Reward-modulated spike-timing-dependent plasticity (STDP) has recently emerged asa candidate for a learning rule that could explain how behaviorally relevantadaptive changes in complex networks of spiking neurons could be achieved in aself-organizing manner through local synaptic plasticity. However, thecapabilities and limitations of this learning rule could so far only be testedthrough computer simulations. This article provides tools for an analytictreatment of reward-modulated STDP, which allows us to predict under whichconditions reward-modulated STDP will achieve a desired learning effect. Theseanalytical results imply that neurons can learn through reward-modulated STDP toclassify not only spatial but also temporal firing patterns of presynapticneurons. They also can learn to respond to specific presynaptic firing patternswith particular spike patterns. Finally, the resulting learning theory predictsthat even difficult credit-assignment problems, where it is very hard to tellwhich synaptic weights should be modified in order to increase the global rewardfor the system, can be solved in a self-organizing manner throughreward-modulated STDP. This yields an explanation for a fundamental experimentalresult on biofeedback in monkeys by Fetz and Baker. In this experiment monkeyswere rewarded for increasing the firing rate of a particular neuron in thecortex and were able to solve this extremely difficult credit assignmentproblem. Our model for this experiment relies on a combination ofreward-modulated STDP with variable spontaneous firing activity. Hence it alsoprovides a possible functional explanation for trial-to-trial variability, whichis characteristic for cortical networks of neurons but has no analogue incurrently existing artificial computing systems. In addition our modeldemonstrates that reward-modulated STDP can be applied to all synapses in alarge recurrent neural network without endangering the stability of the networkdynamics. A major open problem in computational neuroscience is to explain how learning,i.e., behaviorally relevant modifications in the central nervous system, can beexplained on the basis of experimental data on synaptic plasticity.Spike-timing-dependent plasticity (STDP) is a rule for changes in the strengthof an individual synapse that is supported by experimental data from a varietyof species. However, it is not clear how this synaptic plasticity rule canproduce meaningful modifications in networks of neurons. Only if one takes intoaccount that consolidation of synaptic plasticity requires a third signal, suchas changes in the concentration of a neuromodulator , then meaningful changes in thestructure of networks of neurons may occur. We provide in this article ananalytical foundation for such reward-modulated versions of STDP that predictswhen this type of synaptic plasticity can produce functionally relevant changesin networks of neurons. In particular we show that seemingly inexplicableexperimental data on biofeedback, where a monkey learnt to increase the firingrate of an arbitrarily chosen neuron in the motor cortex, can be explained onthe basis of this new learning theory. Thiseffect is called spike-timing-dependent plasticity (STDP). But a major puzzle forunderstanding learning in biological organisms is the relationship betweenexperimentally well-established rules for STDP on the microscopic level, andadaptive changes of the behavior of biological organisms on the macroscopic level.Neuromodulatory systems, which send diffuse signals related to reinforcements(rewards) and behavioral state to several large networks of neurons in the brain,have been identified as likely intermediaries that relate these two levels ofplasticity. It is well-known that the consolidation of changes of synaptic weightsin response to pre- and postsynaptic neuronal activity requires the presence of suchthird signals Numerous experimental studies  is an eligibility traceof this synapse which collects weight changes proposed by STDP, andd(t) = h(t)−h̅results from a neuromodulatory signal h(t) withmean value h̅. It was shown in Corresponding spike-based rules for synaptic plasticity of the formd(t)which is transmitted to all synapses between excitatory neurons in the networkwhenever the first neuron fired, and decreased this reward signal whenever thesecond neuron fired (the resulting composed reward corresponds to the displacementof the meter arm that was shown to the monkey in these more complex operantconditioning experiments).We also provide a model for the remarkable operant conditioning experiments of Our theory and computer simulations also show that reward-modulated STDP can beapplied to all synapses within a large network of neurons for long time periods,without endangering the stability of the network. In particular this synapticplasticity rule keeps the network within the asynchronous irregular firing regime,which had been described in W(Δt) of the synaptic weight of anexcitatory synapse in dependence on the time differenceΔt = postt−pretbetween the firing times pret andpostt of the pre- and postsynaptic neuron, is basedon numerous experimental data are collected in an eligibility tracejic(t) at the site of the synapse. Thecontribution to ijc(t) of all spikepairings with the second spike at timet−s is modeled fors>0 by a functioncf(s) (see ji at time t isgiven byt for reward-modulated STDP is theproductijc(t)·d(t)of the eligibility trace with the reward signald(t) as defined by Equation 1. Since this simplemodel can in principle lead to unbounded growth of weights, we assume that weightsare clipped at the lower boundary value 0 and an upper boundarymaxw.The model analyzed in this article is based on the assumption that positive andnegative weight changes suggested by STDP for all pairs of pre- and postsynapticspikes at synapse c(s) see ; the timThe network dynamics of a simulated recurrent network of spiking neurons where allconnections between excitatory neurons are subject to STDP is quite sensitive to theparticular STDP-rule that is used. Therefore we have carried out our networksimulations not only with the additive STDP-rule in Equation 3, whose effect can beanalyzed theoretically, but also with the more complex rule proposed in jiw over some sufficiently long time intervalT to statistical properties of the joint distribution ofthe reward signal d(t) and pre- andpostsynaptic firing times, under the assumption that the weight and correlationsbetween pre- and postsynaptic spike times are slowly varying in time. We treatspike times as well as the reward signal d(t)as stochastic variables. This mathematical framework allows us to derive theexpected weight change over some time interval T  = 〈jS(t)iS(t−r)〉E describes correlations between spike timings of neuronsj and i, i.e., it is the probability densityfor the event that neuron i fires an action potential at timet−r and neuronj fires an action potential at time t. Forsynapses subject to reward-modulated STDP, changes in efficacy are obviouslydriven by co-occurrences of spike pairings and rewards within the time scale ofthe eligibility trace. Equation 6 clarifies how the expected weight changedepends on how the correlations between the pre- and postsynaptic neuronscorrelate with the reward signal.In this section, we derive a learning equation for reward-modulated STDP. Thislearning equation relates the change of a synaptic weightal T see ,with thelds see (6)This frd after the pairing, the weight update will beproportional to cf(rd)instead ofcf(rd+r).The approximation is justified if the temporal average is performed on a muchlonger time scale than the time scale of the learning window, the effect of eachpre-post spike pair on the reward signal is delayed by an amount greater thanthe time scale of the learning window, and cfchanges slowly compared to the time scale of the learning window (see d(t) = d0.Then also the reward correlation is constant and given byD = d0.We recover the standard STDP learning equation scaled byd0 if the eligibility function is aninstantaneous delta-pulsecf(s) = δ(s).Furthermore, if the statistics of the reward signald(t) is time-independent and independent fromthe pre- and postsynaptic spike statistics of some synapse ji,then the reward correlation is given byjiD = 〈d(t)〉E = d0 forsome constant d0. Then, the weight change forsynapse ji is jiνThe asThe learning Equation 8 provides the mathematical basis for our followinganalyses. It allows us to determine synaptic weight changes if we can describe alearning situation in terms of reward correlations and correlations between pre-and postsynaptic spikes.We now apply the preceding analysis to the biofeedback experiment of d(t). This enables us to calculate synapticweight changes for this particular scenario. We consider as model a recurrentneural circuit where the spiking activity of one neuron k isrecorded by the experimenter  is produced whichdepends on the visual feedback  as well as previously received liquid rewards, andthat this signal d(t) is delivered toall synapses in large areas of the brain. We can formalizethis scenario by defining a reward signal which depends on the spike rate of thearbitrarily selected neuron k (see rε(r) (thereward kernel) is produced with some delay rd everytime the neuron k produces an action potentiald(t) = h(t)−h̅is defined in Equation 1 as a signal with zero mean. In order to satisfy thisconstraint, we assume that the reward kernelrε has zero mass, i.e., k is thenapproximately This rate see . Howeverj≠k is given byjν(t) = 〈jS(t)〉E is the instantaneous firing rate of neuron j at timet. This equation indicates that a non-reinforced neuron istrained by STDP with a learning rate proportional to its correlation with thereinforced neuron given bykjν/jν(t−s).In fact, it was noted in j is uncorrelated withthe reinforced neuron k, we can decompose the joint firing rateintokjν = kν(t−rd−r′)jν(t−s).In this case, the learning rate for synapse ji is approximatelyzero . The circuit was composed of 4000 LIF neurons, with 3200 beingexcitatory and 800 inhibitory, interconnected randomly by 228954 conductancebased synapses with short term dynamics .At the middle of the simulation (simulation timet = 10 min), we changed thedirection of the reinforcements by negatively rewarding the firing of neuron Aand positively rewarding the firing of neuron B  predicts thatreward-modulated STDP affects in the long run only those excitatory synapseswhere the firing of the postsynaptic neuron is correlated with the rewardsignal. In other words: the reward signal gates the effect of STDP in arecurrent network, and thereby can keep the network within a given dynamicregime. This prediction is confirmed qualitatively by the two panels of The preceding model for the biofeedback experiment of Fetz and Baker focused onlearning of firing rates. In order to explore the capabilities and limitationsof reward-modulated STDP in contexts where the temporal structure of spiketrains matters, we investigated another reinforcement learning scenario where aneuron should learn to respond with particular temporal spike patterns. We firstapply analytical methods to derive conditions under which a neuron subject toreward-modulated STDP can achieve this.d(t) is givenin dependence on how well the output spike train j matches some rather arbitraryspike train S* .S* is produced by a neuronμ* that receives the same ninput spike trainsS1,…,nS asthe trained neuron j, with some arbitrarily chosen weights μ* receivesn′−n further spiketrainsnS+1,…,nS′with weights jw1,…,jnwmatch those of the neuron μ* for thosen input spike trains which both of them have in common. Thereward d(t) at time t dependsin this task on both the timing of action potentials of the trained neuron andspike times in the target spike train S*κ(r)with r between a postsynaptic spike and a target spike, andrd>0 is the delay of the reward.In this model, the reward signal ν* is the output rate of neuronμ*, ε(s), and Our theoretical analysis see predictsw* . To get an intuitiveunderstanding of these inequalities, we first examine the idea behind Constraint13. This constraint assures that weights of synapses i with iS with S*. In the linear Poisson neuron model, this leads toweight changes similar to STDP which can be described by two terms. First, allsynapses are subject to depression stemming from the negative part of thelearning curve W and random