretch. We assume that a higher local stretch unfolds cryptic binding sites24k, pon,R can vary along the chain with higher values at regions where the fiber is weaker due to more frequent visits of D particles. Consequently, since pon,R is higher at such locations, R particles tend to visit these sites with a higher probability. However, as soon as the R particles start to increase k, pon,R naturally decreases recovering a value which corresponds to the isotropic diffusion-reaction case.where the new parameter F is assumed to be constant but k along the fiber shows substantial heterogeneity, as we have confirmed by the divergence in σk for both the random walk model without control and the TCM. To test whether the STCM can control the global elasticity while preserving fiber homogeneity, we carry out simulations with the STCM for different values of f and tu. We also examine the effect of F by varying it between 0.04 and 10. For all cases, the global fiber stiffness K is well controlled as in the TCM. However, σk no longer diverges. The main plot in σk reaches a steady state although its value σs depends on F. Here, σs is the value around which σk fluctuates after it has reached a steady state.During the digestion/repair processes F, tu and f in the STCM. For all parameter combinations, σk always reaches a steady state with σs depending on the actual parameters. We plot σs as a function of F for fixed tu = 10 and three values of the fraction f in σs presents a minimum as a function of F that occurs at F ≈ 0.63. The maximum homogeneity of stiffness along the fiber is thus achieved when σs is minimum which depends on the applied force as well as the strength of cellular control modeled by the fraction of particles f replaced during the fiber maintenance process. The decrease in σs for larger values of f results from the stronger and more effective feedback to regulate global stiffness through a higher concentration of control particles in the system. The presence of a minimum can be explained by recalling that the process of degradation and repair is similar to a random walk when F = 0 which results in a divergence of σk. For any small positive value of F, the local control results in finite σk and with increasing F, the control becomes stronger and σk decreases. However, when F further increases, the control of the R particles becomes much faster than that of D particles leading to overshoots in repair and a subsequent increase in σk which we have verified by examining the local time variation of individual springs (not shown). Similarly to σs, the mean fiber stiffness also shows a minimum for F ≈ 0.63  and p(nR), approach a Gaussian distribution at any instant in time. It can be shown that the distribution of α = nD − nR, which determines k, also approaches a Gaussian  ii) dμα/dt = 0. Examining ξ = 1. Condition (ii) is equivalent to For ξ reaches and slightly fluctuates near unity only for the STCM. To corroborate that the average number of visits has the same value for both the D and R particles, we plot in t = 103 and t = 106. The color maps are identical for both types of particles at longer time points, which is in agreement with the calculations in the case of STCM. Thus, the STCM as a model of biological regulation of fiber maintenance fulfills the requirement to keep both elasticity and homogeneity of a fiber within a narrow range in the presence of continuous degradation and repair. This can be achieved only in the presence of tension on the fiber which places part of the regulatory mechanism outside the cell because the binding affinity becomes a function of the applied force as well as the local stiffness along the fiber.The conditions obtained above are confirmed by the simulation results in Nc that pass the cross section A of the fiber. If we assume that the cross-link density is constant along the fiber, the local stiffness should be proportional to Nc. Since A is the sum of the cross sectional areas of individual monomers, A is also proportional to Nc implying that fiber diameter is proportional to the square root of Nc. Thus, we compute the distribution of k1/2 and compare it with the distribution of diameters along individual collagen fibrils.Comparison of our results with experimental data would require measurements of the variation of the Young’s modulus of individual collagen fibrils along its axis. To our knowledge, no such Young’s modulus measurements in the axial direction are available along the collagen fibers. Atomic Force Microscopy measurements along the fibril in indentation mode showed significant axial heterogeneity of stiffnessk1/2 for 3 values of F in F = 0.6, which corresponds to the minimum of σs in Images of the thoracic aorta of normal rats were obtained by scanning electronic microscopy . After iIn this study, we investigated the cellular long-term maintenance of an elastic fiber under tension including degradation and repair processes combined with diffusion of regenerative and degradative particles by various computational models. Our main finding is that a homeostatic fiber stiffness can be achieved easily by assuming that cells periodically probe the overall stiffness of the fiber and properly adjust the production and release of degradative enzymes and regenerative monomers. However, this control mechanism fails to maintain a homogeneous fiber that can be seen on images of collagenous tissues. We also introduced the idea that part of the control mechanism is locally governed by how the biophysical properties of the fibers including binding affinity are modulated by the applied force on the fiber. This