This condition assumes that the total renal CO 2 production is distributed into all forms of CO 2 on venous return, i. Condition 2 : Unbalanced CO 2 distribution on the venous return. This condition assumes that the total renal CO 2 production is distributed into all forms of CO 2 except HCO 3 - in plasma on venous return.
The above given BCs ensure for both conditions that total oxygen and carbon dioxide delivery throughout the kidney is conserved, i. Figure 3.
The shaded regions represent the cortex and the medulla. Solid arrows symbolize blood flow, whereas dashed arrows represent oxygen and carbon dioxide flux. Blood enters the arterial tree at order 10 and exits the explicitly modeled cortical domain at order 0. Blood enters cortical domain again at the venous side at order 0 and exits at order Positive values designate flux from vessels to the tissue, whereas negative values stand for oxygen or carbon dioxide transfer from the tissue into the vessels.
All carbon dioxide produced in the cortex is assumed to be taken up by capillaries, i. As to the outlet BCs, convective flux boundary conditions are imposed on all vessel outlets by setting the diffusive flux to zero. On all lateral surfaces, diffusive flux is set to zero.
At the vessel-tissue interfaces, there is continuity of oxygen and carbon dioxide partial pressure and oxygen and carbon dioxide flux such that:. The base case is derived from in vivo P O 2 measurements with oxygen-sensitive ultramicroelectrodes in normotensive WKY rats as reported by Welch et al. Relevant values for the base case are summarized in Table 4.
To set the carbon dioxide production rate in dependence of the oxygen consumption rate, we assume a respiratory quotient RQ of 0. Prescribing the reference renal artery P O 2 , P O 2 , RA , on the renal artery inlet, the total heme group concentration is set such that the renal artery oxygen delivery D O 2 , inlet, a, 10 matches the values given in Table 4.
We set capillary P O 2 , P O 2 , c , to an average of afferent arteriole outlet and venous return inlet, i. See Olgac and Kurtcuoglu a for details on capillary P O 2.
We first present the output of the model employing two different boundary conditions on the venous return. Condition 1 distributes total renal CO 2 production into all forms of CO 2 in the venous return, whereas Condition 2 excludes plasma bicarbonate in this distribution. Under Condition 2 , the increase is to The lower increase in P CO 2 under Condition 1 is due to the fact that CO 2 production is distributed into all forms of CO 2 on the venous return, including the dominant plasma bicarbonate.
Conversely, as there is no plasma bicarbonate added to the venous return under Condition 2 , the same rate of renal CO 2 production results in a higher increase in P CO 2. This is also evident in the pH profiles: Under Condition 1 , the pH profiles are almost flat with a slight overall decrease in plasma and RBC pH on the venous side due to the increased acidity added renal CO 2 production. This increased acidity is again owed to the addition of produced CO 2 to the venous return in forms other than plasma bicarbonate.
Figure 4C shows for both conditions the flux of carbon dioxide between artery walls and the tissue. As indicated by the negative fluxes, there is venous-to-arterial carbon dioxide shunting under both conditions, with more shunting under Condition 2. Overall, approximately 0. The larger amount of carbon dioxide shunting under Condition 2 is primarily due to the higher P CO 2 gradient between the venous and the arterial sides compared to Condition 1.
Figure 4. Comparison of results for the base case under Condition 1 left and Condition 2 right. Cumulative values as well as values for each individual order are shown. Positive flux represents flux from the vessel into the tissue, whereas negative flux denotes the opposite, i.
The investigated Conditions 1 and 2 , i. The real state must lie between these two. We performed O 2 transport calculations with a constant P 50 , and a variable P 50 whose dependence on the local P CO 2 and pH is given by Equation 6 a — c. The O 2 transport calculations with variable P 50 are based on the P CO 2 and pH fields obtained from carbon dioxide transport calculations under Condition 2 , because under this condition, the maximum possible increase in P CO 2 and decrease in pH in the preglomerular vasculature compared to the systemic arterial blood are reached.