pre-post spike pairs. This weightchange is bounded from below by α. On theother hand, the positive influence of input spikes on postsynaptic firing leadsto potentiation of the synapse bounded from above by iwith S*. Therefore, the probability of a delayed rewardsignal after a presynaptic spike is larger. This additional drive leads topositive weight changes if Inequalities 14 and 15 are fulfilled  are important, since they may lead toreward signals that can be exploited by the learning rule. It is obvious that inreward-modulated STDP, a silent neuron cannot recover from its silent state,since there will be no spikes which can drive STDP. But in addition, Condition13 shows that in this learning scenario, the minimal output rate κε is adjusted accordingly.For example, instead of a standard STDP learning window W withW(r)≥0 forr>0 and W(r)≤0for r<0 and a corresponding reward kernelκ, one can use a reversed learning windowW′ defined byW′(r)≡W(−r)and a reward kernel κ′ such thatκε′(r) = κε(−r).If Condition 15 is satisfied for W andκ, then it is also satisfied forW′ and κ′ . This reflects the fact that inreward modulated STDP the learning window defines the weight changes incombination with the reward signal.Conditions 13–15 also reveal how parameters of the model influence theapplicability of this setup. For example, the eligibility trace enters theequations only in the form of its integral and its value at the reward delay inEquation 15. In fact, the exact shape of the eligibility trace is not important.The important property of an ideal eligibility trace is that it is high at thereward delay and low at other times as expressed by the fraction in Condition15. Interestingly, the formulas also show that one has quite some freedom inchoosing the form of the STDP window, as long as the reward kernelκ are suitable for this learning setup. FromCondition 15, we can deduce that the integral over κshould be small (but positive), whereas the integral W with W(r)≥0 forr>0 andW(r)≤0 for r<0,the convolutionκε(r) of the rewardkernel with the PSP should be positive for r>0 andnegative for r<0. In the computer simulation we used asimple kernel depicted in κt from the origin.The optimal offset κt is always negative andin the order of several milliseconds for usual PSP-shapesε. We conclude that for successful learning in thisscenario, a positive reward should be produced if the neuron spikes around thetarget spike or somewhat later, and a negative reward should be produced if theneuron spikes much too early.For a given STDP learning window, the analysis reveals what reward kernelsμ* which produced the target spike trainS* both received inputs from 100 input neuronsemitting spikes from a constant rate Poisson process of 15 Hz. The synapses tothe trained neuron were subject to reward-modulated STDP. The weights of neuronμ* were set to i<50 and i<100. In order tosimulate a non-realizable target response, neuronμ* received 10 additional synaptic inputs (withweights set to maxw/2). During the simulations weobserved a firing rate of 18.2 Hz for the trained neuron, and 25.2 Hz for theneuron μ*. The simulations were run for 2 hourssimulated biological time.In order to explore this learning scenario in a biologically more realisticsetting, we trained a LIF neuron with conductance based synapses exhibitingshort term facilitation and depression. The trained neuron and the neuronS* after learning, we performed additional simulationswhere the same spike input was applied to the trained neuron before and afterthe learning. Then we compared the output of the trained neuron before and afterlearning with the output S* of neuronμ*. S* which is accessible to itquite well. We performed 5 repetitions of the experiment, each time with different randomlygenerated inputs and different initial weight values for the trained neuron. Ineach of the 5 runs, the average synaptic weights of synapses with Both the theoretical results and these computer simulations demonstrate that aneuron can learn quite well through reward-modulated STDP to respond withspecific spike patterns.maxw, or for the learning of weightswith target value 0. Equations 13–15 predict under which relationships between theparameters involved the learning of particular spike responses throughreward-modulated STDP will be successful. We have tested these predictions byselecting 6 arbitrary settings of these parameters, which are listed in P andN of its presynaptic neurons, by responding with more spikes topattern P than to pattern N. Our analysis isbased on the assumption that there exist internal rewardsd(t) that could guide such patterndiscrimination. This reward based learning architecture is biologically moreplausible than an architecture with a supervisor which provides for each inputpattern a target output and thereby directly produces the desired firingbehavior of the neuron (since the question becomes then how the supervisor haslearnt to produce the desired spike outputs).We examine here the question whether a neuron can learn through reward-modulatedSTDP to discriminate between two spike patterns n presynapticneurons. A pattern X consists of n spiketrains, each of time length T, one for each presynaptic neuron.There are two patterns, P and N, which arepresented in alternation to the neuron, with some reset time betweenpresentations. For notational simplicity, we assume that each of then presynaptic spike trains consists of exactly one spike.Hence, each pattern can be defined by a list of spike times: i spikesfor pattern X∈{P,N}.A generalization to the easier case of learning to discriminate spatio-temporalpresynaptic firing patterns (where some presynaptic neurons produce differentnumbers of spikes in different patterns) is straightforward, however the maincharacteristics of the learning dynamics are better accessible in thisconceptually simpler setup. It had already been shown in spatial presynaptic firing patterns. But in the light ofthe analysis of temporal presynaptic firing patterns.We consider a neuron that receives input from d(t)rewards—after some delayrd—action potentials of the trained neuronif pattern P was presented, and punishes action potentials ofthe neuron if pattern N was presented. More precisely, weassume thatrεand constantsNα<0<Pα.The goal of this learning task is to produce many output spikes for patternP, and few or no spikes for pattern N.We assume that the reward signal i of the trained neuron for the presentation of patternP, followed after a sufficiently long timeT′ by a presentation of pattern NEX| is the expectation over the ensemblegiven that pattern X was presented. This weight change can beestimated as (see Xν(t)is the postsynaptic rate at time t for patternX, and the constants X∈{P,N} are given bycf(r) is non-negative, a naturalway to achieve this is to choose a positive reward kernelrε(r)≥0 forr>0 andrε(r) = 0for r<0  andrε(r) must not beidentical to zero for all r).The main result of our analysis is an estimate of the expected weight change ofsynapse d as see (17)whereP than for input pattern N. The reason is thateach presynaptic neuron emits the same number of spikes in both patterns (namelyone spike). This simple fact implies that it is impossible to train a linearPoisson neuron (with any learning method) to respond to patternP with more spikes than to pattern N. ButEquation 17 implies that reward-modulated STDP increases the variance of themembrane potential for pattern P, and reduces the variance forpattern N. This can be seen as follows. Because of the specificform of the STDP learning curve W(r), which ispositive for  positive r, negative for  negativer, and zero for large r, i if thepostsynaptic rate for pattern P is larger  shortly after the presynaptic spike at this synapsei than before that spike. This tends to further increasethe membrane potential after that spike. On the other hand, since Nhas a depressing effect on synapse i, which counteracts theincreased membrane potential after the presynaptic spike. Dually, if thepostsynaptic rate shortly after the presynaptic spike at synapsei is lower than shortly before that spike, the effect onsynapse i is depressing for pattern P. Thisleads to a further decrease of the membrane potential after that spike. In thesame situation for pattern N, the effect is potentiating, againcounteracting the variation of the membrane potential. The total effect on thepostsynaptic membrane potential is that the fluctuations for patternP are increased, while the membrane potential for patternN is flattened.We use Equation 17 to provide insight on when and how the classification oftemporal spike patterns can be learnt with reward-modulated STDP. Assume for themoment that P for these neuron models, while it tends to decrease thenumber of spikes for pattern N, thereby enabling adiscrimination of these purely temporal presynaptic spike patterns.For the LIF neuron model, and most reasonable other non-linear spiking neuronmodels, as well as for biological neurons in-vivo and in-vitro P and N, had 200input channels, with 1 spike per channel .The spike times were drawn from an uniform distribution over a time interval of500 ms, which was the duration of the patterns. We performed 1000 trainingtrials where the patterns P and N werepresented to the neuron in alternation. To introduce exploration for thisreinforcement learning task, the neuron had injected 20% of theOrnstein-Uhlenbeck process conductance noise  we could observe the membrane potential fluctuations undisturbed bythe reset mechanism after each spike (see P from 2.49(mV)2 to 5.43 (mV)2 (N (2 to 1.33 (mV)2. Thecorresponding plots with the firing threshold included are given in panels E andF, showing an increased member of spikes of the LIF neuron for patternP, and a decreased number of spikes for patternN. Furthermore, as P led to astable temporal firing pattern in response to pattern P.The theoretical analysis predicted that the membrane potential will have afterlearning a higher variance for pattern pike see . The var43 (mV)2 , and dec(mV)2  that we used in the computersimulations. Finally we provide technical details to each of the 5 computersimulations that we discussed in the preceding section.jR(t).The effect of a spike of presynaptic neuron i at timet′ on the membrane potential of neuronj is modeled by an increase in the instantaneous firing rate byan amountjiw(t′)ε(t−t′),where ε is a response kernel which models the timecourse of a postsynaptic potential (PSP) elicited by an input spike. Since STDPaccording to jiw≥0 for alli and ε(s)≥0for all s. Because the synaptic response is scaled by thesynaptic weights, we can assume without loss of generality that the responsekernel is normalized to S1,…,nS arethe n presynaptic spike trains. Since the instantaneous firingrate R(t) is analogous to the membranepotential of other neuron models, we occasionally refer toR(t) as the “membranepotential” of the neuron.In our theoretical analysis, we use a linear Poisson neuron model whose outputspike train xgiven that neuron k spikes at time t andneuron i spikes at time t′. We willalso sometimes indicate the variablesY1,Y2,…over which the average of x is taken by writing In the following, we denote by t and t+TjiD = 〈d(t)|Neuronj spikes att−s, and neuroni spikes att−s−r〉E, and the joint firing ratejiν = 〈jS(t)iS(t−r)〉E describes correlations between spike timings of neuronsj and i. The joint firing ratejiνdepends on the weight at timet−s. If the learning ratedefined by the magnitude of W(r) is small,the synaptic weights can be assumed constant on the time scale ofT. Thus, the time scales of neuronal dynamics are separatedfrom the slow time scale of learning. For slow learning, synaptic weightsintegrate a large number of small changes. We can then expect that averagedquantities enter the learning dynamics. In this case, we can argue thatfluctuations of a weight jiw about its mean arenegligible and it can well be approximated by its average〈jiw〉E  is vanishing for large|r|. Hence we can approximate the integral over thelearning window by a bounded integral WT>0 andWT≪T. In theanalyzes of this article, we consider the case where reward is deliveredwith a relatively large temporal delay. To be more precise, we assume that apre-post spike pair has an effect on the reward signal only after someminimal delay rd and that we can write d0and a part which depends on the timing of pre-post spike pairs