model predicts diameter variations along the fiber that are in quantitative agreement with experimental data when the applied force is in the range where the variance of local stiffness is at its minimum. Thus, our model predicts a strong involvement of the fibers in their own repair that warrants further experimental studies. While little is known about how tensile forces regulate fiber repair15172528Various computational models have been developed to describe tissue remodeling and homeostasis3031α is the same in the 2-layer and 5-layer models. We also test another model, called the ring configuration . Finally, to account for the observed experimental fact that the enzyme carries out a biased random walk moving essentially in one direction along the fiberB times more likely than in the other direction. Interestingly, this reduces σk in the steady state because the enzyme spends less time at a binding site that may not need cleaving. B suggesting that the efficiency of the control mechanism can be improved by specific features of the interaction of the collagen and its degradative enzymes. For larger and more mature fibers, cleaving or adding a monomer should have less of an effect. We test this by examining the sensitivity of stiffness and variance to γ. As the value of γ approaches unity, the fiber stiffness also approaches unity and σk decreases  were chosen randomly before the periodic relabeling process took place. At each time step, all 100 particles were allowed to move sequentially according to the rules described in the main text. In all simulations the averages were taken over 500 and occasionally 1000 realizations, which we verified to produce adequate convergence.In all numerical simulations described in the main text, the chain was formed by n = 3) were sacrificed and the thoracic aorta was isolated as described previouslyAll procedures were approved by the Institutional Animal Care and Use Committee of Boston University (Protocol # 12-031) and the experiments were performed in accordance with relevant guidelines and regulations. Rats .


Fatigue is a major contributor to workplace accidents, morbidity, and mortality. To prevent the disruption of homeostasis and to concurrently accomplish an assigned workload, it is essential to control the level of workload based on the subjective estimation of the level of fatigue that will be experienced in the near future. In this study, we aimed to clarify the neural mechanisms related to predicting subjective levels of fatigue that would be experienced 60 min later, using magnetoencephalography. Sixteen healthy male volunteers participated in this study. In relation to the prediction, a decrease of alpha band power in the right Brodmann’s area (BA) 40 and BA 9 at 1200 to 1350 ms and that in the right BA 9 at 1350 to 1500 ms, and a decrease of gamma band power in the right BA 10 at 1500 to 1650 ms were observed. In addition, the decreased level of alpha band power in BA 9 at 1200 to 1350 ms was positively associated with the daily level of fatigue. These findings may help increase our understanding of the neural mechanisms activated to indicate the need to take a rest based on the prediction of the subjective fatigue in the future. Fatigue is prevalent in modern societies. It has been reported that 20–30% of the general population in Europe and the United States experience substantial fatigue12347Fatigue is defined as a decline in the ability to perform or the efficiency of performance of mental and/or physical activities caused by excessive mental or physical activity or disease and is often accompanied by a peculiar sense of discomfort, a desire to rest, and a decline in motivation, referred to as fatigue sensationIn our previous study, we focused on the neural mechanisms related to the decision to rest in the presence of fatigue11In the present study, we aimed to clarify the neural mechanisms related to predicting the subjective level of fatigue that will be experienced in the future as a first step in examining the neural mechanisms of the decision to rest based on the future level of fatigue. Because the neural mechanisms related to the prediction of the subjective level of fatigue may involve several brain regions, and the temporal sequences among these brain regions may provide valuable clues, we used MEG with high temporal and spatial resolutions to record neural activities related to the prediction of the subjective level of fatigue. We enrolled healthy participants in this study and assessed oscillatory brain activities, which reflect time-locked cortical activities1314Sixteen healthy male volunteers (21.9 ± 1.7 years of age [mean ± SD]) participated in this study. All participants were right-handed according to the Edinburgh Handedness InventoryThe experiment consisted of two conditions: a prediction condition and a control condition. The two conditions were conducted in a crossover fashion and on different days. Both in the prediction and control conditions, participants lay on a bed in a magnetically shielded room in the supine position with a screen in front of their eyes, and MEG was recorded (MEG sessions). During the MEG sessions, they performed reverse Stroop test trials projected onto the screen by a video projector . The reverse Stroop test used in this study was the same as one used in our previous studyIn the prediction condition, after every 3 to 5 reverse Stroop test trials, participants were asked to predict the subjective level of fatigue that would be experienced 60 min later if they continued performing the reverse Stroop test trials for another 60 min . They