Understanding the Sub-Cellular Dynamics of Silicon Transportation and Synthesis in Diatoms Using Population-Level Data and Computational Optimization
[['Diatoms are the eukaryotic unicellular organisms , living in marine and fresh water environments .', 'Diatoms are producers in the food chain .', 'They generate around 40% of all organic carbon in the sea [9] .', "They contribute to the global carbon cycle , by photosynthetic carbon fixation as much as all the terrestrial rain forests do [10] , [11] and therefore , it's likely that they have influenced the global climate over millions of years , by the inward flux of carbon dioxide to the oceans [12] .", 'Moreover , they are major players in the silicon cycle of the oceans [13] .', 'The distinctive feature of diatoms is that they synthesize a wall around themselves , called frustule , made of amorphous silica , which is delicately patterned down to the scale of nanometers .', 'The frustule structure varies between different species of diatoms and also between different growth conditions .', '[14]–[16] .', 'The precision in controlled mineralization is one of the reasons that they have been attracting increasing interest for a long time , from a material science perspective [14] , [17]–[21] .', 'The oldest diatom fossils have been dated back to 185 Mya [22] .', 'It is suggested that the abundance and ecological success of diatoms can be a result of their silica walls - living in a “glass house” [23] , [24] .', 'Diatom frustules are typically composed of two parts: the valve , which forms the larger outer surface and girdle bands , which are rings of silica being produced during cell growth ( Figure 1A ) .', 'The necessity of silica formation for diatom cells imposes special steps in their cell cycle .', 'Figure 1A depicts the asexual cell cycle of a typical diatom .', 'Before a cell divides , new silica valves for the next generation are formed inside a specialized vesicle , the Silica Deposition Vesicle ( SDV ) [25] , [26] .', 'After this event , daughter cells separate and start growing , which includes the growth in the cell volume and also the silica girdle bands until the cell reaches its largest size .', 'If the amount of silicon in the environment is depleted to almost zero; most cells will be arrested in the G1-phase or G2-M phase , with the G1 arrest point being generally predominant [27]–[29] .', 'This property has been very useful in diatom studies because under silicon starvation condition , cells become mostly synchronized in their cell cycle and therefore , an individual cell can be studied easier with the data from population-level quantities .', 'However , even in the best case usually up to 80% of the cells are synchronized and , therefore , there will be an error in downscaling to a single cell dynamics from macroscopic quantities .', 'Because of the specific cell division form , including one valve growing inside another , in many species of diatoms , one of the daughter cells becomes smaller after each generation .', 'To overcome this problem , after many generations , cells that are smaller than a critical threshold will be regenerated to the original size via sexual reproduction [30] .', 'For some species of diatoms , however , sexual reproduction has never been observed .', '[31] , [32] .', "A study on the frustule formation based on fluorescence imaging of the species Thalassiosira pseudonana , suggests that sometimes girdle bands close to the cell center expand and are thus able to accommodate a new valve , which is not smaller than parent's valves [29] .", 'The silica wall architecture is a species-specific characteristic of diatoms , which is an indication that the synthesis of silica is highly genetically controlled , in addition to being chemically and physically controlled .', 'Since the entire genome of some species of diatoms has been sequenced ( Thalassiosira pseudonana: [33] and Phaeodactylum tricornutum: [34] ) , there have recently been greater insights into this genetic control [35] , [36] .', 'Figure 2 is a diagram showing cell control mechanisms .', 'It is believed that such control takes place mainly through two processes .', 'Firstly , via synthesizing and providing special membranes like SDV and secondly , via producing functional biomolecules .', 'The first type of silicification-related biomolecules regulate uptake and transport of silicon and the second type are involved in deposition of silica including proteins and polyamines , which play the role of catalyst or a structure forming scaffold [4] , [5] , [37]–[39] .', 'Our model organism is Thalassiosira pseudonana .', 'Figure 1B and 1C shows a scanning electron microscope ( SEM ) image of this species .', 'In Figure 1B the silica structure of valves , which is specific for this species , and girdle bands , which have a finer and more regular structure , are presented .', 'Figure 1C shows the image of a diatom captured during the last step of cell division .', 'It is clear in this image that the daughter cells already have completed valves before division takes place .', 'Diatoms uptake silicon mostly in the form of neutral orthosilicic acid Si ( OH ) 4 [40] , [41] .', 'The low concentration of silicic acid in present oceans might be the reason for the development of active transportation .', 'Cells synthesize special silicic acid transporter proteins ( SITs ) to act on the membrane for making an inward silicon flux in the cell .', 'The role of SITs has been discussed in several studies [e . g . 