with s<rd andrd>WT. Wecan then approximate the second term of Equation 6:jiν〉T≈〈jiν〉T forr∈and WT≪T. Since s≤WT, the second term inthe brackets is equivalent to cf(s+r)≈cf(s)for s≥rd and|r|<WT. We canthus approximate the second term of Equation 6 asIn order to simplify this equation, we first observe thatrε is delivered for each postsynaptic spikewith a delay rd. The reward as timet is thereforeWe assume that a reward with the functional formki afferent to thereinforced neuron is cf(s)≈cf(s−r′)and〈kiν〉T≈〈kiν〉T forr′∈.Here, WT is the time scale of the learning window(see above), and εT is time scale of thePSP, i.e., we have ε(s)≈0 fors≥εT. Since kiw. For neuronswith many input synapses we have kiw≪1. Thusthe second term in the brackets of Equation 20 is small compared to the firstterm. We therefore haveThe reward correlation for a synapse ji to a non-reinforcedneuron j is given byjν(t−s)in the denominator results from many PSPs. Hence, the single PSPjiεw(r)is small compared tojν(t−s).Similarly, we assume that with weights kiw,jiw≪1, the second term in thenominator is small compared to the joint firing ratekjν.We therefore approximate the reward correlation byj≠kis thereforejν(t−s)is zero, since it appears in the denominator of the fraction. Note that in thiscase, bothkjνandjiνare zero. In fact, if we take the limitjν(t−s)→0,then both of these factors approach zero at least as fast. Hence, in the limitofjν(t−s)→0,the term in the angular brackets evaluates to zero. This reflects the fact thatsince STDP is driven by pre- and postsynaptic spikes, there is no weight changeif no postsynaptic spikes occur.The reward correlation of a synapse k, j,kjνcan be factorized intokν(t−rd−r′)jν(t−s),and we obtaink is constant on the time scale of the rewardkernel.For uncorrelated neurons Y1,Y2,…over which the average of x is taken by writing it, andν*(t) = 〈S*(t)〉E denotes the instantaneous rate of the target spike train at timet. Since weights are changing very slowly, we havejiw(t−s−r)≈jiw(t).In the following, we will drop the dependence of jiwon t for brevity. For simplicity, we assume that input ratesare stationary and uncorrelated. In this case (since the weights are changingslowly), also the correlations between inputs and outputs can be assumedstationary,jiν = jiν(r).With constant input rates, we can rewrite Equation 21 asji. With stationary correlations, we candrop the dependence of jiν ont and writejiν = jiν(r).Furthermore, we define cf(rd)≈cf(rd+r)if |r| is on the time scale of a PSP, the learning window, orthe reward kernel, and that rd is large compared tothese time scales. Then, we havejiBelow, we will indicate the variablesji is thenFor uncorrelated Poisson input spike trains of rate jiwith jk with i with jiw ismaxw and jiw = maxw,this inequality is fulfilled. This could be guaranteed by some noise current.Given such minimal output rate, we can state the first inequality whichguarantees convergence of weights jiw with ji with w*. The secondcondition is less severe, and should be easily fulfilled in most setups. If thisis the case, the first Condition 13 ensures that weights withw* = 0 are depressedwhile the third Condition 15 ensures that weights withw* = maxware potentiated.We will now bound the expected weight change for synapses t = 0. We compute theweight change for a single trial given that patternX∈{P,N} waspresented with the help of Equations 1, 3, and 4 asX was presented:cf is approximatelyconstant on the time scale of the learning window W, we cansimplify this toXν(t) = 〈postS(t)〉EX| is the ensemble average rate at timet given that pattern X was presented. Ifan experiment for a single pattern runs over the time interval, we can compute thetotal average weight change X was presented asWe assume that a trial consists of the presentation of a single pattern startingat time We describe here the models and parameter values that were used in all ourcomputer simulations. We will specify in a subsequent section the values ofother parameters that had to be chosen differently in individual computersimulations, in dependence of their different setups and requirements of eachcomputer simulation.mV(t)of this neuron model is given by:mC is the membrane capacitance,mR is the membrane resistance,restingV is the resting potential, andegj,(t)andigj,(t)are the eK and iKsynaptic conductances from the excitatory and inhibitory synapses respectively.The constants eE and iEare the reversal potentials of excitatory and inhibitory synapses.noiseI represents the synaptic backgroundcurrent which the neuron receives (see below for details).For the computer simulations LIF neurons with conductance-based synapses wereused. The membrane potential threshV, the neuron produces a spike, and itsmembrane potential is reset to the value of the reset potentialresetV. After a spike, there is a refractoryperiod of length refractT, during which the membranepotential of the neuron remains equal to the valuemV(t) = resetV.After the refractory period mV(t)continues to change according to Equation 24.Whenever the membrane potential reaches a threshold valueg(t) is defined byA(t) is the amplitude ofthe postsynaptic response (PSR) to a single presynaptic spike, which varies overtime due to the inherent short-term dynamics of the synapse, and{tk)whenever the presynaptic neuron spikes.For a given synapse, the dynamics of the synaptic conductancemR = 100MΩ, the membrane capacitancemC = 0.3 nF, theresting potential, reset potential and the initial value of the membranepotential had the same value ofrestingV = resetV = mV(0) = −70mV, the threshold potential was set tothreshV = −59mV and the refractory periodrefractT = 5 ms.For the synapses we used a time constant set tosynτ = 5ms, reversal potentialeE = 0 mV for theexcitatory synapses andeE = −75mV for the inhibitory synapses. All synapses had a synaptic delay ofdelayt = 1ms.In all computer simulations we used the following values for the neuron andsynapse parameters. The membrane resistance of the neurons waskA = A(kt+delayt)of the postsynaptic response for the kth spike in a spike trainwith inter-spike intervals Δ1,Δ2,…,Δk−1 is calculated with the following equationsu∈ andR∈ whose initial values for the1st spike areu1 = Uand R = 1  andig(t) are time-dependentexcitatory and inhibitory conductances. The values of the respective reversalpotentials wereeE = 0 mV andiE = −75mV. The conductances eg(t) andig(t) were modeledaccording to eg0 = 0.012µS, noise-diffusion constanteD = 0.003µS and time constanteτ = 2.7ms for the excitatory conductance, and meanig0 = 0.057µS, noise-diffusion constantiD = 0.0066µS, and time constantiτ = 10.5ms for the inhibitory conductance.χ1(t) andχ2(t) are Gaussian white noiseof zero mean and unit standard deviation.To reproduce the background synaptic input cortical neurons receive in vivo, theneurons in our models received an additional noise process as conductance input.The noise process we used is a point-conductance approximation model, describedin N1 andN2 are normal random numbers  and eA,iA are amplitude coefficients given by:Since these processes are Gaussian stochastic processes, they can be numericallyintegrated by an exact update rule:W(r):A+ = 0.01maxw,A−/A+ = 1.05,τ+ = τ− = 30ms. maxw denotes the hard bound of the synapticweight of the particular plastic synapse. Note that the parameterA+ can be given arbitrary value in thisplasticity rule, since it can be scaled together with the reward signal, i.e.multiplying the reward signal by some constant and dividingA+ by the same constant results inidentical time evolution of the weight changes. We have setA+ to be 1% of the maximumsynaptic weight.For the computer simulations we used the following parameters for the STDP windowfunction α-function to model the eligibility tracekernel cf(t)eτwas set toeτ = 0.4 sin all computer simulations.We used the μ = 0.4,α = 0.11,τ+ = τ− = 20ms. The w0 parameter was calculated according to theformula: maxw is the maximum synapticweight of the synapse. For computer simulations 1 and 4 we performed control experiments see  with themaxw/2. The standard deviation was set tomaxw/10 bounded within the range.The synaptic weights of excitatory synapses to the trained neurons in experiments2–5 were initialized from a Gaussian distribution with meanhttp://www.lsm.tugraz.at/pcsim). PCSIM is a parallel simulatorfor biologically realistic neural networks with a fast c++simulation core and a Python interface. It has been developed by ThomasNatschläger and Dejan Pecevski. The time step of simulation was set to0.1 ms.All computer simulations were carried out with the PCSIM software package. Each of the computersimulations in this article modeled a specific task or experimental finding.Consequently, the dependence of the reward signal on the behavior of the systemhad to be modeled in a specific way for each simulation  received downscaled OU noise , sincefor learning the classification of temporal patterns the temporal variation ofthe voltage of the postsynaptic membrane turns out to be of critical importance(see the discussion after Equation 17).This temporal variation depends less on the shape of a single EPSP and more onthe temporal pattern of presynaptic firing when the number of synapses isincreased. In computer simulation 5 the readout neuron received inputs from all432 excitatory neurons in the circuit. The synaptic weights were chosen inaccordance with the number of synapses in order to achieve a firing ratesuitable for the particular task, and to balance the synaptic input and thenoise injections in the neurons.w* = 0 synapses do notconverge to 0. If the noise is too strong,w* = maxwsynapses do not converge to maxw. To achieve thedesired learning result, the noise level should be in a range where it reducesthe correlations of the synapses withw* = 0 so that thedepression of STDP will prevail, but at the same time is not strong enough to dothe same for the other group of synapses withw* = maxw,since they have stronger pre-before-post correlations. For our simulations, wehave set the noise level to the full amount of OU noise.For the pattern discrimination task (computer simulation 4) and the speechrecognition task (computer simulation 5), the amount of noise had to be chosento be high enough to achieve sufficient variation of the membrane potential fromtrial to trial near the firing threshold, and low enough so that it would notdominate the fluctuations of the membrane potential. In the experiment where theexact spike times were rewarded (computer simulation 2), the noise had adifferent role. As described in the eep = 0.02,eip = 0.02,iep = 0.024and iip = 0.016where the ee, ei, ie, ii indices designate the type of the presynaptic andpostsynaptic neurons (e = excitatory ori = inhibitory). For the other neurons thecorresponding connection probabilities were downscaled by 0.4. The resultingfiring rates and correlations for both types of excitatory neurons are plottedin The cortical microcircuit model consisted of 4000 neurons with twenty percent ofthe neurons randomly chosen to be inhibitory, and the others excitatory. Theconnections between the neurons were created randomly, with differentconnectivity probabilities depending on whether the postsynaptic neuron receivedthe full amount of OU noise, or downscaled OU noise with an additionalcompensatory synaptic input from the circuit. For neurons in the lattersub-population, the connection probabilities wererε(t) was chosen as adifference of two α-functionsα-pulse with a peak at 0.4sec after the corresponding spike, and one long-tailed negativeα-pulse which makes sure that the integral over thereward kernel is zero. The parameters for the reward kernel were rd = 0.2 s, whichproduced a peak value of the reward pulse 0.4 s after the spike that causedit.The shape of the reward kernelκ(r)κt defines theoffset of the zero-crossing from the origin. The parameter values used in oursimulations were κt = −1ms. The reward delay was equal tord = 0.4 s.We used the following function for the reward kernelmaxw. The input spike trains were Poisson processeswith a constant rate ofprer = 6 Hz, exceptin experiment # 6 where the rate wasprer = 3 Hz. Theweights of the target neuron were set to i<50 and i<100.We used a linear Poisson neuron model as in the theoretical analysis with staticsynapses and exponentially decaying postsynaptic responses κt was always set to an optimalvalue such that the