were instructed to self-evaluate the subjective level of fatigue experienced at that moment and to predict the subjective level of fatigue that would be experienced 60 min later based on their current subjective level of fatigue. In the control condition, after every 3 to 5 reverse Stroop test trials, participants were asked to evaluate the subjective level of fatigue that was experienced at the time . They were instructed to predict and to evaluate the subjective level of fatigue in time with visual cues that lasted 1800 ms in the prediction and control conditions. Just before the MEG sessions, they performed the reverse Stroop test, prediction, and control trials to practice predicting and evaluating the subjective level of fatigue, to the point that they thought they were able to perform the prediction and control trials adequately as instructed. The mean ± SD interval between the reverse Stroop test trials and the prediction and control trials was 1500 ± 150 ms . The jitOn each experimental day, the daily level of fatigue was assessed using the Japanese version of Chalder’s fatigue scale181/2 in the white-noise region. The sensor and reference coils were gradiometers with 15.5-mm diameter and 50-mm baseline, and the two coils were separated by 23 mm. The sampling rate was 1,000 Hz, and data were high-pass filtered at 0.3 Hz.MEG recordings were performed in the MEG sessions using a 160-channel whole-head type MEG system  with a magnetic field resolution of 4 fT/HzThe magnetic noise that originated from outside the magnetically shielded room was eliminated by subtracting the data obtained from reference coils using specialized software . Epochs of the raw MEG data that included the artifacts caused by eye blinks and those originated from outside of the magnetically shielded room which remained after the subtraction of the data obtained from reference coils were visually identified and excluded from the analyses before band pass filtering and averaging. The mean numbers of the trials remaining after the rejection of the epochs with artifacts were 82.6  and 89.1  for the prediction and control conditions, respectively. Spatial filtering analysis of the MEG data was performed to identify changes in the oscillatory brain activity that reflected time-locked cortical activities131420t}). The SPM{t} was transformed to units of normal distribution (SPM{Z}). The significance of the changes in oscillatory band power caused by the prediction and evaluation and the significance of any difference in those between the prediction and control conditions were assessed using t statistics  on a voxel-by-voxel basist} of the one sample t test was set at P < 0.0015 (familywise-error corrected for multiple comparisons for voxels), considering multiple comparisons among the frequency bands and the time windows. The threshold for the SPM{t} of the paired t test was set at P < 0.05 (familywise-error corrected for multiple comparisons for voxels).Data were then analyzed using statistical parametric mapping , implemented in Matlab . The MEG parameters were transformed into the Montreal Neurological Institute T1-weighed image templateAnatomical MR imaging was performed using a Philips Achieva 3.0 TX  to permit registration of magnetic source locations with their respective anatomical locations. Before MR scanning, five adhesive markers  were attached to the skin of the head: two markers 10 mm in front of the left and right tragus, one marker 35 mm above the nasion, and two markers 40 mm to either side of the marker above the nasion. The MEG data were superimposed on MR images using information obtained from these markers and MEG localization coils.P values were two-tailed, and values less than 0.05 were considered statistically significant. Statistical analyses were performed using IBM SPSS 21.0 software .Values are presented as mean and SD unless otherwise stated. Two-way analysis of variance (ANOVA) with repeated measures was performed to assess the effect of condition (the prediction and control conditions) and time point (just before and after the MEG sessions) on the subjective level of fatigue. A paired t test with Bonferroni correction was used to compare the subjective level of fatigue across different time points in the prediction and control conditions. Relationships between changes in oscillatory band power and the VAS scores and those among changes in oscillatory band power were evaluated using Pearson’s correlation analyses. All P < 0.001], but there was no main effect of condition  or condition × time point interaction . The subjective level of fatigue just after the MEG session was higher than that just before the MEG session both in the prediction and control conditions .Subjective levels of fatigue assessed by VAS just before and after the MEG sessions in the prediction and control conditions are shown in P = 0.120, paired t test).The level of the daily level of fatigue in the prediction condition was not different from that in the control condition (Decreases of the oscillatory power ratio were observed across the frequency bands and the time windows (one sample t test) in the prediction and control conditions. To identify changes in the neural activity caused by predicting subjective level of fatigue that will be experienced in the future, the oscillatory power ratio in the alpha, beta, and gamma frequency bands was compared between the prediction and control conditions. There were several clusters of voxels in which a decrease of oscillatory band power in the prediction condition was significantly greater than that in the control condition .