In other words, this condition captures the highest possible effect of CO 2 transport on O 2 transport. Figures 5A,B show P O 2 profiles in arteries, veins and tissue, as well as oxygen fluxes between vein walls and tissue. The P O 2 profiles for the constant and variable P 50 cases are very similar, with a slight overall increase in P O 2 for the variable P 50 case due to higher P 50 compared to the constant P 50 case.
For the constant P 50 case, cumulatively 0. Hence, for this case, the total preglomerular AV oxygen shunting is 0. Note that these results are slightly different from the ones given in our previous study Olgac and Kurtcuoglu, b. Figure 5. Comparison of results for the base case with constant P 50 left and variable P 50 dependent on the local P CO 2 and pH based on Condition 2 right.
Under variable P 50 conditions, oxygen shunting along the wrapped vessels decreases, with overall preglomerular AV oxygen shunting reducing to 0. This is because the increase in acidity and hence the decrease in the affinity of hemoglobin to oxygen is more pronounced on the venous compared to the arterial side.
To test the influence of buffering capacity, we performed calculations on a modified base case with a 10 fold decrease in plasma and RBC buffering capacities. Figures 6A—C represent, on the left panel under Condition 1 and on the right panel under Condition 2 , P CO 2 , pH and carbon dioxide flux profiles for this modified case.
P CO 2 increases to Furthermore, pH profiles vary more compared to the rather flat profiles in Figure 4. On the venous return, plasma and RBC pH are 7. VA CO 2 shunting is also increased due to the increased P CO 2 gradient between the venous and the arterial side, with 1. Figure 6. We have made the following key observations: 1 Increase in acidity in the preglomerular vasculature compared to systemic arterial blood is marginal.
In the following we will discuss these observations. We calculated the P CO 2 at the outlet of the afferent arteriole and on the venous return to be in the range of Plasma and RBC pH on the venous return decrease to somewhere between 7. Taken together, we conclude that the increase in acidity in the preglomerular vasculature is not substantial. The main reason for this is the high buffering capacity of blood. When we lowered the buffering capacity in our model, acidity increased substantially.
Our current model does not include these parts. Previous modeling studies by Bidani et al. They indicated that substantial venous-to-arterial CO 2 shunting would be necessary to preserve this P CO 2 of 65 mmHg in the renal cortex. We further calculated the shunting of CO 2 from the veins to the arteries to be approximately between 0. We conclude that just as the increase in acidity, the venous-to-arterial CO 2 shunting in the preglomerular vasculature is also only marginal.
This is mainly because the increase in acidity is higher on the venous side, which leads to a lower affinity of hemoglobin to oxygen compared to the arterial side. This lower affinity on the venous side makes it slightly harder for the oxygen to bind to hemoglobin, diminishing the oxygen transfer from the tissue into the veins, hence decreasing AV O 2 shunting.
Therefore, our model does not support the hypothesis initially proposed by Schurek et al. The current model thus also confirms our previous findings that preglomerular AV O 2 shunting is marginal, and that if substantial renal oxygen shunting exists, it should be along the post-glomerular vasculature, i.
The main limitation of the model is that the distribution of the different forms of CO 2 in the venous return is unknown. To address this, two different conditions representing extreme cases were employed and ranges of values reported.
The actual values representing the real state are expected to lie within the given ranges. More accurate calculations would require that CO 2 transport dynamics in the peritubular capillary network be taken into account, which would necessitate explicit treatment of the postglomerular vasculature and the tubular system. Modeling bicarbonate reabsorption in this domain would yield an estimate of what fraction of the carbon dioxide produced in the tubular cells reaches the capillaries in bicarbonate and CO 2 form, respectively.
This fraction is unknown in the current model. Nevertheless, the two conditions employed on the venous return provide solid boundaries for the ranges of P CO 2 and pH in the preglomerular vasculature, and the conclusions reached in this study are valid for both conditions. A further limitation of this computational study is produced by the fact that there are no comparable experimental studies of renal carbon dioxide transport which could be used for validation.
The experimental P CO 2 and pH measurements referred to in the Introduction section have been performed on tubules and stellate vessels, and can thus not be compared with our results. Quantitative cortical tissue and afferent arteriole P CO 2 and pH values have, to our knowledge, not been published.