42 , 43] .', 'In T . pseudonana three distinct SIT genes have been analyzed for their regulatory mechanisms .', 'It has been shown that SIT protein levels change during a synchronized cell cycle ( up to 50% changes around an average value ) and that the peaks of their profile occur during silica deposition periods of the cell cycle .', 'Moreover , the peaks in mRNA levels happen in S-phase , where the period prior to valve formation shows the highest uptake rate [44] .', 'This causes non-classical enzyme kinetics , which is when the kinetic coefficients are time-dependent in contrast to classical enzyme kinetics when the coefficients are assumed to be constant .', 'In this case , the maximum uptake rate is not constant , but it is a dynamic quantity due to the flux of enzyme production and dynamic enzyme activities [44] .', 'This effect changes the chemical pathways [45] .', 'More interestingly , the SIT3 mRNA level is much lower than SIT1 and SIT2 and also SIT3 is not up-regulated in response to silicon starvation or cell cycle as much [33] , [44] .', 'This suggests that SIT3 might act as a sensor for external silicon concentration [46] .', 'The sensor role of some proteins has been observed in other cells like yeast ( e . g . [47] ) .', 'In that case when the nutrient concentration is lower than a threshold a different type of transporter with a high affinity is produced .', 'This behavior is associated with a dual-transport system , which has been shown in the case of yeast that it prolongs the preparation for starvation and it facilitate the subsequent recovery of cells [47] .', 'After cell uptakes silicon it stores it partly in a soluble silicon pool and then transports it through cytoplasm to reach the SDV , the location of the new synthesizing walls .', 'Currently , the intracellular location of the pool and the mechanisms by which it transports to SDV is not completely understood .', 'Interestingly , if we consider all the intracellular silicon pool in the form of monosilicic acid , considering the small volume of the cell , it should have a concentration higher than the solubility of monosilicic acid , which is around 2mM at pHs below 9 [48] .', 'It has thus been an open question as to how the cell can maintain this concentration without deposition .', 'There are different scenarios for explaining the storage and transport of silicon in the pool .', 'One of these scenarios assumes that the silicic acid binds to some type of organic molecule and thus makes a soluble silicon pool [49] and therefore it turns the silicic acid into another chemical form .', 'This explanation is in agreement with the uptake behavior of diatoms after different starvation conditions [50] .', 'Another scenario assumes the existence of special silicon transport vesicles ( STVs ) , which transport silicic acid from the cell membrane and release their content into SDV by fusing to its membrane [51] , however , the existence of silicon inside such vesicles , to the best of our knowledge , has not been proved .', 'A third scenario shows that oligomerization indeed starts inside the cell as soon as there is some monosilicic acid available in cytoplasm , generating precursors for later deposition inside SDVs .', 'This explanation is based on NMR data from silicon pools ( see the following ) .', 'Recently , the NMR chemical shift technique has been a powerful way for understanding the forms of silicic acid based on their connections to other molecules .', 'With this data it has been shown that the majority of silicon in the entire cell is in a polymerized form [52] .', 'However , this data does not necessarily exclude the possibility that the first explanation could have a role ( because this method cannot distinguish between free monosilicic acid and its attachment to an organic molecule ) , but it shows clearly that intracellular silicon is mostly in the form of oligomers .', 'Finally , after the nutrient ( oligomers of silicic acid and pre-synthesized silica ) is provided for SDV , silica precipitation and pattern formation occurs .', 'In this study , we model silicon uptake , transportation and synthesis in diatoms .', 'We use the nonlinear Michaelis-Menten kinetics for protein activities as mass transport equations .', 'The model is composed of four compartments: external environment , cytoplasm , SDV and deposited silica .', 'In order to find the unknown parameters of our compartmental model , scatter search , ( a global optimization technique ) , has been applied for fitting the model to experimental data on silicon consumption and cell population growth .', 'To add constraints to the model , a penalty term is added to the objective function .', 'Additionally , the optimized solutions have been tested with sensitivity and perturbation analysis .', 'The resulting robust optimized solutions predict silicon dynamics and intracellular biosilicification rates which are in agreement with experimental measurements .', 'With the insight from SITs expression level data , we then impose a flux of proteins during the cell cycle and investigate its effect on silicon uptake rates .'], ['In order to model the distribution and transportation of materials in cells , two computational methods have been commonly used .', 'In the first method , spatial and temporal quantities