Out of all photosynthetic organisms, microalgae, due to their fast growth rates and their ability to grow on non-arable land using saline water, have been identified as potential source of raw material for chemical energy production. Electrical energy can also be produced from this same solar resource via the use of photovoltaic modules. In this work we propose a novel method of combining both of these energy production processes to make full utilisation of the solar spectrum and increase the productivity of light-limited microalgae systems. These two methods of energy production would appear to compete for use of the same energy resource (sunlight) to produce either chemical or electrical energy. However, some groups of microalgae (i.e. Chlorophyta) only require the blue and red portions of the spectrum whereas photovoltaic devices can absorb strongly over the full range of visible light. This suggests that a combination of the two energy production systems would allow for a full utilization of the solar spectrum allowing both the production of chemical and electrical energy from the one facility making efficient use of available land and solar energy. In this work we propose to introduce a filter above the algae culture to modify the spectrum of light received by the algae and redirect parts of the spectrum to generate electricity. The electrical energy generated by this approach can then be directed to running ancillary systems or producing extra illumination for the growth of microalgae. We have modelled an approach whereby the productivity of light-limited microalgae systems can be improved by at least 4% through using an LED array to increase the total amount of illumination on the microalgae culture.The Earth receives around 1000 W.m The irradiance from the sun varies widely with wavelength and has been well characterised . The spe‘the direct component contributed to the total hemispherical  radiation on a 37°-tilted surface’[There are two standard spectra defined in the standards . The fir surface’.A plot of the extra-terrestrial irradiance and the two spectra described in the ASTM G-173-03 standard is shown in Figure a, have oxygenic photosynthesis and have no specialised organelles [2, shear, CO2, pH and nutrients effecting and limiting the growth of microalgae [6 EJ of total solar energy each year [−2 to 120 W.m−2). It is to be noted that, to date, the average PE is between 2% and 5% [Algae are plant like organisms which contain Chlorophyll ganelles . Algae dganelles . Algae cganelles . All phoganelles  and algaganelles . Microalganelles ,8. Therecroalgae . Howevercroalgae ,10. Photcroalgae . The algcroalgae . The maicroalgae . This dicroalgae . Photosycroalgae . Energy croalgae . It is wcroalgae . The earach year . The phoach year , the the% and 5% . The maiThe main spectral absorption peaks for Chlorophylls a, b, and c  and seveThe use of photovoltaics, or solar cells, has been described as the ‘art of converting sunlight directly into electricity’. These solid state devices take incident illumination and produce a supply of electrons which can be used by an external circuit . PhotovoThe first solar cell was produced from crystalline silicon and had a conversion efficiency of 6% . ThroughLight emitting diodes (LEDs) are highly efficient solid state devices that can convert electrical current into light. The internal quantum efficiency of high quality LEDs can exceed 99%, however there are difficulties in extracting the light from the LED which leads to low external quantum efficiencies (EQE) in the order of a few per cent .There are a range of different technologies and materials used to produce LEDs and a large amount of research going into increasing the external quantum efficiency of these LEDs. These include blue emitting InGaN-GaN LED’s with a EQE of 40% , thin fiThese LEDs with high external quantum efficiencies (60.9% ) for parblackbox filter and how the light is split between these two purposes is not a subject of this current work. We will assume that the filter can selectively transmit or redirect the different parts of the spectrum to different purposes with minimal energy loss. However, there are several candidate options, including a specifically tailored semitransparent thin film PV, luminescent solar concentrators, or other advanced energy harvesting flat glass panel that match the spectrum not used by the microalgae. One excellent candidate technology system can transmit arbitrary visible light wavebands, capture the infrared part of the spectrum, concentrate it on the edge of a glass panel and convert this to electricity [In this work we propose introducing a filter above the algae pond to allocate the incident illumination to different purposes. The spectrum the filter transmits is allowed to be incident upon the algae pond, while the remainder is provided to a solar cell for electricity production. The nature of this ctricity .blackbox filter. The ideal spectrum to allocate to different uses will be dependent on the type of algae, response of growth rate and yield to different spectra and which parts of the spectrum are necessary for viable growth.In this work we have allocated the solar spectrum to different purposes using readily available lighting filters as model for the The models described in this work are designed to determine