τ− of the negative part of theSTDP window function W(r) was set toτ+. The reward signal wasdelayed bydτ = 0.4 s.The simulations were performed for varying durations of simulated biologicaltime  wasτ = 100 ms.The pulses in the reward were delayedrd = 300 msfrom the spikes that caused them.We performed 2000 training trials, where for each trial a spikerepresentation of a randomly chosen utterance out of 10 utterances for onedigit was injected into the circuit. The digit changed from trial to trial.Whenever the readout neuron spiked during the presentation of an utteranceof digit “two”, a positive pulse was generated in thereward signal, and accordingly, for utterances of digit“one”, a negative pulse in the reward was generated. Weused the reward signal from Equation 16. The amplitudes of the positive andnegative pulses wereThe cortical microcircuit model consisted of 540 neurons with twenty percentof the neurons randomly chosen to be inhibitory, and the others excitatory.The recurrent connections in the circuit were created randomly with aconnection probability of 0.1. Long-term plasticity was not modeled in thecircuit synapses.eτ = 3ms and amplitudeinputw = 0.715nA.The synapses for the connections from the input neurons to the circuitneurons were static, current based with axon conduction delay of 1 ms, andexponentially decaying PSR with time constantWe have presented in this article analytical tools which make it possible to predictunder which conditions reward-modulated STDP will achieve a given learning goal in anetwork of neurons. These conditions specify relationships between parameters andauxiliary functions  that are involved in the specification of the reward-modulated STDP learningrule. Although our analytical results are based on some simplifying assumptions, wehave shown that they predict quite well the outcomes of computer simulations ofquite complex models for cortical networks of neurons.We have applied this learning theory for reward-modulated STDP to a number ofbiologically relevant learning tasks. We have shown that the biofeedback result ofFetz and Baker how fast aneuron can learn to produce a desired temporal output pattern. An interesting aspectof Whereas this learning task focused on firing rates, we have also shown see  that neuWe have also addressed the question to what extent neurons can learn viareward-modulated STDP to respond with different firing rates to differentspatio-temporal presynaptic firing patterns. It had already been shown in P, it automatically started to respond to this patternP with a specific temporal spike pattern, that advanced in timeduring training  which guaranteed successfullearning. For example, in the biofeedback learning scenario (d(t). The shape of this change was definedby the reward kernel ε(r). Our analysisrevealed that this reward kernel can be chosen rather arbitrarily as long as theintegral over the kernel is zero, and the integral over the product of the kerneland the eligibility function is positive. For another learning scenario, where thegoal was that the output spike train j approximates the spike timingsof some target spike train S* . Our analysis showed that thereward kernel has to be chosen for this task so that the synapses receive positiverewards if the postsynaptic neuron fires close to the time of a spike in the targetspike train S* or somewhat later, and negative rewards whenan output spike occurs in the order of ten milliseconds too early. In the patterndiscrimination task of rε. There are currently no dataavailable on the shape of reward kernels in biological neural systems. The previoussketched theoretical analysis makes specific prediction for the shape of rewardkernels  which can potentially be tested through biological experiments.The new learning theory for reward-modulated STDP will also be useful for biologicalexperiments that aim at the clarification of details of the biologicalimplementation of synaptic plasticity in different parts of the brain, since itallows to make predictions which types and time courses of signals would be optimalfor a particular range of learning tasks. For each of the previously discussedlearning tasks, the theoretical analysis provided conditions on the structure of thereward signal scenario , every atrain S* , the rewAn interesting general aspect of the learning theory that we have presented in thisarticle is that it requires substantial trial-to-trial variability in the neuralcircuit, which is often viewed as “noise” of imperfectbiological implementations of theoretically ideal circuits of neurons. This learningtheory for reward-modulated STDP suggests that the main functional role of noise isto maintain a suitable level of spontaneous firing , which should vary from trial totrial in order to explore which firing patterns are rewarded Click here for additional data file.Figure S2Variations of (0.06 MB PDF)Click here for additional data file.Figure S3μ = 0.4,α = 0.11,τ+ = τ− = 20ms, λ = 0.1 andw0 = 272.6pS. The w0 parameter was calculated according tothe formula: maxw is the maximumsynaptic weight of the synapse. The amplitude parameters Variation of (0.09 MB PDF)Click here for additional data file.Figure S4Variation of (0.06 MB PDF)Click here for additional data file.Figure S5ετ = 5ms. The value of the maximum synaptic weight wasmaxw = 32.9 pA.All other parameter values were the same as in computer simulation 2.Variation of (0.17 MB PDF)Click here for additional data file.Figure S6w of the trained neuron at the end of the simulation andthe weight vector w* of the neuronμ*) is taken as measure for the learningperformance, and plotted for 9 simulations with different noise levels thatare given on the X axis (in term of multiples of the noise level chosen forDependence of the learning performance on the noise level in computersimulation 2. The angular error (defined as the angle between the weightvector (0.02 MB PDF)Click here for additional data file.Figure S7μ = 0.4,α = 0.11,τ+ = τ− = 20ms, λ = 0.1 andw0 = 72.4pS. The w0 parameter was calculated according tothe formula: maxw is the maximumsynaptic weight of the synapse. The amplitude parameters of the rewardkernel were set toPα = −Nα = 1.401.All other parameter values were the same as in computer simulation 4. Thevariance of the membrane potential increased for pattern Pfrom 2.35 (mV)2 to 3.66 (mV)2 (C), and decreased forpattern N (D), from 2.27 (mV)2 to 1.54(mV)2.Variation of (0.31 MB PDF)Click here for additional data file.Figure S8ετ = 5ms. The value of the maximum synaptic weight wasmaxw = 106.2 pAAll other parameter values were the same as in computer simulation 4. Thevariance of the membrane potential increased for pattern Pfrom 2.84 (mV)2 to 5.89 (mV)2 (C), and decreased forpattern N (D), from 2.57 (mV)2 to 1.22(mV)2.Variation of (0.31 MB PDF)Click here for additional data file.Figure S9ετ = 5ms. The synaptic weights of the excitatory and inhibitory synapses in thecortical microcircuit were set toexcw = 65.4 pAand inhw = 238pA respectively. The maximum synaptic weight of the synapses to the readoutneuron wasmaxw = 54.3 pA.All other parameter values were the same as in computer simulation 5.Variation of (0.27 MB PDF)Click here for additional data file.Figure S10Spike encodings of 10 utterances of digit “one” by onespeaker with the Lyon cochlea model (0.05 MB PDF)Click here for additional data file.Figure S11Spike encodings of 10 utterances of digit “two” by onespeaker with the Lyon cochlea model (0.05 MB PDF)Click here for additional data file.


Buccinum tenuissimum shell was explored to evaluate the efficiency of shell biomass as sorbent for REEs. In this work, four kinds of sieved shell samples: (a) “Ground original sample”, (b) “Heat-treatment  sample”, (c) “Heat-treatment  sample” and (d) “Heat-treatment  and water added sample” were used. Furthermore, to confirm the characteristics of the shell biomass, the crystal structure, the surface morphology, and the specific surface area of these shell samples were determined. Consequently, the following matters have been mainly clarified. (1) The crystal structure of the shell biomass was transformed from aragonite (CaCO3) into calcite (CaCO3) phase by heat-treatment ; then mainly transformed into calcium oxide (CaO) by heat-treatment , and calcium hydroxide (Ca(OH)2) by heat-treatment  and adding water. (2) The shell biomass showed excellent sorption capacity for lanthanides. (3) Adsorption isotherms using the shell biomass can be described by Langmuir and Freundlich isotherms satisfactorily for lanthanides except “heat-treatment  sample”. (4) Shell biomass  can be an efficient sorbent for lanthanides in future.Biosorption experiment from aqueous solutions containing known amount of rare earth elements (REEs) using pre-treated  Rare earth elements (REE) have gained considerable attention owing to their unique properties and a wide range of applications –4. TheseBiosorption studies using various low-cost biomasses as adsorbents have been widely performed for the removal of heavy metals from aquatic effluent in large parts of the world recently –19. HoweBuccinum tenuissimum shell biomass has been performed recently [In our research, the objective elements are mainly rare earth elements (REEs) and uranium (U) from the viewpoint of resources recovery, although REEs do not represent a common toxic threat. In a previous paper , we carrrecently . ConsequBuccinum tenuissimum were also used for comparison in present work. Furthermore, the effect of competitive ion on uptake potential of REEs was also studied using original sample to investigate the efficiency of seaweed biomass as sorbent for REEs for more practical use. Among REEs, lanthanides  were selected in this study, and sorption isotherms of lanthanides were analyzed using Langmuir and Freundlich equations. Moreover, to evaluate the characteristics of the shell biomass used in this work, the crystal structure, the surface morphology, and the specific surface area of the biomass (four kinds of sieved shell samples) were determined by XRD (X-ray powder diffraction), by SEM (Scanning Electron Microscope), and by BET  and Langmuir method, respectively.In addition to ground original sample and heat-treatment  sample used in our preliminary work , heat-tr−3 5% HNO3 solution) purchased from SPEX CertiPrep, Inc. (USA). All other chemical reagents were purchased from Kanto Chemical Co., Inc. (Japan). All reagents used were of analytical grade, and water  which was treated by an ultrapure water system  was employed throughout the work. Lanthanides standard solutions used for making the calibration curve were prepared by diluting the multielement standard solutions  gas was used to determine the adsorption isotherms. The crystal structure and the surface morphology of biomass were determined by X-ray powder diffraction  and by SEM , respectively. The measurement of pH in solution was carried out using a pH meter .An ICP-MS instrument  was employed to determine the concentration of REEs. The operating condition of ICP-MS is shown in Buccinum tenuissimum shellfish samples used for shell biomass in this work were collected at fshermen's cooperative association on the coast of Niigata Prefecture, Japan in June, 2008. After being separated from the meat by boiling, organism shells were washed thoroughly with ultrapure water after being washed with tap water repeatedly. Afterwards, dried overnight in an electric drying oven  at 60°C, the biomass was ground and sieved through a sieve (SANPO Test Sieves) to remove particles having size more than 600 μm. Afterwards, a part of this sieved materials was heated for 6 hours at 480°C or 950° C in an electric furnace . Moreover, adequate ultrapure water was added to a part of heat-treatment  samples that were heated at 100°C on a hotplate for evaporation to near dryness (removing water) and finally dried in an electric drying oven at 60°C. Based on the above-mentioned procedure, four kinds of sieved samples: (a) ground original sample, (b) heat-treatment  sample, (c) heat-treatment  sample, and (d) heat-treatment  and water-added sample have been prepared for sorption experiments of lanthanides in this work. Buccinum tenuissimum shell biomass. Each sample of 0.2 g was contacted with 100 cm3 of multielement standard solution (prepared by XSTC-1) including known initial lanthanide concentration (10 to 500 μg · dm−3) in a 200 ml conical flask. Afterwards, the suspensions were shaken for 30 minutes in a water bath at room temperature (25°C) at pH 5. Experimental conditions  in this work were determined based on our preliminary experiments [−3HNO3/0.1 mol·dm−3 NH3aq. Following with each sorption experiment, the suspension containing biomass and lanthanides standard solution was filtered through a 0.10 μm membrane filter  to remove lanthanides that have been adsorbed into the shell, and the concentration of these metals in the filtrate was determined with an ICP-MS.The following sorption experiments were performed using eriments . The pH μg·dm−3based on preliminary experiments [3 of lanthanide solution under the presence of calcium (Ca), magnesium (Mg), sodium (Na), and potassium (K) ion at different concentrations 50, 100, and 200 mg·dm−3. Other experimental conditions and methods were basically the same as that mentioned above in μm membrane filter, the matrix in the filtration was removed using chelate disk (47 φmm) (Empore Sumitomo 3M Co.) according to the procedure of Takaku et al. [The effect of competitive ion on the sorption of lanthanides was studied as the following experiment. In this experiment, the initial lanthanides concentration was taken as 100 eriments . In a 20u et al. , and theThe uptake of lanthanides by each sample was calculated using the following mass balance equation :q = metal uptake (mg · g−1); Co= initial metal concentration (μg·dm−3); Ce= final (after sorption at equilibrium) metal concentration (μg·dm−3); V= volume of the solution (cm3); and W= dry weight of each sample (g).