are both important and a system of PDEs should be solved with some degree of accuracy .', 'However , in many cases , cell processes are not diffusion-limited , meaning that the rate of another event that plays the role of a sink or a source , is slower than diffusion rate and thus diffusion is fast enough to keep the distribution of materials homogenous in the time-scale of interest .', 'To investigate the effect of diffusion on transport of silicon two types of diffusion rates have been calculated .', 'For the detailed calculation see Text S1 from supplementary materials .', 'The first type is diffusion through membrane .', 'Even though the membrane is semi-permeable for monosilicic acid , which is a small , uncharged molecule , the rate of diffusion is much smaller than the observed uptake rate [53]–[56] .', 'Therefore , it seems that active transporters are the most important method for the transport .', 'The second type of diffusion is responsible for distribution of materials close to the membrane in each of its sides .', 'In text S1 we show that diffusion of silicic acid in water is fast enough compared to the rate of uptake , that it will not be a controlling factor ( See Figure S2 in Text S1 ) .', 'The diffusion-mediated Michaelis-Menten equation also shows that the effect of diffusion on the total rate is negligible [45] .', 'This allows us to use compartmental modeling as a good approximation .', 'If cells have several compartments , the chemical and physiological characteristics of inside and outside compartments can differ significantly .', 'This is an efficient mechanism for regulating special events and as expected it requires energy for synthesizing new biomaterials for membranes .', 'In such a process that is not diffusion-limited the second modeling approach , compartmental modeling , is suitable .', 'Compartmental modeling includes a system of ODEs that describes the dynamics of materials inside and its transportation between compartments .', 'There are several reasons that the uptake of silicon , in the form of mono silicic acid , is mostly controlled by enzymatic reactions .', 'For instance , cells use the so-called SIT ( silicon transporters ) genes to produce proteins with active uptake sites and subsequently lower the energy barrier for silicon uptake through membranes .', 'Although in most studies of SITs , the focus is on the SITs on cell membranes , but the expression level and other relevant data usually is derived from the whole cell proteins analysis .', "Since in diatom cells , there is a specialized compartment for silica synthesis and deposition which is surrounded by a membrane , there is no reason why this membrane shouldn't be equipped with SITs; either in the same form or a similar form .", 'Moreover , the permeability of intracellular membranes to silicic acid is low enough that transporter proteins still are likely the major way of transportation [53] .', 'Our compartmental model includes four compartments ( see Figure 3 ) and we aim to model the temporal changes in amount of silicon ( mol ) , regardless of the form of the silicon compound , inside those four parts .', 'Once silicic acid is inside the cell , it will likely undergo polymerization [52] .', 'The silica polymerization chain of reactions contains many reaction terms , giving rise to a high degree of complexity .', 'Moreover , there is not much known about the oligomer form of silicic acid in diatoms .', 'Therefore , a useful and applicable approach is to consider the total amount of silicon in each compartment and calculate the temporal changes of this quantity .', 'In order to include the deposition of silica in the SDV , we consider deposited amorphous silica as one compartment .', 'Biological molecules , which consist mainly of proteins and long chain polyamines ( LCPAs ) , have a major role in silica polymerization and pattern formation [35]–[39] .', 'The process by which they guide biomineralization is studied to some extent but still not completely understood .', 'Moreover , there are a variety of complex events happening in SDV , including self-aggregation of organic molecules and organic matrix formation , polymerization of silicic acid and formation of oligomers both from monosilicic acid and also from precursors of oligomers , nucleation and phase separation and formation of silica under a controlled condition of concentrations and pH values .', 'Also those events have different time and spatial scales [4]–[6] .', 'It is apparent that the entire process is too complex to study it in a single model .', 'In our model , we present the equilibrium condition of the SDV membrane to be described by a catalytic process .', 'Moreover , we introduce the phase separation event , the transport between the soluble and deposited silica in SDV , as the transport between compartments 3 and 4 .', 'Figure 3 also shows the cell control over level of SITs , which is regulated in response to changes in external concentrations of silicic acid and internal consumption of silicon , as discussed earlier in the introduction .', 'We introduce this control in one of our experiments by adding a flux term to the rate equation of the SITs .', 'In this model the focus is on uptake and transportation of silicic acid through the cell membrane and cytoplasm .', 'This step is vital in providing the material for the silica depositing compartment and , consequently , vital for the cell division .'], ['Using scatter search simulation in the search space of parameter values , the minimum for the objective function has been achieved .', 'The search space that we have used here is listed in table 1 .', 'The approximate values for proteins came from literature , which are mostly based on macroscopic properties of enzyme kinetics .', 'Figure 5 shows the best values for the objective function .', 'The algorithm stops searching when the acceptance criteria is achieved , which is when the algorithm has not found any better solution for a long time and the objective function is close to the optimum value .', 'Since we have considered a weighted objective function for 10 data points ( eq . 