the portion of light that can be converted into electricity if different portions of the spectrum are redirected to the algae pond. This energy could be used to run ancillary systems in an algae pond or could be used to increase the illumination upon the pond using specific spectra generated by highly efficient LED lighting. These models also describe the potential improvement in yield if light is the limiting factor.blackbox filter which divides the spectrum for different purposes. What the filter transmits will be allocated to the algae, what the filter does not transmit will be allocated to the solar cell. The ideal spectrum to allocate to different uses will be dependent on the type of algae, response of growth rate and yield to different spectra and which parts of the spectrum are necessary for viable growth and will be tailored in future experimental work.We can model the concept of transmitting a portion of the solar spectrum to a microalgae pond and converting the remainder of the light into electricity via a conventional solar panel. This allows us to determine the viability of a cultivation system based on this concept in terms of generating electivity or increasing the portion of specifically targeted PAR available for cultivation. For this model we are not concerned with how the light will be collected by a solar panel but are investigating the allocation of the solar spectrum to different purposes. To this end we will use typical commercially obtainable filters as a model for the The filters used in this study are LEE 026 Bright Red, LEE 363 Medium Blue and LEE 128 Bright Pink filters. The transmission of each of these was measured using ultraviolet and visible spectroscopy and is shown below in Figure For photovoltaic devices, the absorption of light is determined by the band-gap. This needs to be close to the peak of the energy range of the AM1.5 spectrum (1 eV to 3 eV) and not all semiconductors are suitable for use as solar cells, the most suitable band-gap for which is about 1 to 1.6 eV . AlthougThe spectral response of a solar cell is usually defined as the output current under short-circuit conditions per unit power of incident monochromatic light as a function of wavelength  and is aThere are several different technologies used in photovoltaic devices, including but not limited to: crystalline silicon ,25, amorFrom the reported spectral response graphs and parameters for crystalline silicon  and amorSC) generated by the solar cell is calculated from:The short circuit current density (Jλ)AM1.5 is the photon flux density calculate from the AM1.5  solar spectrum, T(λ) is the transmittance of the filter as measured from spectroscopy measurements and q is the charge of an electron.Where EQE(λ) is the external quantum efficiency as a function of wavelength, Φ(OC) of the solar cell is also dependent on the short circuit current density and will vary with the irradiance incident upon the cell. This can be calculated from [The open circuit voltage  in W.mFF) is the value published in the literature for each cell type.Where the fill factor  arrays can be used.PAR) in Wm−2 that can be produced using the power generated (Pin) using the system modelled above can be calculated from:The additional PAR power  when allocated the spectra not transmitted by the −2 or 1982 μ mole photons.s−1.m−2 would be available for use in the PAR section of the solar spectrum. The calculations from the three filters reflect the fact that smaller portions of the solar spectrum are being transmitted to the algae. Under AM1.5 illumination the highly efficient crystalline silicon cell would produce more electrical power than a less efficient amorphous silicon solar cell. However, from Figure The power from the spectra transmitted through the various filters and onto the algae is shown below in Table −1.m−2 have also been calculated and are shown in Table −2 ; the rest is either reflected or heats up the growth media. The use of photovoltaics, or solar cells, is a second well established method for converting light into useable energy and has been described as the ‘art of converting sunlight directly into electricity’ . WherebyThese two methods of energy production would appear to compete for use of the same energy resource (sunlight) to produce either chemical or electrical energy. However, some groups of microalgae (i.e. Chlorophyta) generally only require the blue and red portions of the spectrum whereas solar cells are generally produced with a very broad spectral response to be able to efficiently collect as much of the solar spectrum as possible. Some technologies have a broader response than others as illustrated in Figure blackbox filter above an algae pond has been modelled and it has been shown in Table −2 is available for algae growth. With the filter in place the available PAR power is reduced to between 47 W.m−2 and 148 W.m−2.The addition of a −2 is required for this process, the remainder is not fully utilised. This can be calculated under the assumption that the largest contribution to photosynthesis is from regions where the normalised absorbance is greater than 60% and the remainder is not critical for growth. For example, the normalised absorption of Chlorella with Chlorophylls a and b and β-carotene, is greater than 60% in the regions of 378 – 485 nm and 654 – 670 