μg·dm−3 under optimized condition of pH, contact time, and biosorbent dosage in this work. The adsorption data obtained for lanthanides were analyzed using Freundlich and Langmuir equations.Adsorption isotherms of sorption data were studied at varying initial concentration from 10 to 500 Two common adsorption model, Langmuir and Freundlich isotherm model was applied based on Dahiya et al. , 14 to eLangmuir model assumes monolayer sorption onto a surface and is given byCe (mg·dm−3) is the concentration of metal ion at equilibrium in the aqueous solution, qe(mg · g−1) is the amount of adsorption at equilibrium, a (mg · g−1) is the maximum adsorption capacity, and b (dm3 · mg−1) is the equilibrium adsorption constant (Langmuir constant) [Ce/qe versus Ce gives a straight line with slope of1/a, and intercept is 1/(ab); b can be related to the adsorption free energy ∆G ads (J · mol−1) by onstant) , 25. A p−1 · mol−1), T is the absolute temperature (K) at equilibrium.b) can be used to determine the suitability of the adsorbent to adsorbate by using dimensionless parameter, Hall separation factor (RL) [The Langmuir constant (or (RL) , which iC0(mg·dm−3) is the initial concentration. The slope of the linearized Langmuir isotherm can be used to interpret the type of sorption using the value of RL as follows: RL < 0 unfavorable; RL > 1 unfavorable; RL = 1 favorable; RL < 1 favorable; 0 <  RL = 0 irreversible. On the other hand, Freundlich isotherm can also be used to explain adsorption phenomenon as given below:KF and 1/n indicate the adsorption capacity and the adsorption intensity of the system, respectively. It is shown that 1/n values between 0.1 and 1.0 correspond to beneficial adsorption. The linearized Freundlich model isotherm is represented by 10 qe versus log 10 Ce gives a straight line with slope of 1/n and intercept islog 10 KF.Buccinum tenuissimum shell biomass samples are shown in 3) into calcite (CaCO3) phase by heat treatment . Moreover, the crystal structure of the shell biomass was mainly transformed into calcium oxide (CaO) by heat treatment  and was mainly transformed into calcium hydroxide (Ca(OH)2) by adding water after heat treatment . X-ray powder diffraction (XRD) patterns of the four kinds of μm) was observed in (d) heat-treatment  and water-added sample. SEM pictures of the four kinds of sieved shell biomass samples: (a) ground original sample, (b) heat-treatment  sample, (c) heat-treatment  sample, and (d) heat-treatment  and water-added sample are shown in 2/g to 0.390 m2/g for BET, or from 5.35 m2/g to 0.612 m2/g for Langmuir) was found after heat treatment . It is suggested that the crystal structure transformation  into calcite (CaCO3) phase) and also the difference of the surface morphology can be closely related to the remarkable decrease of specific surface area of the shell biomass. On the other hand, the surface area of heat-treatment  sample was 1.88 m2/g for BET or 3.10 m2/g for Langmuir, respectively, and that of “heat-treatment  and water-added sample” was 6.37 m2/g for BET or 9.91 m2/g for Langmuir, respectively.Furthermore, the measurement of specific surface area of the four kinds of sieved samples was performed in this study; and the results are shown in  Buccinum tenuissimum shell samples is shown in μg · dm−3. From this figure, it is found that all kinds of sieved samples showed excellent sorption capacity under this experimental condition. However, the sorption capacity in sample (b)  decreases slightly relative to that of the original material  the main phase is aragonite) and others. The decrease of sorption capacity in sample (b) may be attributable to the remarkable decrease  of specific surface area of the biomass. The comparison for sorption capacity of lanthanides by four kinds of sievedPrieto et al.  pointed 2+, Mg2+, Na+, and K+) at different concentrations 50, 100, and 200 mg · dm−3 is shown in −3, the percentage removal of light REE (LREE) such as La or Ce decreased slightly (2–3%) whereas the removal decreased about 5% for heavy REE (HREE) such as Yb or Lu. This implies that the shell biomass can be an efficient adsorbent for lanthanides in aqueous environment such as seawater, although it requires further investigations to apply the shell biomass to use as an adsorbent for lanthanides more practically.The percentage removal of REEs under the presence of common ions (CaX-ray diffraction (XRD) patterns of four kinds of sieved samples after adsorption of metals are shown in 2) and calcite (CaCO3) after exposing metals and that of (d) heat-treatment (950°C) and water added sample was transformed from calcium hydroxide(Ca(OH)2) to calcite (CaCO3) after adsorption of metals. These changes may be due to the reaction with water or carbon dioxide in atmosphere. Moreover, according to XRD analysis, the main crystal structure of (c) heat-treatment (950°C) sample was transformed from calcium oxide (CaO) to the mixture of calcium hydroxide (Ca(OH)SEM pictures of the shell biomass after adsorption of metals are shown in μm) was observed in sample (b) even after adsorption of metal. In case of Cd conducted by Kohler et al. [In contrast to sample (a), clear crystal structure  and (d) after exposing metals have changed largely compared to that before adsorption of metals . This isBuccinum tenuissimum shell biomass were analyzed using Langmuir and Freundlich equations. The adsorption data obtained for lanthanides using R2) of Langmuir and Freundlich isotherms for lanthanides using ground original shell biomass is shown in R2 value for lanthanides is comparatively high. It indicates the applicability of these adsorption isotherms satisfactorily for lanthanides in this sample. The dimensionless parameter Hall separation factor (RL) for lanthanides is in the range of 0 < RL < 1, which means that the sorption for lanthanides by this shell biomass is favorable. Furthermore, the negative value of ∆G indicates that the sorption is spontaneous. The higher R2 value for Freundlich model rather than for Langmuir isotherm (0.638–0.886 for Langmuir isotherm and 0.844–0.932 for Freundlich one) suggests that the adsorption on this sample is due to multilayer coverage of the adsorbate rather than monolayer coverage on the surface. It is noted that the value of 1/n less than unity indicates better adsorption mechanism and formation of relatively stronger bonds between adsorbent and adsorbate [The correlation coefficient (dsorbate . That isR2 and other parameters of Langmuir and Freundlich isotherms for lanthanides using heat-treatment (480°C) sample is shown in R2 value for REEs in this sample is still more large (0.947–0.982 for Langmuir isotherm and 0.948–0.975 for Freundlich one), compared with the original ground sample  and other parameters of Langmuir and Freundlich isotherms for lanthanides using heat-treatment (950°C) sample is shown in 2R value for lanthanides in this sample is fairly small compared with the values of ground original sample or heat-treatment (480°C) sample . The low correlation coefficient (R2) in this heat-treatment (950°C) sample may indicate that the removal of lanthanides occurred not by adsorption mechanism, Particularly 2R value is remarkably small for Langmuir isotherm, and then other relevant parameters cannot be estimated. As for Freundlich one, not only R2 value is relatively small (0.157–0.625), but the value of 1/n for most lanthanide is more than unity. That is to say, the almost perfect removal of lanthanides for this sample (as shown in The correlation coefficient (R2 and other parameters of Langmuir and Freundlich isotherms for lanthanides using heat-treatment (950°C) and water-added sample is shown in R2 value for lanthanides in this sample is fairly large particularly for Langmuir isotherm (0.992–0.999 for Langmuir isotherm and 0.885–0.951 for Freundlich one). This result is similar to that for heat-treatment (480°C) sample and indicates the stronger the monolayer adsorption on this sample. Judging from the value of R L or 1/n in Finally, qm) of the biomass for lanthanides in the present study with that of different biosorbents (for lanthanides and other elements) in the literatures [Buccinum tenuissimum shell biomass for lanthanides in this work is smaller than that of the presented biomasses. However, the sorption experiments in this work were carried out under low concentration of lanthanide ) instead of that in single component system.As mentioned above, biosorption studies have been mainly focused on toxic metals elements such as Cd, Pb, As, and Cr so far, and a few reports are focused on lanthanides. Hence, the comparison of maximum adsorption capacity 3 · 6H2O, Eu(NO3)3 · 6H2O, or Yb(NO3)3 · 3H2O  and this Buccinum tenuissimum shell biomass.Then, sorption experiment for three lanthanides  in single component system is being planned using the solution individually prepared by each nitrate salt: La up to the concentration of 200 mg · dm−3 on the sorption capacity of lanthanides is considerably small. From these results, it was quantitatively clarified to some extent that shell biomass can be an efficient sorbent for lanthanides. It is very significant information from the viewpoint of environmental protection that the shell  can be converted into a biosorbent for lanthanides.The shell biomass samples showed excellent sorption capacity for lanthanides under this experimental condition, and the effect of all the common ions (Ca


Carboplatin clearance depends on the glomerular filtration rate (GFR), and Calvert's formula is frequently used to achieve a target area under the time vs concentration curve (mg ml(-1) min). Creatinine clearance is a substitute for GFR when creatinine values are determined by the JaffÃ© method, which is being replaced by the enzymatic method. When the enzymatic method is used, the corresponding creatinine clearance theoretically exceeds GFR, and the use of creatinine clearance as GFR in Calvert's formula results, accordingly, in overdosing of carboplatin. In this study, we have established a model for adjusting the creatinine clearance to offset this bias based on a relationship between creatinine values measured by the JaffÃ© method and by the enzymatic method: adjusted creatinine clearance (ml min(-1)) = creatinine clearance (ml min(-1)) x [serum creatinine (mg dl(-1))]/[serum creatinine (mg dl(-1)) + 0.2]. Subsequently, we validated this model using the data from 35 lung cancer patients. Estimated clearances of carboplatin with the original equation [creatinine clearance + 25] were systematically higher than observed clearances [mean prediction error (MPE) +/- standard error (s.e.) = 26 +/- 5%]. This positive bias was corrected by the adjustment (MPE +/- s.e. = 5 +/- 4%). When the enzymatic method is used, the adjusted creatinine clearance should be used in Calvert's formula.