13 ) the best meaningful value for objective function is 10 and if the search algorithm arrives at values less than 10 , all of those solutions are acceptable and there is no preference among them , in order to avoid overfitting problem .', 'In the simulation shown here , the objective function is around 15 .', 'So , with the considered search space for parameters , this model is able to closely reproduce the experimental data with a relatively small fitting violation .', 'The solution does not change by repeating the scatter search or by changing the initial point ( results are not shown ) .', 'We also make sure that the model equations hold the conservation law for nutrients and enzymes .', 'Figure 6A shows that the relative error in conservation of silicon is of the order of and Figure 6B shows the relative error of total protein conservation is , both of which show a very good accuracy of the numerical solvers .', 'The problem has several solutions all in the same range of the minimum cost function value .', 'These accepted parameters are shown in a scatter plot of parameters in Figure 7 .', 'To clarify the role of penalty terms , two cases of simulation have been performed , as discussed in previous section .', 'In the first case , no penalty function imposed to the model ( Figure 7A ) and in the second one penalty terms are added to cost function ( Figure 7B ) .', 'From the results it is clear that with no penalty , parameter values are mostly scattered , but applying the penalty , besides and , they mostly form one cluster and are not significantly scattered .', 'This means that in the second case , most parameters are very well identified .', 'Moreover , with the optimized parameters , we return to the forward problem and calculate temporal dynamics of intercellular quantities .', 'Applying an accepted set of parameters , we test the variations in the model variables to make sure there is not a different behavior when changing from one solution to another .', 'Figure 8 shows the concentration dynamics of silicon and enzymes in all cell compartments with and without the penalty term .', 'With no penalty , the dynamics of most variables changes for different set of parameters , however , after applying penalty , although there are some variations in few of the variables , still there is the same dynamics for concentrations , especially concentration of silicon in different compartments .', 'In Figure 9 , experimental values for silicon concentration in the medium together with the model output is shown .', 'The fitting to data , considering experimental error is appropriate .', 'This figure also shows the two curves illustrating the effect of the two terms in eq .', '( 5 ) , which was discussed in earlier .', 'We calculated the integral of each term , with a trapezoidal method , to calculate their contribution in silicon consumption .', 'It appears that term 2 in the beginning does not have a significant effect and term 1 has the major role .', 'However , the absolute value of term 2 starts to grow through time and reaches a considerable value .', 'This effect is consistent with the behavior of the diatom cell cycle in a bulk .', 'First , cells are not dividing , but instead up-taking silica with the highest rate in order to build the silica valves for daughter cells .', 'Even though , some cells divide earlier than others , they are only in the beginning of girdle band growth and the uptake rate is not very high and therefore , the first term becomes dominant .', "By the end of the experiment's duration , the second term has a considerable role , which shows that it has to be included in the calculations of synchronized cell cultures .", 'To this point we concluded to the solution of compartmental dynamics based on our mathematical model .', 'The fact that parameters are mostly not scattered is a good sign .', 'However , if a model is very sensitive to certain parameters , even a small change can possibly affect the dynamics significantly .', 'Therefore , in order to check the robustness of our model , we first performed sensitivity analysis on solutions and then measured the effect more clearly by means of perturbation analysis .', 'Figure 10 shows the normalized sensitivity of observables by changing parameters .', 'Since we have only used the data from medium concentration and deposited silica , we investigate their sensitivity .', 'is most sensitive to parameters and , especially at the end of the experiment where decrease has a smaller slope .', 'shows greatest sensitivity to .', 'To bring an understanding of the amount of change that can be produced by these important parameters , we have again performed perturbation