nm. The amount of solar energy contained in these regions of the AM1.5 spectrum  radiation or 241 to 482 MJm−2y−1, depending on location in Australia, can be generated by a highly efficient crystalline silicon solar cell which when coupled with an LED array and the light passing through the filter allows 177 W.m−2 of PAR to illuminate the algae. Assuming a photosynthetic biofuel production rate of a green alga (i.e. Chlorella) with Chlorophylls a and b and β-carotene = 20 g.m−2.d−1[−1, the annual production rate of biofuel will be between 109 and 146 MJm−2 year−1. In a light limited system, by increasing the amount of useable PAR, this could be increased. If only 170 W.m−2 is required for achieving a successful productivity of 20 g.m−2.d−1 the increased illumination (177 W.m−2) modelled here could potentially increase the annual algae productivity rate by at least 4%. This may be improved if the selection of microalgae is such that the biofuel production of 20 g.m−2.d−1 can be achieved using just the portion of the spectrum absorbed by Chlorophyll a.The amount of energy production has been calculated for the filter and solar cell combination modelled above that generates the largest amount of total PAR power. These calculations indicate up to 49 Wmg.m−2.d−1, and a cThere are a number of assumptions and limitations in this model. For the total amount of useable PAR with the proposed filter system to be increased relative to the useable PAR without the filter we require a few high efficiency devices. Firstly, the solar cells need to be able to absorb the portions of the spectrum provided to them with very high quantum efficiency and preferably have a broad wavelength response. This would increase the absorption of light in the blue and red portions of the spectrum which are outside of the range of PAR (400 nm - 700 nm). The modelled system also relies on highly efficient LEDs. These can be produced in the lab with external quantum efficiencies ranging up to 60% . A LED wWe recognise that, if the solar cells are in the order of 25% efficient, they would be producing more electrical energy per year from the spectrum they receive than the algae are storing as energy. However, the advantage of our proposed method is the production of chemical energy for transportation. We also recognise that the power used to produce extra illumination could be provided by a connection to the electricity grid. However, microalgae are often cultivated in remote areas where an independent power supply may be advantageous. On the other hand, some cultivation systems may have limited amounts of land available for cultivation. In this situation, co-locating the solar array and the algae ponds would result in an increased growth. Additionally there are some other benefits from filtering the light before it is incident upon the algae. The removal of the parts of the spectrum not required by the algae would reduce the heating and evaporation from the algae pond.blackbox filters. This hypothetical filter allows the transmitted light through to the algae and used the remainder to generate electricity using either a highly efficient crystalline silicon solar cell or an amorphous silicon solar cell. Using this system up to 151 W.m−2 of electrical power can be produced. Introducing a method of cogeneration of electrical energy has benefits in the often remote areas microalgae cultivation occurs. This can reduce the costs associated with production, dewatering and extraction of oil from microalgae. This allows for the cheaper and more efficient production of biofuel or value added crops in remote locations which are located away from sources of electrical power. Additionally, we have shown that the total amount of useable PAR incident on an algae pond can be increased by introducing a filter system above an algae pond that directs part of the light to the algae and part to a highly efficient crystalline silicon solar cell and using the generated electricity to produce additional targeted PAR. This can result in a total available PAR of 177 W.m−2 which can be used to increase the productivity and value of algae cultivation.Whilst other factors can influence actual productivity, photosynthesis stipulates the potential upper limit on the effectiveness with which solar energy can be transformed into stored chemical energy (i.e. biofuel). As such, the solar spectrum is the ultimate source of all biomass production. Solar panels have also been recognised as a potential electrical energy production system. By combining two energy production systems we can fully utilize the solar spectrum and light incident on a surface. This would allow both the production of biofuel and electricity from the one facility making efficient use of available land. We propose introducing a filter above the algae pond that will allocate the incident illumination to different purposes. We have modelled this by using commercially available lighting filters as The authors declare that they have no competing interests.DP and NM jointly developed the model and conceptual framework for the distribution of solar radiation between microalgae and photovoltaics. DP performed numerical modelling and drafted the manuscript. NM contributed specifically in the area of biology and photosynthesis. Both authors read and approved the final manuscript.