One AgI atom has a Y-shaped geometry defined by one N atom from one IN ligand, one O atom from another IN ligand and one O atom from an oxalate ligand. The other AgI atom is coordinated by two IN ligands and one O atom from an oxalate ligand. One of the IN ligands is disordered over an inversion center and forms a bridge between two centrosymmetric AgI ions. Due to the disorder, this IN ligand coordinates to the Ag atom through either the pyridyl N or the carboxylate O atoms. The IN and oxalate ligands link the Er and Ag atoms into a three-dimensional coordination framework. O—H⋯O and C—H⋯O hydrogen bonds are observed in the crystal structure.In the title coordination polymer, {[Ag DOI: 10.1107/S160053680901842X/hy2195Isup2.hkl            Structure factors: contains datablocks I. DOI:  crystallographic information; 3D view; checkCIF report            Additional supplementary materials:


P=0.299). Genotype distribution showed neither an association with histopathological characteristics of the tumours nor with prognosis. Age at disease onset was also not modified by the SNP. This first study of the Mdm2 SNP309 in prostate cancer patients suggests no correlation between a certain allelic variant and an increased cancer risk.The search for inherited cancer susceptibility factors is a major focus of epidemiologic cancer studies. Analyses of single-nucleotide polymorphisms (SNP) in a variety of genes revealed a correlation between a specific allele variant and cancer predisposition. Human mouse double-minute 2 protein (Mdm2) is a cellular E3 ligase capable of ubiquitination and degradation of p53. Therefore, Mdm2 is a crucial factor of cell cycle control and cell survival. The Mdm2 promoter SNP309 was shown to increase Mdm2 expression and can, thereby, inhibit the p53 pathway. This SNP was found to be associated with increased risk and early onset of various malignancies. For prostate cancer no studies are reported to date. In a case–control study we determined the distribution of the Mdm2 SNP309 in 145 male subjects with prostate cancer and in 124 male controls without any malignancy using RFLP analysis. Cases and controls showed a similar distribution of the SNP ( Genomic integrity and the ability of accurate repair of cellular damage are crucial prerequisites for controlled proliferation and differentiation. These processes are highly regulated and disruption of components of this network favours malignant transformation.The p53 protein is one of the most important coordinators of cellular response to genotoxic stress . The tumProstate cancer (PCa) poses one of the major health care problems today. PCa is responsible for approximately 11% of all male cancers in Europe, and about 9% of all cancer deaths in men are caused by this malignancy within the European Union, the course of this malignancy is unpredictable and therapy not warranted in all patients  or from the prostatectomy specimens (n=114). For comparison 124 samples from a male control group of patients without any malignancy acquired at the Department of Urology, University of Regensburg was investigated.Overall, 145 patients with PCa were included in our study. All PCa patients underwent a radical prostatectomy. Formalin-fixed and paraffin-embedded tissue samples from these patients were available from prior transurethral resection , whereas 45 tumours did not recur within at least 5 years. Prior IRB approval was obtained for the study.All tumours were diagnosed according to the 2004 WHO classification of prostate tumours . CharactDNA was extracted from normal prostate tissue or peripheral blood using the High Pure PCR Template Preparation Kit  according to the manufacturer's instructions.Msp A1I site (5′-CMGCKG-3′) in presence of the G-allele  of the promoter region which contains an μl containing approximately 100 ng DNA, 0.2 mM dNTP (Roche Diagnostics), 0.18 μM primers and 0.0025 U μl−1 GoTaq . The thermal cycling conditions were as follows: initial denaturation for 3 min at 95°C, 35 cycles of denaturation at 95°C for 1 min, annealing at 61°C for 1 min, elongation at 72°C for 1 min and final primer extension at 72°C for 10 min.Single-nucleotide polymorphism region was amplified by PCR using primers  obtained from Metabion  in a total volume of 25 Msp A1I  and 100 μg ml−1 BSA at 37°C in a total volume of 30 μl to ensure complete digestion. Restriction fragments were separated by capillary electrophoresis using an ABI PRISM 310 genetic analyser  and analysed with the GeneScan Analysis Software. Representative examples of genotyping are shown in PCR products were incubated overnight with 5 U http://ihg.gsf.de/cgi-bin/hw/hwa1.pl was used. χ2 statistics (two-sided Fisher's exact test) were used to evaluate case-control differences in the distribution of genotypes and to analyse associations between genotypes and clinical or histopathological characteristics. P<0.05 was interpreted as statistically significant.To test if the genotype distribution followed Hardy–Weinberg equilibrium, the public software at P=1.000) and controls (P=0.578). Genotype distribution between cases and controls did not differ significantly. Although there was a higher frequency of T/T genotypes in prostate cancer patients this difference did not reach statistical significance (P=0.299, vs T/G+G/G; P=0.131, vs >60 years, All analysed samples gave interpretable results. The genotype distribution in our cohorts followed the Hardy–Weinberg equilibrium in cases (P=0.299, . There wThe Mdm2 SNP309 is a plausible cancer predisposing allele due to the crucial role of Mdm2 in the cellular p53 pathway. The T to G variant was shown to result in increased Mdm2 synthesis and was found to be correlated with the risk of cancer or an early onset of tumour formation at various organ sites (Overexpression of Mdm2 and its clinical consequences were already described in PCa (Mdm2 overexpression could be linked to gene amplification in several malignancies (eg, malignant melanoma, non-small cell lung cancer and lipomatous tumours (The G-variant of the Mdm2 promoter polymorphism increases the affinity of transcription factors for example, Sp1. As long as Mdm2 gene amplification is not analysed in detail in PCa, overexpression of Sp1 might be speculated as an activator of increased Mdm2 synthesis. Numerous studies have documented that Sp1 activity and/or Sp1 expression levels are elevated in various human cancers and are associated with prognosis (Mdm2 is still discussed as a promising target for a therapeutical approach . The ideIn conclusion, our case–control study suggests that the Mdm2 promoter polymorphism SNP309 has no influence on PCa risk or prognosis, and relevant inherited alterations in PCa-related genes remain to be uncovered.