analysis .', 'In Figure 11 the results of parameter perturbation are shown in terms of objective function and temporal dynamics of concentrations .', 'We can see that with a relatively large change in the parameters ( 10% perturbation ) , the behavior of solutions remains the same .', 'For a nonlinear system , this is a reasonable amount of change and it means that our model is robust and stable .', 'Figure 12A shows the silicon content dynamics in different compartments .', 'From the total amount of silicon uptake by cell , the biggest amount becomes in the form of deposited silica , as we desired .', "However , there is some silicon in cytoplasm or , as it's called , the silicon pool .", 'The concentration of non-deposited ( dissolved ) silicon in SDV ( ) is very low .', 'This makes sense considering very small volume of SDV and also the fact that SDV grows together with silica valves and thus leaving only a small portion of the compartment for non-deposited silicon .', 'As we discussed previously , cells control the uptake and transport of silicon through changing the expression level of SITs .', 'To test the effect of these changes on uptake rates by the cell , we have added a flux term to equations S2–3 and S2–6 for the amount of free enzymes ( SITs ) during time and again solved the inverse problem .', 'We have chosen this flux as a function of time based on changes in protein level from the experiments [44] .', 'The relative change of SITs that we applied to our model is shown in Figure 13 .', 'This function is chosen based on experimental data , but it only shows the behavior of the SITs expression level .', 'The main idea is that during the S-phase , while silicon deposition is minimum , the amount of proteins is also at its minimum .', 'Figure 12B is the result of imposing the protein flux on the silicon amount in different compartments .', 'It shows that even though the total dynamics are more or less the same , but there are some differences .', 'For example , in experimental measurements it seems that silicon deposition happens in a low rate immediately after adding silicon to the starved cells .', 'This might be because of silicon storage in cytoplasm in the beginning [29] .', 'The dynamics in Figure 12B is closer to this behavior than in Figure 12A .', 'An important measure in nutrient uptake is the uptake rate .', 'In Figure 14A we have shown uptake rates versus medium concentration , measured by imposing different initial values for silicic acid concentration in the medium or cell culture ( ) and then the calculating the uptake rates at different time points .', 'The uptake rate-silicic acid concentration curve is a saturated curve as expected .', 'Uptake rates in the first time step , after 2 minutes , are much higher than later uptake rates .', 'This can be a result of the initial condition of the model , zero value of silicon inside the cell , which we assumed based on the fact that cells have been kept in silicon starvation for a long time ( 24 hours ) prior to the measurement .', 'Also this big drop shows the nonlinear nature of the system .', 'This sudden decrease has been seen in experiments on diatoms .', 'It is called surge-uptake .', 'Also experiments suggest that in low concentrations of silicic acid , uptake is almost linear and thus it is referred to as externally controlled ( cells uptake as fast as the diffusion of external nutrient allows them ) .', 'However , in high concentrations of silicic acid , the uptake rate reached its maximum value and , therefore , it is called internally controlled uptake .', 'Interestingly , this model is able to produce all three phases of uptake: ( surge uptake , internally controlled and externally controlled ) , with only the enzyme kinetics and considering cell compartments and without any other assumptions on the presence of different phases of uptake in diatom cells .', 'Figure 14B is the same measure for the case when we applied changes to the total amount of SITs .', 'Compared to 14A , the decrease in uptake rates accrues slower , which is closer to some experimental data of uptake rates in different incubation times [50] .', 'Moreover , the uptake rate increases again at the time of starting valve formation , when the cell needs a high amount of silicon .'], ['Studying intracellular processes is a difficult task , largely because of the difficulties of in-vivo measurements at such small scales .', 'As a consequence of this , the modeling approach is a good candidate for understanding the different mechanisms and temporal behavior , such as nutrient uptake and transportation of materials .', 'We have introduced a multi-compartmental model for silicon transport and synthesis in diatoms .', 'This is the first nonlinear compartmental model designed for this purpose .', 'The model uses experimental population-level ( macroscopic ) data and therefore an accurate equation for the connection of macroscopic data to sub-cellular data has been derived .', 'This equation accounts for the effect of a portion of cells that are not synchronized in the cell culture .', 'To estimate the free parameters of the model , we have solved the inverse problem of parameter estimation , which includes the constraints related to enzyme kinetics via the penalty method .', 'The use of constraints together with sensitivity and perturbation analysis makes it possible to infer the sub-cellular