To test the robustness of our conclusions, we performed sensitivity analyses in which we altered renal artery inlet boundary conditions. First, we established alternative chemical equilibria at the renal artery inlet corresponding to renal artery P CO 2 values of 35 mmHg and 45 mmHg, respectively. This accounts for possible variation in renal artery P CO 2 in the physiologic range. We calculated maximum P CO 2 at the outlet of the afferent arteriole and on the venous return to be These extreme cases show relative increases in P CO 2 in the preglomerular vasculature with respect to renal artery P CO 2 that are similar to the base case.
Plasma and RBC pH on the venous return decrease to minima of 7. These relative decreases in pH in the preglomerular vasculature with respect to renal artery pH in the extreme cases are similar to that in the base case. Furthermore, oxygen transport calculations in these extreme cases under variable P 50 conditions show impaired AV oxygen shunting compared to under constant P 50 conditions, just as it was observed in the base case Supplementary Figures 2, 3.
There, under variable P 50 conditions, overall preglomerular oxygen shunting reduced to 0. In the extreme cases, this reduction was to 0. We calculated for this case maximum P CO 2 at the outlet of the afferent arteriole and on the venous return to be In these extreme cases, AV O 2 shunting reduced from 0.
In comparison, in the base case, AV O 2 shunting reduced from 0. We conclude that our first main observation, namely that increase in acidity in the preglomerular vasculature compared to systemic arterial blood is marginal, is robust unless RBF is substantially reduced. Our second main observation, i. Because changes in the carbon dioxide partial pressure can modify blood pH, increased partial pressures of carbon dioxide can also result in right-ward shifts of the oxygen-hemoglobin dissociation curve.
The relationship between carbon dioxide partial pressure and blood pH is mediated by carbonic anhydrase which converts gaseous carbon dioxide to carbonic acid that in turn releases a free hydrogen ion, thus reducing the local pH of blood. Significance The Bohr Effect allows for enhanced unloading of oxygen in metabolically active peripheral tissues such as exercising skeletal muscle.
Increased skeletal muscle activity results in localized increases in the partial pressure of carbon dioxide which in turn reduces the local blood pH. Because of the Bohr Effect, this results in enhanced unloading of bound oxygen by hemoglobin passing through the metabolically active tissue and thus improves oxygen delivery. Importantly, the Bohr Effect enhances oxygen delivery proportionally to the metabolic activity of the tissue. As more metabolism takes place, the carbon dioxide partial pressure increases thus causing larger reductions in local pH and in turn allowing for greater oxygen unloading.
This is especially true in exercising skeletal muscles which may also release lactic acid that further reduces local blood pH and thus enhances the Bohr Effect. This gives you the sigmoidal S-shaped curve. So how to keep it from dumping it all too soon? And from just retaking what it dumps?
So we need a way to shift the curve in different tissues based on their oxygen needs. And this requires changing the affinity, not just the oxygen concentration. And this is where the Bohr effect comes in, shifting the curve to the right favoring release at lower oxygen concentrations in the tissues that need oxygen. Enzymes are usually proteins e. They bind to specific substrate s and provide the optimal conditions in their "active site" for a reaction to occur.
So, after they help out with some reaction, they can do it again and again and again. I say "help out" because the enzyme doesn't really "do" anything - it can only help make something that was "possible," "likely.
Instead, enzymes lower the activation energy required to get the reaction going. And this takes us to an aside about acids. One of 3 main types of subatomic particles parts of atoms. Protons hang out with neutral neutrons in a dense central nucleus and are surrounded by a cloud of negatively-charged electrons. The number of protons an atom has determines what element it is e.
The number of protons is also referred to as the "atomic number," abbreviated Z. Elements are ordered by increasing atomic number in the periodic table of elements. Atoms are the basic units of elements hydrogen, carbon, oxygen, etc. Atoms can share pairs of electrons to form strong covalent bonds.
So, the process is reversible. Concentrate on the concentrations! And the more protons there are, the more acidic the solution lower the pH. But pH is just a measurement — it tells us about how many protons are on the loose, but not what they then do….
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