However, a quantitative understanding of the kinetics of VEGF cleavage and the efficiency of cell-mediated VEGF release is currently lacking. To address these uncertainties, we develop a molecular-detailed quantitative model of VEGF proteolysis, used here in the context of an endothelial sprout.VEGF proteolysis by plasmin or matrix metalloproteinases (MMPs) is believed to play an important role in regulating vascular patterning 165 to VEGF114 (the expected MMP cleavage product of VEGF165) and VEGF receptor-mediated recapture. Using experimental data, we estimated the effective bimolecular rate constant of VEGF165 cleavage by plasmin to be 328 M−1s−1 at 25°C, which is relatively slow compared to typical MMP-ECM proteolysis reactions. While previous studies have implicated cellular proteolysis in growth factor processing, we show that single cells do not individually have the capacity to cleave VEGF to any appreciable extent (less than 0.1% conversion). In addition, we find that a tip cell's receptor system will not efficiently recapture the cleaved VEGF due to an inability of cleaved VEGF to associate with Neuropilin-1.To study a cell's ability to cleave VEGF, the model captures MMP secretion, VEGF-ECM binding, VEGF proteolysis from VEGF165 cleavage in vivo is likely to be mediated by the combined effect of numerous cells, instead of behaving in a single-cell-directed, autocrine manner. We show that heparan sulfate proteoglycans (HSPGs) potentiate VEGF cleavage by increasing the VEGF clearance time in tissues. In addition, we find that the VEGF-HSPG complex is more sensitive to proteases than is soluble VEGF, which may imply its potential relevance in receptor signaling. Finally, according to our calculations, experimentally measured soluble protease levels are approximately two orders of magnitude lower than that needed to reconcile levels of VEGF cleavage seen in pathological situations.Overall, VEGF The cytokine vascular endothelial growth factor A (VEGF) is a critical mediator of adult neovascularization. Inducing blood vessel growth can be beneficial in alleviating tissue ischemia and in synthetic graft acceptance; however, neovascularization is also responsible for supporting pathological processes such as tumor growth. Controlling the activity of VEGF is thus an area of significant interest.121, VEGF165, and VEGF189. The longer VEGF isoforms contain basic residues encoded by exons 6 and/or 7 of the VEGF gene, which results in differential binding to VEGF receptors (VEGFRs), Neuropilin-1 (NRP1) VEGF activity and patterning in tissues is regulated by its binding to the extracellular matrix (ECM), which is determined both by alternate splicing of VEGF and by processing of VEGF and the ECM by proteases and heparinases, resulting in a range of vascular phenotypes Proteolytic release of VEGF, also referred to as VEGF release (as distinct from secretion of the unproteolyzed ligand by cells), can occur by cleavage of matrix-bound VEGF at its C-terminal domain or by cleavage of the ECM and results in a diffusible VEGF 164, the murine form of VEGF165, displays susceptibility to the MMPs, the most potent being MMPs -3, -7, -9, -12, and -19 VEGF cleavage can occur readily via the proteases plasmin, MMPs, and elastase in vitro endothelial cell spheroid model, while Hawinkels et al. VEGF release occurring through the cleavage of the ECM can occur through proteoglycan core protein digestion by plasmin, elastase, or a subset of the MMPs  in vitro fibrin-based system, a significant release-dependent cellular response occurred without any detectable VEGF release in vivo protease levels in plasma and in pathological fluid samples are typically lower, between 100 pM–20 nM Much remains to be determined about the nature of VEGF proteolysis and cell-mediated release. For example, endothelial cells The efficiency of VEGF cleavage and release may be tied to intense but tightly localized pericellular events  in vivo. For example, while it is generally assumed that matrix binding localizes a growth factor to the ECM, generating local deposits of VEGF off = 0.01 s−1) in vivo and in vitro.Quantitative understanding of these processes is essential to determine their relative importance To clarify the process of VEGF release, we develop a molecular-detailed quantitative model of VEGF cleavage based on an endothelial tip cell cleaving and releasing nearby VEGF. This model extends our efforts to quantify the interactions between VEGF, VEGF receptors, and the MMP systems to mechanistically understand angiogenesis and drug treatments to reduce angiogenesis in pathological situations 165; its transport includes diffusion, protease interactions, and binding to HSPGs and VEGFRs . The sprout, idealized as a cylinder, consists of a single tip cell followed by stalk cells, is surrounded by a thin basement membrane (BM), and is immersed in a volume of ECM. We assume that the endothelial tip cell is “activated” and can secrete a generic protease capable of cleaving both free and ECM-bound VEGF165 into VEGF114. Along with diffusion of protease, VEGF165, and VEGF114, the model simulates the following reactions:We developed a computational model to calculate the proteolytic cleavage of VEGF by a protease-secreting endothelial sprout . We cons165 + HSPG ↔ VEGF165·HSPGVEGF165 + Protease → VEGF114 + ProteaseVEGF165·HSPG + Protease → VEGF114 + Protease + HSPGVEGF165 + VEGFR2 ↔ VEGF165·VEGFR2VEGF114 + VEGFR2 ↔ VEGF114·VEGFR2VEGF165 binding to HSPGs is modeled as a single-step reaction 165 cleavage to VEGF114 is in reality a two-step reaction 165-114, we assume an effective single cleavage step . VEGFR2 is inserted into and internalized from the cell surface. Protease is secreted into the basement membrane layer and diffuses out into the ECM volume .For simplicity our current model does not incorporate VEGFR1 or NRP1, receptors for which we have previously developed biochemically-detailed models av, represents the fraction of space that is accessible to a molecule for diffusion and depends on the molecule's size and matrix fiber composition fluid, or “local” concentration, differs from the volume-averaged “bulk” concentration, Cbulk, of the species in a tissue by the relation Cbulk = Cfluid·Kav. The ECM and basement membrane are physically distinct, which is reflected in our model by different values for the protein diffusivities, Kav, HSPG density, and reactive components (see Parameters). While our governing equations are formulated in terms of bulk concentrations, we will refer to a species' interstitial fluid concentration in our results and figures unless explicitly stated.The basement membrane covering vessels may not always be structurally integral, e.g. in tumors C is the effective diffusivity of a molecular species C in the porous environment and [C] is the bulk or pore-averaged concentration of C. For each species, these differential equations (Eqns. 2–6) are coupled to their appropriate boundary conditions .Our system is formulated mathematically as reaction-diffusion partial differential equations:165 in the domain:on and koff, reflect the binding of VEGF165 to the HSPG, while kP denotes the effective bimolecular rate constant of proteolysis between VEGF165 and protease, given by [P].We first consider the transport of VEGF114 is generated from cleavage of either free or matrix-bound VEGF165d of matrix interaction, and thus does not saturate existing binding sites.VEGFm of VEGF proteolysis by plasmin  is much larger than the VEGF concentration and allows us to use first-order, rather than Michaelis-Menten, kinetics for the cleavage and neglect changes in the protease concentration due to VEGF binding. To account for possible protease inactivation due to inhibition or degradation, we impose an autolytic degradation rate constant, kdeg. Thus, the protease distribution after its secretion is governed by:Our estimated K165-HSPG ([V165H]), are described as ordinary differential equations (ODEs) since they do not diffuse but do interact with VEGF and protease:The matrix components, HSPG ([H]) and VEGFTypically, boundary conditions are imposed by specifying either the concentration or the flux at each face. We assume a cylindrical coordinate system and thus must specify four external boundary conditions: the leading face, z = +L; trailing face, z = −L; radial edge, r = R; and the central axis in the region excluding the sprout, i.e. r = 0 and z>0 see . The vesFor the central axis (r = 0), we have ∂V/∂r = 0 due to symmetry. We consider two cases of the model:165] = V0, [V114] = 0, and [P] = P0 at all outer boundaries, r = R and z = ±L.Case 1: The sprout is considered in isolation, with an imposed background of VEGF or protease. Thus we use a Dirichlet boundary condition: [VDiffusion∼L2/D∼1.5 min) compared to in vivo clearance rates on the order of hours 165 secretion rate from the surface z = +L: −D·∂[V165]/∂z = −q, which was balanced by a first-order VEGF clearance at z = −L, −D·∂[V165]/∂z = −kclear[V165]. The secretion rate q and kclear were pre-calculated to give the desired VEGF concentration in the absence of proteases, V0 at z = 0 and VEGF gradient, g0 over the domain length (see Model Implementation). For VEGF114, ∂[V114]/∂z = 0 at z = +L (no secretion), and −D·∂[V114]/∂z = −kclear[V114] at z = −L. The overall clearance rate, kclear/(2·L) ∼5.41·10−4 s−1, is similar in magnitude to clearance times in vivoCase 2: The sprout is considered as one of many sprouts migrating up an imposed gradient of VEGF. The computational domain is assumed representative of its surrounding tissue in the radial direction. Thus, we use a no-flux condition, ∂V/∂r = 0 at r = R. With the VEGF gradient in the z-direction, Dirichlet boundary conditions would overestimate VEGF diffusion through the boundaries (τout) are continuous (refer to ):Basement membranes around vessels are thin ∼43 nm . Thus, t−2 µm2/s Da = koff·Lsprout2/D = 160). As a result, the cell-surface distributions of soluble species and receptors can be approximated by ordinary differential equations (Eqns. 9–16)Cell-surface reactions are assumed to occur in the basement membrane volume and lateral diffusion along the cell surface is negligible  behaves similarly to VEGF121165 or VEGF121. In the current model, we assume that only free VEGF can interact with VEGF receptors. That is, VEGF165 bound to HSPG in the basement membrane layer cannot interact with the receptor population. The kinetic parameters describing these reactions are described below , spacing was 4–8 µm. Due to the thinness of the basement membrane layer, its radial dimension was approximated by a single node. Jout, previously given implicitly, was derived such that fluxes and concentrations were continuous (refer to section SIV).The computational domain was represented in cylindrical coordinates and the VEGF and HSPG transport equations were solved using the finite volume method on a 2D grid (z and r). The basement membrane layer was used to approximate cell-surface and basement membrane volume reactions. The control volume spacing in the z-direction was 8 µm. In the r-direction, one voxel was used to represent the sprout radius, from r = 0 to r = Rt+1 = 2·yt−yt−1. The convergence criteria at each time step was set to a maximum fractional change in any computational node less than or equal to 10−7/iteration.The first order derivatives in time were discretized using a first order fully-implicit scheme, while second order spatial derivatives used a central difference approximation. Nonlinear solution of the equations was found by iteration using the successive over-relaxation (SOR) update formulation and a Red-Black node ordering 0, and gradient, g0, and thus required a sequence of simulation steps.The initial condition for the protease secretion simulations consists of a fully-formed VEGF distribution after taking into account VEGF depletion by receptor-mediated internalization. For case 1, this consisted of finding the steady-state distribution in the absence of protease secretion. In the case of an imposed VEGF gradient (case 2), we used Neumann boundary conditions fitted to produce a mean concentration, V0 (see Parameters) and the mean VEGF concentration at z = 0, V0: at z = +L, [V165] = V0·(1+g0·L/Ltip), at z = −L, [V165] = V0·(1−g0·L/Ltip)). This was done in the absence of HSPGs to allow faster convergence. After equilibration of the VEGF receptor population, the Dirichlet boundary conditions were converted into the appropriate ‘case 2’ boundary conditions by calculating q and kclear using the following formulas,0 and V0, this approximation is justified since the error is small for our domain size and gradient. HSPGs were finally directly imposed by the equilibrium relations [V165H] = [V]·[H]Total/(Kd+[V]), as the distribution of soluble VEGF at steady state is independent of HSPGs in the absence of proteases.We first specified Dirichlet boundary conditions in the absence of receptors to satisfy gedge = 1200 µm (case 1) and L = 80 µm and Redge = 50 µm (case 2) (The domain sizes were L = R(case 2) . The cassection SV; Table S2). While the diffusivities of various VEGF isoforms would be different in vivo, we assumed each had a diffusivity equal to that of VEGF165. Available volume fractions were taken as limiting cases for matrix connectivities as derived in ECM = 0.85, KBM = 0.2).The diffusivity and available volume fractions depend on the structure of the interstitial matrix. We estimated diffusivities directly from the properties of the ECM  from zymographic and VEGF mitogenicity data with a