dynamics even with sparse and noisy data .', 'Taking into account the amount of silicon ( mol ) in the model in order to simplify different polymerization and other reactions in cells , the model is still able to produce the transport and the dynamics of nutrients with a good agreement to experimentally obtained evidence .', 'For example , the equations of the model can generate different regimes of uptake , namely: surge , externally-controlled and internally-controlled .', 'This model constitutes a framework by which to study cell compartments and to infer dynamics based on the known facts and data .', 'More importantly , it brings with it the ability to manipulate cell processes such as uptake rates and protein regulation , which are normally difficult to manipulate experimentally .', 'As an example , we have imposed changes in the total amount of SITs through time; a mechanism for cells to control the uptake and transport of materials .', 'We have observed that applying a protein flux results in more realistic silicon dynamics and uptake rates , and can postpone the start of silica deposition in favor of silicon storage in the silicon pool .', 'The model presented here can be generalized to other chemical pathways by changing only the system of ODEs , which lie at the core of the model , and then applying the same procedure .', 'One interesting area in this framework would be to introduce changes in the expression level of enzymes during time as a function of the internal and external changes , and try to connect the cell cycle and silicon cycle of diatoms together .', "Another interesting addition to this type of model would be to consider the statistical distribution of individual cells' dynamics in the culture , which will introduce more complexities .", 'This can be achieved by applying individual-based modeling , or with an ensemble based modeling to fulfill the role of cells in different phases .']]
['Introduction', 'Materials and Methods', 'Results', 'Discussion']
['Controlled synthesis of silicon is a major challenge in nanotechnology and material science .', 'Diatoms , the unicellular algae , are an inspiring example of silica biosynthesis , producing complex and delicate nano-structures .', 'This happens in several cell compartments , including cytoplasm and silica deposition vesicle ( SDV ) .', 'Considering the low concentration of silicic acid in oceans , cells have developed silicon transporter proteins ( SIT ) .', 'Moreover , cells change the level of active SITs during one cell cycle , likely as a response to the level of external nutrients and internal deposition rates .', 'Despite this topic being of fundamental interest , the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood .', 'One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales , and even when possible , data often contain large errors .', 'Therefore , using computational techniques seems inevitable .', 'We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment , cytoplasm , SDV and deposited silica .', 'The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations .', 'In order to find the free parameters of the model from sparse , noisy experimental data , an optimization technique ( global and local search ) , together with enzyme related penalty terms , has been applied .', 'We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells .', 'Our model is robust , proven by sensitivity and perturbation analysis , and predicts dynamics of intracellular nutrients and enzymes in different compartments .', 'The model produces different uptake regimes , previously recognized as surge , externally-controlled and internally-controlled uptakes .', 'Finally , we imposed a flux of SITs to the model and compared it with previous classical kinetics .', 'The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations .']
['Understanding complex biological systems , especially at intracellular scales , has always been a big challenge , owing to the difficulties in measuring and manipulating such small quantities .', 'Computational modeling brings promising possibilities to this area .', 'The model organism we have studied here is the diatom , a single cellular silicifying organism .', 'Diatoms live in most water habitats and they use the very low concentrations of silicon in the oceans to develop beautifully complex silica structures .', 'The cell control strategies acting on this process have been a long-standing open question .', 'In this work , we have modeled the silicon uptake , transport and synthesis in diatoms in different cell compartments .', 'To find the best set of free parameters of the model we solved the inverse problem using parameter identifiability , global optimization , sensitivity and perturbation techniques .', 'The resulting model is a framework for manipulating and testing different properties of cells; for example , we have tested the cell control on silicon uptake by changing the expression level of the transporter proteins .', 'Such modeling , described in this work , is both a necessary and important tool for understanding the cell strategies over control of material transport and synthesis .']
['systems biology', 'biochemistry', 'biochemical simulations', 'physiological processes', 'biomineralization', 'physiology', 'earth sciences', 'marine and aquatic sciences', 'biology and life sciences', 'computational biology', 'marine biology']