We report a model for atomic force microscopy by means of computer simulations of molecular brushes on surfaces of biological interest such as normal and cancerous cervical epithelial cells. Our model predicts that the force needed to produce a given indentation on brushes that can move on the surface of the cell  is the same as that required for brushes whose ends are fixed on the cell’s surface , as long as the tip of the microscope covers the entire area of the brush. Additionally, we find that cancerous cells are softer than normal ones, in agreement with various experiments. Moreover, soft brushes are found to display larger resistance to compression than stiff ones. This phenomenon is the consequence of the larger equilibrium length of the soft brushes and the cooperative association of solvent molecules trapped within the brushes, which leads to an increase in the osmotic pressure. Our results show that a careful characterization of the brushes on epithelial cells is indispensable when determining the mechanical response of cancerous cells. The brushes we are interested in modeling are very large . Our model for the brush on normal cells is depicted in 34569h, than the stiff brushes. The liquid or solid nature of the brush is found to play a secondary role12345In the rest of this work we focus on brushes on cancerous cells only, taking advantage of the fact that the simulations allow one to have control over the softness and mobility of the brushes on the cell’s surface. The motion of the chains that make up the so called liquid brushes on the surface of the cell can be considerable, as Lsoft, i.e. its length when is not yet compressed by the AFM tip, is larger than that of the stiff brush, Lstiff, see snapshots in h/rc ≤ 5 and compared with the corresponding interval in To determine why soft brushes are harder to compress than stiff ones, we show in h/L < 0.9. Since the simulations show Lsoft > Lstiff, from Fsoft > Fstiff at a given value of h.in vitro, since it can enhance or reduce the brush thickness, just as it occurs with grafted polymers under good or theta solvent conditionsIn conclusion, our simulations show that the lack of uniformity in thickness of the brushes on epithelial cancerous cells is responsible for their softness in comparison with normal cells. Biological brushes such as those on the surfaces of cells, as well as proteins on membranes, can move on the surface of the cell or membrane. However, we have shown for the first time that if the area of the AFM tip probes the entire surface on which the brushes are mobile, then the AFM tip records the same force for liquid and for solid brushes. This conclusion is important for those workers carrying out research with colloidal—sized AFM probes; for nanometer—sized probes a smaller force is expect for liquid brushes because some of the chains can relieve pressure by moving out of the area of compression. Our calculations show that larger forces are needed to produce indentation in soft brushes than in stiff ones on cancerous cells because the former allow for the penetration of more solvent particles, increasing the osmotic pressure. This stresses the need for the careful consideration of the buffer in AFM experiments with cells κ =  100 (kBT/rc2). Stiff brushes on cancerous cells were modeled with spring constant κ=2000 (kBT/rc2); soft ones with κ = 100 (kBT/rc2). The area of the cells studied in all cases was A = 20.5 nm2; the radius of the AFM tip was chosen as R = 2.5 μm, and the distance range between it and the cell was 2.8 nm ≤ h ≤ 17.5 nm. The simulations were carried out using the Monte Carlo method, solved with the Metropolis algorithm, for a fluctuating number of solvent particles to keep the chemical potential fixed . Full details and additional analysis are presented in the The DPD model23How to cite this article: Gama Goicochea, A. and Alas Guardado S. J. Computer simulations of the mechanical response of brushes on the surface of cancerous epithelial cells. Sci. Rep.5, 13218; doi: 10.1038/srep13218 (2015).