half-life of 1–4 h, equating to kP ∼1.2·103–5·103 M−1s−1165 cleavage by plasmin at 37°C (kp = 631 M−1s−1) was derived by directly fitting kinetic data from Keyt et al. section S1; Fig. S1A).The kinetic parameters for VEGF binding to VEGFR2 have been previously characterized 4 VEGFR2/cell Interstitial VEGF levels were previously reported at ∼1 pM in vitro and in vivo biological systems is not exactly known. MMP and plasmin concentrations in the circulation have been determined previously to be <20 nM The level of active proteases in 5–2·105 molecules/cell/h 4–107 molecules/cell/h 6 active protease molecules/cell/h. We expect that this serves as an upper bound to the real value of protease activity.The rate of MMP secretion is also a critical parameter affecting MMP localization and activity, and depends on cell type and factors used for cell stimulation. However as most cells, with the exception of neutrophils, secrete TIMPs in conjunction with proteases, the protease secretion rate itself is of limited use. For example, rabbit brain capillary endothelial cells secrete as much MMP as rabbit synovial fibroblasts, however the MMPs remain inactive, unlike in the latter, even after activators are present 165 by plasmin yielded a bimolecular rate constant of kP = 631 M−1s−1 at 37°C, which is at the low end of typical ECM enzyme-substrate reactions for the MMPs . With low nM levels of MMPs in vivo, cleavage of VEGF would seem negligible as its time constant ∼100 h. These results motivate us to study the possibility of pericellular localization of MMPs upon their secretion.An analysis of kinetic data of cleavage of VEGF6 active protease molecules/h in a 3D reaction-diffusion model  is not affected by proteases.Assuming that the secreted proteases are not inhibited or inactivated, a single cell secreting proteases in isolation provides a very low proteolytic load (∼0.31 nM in the available pores) at the secreting cell's surface . Additio·10−4 pM , relativroteases . The tot114 levels found in its vicinity . Imposing protease degradation to mimic the effects of inhibition . However, as the basement membrane diffusivity decreases, the increase in protease levels does not lead to a concomitant increase in VEGF cleavage, shown by cleaved VEGF not becoming significant until the basement membrane diffusivity reached 1/10,000th of the ECM diffusivity (∼0.01 µm2/s) (not shown).While protease levels reached only 0.3 nM at the cell surface in our model, hindering basement membrane diffusion by increasing its thickness or decreasing the diffusivity may be able to increase pericellular protease levels and subsequently increase VEGF conversion. We find that pericellular protease levels are relatively sensitive to the basement membrane thickness and diffusivity (noticeable changes in its concentration begin at D1 µm2/s) . Thus, o1 µm2/s) . Removinnot shown).Further localization of MMP activity, e.g. to specific microdomains on the tip cell, may also increase local MMP concentrations and VEGF cleavage. To test this, we concentrated the entire MMP secretion to the leading edge of the tip cell. Similar to the above trends, increases in local MMP levels were substantial (to ∼5.5 nM) while increases in cleaved VEGF were not . VEGF165 levels in the basement membrane dropped by an identical amount, indicating that VEGF165 levels in the ECM, and thus VEGF165-HSPG levels in the ECM, are not significantly altered (not shown). Unexpectedly, we notice a very sharp depletion of basement membrane VEGF165-HSPG (from 540 pM to 160 pM) (not shown).As a baseline, we consider the tip cell having 10165-HSPG in the basement membrane to cell-surface proteases is more poignantly captured by testing a range of protease concentrations , an unphysiological level.The sensitivity of VEGFtrations . The basroteases  . We find that the difference in the susceptibilities of VEGF165 and VEGF165-HSPG to cell surface proteolysis stems from differences in their rates, per molecule basis, of being replenished after proteolysis. While VEGF165 is quickly replenished by diffusion (at a rate 1059 s−1), VEGF165-HSPG is replenished only as quickly as another complex can dissociate (i.e. koff = 0.01 s−1). In our model, the rate of proteolysis per molecule VEGF is kP·[P] = 0.0236 s−1 .To understand why basement membrane VEGFGeometrical and Transport Parameters). We assume that a VEGF gradient is established through a balance of VEGF secretion in front of the sprout and VEGF clearance behind the sprout .As we have shown that an isolated cell is unable to alter its local soluble VEGF concentration, we attempted to simulate the proteolytic contribution of other cells by simulating VEGF release in a spatially constrained environment. We assume the modeled sprout is one of several sprouts separated by 100 µm  simultaneously migrating towards a distant VEGF source (e.g. tumor) (see 165 is predicted to be approximately 27% (0.97 pM to 0.71 pM), however the total soluble VEGF is unchanged due to a concomitant increase in VEGF114 . We find that HSPGs do not increase the effective rate of VEGF proteolysis, e.g. by providing additional sites for cleavage. Instead HSPGs increase the time VEGF spends in the proteolytic environment, by decreasing the effective VEGF clearance and internalization ∼33-fold in our model. Consequently, our results imply that mechanisms that would increase VEGF clearance or internalization, e.g. increased VEGFR2 expression, would cause VEGF molecules to spend less time in the interstitium and decrease VEGF conversion (not shown).We also find that HSPGs significantly increase VEGF VEGF114 , which win vivo. The useful measure to determine VEGF cleavage in any physiological system is the total clearance rate of a VEGF molecule (i.e. the sum of nonspecific and receptor-mediated mechanisms). Experimental studies indicate a VEGF half-life in the plasma of ∼1 h P = 631 M−1s−1, ∼305 nM protease would result in 50% VEGF cleavage. These protease levels are however significantly greater than what is expected to be found in vivo.We can similarly use this analysis to estimate the necessary protease concentration for VEGF proteolysis 165 proteolysis to VEGF114, and VEGF clearance. While simplified, it allows us to make broad conclusions regarding the extent and determinants of VEGF proteolytic release.In this study, we developed a computational model of the cellular proteolysis of VEGF. The model includes the secretion of proteases, binding of VEGF to HSPGs and VEGFR2, VEGF6 active protease molecules/cell/h) and accounting for mechanisms of increased cell-surface MMP localization, we find that an isolated cell would have difficulty in causing significant VEGF conversion. Reconciling the in vivo observation of VEGF cleavage requires a mechanism of protease accumulation, e.g. geometric constraints and/or simultaneous protease secretion by numerous cells. We thus propose VEGF cleavage is not mediated by single cells but rather by the collective behavior of a tissue, dependent upon total cell density and the whole-tissue MMP concentration.Kinetic fitting of experimental data shows that VEGF cleavage by plasmin is a slow reaction. Using a reaction-diffusion model of a cellular microenvironment, and after overestimating protease secretion  of VEGF165 and VEGF114 are indistinguishable, which was assumed in our model and was approximately observed in the plasma of mice 165 in equilibrium with HSPGs. This effect was especially notable close to the cell surface, for VEGF165-HSPG within the range of cell-surface proteases. Thus, we suspect that matrix-bound VEGF may represent a more responsive signaling modality than free VEGF, at least to the presence of proteases. This coupled with a recent finding that matrix-bound VEGF induced prolonged receptor activation compared to soluble VEGF off = 10−3 s−1) compared to HSPGs (koff = 10−2 s−1), they may mediate an even more sensitive protease response curve than that seen with HSPGs . Our model predicts that HSPGs increase the proteolytic conversion of matrix-binding VEGF isoforms by increasing the residence time of a VEGF molecule in a tissue's proteolytic environment. As a result, assuming each VEGF isoform has similar susceptibility to proteases, cleavage of non-HS binding VEGF isoforms  would be expected to be negligible, while cleavage of VEGF145189165. In contrast, factors that increase total VEGF clearance, e.g. VEGFR-mediated internalization, result in decreased proteolytic conversion.HSPGs are thought to reduce the effective rate of VEGF diffusion by rapidly binding VEGF  than structural changes such as vessel reorganization and angiogenesis, which may take several hours to days and are thus relatively static. While our system's overall time scale was ∼10 h (refer to section SVI.2), we did not represent the full extent of the vasculature and vessel-mediated internalization in our model. Our previous computational model, representing the whole body microenvironment, estimated a VEGF tissue clearance rate of ∼30 min, primarily due to receptor-mediated internalization 1/2∼1 h Our model makes several important assumptions that are worth clarifying, the most important being the consideration of steady state. Steady state is justified in that the net rate of VEGF clearance 164in vivo protease concentration required to explain the significance of VEGF proteolysis. The role of such proteases may instead be the cleavage of HSPG core protein to enable diffusion of HS-bound VEGF, which was shown for MMP9 in a HT29 colon carcinoma spheroid model Another important assumption we made was that HSPGs do not protect VEGF against proteolysis, as seen by Lee et al. for MMP3 ). We simulated concentration of proteases to microdomains and the presence of concave pockets (not shown); local proteases concentrations do increase, however, not enough to increase pericellular VEGF cleavage to significant levels (not shown).Finally, an endothelial tip cell is structurally more complex more than the simple cylindrical tube we have assumed 165 and VEGF189 are typically thought to be tightly bound to HSPGs , the dissociation rate is rapid (koff = 0.01 s−1) and VEGF165 is always near dynamic equilibrium with HSPGs (τ = 3.1 s). This indicates that VEGF165 should not form any stationary deposits as they will quickly equilibrate. Deposits of VEGF could instead reflect spatial inhomogeneities in the underlying HSPG itself, which would have a longer lifetime due to the decreased motility of HSPG within the ECM. These inhomogeneities may be important to cellular guidance 165 is more likely to simply dissociate than be cleaved and released in a directed manner by a cell. Directed proteolysis could occur for covalently tethered VEGF 189While the affinity of VEGF165 release  (DaVEGF-Proteolysis≪DaCol1-Proteolysis∼1). Moreover, pericellular VEGF cleavage remains insensitive to changes in MMP localization brought about by changes in basement membrane diffusion (not shown). Due to physiological limits in the number of proteases a cell can secrete and the rate of VEGF cleavage, proteases cannot be both localized to an isolated cell and induce significant VEGF cleavage at the same time. Instead, Pericellular proteolysis is significant for many processes usivity) , 3, 4. Tiffusion  and micrsection SVI.1): at steady state, the capture probability was only 0.8% for our tip cell with 104 VEGFR2 . In contrast to our results, a previous analysis 2/s not shown) and have no effect at steady state. Finally, our results imply that autocrine VEGF release and recapture would be even less likely in the presence of interstitial flow. This contradicts the hypothesis of a previous finding that the autocrine detection of convection-driven gradients of proteolytically-released VEGF may enhance capillary morphogenesis Even if VEGF is cleaved and released at the cell surface, diffusion away from the cell surface is significantly faster than VEGFR2 binding and internalization , VEGF conversion could be significant (resulting in a significant fraction of plasma VEGF being cleaved) Since VEGF cleavage is a multi-cellular phenomenon, its effectiveness for any single cell capable of sensing VEGF depends on the total density of cells secreting or cleaving VEGF, as well as overall tissue clearance and receptor-mediated uptake rates. While our model did not explicitly account for the multiple cell types involved in angiogenesis  in vivo.We developed a computational model to simulate the proteolytic cleavage of VEGF in the vicinity of an endothelial sprout. We found that VEGF proteolysis by plasmin is slow compared to other proteolysis reactions. In order for VEGF conversion to be significant, we required a model where protease production is not limited to a single cell. Our results suggest autocrine effects can only be supported by ECM-cleaving VEGF release, which would preserve VEGF's ability to bind to co-receptors, while paracrine effects are expected for VEGF-cleaving VEGF release. Localization of proteases and receptors to cell surface microdomains can significantly improve autocrine capture, however it has no significant effect on VEGF proteolysis. Our analysis also shows two distinct roles for HSPGs: they increase VEGF conversion by decreasing the overall VEGF clearance rate in tissues and also provide a unidirectional signaling modality in the presence of proteases. Future experiments should test the cell density dependence on VEGF cleavage as well more accurately estimate the quantity of proteases present Supplement S1(0.60 MB DOC)Click here for additional data file.